{"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 2], [4, 2], [4, 0], [6, 0]]}, {"polygon": [[4, 2], [4, 1], [5, 2]]}], "meta": {"seed": 4201001, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 1, "strictValidation": true}, "imageAssets": {"target": "../images/voi-000/target.png", "shapes": {"S1": "../images/voi-000/shape_S1.png", "S2": "../images/voi-000/shape_S2.png"}}, "ID": "voi-000", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [4, 2]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [5, 2]}]}, "legacy_answer": "S1 180 V2 [4,2]\nS2 90 V3 [5,2]", "solutionText": "S1 180 V2 [4,2]\nS2 90 V3 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-000\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-000/target.png", "shapes": {"S1": "images/voi-000/shape_S1.png", "S2": "images/voi-000/shape_S2.png"}}, "__sample_id__": "voi-000"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [3, 2], [5, 4]]}, {"polygon": [[5, 1], [5, 3], [3, 3], [3, 1]]}], "meta": {"seed": 4201002, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 2, "strictValidation": true}, "imageAssets": {"target": "../images/voi-001/target.png", "shapes": {"S1": "../images/voi-001/shape_S1.png", "S2": "../images/voi-001/shape_S2.png"}}, "ID": "voi-001", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [3, 4]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [3, 1]}]}, "legacy_answer": "S1 90 V1 [3,4]\nS2 270 V4 [3,1]", "solutionText": "S1 90 V1 [3,4]\nS2 270 V4 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-001\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-001/target.png", "shapes": {"S1": "images/voi-001/shape_S1.png", "S2": "images/voi-001/shape_S2.png"}}, "__sample_id__": "voi-001"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [3, 4], [5, 6]]}, {"polygon": [[5, 5], [3, 5], [3, 3], [5, 3]]}], "meta": {"seed": 4201003, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 3, "strictValidation": true}, "imageAssets": {"target": "../images/voi-002/target.png", "shapes": {"S1": "../images/voi-002/shape_S1.png", "S2": "../images/voi-002/shape_S2.png"}}, "ID": "voi-002", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [3, 6]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [5, 5]}]}, "legacy_answer": "S1 90 V1 [3,6]\nS2 180 V1 [5,5]", "solutionText": "S1 90 V1 [3,6]\nS2 180 V1 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-002\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-002/target.png", "shapes": {"S1": "images/voi-002/shape_S1.png", "S2": "images/voi-002/shape_S2.png"}}, "__sample_id__": "voi-002"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 1], [3, 3], [1, 1]]}, {"polygon": [[3, 4], [1, 4], [1, 2], [3, 2]]}], "meta": {"seed": 4201004, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 4, "strictValidation": true}, "imageAssets": {"target": "../images/voi-003/target.png", "shapes": {"S1": "../images/voi-003/shape_S1.png", "S2": "../images/voi-003/shape_S2.png"}}, "ID": "voi-003", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 1]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 4]}]}, "legacy_answer": "S1 270 V1 [3,1]\nS2 180 V1 [3,4]", "solutionText": "S1 270 V1 [3,1]\nS2 180 V1 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-003\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-003/target.png", "shapes": {"S1": "images/voi-003/shape_S1.png", "S2": "images/voi-003/shape_S2.png"}}, "__sample_id__": "voi-003"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 4], [4, 4], [4, 6], [2, 6]]}, {"polygon": [[2, 3], [4, 3], [2, 5]]}], "meta": {"seed": 4201005, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 5, "strictValidation": true}, "imageAssets": {"target": "../images/voi-004/target.png", "shapes": {"S1": "../images/voi-004/shape_S1.png", "S2": "../images/voi-004/shape_S2.png"}}, "ID": "voi-004", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [4, 6]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 3]}]}, "legacy_answer": "S1 0 V3 [4,6]\nS2 0 V1 [2,3]", "solutionText": "S1 0 V3 [4,6]\nS2 0 V1 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-004\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-004/target.png", "shapes": {"S1": "images/voi-004/shape_S1.png", "S2": "images/voi-004/shape_S2.png"}}, "__sample_id__": "voi-004"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 4], [5, 5], [4, 4]]}, {"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}], "meta": {"seed": 4201006, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 6, "strictValidation": true}, "imageAssets": {"target": "../images/voi-005/target.png", "shapes": {"S1": "../images/voi-005/shape_S1.png", "S2": "../images/voi-005/shape_S2.png"}}, "ID": "voi-005", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 4]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [5, 4]}]}, "legacy_answer": "S1 270 V1 [5,4]\nS2 270 V1 [5,4]", "solutionText": "S1 270 V1 [5,4]\nS2 270 V1 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-005\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-005/target.png", "shapes": {"S1": "images/voi-005/shape_S1.png", "S2": "images/voi-005/shape_S2.png"}}, "__sample_id__": "voi-005"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 4], [4, 4], [6, 2]]}, {"polygon": [[4, 1], [6, 1], [6, 3], [4, 3]]}], "meta": {"seed": 4201007, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 7, "strictValidation": true}, "imageAssets": {"target": "../images/voi-006/target.png", "shapes": {"S1": "../images/voi-006/shape_S1.png", "S2": "../images/voi-006/shape_S2.png"}}, "ID": "voi-006", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [6, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [4, 1]}]}, "legacy_answer": "S1 180 V1 [6,4]\nS2 0 V1 [4,1]", "solutionText": "S1 180 V1 [6,4]\nS2 0 V1 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-006\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-006/target.png", "shapes": {"S1": "images/voi-006/shape_S1.png", "S2": "images/voi-006/shape_S2.png"}}, "__sample_id__": "voi-006"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 0], [4, 2], [2, 0]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}], "meta": {"seed": 4201008, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 8, "strictValidation": true}, "imageAssets": {"target": "../images/voi-007/target.png", "shapes": {"S1": "../images/voi-007/shape_S1.png", "S2": "../images/voi-007/shape_S2.png"}}, "ID": "voi-007", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [4, 2]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [2, 3]}]}, "legacy_answer": "S1 270 V2 [4,2]\nS2 0 V4 [2,3]", "solutionText": "S1 270 V2 [4,2]\nS2 0 V4 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-007\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-007/target.png", "shapes": {"S1": "images/voi-007/shape_S1.png", "S2": "images/voi-007/shape_S2.png"}}, "__sample_id__": "voi-007"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 6], [2, 6], [4, 4]]}, {"polygon": [[2, 5], [2, 3], [4, 3], [4, 5]]}], "meta": {"seed": 4201009, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 9, "strictValidation": true}, "imageAssets": {"target": "../images/voi-008/target.png", "shapes": {"S1": "../images/voi-008/shape_S1.png", "S2": "../images/voi-008/shape_S2.png"}}, "ID": "voi-008", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [4, 4]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V3 [4,4]\nS2 90 V3 [4,3]", "solutionText": "S1 180 V3 [4,4]\nS2 90 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-008\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-008/target.png", "shapes": {"S1": "images/voi-008/shape_S1.png", "S2": "images/voi-008/shape_S2.png"}}, "__sample_id__": "voi-008"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 4], [3, 4], [5, 2]]}, {"polygon": [[5, 1], [5, 3], [3, 1]]}], "meta": {"seed": 4201010, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 10, "strictValidation": true}, "imageAssets": {"target": "../images/voi-009/target.png", "shapes": {"S1": "../images/voi-009/shape_S1.png", "S2": "../images/voi-009/shape_S2.png"}}, "ID": "voi-009", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 3]}]}, "legacy_answer": "S1 180 V2 [3,4]\nS2 270 V2 [5,3]", "solutionText": "S1 180 V2 [3,4]\nS2 270 V2 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-009\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-009/target.png", "shapes": {"S1": "images/voi-009/shape_S1.png", "S2": "images/voi-009/shape_S2.png"}}, "__sample_id__": "voi-009"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 3], [2, 3], [4, 1]]}, {"polygon": [[3, 1], [3, 3], [1, 1]]}], "meta": {"seed": 4201011, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 11, "strictValidation": true}, "imageAssets": {"target": "../images/voi-010/target.png", "shapes": {"S1": "../images/voi-010/shape_S1.png", "S2": "../images/voi-010/shape_S2.png"}}, "ID": "voi-010", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [2, 3]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [3, 1]}]}, "legacy_answer": "S1 180 V2 [2,3]\nS2 270 V1 [3,1]", "solutionText": "S1 180 V2 [2,3]\nS2 270 V1 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-010\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-010/target.png", "shapes": {"S1": "images/voi-010/shape_S1.png", "S2": "images/voi-010/shape_S2.png"}}, "__sample_id__": "voi-010"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 3], [4, 3], [2, 5]]}, {"polygon": [[3, 5], [3, 3], [5, 3], [5, 5]]}], "meta": {"seed": 4201012, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 12, "strictValidation": true}, "imageAssets": {"target": "../images/voi-011/target.png", "shapes": {"S1": "../images/voi-011/shape_S1.png", "S2": "../images/voi-011/shape_S2.png"}}, "ID": "voi-011", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 3]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 5]}]}, "legacy_answer": "S1 0 V2 [4,3]\nS2 90 V1 [3,5]", "solutionText": "S1 0 V2 [4,3]\nS2 90 V1 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-011\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-011/target.png", "shapes": {"S1": "images/voi-011/shape_S1.png", "S2": "images/voi-011/shape_S2.png"}}, "__sample_id__": "voi-011"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 3], [2, 3], [2, 1], [4, 1]]}, {"polygon": [[2, 4], [2, 2], [4, 4]]}], "meta": {"seed": 4201014, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 13, "strictValidation": true}, "imageAssets": {"target": "../images/voi-012/target.png", "shapes": {"S1": "../images/voi-012/shape_S1.png", "S2": "../images/voi-012/shape_S2.png"}}, "ID": "voi-012", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [2, 1]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 4]}]}, "legacy_answer": "S1 180 V3 [2,1]\nS2 90 V3 [4,4]", "solutionText": "S1 180 V3 [2,1]\nS2 90 V3 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-012\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-012/target.png", "shapes": {"S1": "images/voi-012/shape_S1.png", "S2": "images/voi-012/shape_S2.png"}}, "__sample_id__": "voi-012"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [6, 3], [5, 4]]}, {"polygon": [[6, 3], [6, 5], [4, 5], [4, 3]]}], "meta": {"seed": 4201015, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 14, "strictValidation": true}, "imageAssets": {"target": "../images/voi-013/target.png", "shapes": {"S1": "../images/voi-013/shape_S1.png", "S2": "../images/voi-013/shape_S2.png"}}, "ID": "voi-013", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 4]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 5]}]}, "legacy_answer": "S1 0 V3 [5,4]\nS2 270 V2 [6,5]", "solutionText": "S1 0 V3 [5,4]\nS2 270 V2 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-013\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-013/target.png", "shapes": {"S1": "images/voi-013/shape_S1.png", "S2": "images/voi-013/shape_S2.png"}}, "__sample_id__": "voi-013"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 4], [3, 2], [5, 2], [5, 4]]}, {"polygon": [[5, 5], [3, 5], [5, 3]]}], "meta": {"seed": 4201016, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 15, "strictValidation": true}, "imageAssets": {"target": "../images/voi-014/target.png", "shapes": {"S1": "../images/voi-014/shape_S1.png", "S2": "../images/voi-014/shape_S2.png"}}, "ID": "voi-014", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [5, 2]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [5, 5]}]}, "legacy_answer": "S1 90 V3 [5,2]\nS2 180 V1 [5,5]", "solutionText": "S1 90 V3 [5,2]\nS2 180 V1 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-014\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-014/target.png", "shapes": {"S1": "images/voi-014/shape_S1.png", "S2": "images/voi-014/shape_S2.png"}}, "__sample_id__": "voi-014"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[1, 4], [1, 3], [2, 4]]}], "meta": {"seed": 4201017, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 16, "strictValidation": true}, "imageAssets": {"target": "../images/voi-015/target.png", "shapes": {"S1": "../images/voi-015/shape_S1.png", "S2": "../images/voi-015/shape_S2.png"}}, "ID": "voi-015", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 4]}]}, "legacy_answer": "S1 270 V2 [3,4]\nS2 90 V1 [1,4]", "solutionText": "S1 270 V2 [3,4]\nS2 90 V1 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-015\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-015/target.png", "shapes": {"S1": "images/voi-015/shape_S1.png", "S2": "images/voi-015/shape_S2.png"}}, "__sample_id__": "voi-015"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 0], [4, 0], [2, 2]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}], "meta": {"seed": 4201019, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 17, "strictValidation": true}, "imageAssets": {"target": "../images/voi-016/target.png", "shapes": {"S1": "../images/voi-016/shape_S1.png", "S2": "../images/voi-016/shape_S2.png"}}, "ID": "voi-016", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 0]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 1]}]}, "legacy_answer": "S1 0 V2 [4,0]\nS2 0 V1 [2,1]", "solutionText": "S1 0 V2 [4,0]\nS2 0 V1 [2,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-016\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-016/target.png", "shapes": {"S1": "images/voi-016/shape_S1.png", "S2": "images/voi-016/shape_S2.png"}}, "__sample_id__": "voi-016"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 1], [4, 3], [2, 1]]}, {"polygon": [[4, 4], [2, 4], [2, 2], [4, 2]]}], "meta": {"seed": 4201020, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 18, "strictValidation": true}, "imageAssets": {"target": "../images/voi-017/target.png", "shapes": {"S1": "../images/voi-017/shape_S1.png", "S2": "../images/voi-017/shape_S2.png"}}, "ID": "voi-017", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [4, 1]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [4, 2]}]}, "legacy_answer": "S1 270 V1 [4,1]\nS2 180 V4 [4,2]", "solutionText": "S1 270 V1 [4,1]\nS2 180 V4 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-017\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-017/target.png", "shapes": {"S1": "images/voi-017/shape_S1.png", "S2": "images/voi-017/shape_S2.png"}}, "__sample_id__": "voi-017"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 3], [0, 3], [2, 1]]}, {"polygon": [[0, 2], [0, 0], [2, 2]]}], "meta": {"seed": 4201021, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 19, "strictValidation": true}, "imageAssets": {"target": "../images/voi-018/target.png", "shapes": {"S1": "../images/voi-018/shape_S1.png", "S2": "../images/voi-018/shape_S2.png"}}, "ID": "voi-018", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 3]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [0, 0]}]}, "legacy_answer": "S1 180 V1 [2,3]\nS2 90 V2 [0,0]", "solutionText": "S1 180 V1 [2,3]\nS2 90 V2 [0,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-018\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-018/target.png", "shapes": {"S1": "images/voi-018/shape_S1.png", "S2": "images/voi-018/shape_S2.png"}}, "__sample_id__": "voi-018"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 4], [4, 4], [6, 2]]}, {"polygon": [[4, 5], [4, 3], [6, 5]]}], "meta": {"seed": 4201022, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 20, "strictValidation": true}, "imageAssets": {"target": "../images/voi-019/target.png", "shapes": {"S1": "../images/voi-019/shape_S1.png", "S2": "../images/voi-019/shape_S2.png"}}, "ID": "voi-019", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [6, 4]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S1 180 V1 [6,4]\nS2 90 V3 [6,5]", "solutionText": "S1 180 V1 [6,4]\nS2 90 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-019\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-019/target.png", "shapes": {"S1": "images/voi-019/shape_S1.png", "S2": "images/voi-019/shape_S2.png"}}, "__sample_id__": "voi-019"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 5], [3, 5], [3, 3], [5, 3]]}, {"polygon": [[6, 5], [4, 5], [6, 3]]}], "meta": {"seed": 4201023, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 21, "strictValidation": true}, "imageAssets": {"target": "../images/voi-020/target.png", "shapes": {"S1": "../images/voi-020/shape_S1.png", "S2": "../images/voi-020/shape_S2.png"}}, "ID": "voi-020", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 5]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 180 V1 [5,5]\nS2 180 V2 [4,5]", "solutionText": "S1 180 V1 [5,5]\nS2 180 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-020\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-020/target.png", "shapes": {"S1": "images/voi-020/shape_S1.png", "S2": "images/voi-020/shape_S2.png"}}, "__sample_id__": "voi-020"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [0, 5], [2, 3]]}, {"polygon": [[0, 4], [0, 2], [2, 2], [2, 4]]}], "meta": {"seed": 4201024, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 22, "strictValidation": true}, "imageAssets": {"target": "../images/voi-021/target.png", "shapes": {"S1": "../images/voi-021/shape_S1.png", "S2": "../images/voi-021/shape_S2.png"}}, "ID": "voi-021", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [0, 5]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [2, 2]}]}, "legacy_answer": "S1 180 V2 [0,5]\nS2 90 V3 [2,2]", "solutionText": "S1 180 V2 [0,5]\nS2 90 V3 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-021\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-021/target.png", "shapes": {"S1": "images/voi-021/shape_S1.png", "S2": "images/voi-021/shape_S2.png"}}, "__sample_id__": "voi-021"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 4], [4, 6], [2, 4]]}, {"polygon": [[3, 6], [1, 6], [3, 4]]}], "meta": {"seed": 4201025, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 23, "strictValidation": true}, "imageAssets": {"target": "../images/voi-022/target.png", "shapes": {"S1": "../images/voi-022/shape_S1.png", "S2": "../images/voi-022/shape_S2.png"}}, "ID": "voi-022", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 4]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [1, 6]}]}, "legacy_answer": "S1 270 V3 [2,4]\nS2 180 V2 [1,6]", "solutionText": "S1 270 V3 [2,4]\nS2 180 V2 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-022\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-022/target.png", "shapes": {"S1": "images/voi-022/shape_S1.png", "S2": "images/voi-022/shape_S2.png"}}, "__sample_id__": "voi-022"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 3], [5, 5], [3, 5], [3, 3]]}, {"polygon": [[6, 3], [6, 5], [4, 3]]}], "meta": {"seed": 4201026, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 24, "strictValidation": true}, "imageAssets": {"target": "../images/voi-023/target.png", "shapes": {"S1": "../images/voi-023/shape_S1.png", "S2": "../images/voi-023/shape_S2.png"}}, "ID": "voi-023", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 5]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 270 V2 [5,5]\nS2 270 V3 [4,3]", "solutionText": "S1 270 V2 [5,5]\nS2 270 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-023\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-023/target.png", "shapes": {"S1": "images/voi-023/shape_S1.png", "S2": "images/voi-023/shape_S2.png"}}, "__sample_id__": "voi-023"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 2], [3, 2], [1, 4]]}, {"polygon": [[1, 5], [1, 3], [3, 5]]}], "meta": {"seed": 4201027, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 25, "strictValidation": true}, "imageAssets": {"target": "../images/voi-024/target.png", "shapes": {"S1": "../images/voi-024/shape_S1.png", "S2": "../images/voi-024/shape_S2.png"}}, "ID": "voi-024", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [1, 4]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [1, 3]}]}, "legacy_answer": "S1 0 V3 [1,4]\nS2 90 V2 [1,3]", "solutionText": "S1 0 V3 [1,4]\nS2 90 V2 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-024\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-024/target.png", "shapes": {"S1": "images/voi-024/shape_S1.png", "S2": "images/voi-024/shape_S2.png"}}, "__sample_id__": "voi-024"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [5, 3], [3, 5]]}, {"polygon": [[6, 5], [4, 5], [4, 3], [6, 3]]}], "meta": {"seed": 4201028, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 26, "strictValidation": true}, "imageAssets": {"target": "../images/voi-025/target.png", "shapes": {"S1": "../images/voi-025/shape_S1.png", "S2": "../images/voi-025/shape_S2.png"}}, "ID": "voi-025", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 5]}]}, "legacy_answer": "S1 0 V1 [3,3]\nS2 180 V1 [6,5]", "solutionText": "S1 0 V1 [3,3]\nS2 180 V1 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-025\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-025/target.png", "shapes": {"S1": "images/voi-025/shape_S1.png", "S2": "images/voi-025/shape_S2.png"}}, "__sample_id__": "voi-025"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [4, 6], [6, 4]]}, {"polygon": [[3, 4], [5, 4], [5, 6], [3, 6]]}], "meta": {"seed": 4201029, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 27, "strictValidation": true}, "imageAssets": {"target": "../images/voi-026/target.png", "shapes": {"S1": "../images/voi-026/shape_S1.png", "S2": "../images/voi-026/shape_S2.png"}}, "ID": "voi-026", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [4, 6]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S1 180 V2 [4,6]\nS2 0 V3 [5,6]", "solutionText": "S1 180 V2 [4,6]\nS2 0 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-026\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-026/target.png", "shapes": {"S1": "images/voi-026/shape_S1.png", "S2": "images/voi-026/shape_S2.png"}}, "__sample_id__": "voi-026"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 3], [0, 1], [2, 3]]}, {"polygon": [[2, 0], [2, 2], [0, 2], [0, 0]]}], "meta": {"seed": 4201030, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 28, "strictValidation": true}, "imageAssets": {"target": "../images/voi-027/target.png", "shapes": {"S1": "../images/voi-027/shape_S1.png", "S2": "../images/voi-027/shape_S2.png"}}, "ID": "voi-027", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [2, 3]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [2, 0]}]}, "legacy_answer": "S1 90 V3 [2,3]\nS2 270 V1 [2,0]", "solutionText": "S1 90 V3 [2,3]\nS2 270 V1 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-027\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-027/target.png", "shapes": {"S1": "images/voi-027/shape_S1.png", "S2": "images/voi-027/shape_S2.png"}}, "__sample_id__": "voi-027"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 4], [0, 2], [2, 4]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}], "meta": {"seed": 4201031, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 29, "strictValidation": true}, "imageAssets": {"target": "../images/voi-028/target.png", "shapes": {"S1": "../images/voi-028/shape_S1.png", "S2": "../images/voi-028/shape_S2.png"}}, "ID": "voi-028", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [0, 4]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S1 90 V1 [0,4]\nS2 90 V3 [3,2]", "solutionText": "S1 90 V1 [0,4]\nS2 90 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-028\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-028/target.png", "shapes": {"S1": "images/voi-028/shape_S1.png", "S2": "images/voi-028/shape_S2.png"}}, "__sample_id__": "voi-028"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 1], [3, 1], [3, 3], [1, 3]]}, {"polygon": [[1, 4], [1, 2], [3, 4]]}], "meta": {"seed": 4201032, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 30, "strictValidation": true}, "imageAssets": {"target": "../images/voi-029/target.png", "shapes": {"S1": "../images/voi-029/shape_S1.png", "S2": "../images/voi-029/shape_S2.png"}}, "ID": "voi-029", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [1, 3]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 4]}]}, "legacy_answer": "S1 0 V4 [1,3]\nS2 90 V1 [1,4]", "solutionText": "S1 0 V4 [1,3]\nS2 90 V1 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-029\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-029/target.png", "shapes": {"S1": "images/voi-029/shape_S1.png", "S2": "images/voi-029/shape_S2.png"}}, "__sample_id__": "voi-029"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}, {"polygon": [[5, 2], [5, 3], [4, 2]]}], "meta": {"seed": 4201033, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 31, "strictValidation": true}, "imageAssets": {"target": "../images/voi-030/target.png", "shapes": {"S1": "../images/voi-030/shape_S1.png", "S2": "../images/voi-030/shape_S2.png"}}, "ID": "voi-030", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 1]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 3]}]}, "legacy_answer": "S1 90 V2 [3,1]\nS2 270 V2 [5,3]", "solutionText": "S1 90 V2 [3,1]\nS2 270 V2 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-030\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-030/target.png", "shapes": {"S1": "images/voi-030/shape_S1.png", "S2": "images/voi-030/shape_S2.png"}}, "__sample_id__": "voi-030"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[5, 1], [6, 1], [5, 2]]}], "meta": {"seed": 4201034, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 32, "strictValidation": true}, "imageAssets": {"target": "../images/voi-031/target.png", "shapes": {"S1": "../images/voi-031/shape_S1.png", "S2": "../images/voi-031/shape_S2.png"}}, "ID": "voi-031", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [4, 1]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 1]}]}, "legacy_answer": "S1 270 V4 [4,1]\nS2 0 V2 [6,1]", "solutionText": "S1 270 V4 [4,1]\nS2 0 V2 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-031\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-031/target.png", "shapes": {"S1": "images/voi-031/shape_S1.png", "S2": "images/voi-031/shape_S2.png"}}, "__sample_id__": "voi-031"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 6], [1, 4], [3, 6]]}, {"polygon": [[2, 4], [4, 4], [2, 6]]}], "meta": {"seed": 4201035, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 33, "strictValidation": true}, "imageAssets": {"target": "../images/voi-032/target.png", "shapes": {"S1": "../images/voi-032/shape_S1.png", "S2": "../images/voi-032/shape_S2.png"}}, "ID": "voi-032", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [3, 6]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S1 90 V3 [3,6]\nS2 0 V1 [2,4]", "solutionText": "S1 90 V3 [3,6]\nS2 0 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-032\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-032/target.png", "shapes": {"S1": "images/voi-032/shape_S1.png", "S2": "images/voi-032/shape_S2.png"}}, "__sample_id__": "voi-032"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 3], [2, 1], [4, 1], [4, 3]]}, {"polygon": [[4, 4], [2, 4], [4, 2]]}], "meta": {"seed": 4201036, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 34, "strictValidation": true}, "imageAssets": {"target": "../images/voi-033/target.png", "shapes": {"S1": "../images/voi-033/shape_S1.png", "S2": "../images/voi-033/shape_S2.png"}}, "ID": "voi-033", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [2, 1]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S1 90 V2 [2,1]\nS2 180 V1 [4,4]", "solutionText": "S1 90 V2 [2,1]\nS2 180 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-033\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-033/target.png", "shapes": {"S1": "images/voi-033/shape_S1.png", "S2": "images/voi-033/shape_S2.png"}}, "__sample_id__": "voi-033"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 2], [3, 2], [4, 1]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}], "meta": {"seed": 4201037, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 35, "strictValidation": true}, "imageAssets": {"target": "../images/voi-034/target.png", "shapes": {"S1": "../images/voi-034/shape_S1.png", "S2": "../images/voi-034/shape_S2.png"}}, "ID": "voi-034", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [4, 2]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V1 [4,2]\nS2 0 V3 [4,3]", "solutionText": "S1 180 V1 [4,2]\nS2 0 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-034\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-034/target.png", "shapes": {"S1": "images/voi-034/shape_S1.png", "S2": "images/voi-034/shape_S2.png"}}, "__sample_id__": "voi-034"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 0], [5, 2], [3, 2], [3, 0]]}, {"polygon": [[2, 0], [4, 0], [2, 2]]}], "meta": {"seed": 4201038, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 36, "strictValidation": true}, "imageAssets": {"target": "../images/voi-035/target.png", "shapes": {"S1": "../images/voi-035/shape_S1.png", "S2": "../images/voi-035/shape_S2.png"}}, "ID": "voi-035", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 2]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 0]}]}, "legacy_answer": "S1 270 V3 [3,2]\nS2 0 V1 [2,0]", "solutionText": "S1 270 V3 [3,2]\nS2 0 V1 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-035\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-035/target.png", "shapes": {"S1": "images/voi-035/shape_S1.png", "S2": "images/voi-035/shape_S2.png"}}, "__sample_id__": "voi-035"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [1, 4], [3, 2]]}, {"polygon": [[1, 3], [1, 1], [3, 1], [3, 3]]}], "meta": {"seed": 4201039, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 37, "strictValidation": true}, "imageAssets": {"target": "../images/voi-036/target.png", "shapes": {"S1": "../images/voi-036/shape_S1.png", "S2": "../images/voi-036/shape_S2.png"}}, "ID": "voi-036", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V1 [3,4]\nS2 90 V4 [3,3]", "solutionText": "S1 180 V1 [3,4]\nS2 90 V4 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-036\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-036/target.png", "shapes": {"S1": "images/voi-036/shape_S1.png", "S2": "images/voi-036/shape_S2.png"}}, "__sample_id__": "voi-036"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 0], [3, 2], [1, 2], [1, 0]]}, {"polygon": [[4, 2], [2, 2], [4, 0]]}], "meta": {"seed": 4201040, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 38, "strictValidation": true}, "imageAssets": {"target": "../images/voi-037/target.png", "shapes": {"S1": "../images/voi-037/shape_S1.png", "S2": "../images/voi-037/shape_S2.png"}}, "ID": "voi-037", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [1, 2]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 2]}]}, "legacy_answer": "S1 270 V3 [1,2]\nS2 180 V2 [2,2]", "solutionText": "S1 270 V3 [1,2]\nS2 180 V2 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-037\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-037/target.png", "shapes": {"S1": "images/voi-037/shape_S1.png", "S2": "images/voi-037/shape_S2.png"}}, "__sample_id__": "voi-037"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 3], [0, 3], [0, 1], [2, 1]]}, {"polygon": [[0, 0], [2, 0], [0, 2]]}], "meta": {"seed": 4201041, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 39, "strictValidation": true}, "imageAssets": {"target": "../images/voi-038/target.png", "shapes": {"S1": "../images/voi-038/shape_S1.png", "S2": "../images/voi-038/shape_S2.png"}}, "ID": "voi-038", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [2, 1]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [0, 2]}]}, "legacy_answer": "S1 180 V4 [2,1]\nS2 0 V3 [0,2]", "solutionText": "S1 180 V4 [2,1]\nS2 0 V3 [0,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-038\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-038/target.png", "shapes": {"S1": "images/voi-038/shape_S1.png", "S2": "images/voi-038/shape_S2.png"}}, "__sample_id__": "voi-038"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[1, 1], [3, 1], [1, 3]]}], "meta": {"seed": 4201042, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 40, "strictValidation": true}, "imageAssets": {"target": "../images/voi-039/target.png", "shapes": {"S1": "../images/voi-039/shape_S1.png", "S2": "../images/voi-039/shape_S2.png"}}, "ID": "voi-039", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [1, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 1]}]}, "legacy_answer": "S1 270 V3 [1,4]\nS2 0 V1 [1,1]", "solutionText": "S1 270 V3 [1,4]\nS2 0 V1 [1,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-039\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-039/target.png", "shapes": {"S1": "images/voi-039/shape_S1.png", "S2": "images/voi-039/shape_S2.png"}}, "__sample_id__": "voi-039"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 1], [5, 1], [5, 3], [3, 3]]}, {"polygon": [[5, 0], [5, 2], [3, 0]]}], "meta": {"seed": 4201043, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 41, "strictValidation": true}, "imageAssets": {"target": "../images/voi-040/target.png", "shapes": {"S1": "../images/voi-040/shape_S1.png", "S2": "../images/voi-040/shape_S2.png"}}, "ID": "voi-040", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 3]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 2]}]}, "legacy_answer": "S1 0 V3 [5,3]\nS2 270 V2 [5,2]", "solutionText": "S1 0 V3 [5,3]\nS2 270 V2 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-040\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-040/target.png", "shapes": {"S1": "images/voi-040/shape_S1.png", "S2": "images/voi-040/shape_S2.png"}}, "__sample_id__": "voi-040"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[3, 3], [3, 1], [5, 3]]}], "meta": {"seed": 4201044, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 42, "strictValidation": true}, "imageAssets": {"target": "../images/voi-041/target.png", "shapes": {"S1": "../images/voi-041/shape_S1.png", "S2": "../images/voi-041/shape_S2.png"}}, "ID": "voi-041", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [6, 3]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [3, 1]}]}, "legacy_answer": "S1 270 V2 [6,3]\nS2 90 V2 [3,1]", "solutionText": "S1 270 V2 [6,3]\nS2 90 V2 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-041\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-041/target.png", "shapes": {"S1": "images/voi-041/shape_S1.png", "S2": "images/voi-041/shape_S2.png"}}, "__sample_id__": "voi-041"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 4], [3, 4], [1, 6]]}, {"polygon": [[4, 6], [2, 6], [2, 4], [4, 4]]}], "meta": {"seed": 4201045, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 43, "strictValidation": true}, "imageAssets": {"target": "../images/voi-042/target.png", "shapes": {"S1": "../images/voi-042/shape_S1.png", "S2": "../images/voi-042/shape_S2.png"}}, "ID": "voi-042", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V2 [3,4]\nS2 180 V4 [4,4]", "solutionText": "S1 0 V2 [3,4]\nS2 180 V4 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-042\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-042/target.png", "shapes": {"S1": "images/voi-042/shape_S1.png", "S2": "images/voi-042/shape_S2.png"}}, "__sample_id__": "voi-042"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [1, 5], [3, 3]]}, {"polygon": [[2, 3], [2, 5], [0, 5], [0, 3]]}], "meta": {"seed": 4201046, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 44, "strictValidation": true}, "imageAssets": {"target": "../images/voi-043/target.png", "shapes": {"S1": "../images/voi-043/shape_S1.png", "S2": "../images/voi-043/shape_S2.png"}}, "ID": "voi-043", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 5]}]}, "legacy_answer": "S1 180 V3 [3,3]\nS2 270 V3 [0,5]", "solutionText": "S1 180 V3 [3,3]\nS2 270 V3 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-043\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-043/target.png", "shapes": {"S1": "images/voi-043/shape_S1.png", "S2": "images/voi-043/shape_S2.png"}}, "__sample_id__": "voi-043"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [1, 2], [3, 0]]}, {"polygon": [[2, 0], [2, 2], [0, 2], [0, 0]]}], "meta": {"seed": 4201047, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 45, "strictValidation": true}, "imageAssets": {"target": "../images/voi-044/target.png", "shapes": {"S1": "../images/voi-044/shape_S1.png", "S2": "../images/voi-044/shape_S2.png"}}, "ID": "voi-044", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 0]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [0, 0]}]}, "legacy_answer": "S1 180 V3 [3,0]\nS2 270 V4 [0,0]", "solutionText": "S1 180 V3 [3,0]\nS2 270 V4 [0,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-044\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-044/target.png", "shapes": {"S1": "images/voi-044/shape_S1.png", "S2": "images/voi-044/shape_S2.png"}}, "__sample_id__": "voi-044"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 3], [3, 3], [3, 5], [1, 5]]}, {"polygon": [[1, 2], [3, 2], [1, 4]]}], "meta": {"seed": 4201048, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 46, "strictValidation": true}, "imageAssets": {"target": "../images/voi-045/target.png", "shapes": {"S1": "../images/voi-045/shape_S1.png", "S2": "../images/voi-045/shape_S2.png"}}, "ID": "voi-045", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [1, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 2]}]}, "legacy_answer": "S1 0 V1 [1,3]\nS2 0 V1 [1,2]", "solutionText": "S1 0 V1 [1,3]\nS2 0 V1 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-045\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-045/target.png", "shapes": {"S1": "images/voi-045/shape_S1.png", "S2": "images/voi-045/shape_S2.png"}}, "__sample_id__": "voi-045"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [4, 6], [6, 4]]}, {"polygon": [[4, 3], [6, 3], [6, 5], [4, 5]]}], "meta": {"seed": 4201049, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 47, "strictValidation": true}, "imageAssets": {"target": "../images/voi-046/target.png", "shapes": {"S1": "../images/voi-046/shape_S1.png", "S2": "../images/voi-046/shape_S2.png"}}, "ID": "voi-046", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [6, 6]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [4, 5]}]}, "legacy_answer": "S1 180 V1 [6,6]\nS2 0 V4 [4,5]", "solutionText": "S1 180 V1 [6,6]\nS2 0 V4 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-046\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-046/target.png", "shapes": {"S1": "images/voi-046/shape_S1.png", "S2": "images/voi-046/shape_S2.png"}}, "__sample_id__": "voi-046"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 1], [2, 3], [0, 3], [0, 1]]}, {"polygon": [[3, 3], [1, 3], [3, 1]]}], "meta": {"seed": 4201050, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 48, "strictValidation": true}, "imageAssets": {"target": "../images/voi-047/target.png", "shapes": {"S1": "../images/voi-047/shape_S1.png", "S2": "../images/voi-047/shape_S2.png"}}, "ID": "voi-047", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [2, 1]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [3, 1]}]}, "legacy_answer": "S1 270 V1 [2,1]\nS2 180 V3 [3,1]", "solutionText": "S1 270 V1 [2,1]\nS2 180 V3 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-047\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-047/target.png", "shapes": {"S1": "images/voi-047/shape_S1.png", "S2": "images/voi-047/shape_S2.png"}}, "__sample_id__": "voi-047"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 3], [2, 3], [0, 5]]}, {"polygon": [[0, 4], [2, 4], [2, 6], [0, 6]]}], "meta": {"seed": 4201051, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 49, "strictValidation": true}, "imageAssets": {"target": "../images/voi-048/target.png", "shapes": {"S1": "../images/voi-048/shape_S1.png", "S2": "../images/voi-048/shape_S2.png"}}, "ID": "voi-048", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [0, 3]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [2, 4]}]}, "legacy_answer": "S1 0 V1 [0,3]\nS2 0 V2 [2,4]", "solutionText": "S1 0 V1 [0,3]\nS2 0 V2 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-048\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-048/target.png", "shapes": {"S1": "images/voi-048/shape_S1.png", "S2": "images/voi-048/shape_S2.png"}}, "__sample_id__": "voi-048"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}, {"polygon": [[2, 4], [4, 4], [2, 6]]}], "meta": {"seed": 4201052, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 50, "strictValidation": true}, "imageAssets": {"target": "../images/voi-049/target.png", "shapes": {"S1": "../images/voi-049/shape_S1.png", "S2": "../images/voi-049/shape_S2.png"}}, "ID": "voi-049", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 6]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 270 V3 [3,6]\nS2 0 V2 [4,4]", "solutionText": "S1 270 V3 [3,6]\nS2 0 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-049\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-049/target.png", "shapes": {"S1": "images/voi-049/shape_S1.png", "S2": "images/voi-049/shape_S2.png"}}, "__sample_id__": "voi-049"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 2], [2, 2], [2, 4], [0, 4]]}, {"polygon": [[5, 3], [5, 5], [3, 3]]}, {"polygon": [[4, 5], [2, 5], [2, 3], [4, 3]]}], "meta": {"seed": 4202001, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 51, "strictValidation": true}, "imageAssets": {"target": "../images/voi-050/target.png", "shapes": {"S1": "../images/voi-050/shape_S1.png", "S2": "../images/voi-050/shape_S2.png", "S3": "../images/voi-050/shape_S3.png", "S4": "../images/voi-050/shape_S4.png"}}, "ID": "voi-050", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [0, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [5, 5]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [2, 5]}]}, "legacy_answer": "S1 0 V1 [0,2]\nS3 270 V2 [5,5]\nS4 180 V2 [2,5]", "solutionText": "S1 0 V1 [0,2]\nS3 270 V2 [5,5]\nS4 180 V2 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-050\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-050/target.png", "shapes": {"S1": "images/voi-050/shape_S1.png", "S2": "images/voi-050/shape_S2.png", "S3": "images/voi-050/shape_S3.png", "S4": "images/voi-050/shape_S4.png"}}, "__sample_id__": "voi-050"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 3], [2, 3], [0, 5]]}, {"polygon": [[1, 5], [0, 5], [0, 4], [1, 4]]}, {"polygon": [[1, 4], [3, 4], [3, 6], [1, 6]]}], "meta": {"seed": 4202002, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.150442, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.166667, "difficultyScore": 0.424897, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 52, "strictValidation": true}, "imageAssets": {"target": "../images/voi-051/target.png", "shapes": {"S1": "../images/voi-051/shape_S1.png", "S2": "../images/voi-051/shape_S2.png", "S3": "../images/voi-051/shape_S3.png", "S4": "../images/voi-051/shape_S4.png"}}, "ID": "voi-051", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [0, 3]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [0, 4]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [1, 6]}]}, "legacy_answer": "S2 0 V1 [0,3]\nS3 180 V3 [0,4]\nS4 0 V4 [1,6]", "solutionText": "S2 0 V1 [0,3]\nS3 180 V3 [0,4]\nS4 0 V4 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-051\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-051/target.png", "shapes": {"S1": "images/voi-051/shape_S1.png", "S2": "images/voi-051/shape_S2.png", "S3": "images/voi-051/shape_S3.png", "S4": "images/voi-051/shape_S4.png"}}, "__sample_id__": "voi-051"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [1, 4], [3, 2]]}, {"polygon": [[1, 1], [3, 1], [3, 3], [1, 3]]}, {"polygon": [[4, 6], [2, 6], [2, 4], [4, 4]]}], "meta": {"seed": 4202003, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 53, "strictValidation": true}, "imageAssets": {"target": "../images/voi-052/target.png", "shapes": {"S1": "../images/voi-052/shape_S1.png", "S2": "../images/voi-052/shape_S2.png", "S3": "../images/voi-052/shape_S3.png", "S4": "../images/voi-052/shape_S4.png"}}, "ID": "voi-052", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 1]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [2, 6]}]}, "legacy_answer": "S2 180 V3 [3,2]\nS3 0 V1 [1,1]\nS4 180 V2 [2,6]", "solutionText": "S2 180 V3 [3,2]\nS3 0 V1 [1,1]\nS4 180 V2 [2,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-052\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-052/target.png", "shapes": {"S1": "images/voi-052/shape_S1.png", "S2": "images/voi-052/shape_S2.png", "S3": "images/voi-052/shape_S3.png", "S4": "images/voi-052/shape_S4.png"}}, "__sample_id__": "voi-052"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 6], [0, 4], [2, 4], [2, 6]]}, {"polygon": [[2, 5], [2, 3], [4, 3], [4, 5]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}], "meta": {"seed": 4202004, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.277778, "difficultyScore": 0.137778, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 54, "strictValidation": true}, "imageAssets": {"target": "../images/voi-053/target.png", "shapes": {"S1": "../images/voi-053/shape_S1.png", "S2": "../images/voi-053/shape_S2.png", "S3": "../images/voi-053/shape_S3.png", "S4": "../images/voi-053/shape_S4.png"}}, "ID": "voi-053", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [0, 4]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 2]}]}, "legacy_answer": "S2 90 V2 [0,4]\nS3 90 V4 [4,5]\nS4 90 V2 [1,2]", "solutionText": "S2 90 V2 [0,4]\nS3 90 V4 [4,5]\nS4 90 V2 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-053\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-053/target.png", "shapes": {"S1": "images/voi-053/shape_S1.png", "S2": "images/voi-053/shape_S2.png", "S3": "images/voi-053/shape_S3.png", "S4": "images/voi-053/shape_S4.png"}}, "__sample_id__": "voi-053"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 3], [4, 4], [2, 4], [2, 3]]}, {"polygon": [[3, 4], [2, 4], [3, 3]]}, {"polygon": [[4, 1], [4, 3], [2, 3], [2, 1]]}], "meta": {"seed": 4202005, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 55, "strictValidation": true}, "imageAssets": {"target": "../images/voi-054/target.png", "shapes": {"S1": "../images/voi-054/shape_S1.png", "S2": "../images/voi-054/shape_S2.png", "S3": "../images/voi-054/shape_S3.png", "S4": "../images/voi-054/shape_S4.png"}}, "ID": "voi-054", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [2, 3]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [4, 1]}]}, "legacy_answer": "S1 270 V4 [2,3]\nS2 180 V2 [2,4]\nS4 270 V1 [4,1]", "solutionText": "S1 270 V4 [2,3]\nS2 180 V2 [2,4]\nS4 270 V1 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-054\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-054/target.png", "shapes": {"S1": "images/voi-054/shape_S1.png", "S2": "images/voi-054/shape_S2.png", "S3": "images/voi-054/shape_S3.png", "S4": "images/voi-054/shape_S4.png"}}, "__sample_id__": "voi-054"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 6], [4, 4], [6, 4], [6, 6]]}, {"polygon": [[4, 6], [4, 5], [5, 6]]}, {"polygon": [[4, 2], [6, 2], [4, 4]]}], "meta": {"seed": 4202006, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 100, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 56, "strictValidation": true}, "imageAssets": {"target": "../images/voi-055/target.png", "shapes": {"S1": "../images/voi-055/shape_S1.png", "S2": "../images/voi-055/shape_S2.png", "S3": "../images/voi-055/shape_S3.png", "S4": "../images/voi-055/shape_S4.png"}}, "ID": "voi-055", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [6, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [4, 6]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [4, 2]}]}, "legacy_answer": "S1 90 V3 [6,4]\nS2 90 V1 [4,6]\nS3 0 V1 [4,2]", "solutionText": "S1 90 V3 [6,4]\nS2 90 V1 [4,6]\nS3 0 V1 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-055\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-055/target.png", "shapes": {"S1": "images/voi-055/shape_S1.png", "S2": "images/voi-055/shape_S2.png", "S3": "images/voi-055/shape_S3.png", "S4": "images/voi-055/shape_S4.png"}}, "__sample_id__": "voi-055"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 1], [5, 2], [4, 1]]}, {"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[6, 1], [5, 1], [6, 0]]}], "meta": {"seed": 4202007, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 66, "connectedComponents": 1, "fillRatio": 0.111111, "difficultyScore": 0.457284, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 57, "strictValidation": true}, "imageAssets": {"target": "../images/voi-056/target.png", "shapes": {"S1": "../images/voi-056/shape_S1.png", "S2": "../images/voi-056/shape_S2.png", "S3": "../images/voi-056/shape_S3.png", "S4": "../images/voi-056/shape_S4.png"}}, "ID": "voi-056", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 2]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [4, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 1]}]}, "legacy_answer": "S1 270 V2 [5,2]\nS3 270 V3 [4,3]\nS4 180 V2 [5,1]", "solutionText": "S1 270 V2 [5,2]\nS3 270 V3 [4,3]\nS4 180 V2 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-056\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-056/target.png", "shapes": {"S1": "images/voi-056/shape_S1.png", "S2": "images/voi-056/shape_S2.png", "S3": "images/voi-056/shape_S3.png", "S4": "images/voi-056/shape_S4.png"}}, "__sample_id__": "voi-056"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 2], [4, 2], [3, 3]]}, {"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[1, 1], [3, 1], [1, 3]]}], "meta": {"seed": 4202008, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 58, "strictValidation": true}, "imageAssets": {"target": "../images/voi-057/target.png", "shapes": {"S1": "../images/voi-057/shape_S1.png", "S2": "../images/voi-057/shape_S2.png", "S3": "../images/voi-057/shape_S3.png", "S4": "../images/voi-057/shape_S4.png"}}, "ID": "voi-057", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 2]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 2]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [1, 3]}]}, "legacy_answer": "S1 0 V2 [4,2]\nS2 270 V4 [1,2]\nS3 0 V3 [1,3]", "solutionText": "S1 0 V2 [4,2]\nS2 270 V4 [1,2]\nS3 0 V3 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-057\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-057/target.png", "shapes": {"S1": "images/voi-057/shape_S1.png", "S2": "images/voi-057/shape_S2.png", "S3": "images/voi-057/shape_S3.png", "S4": "images/voi-057/shape_S4.png"}}, "__sample_id__": "voi-057"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 3], [4, 3], [2, 5]]}, {"polygon": [[3, 2], [5, 2], [5, 3], [3, 3]]}, {"polygon": [[2, 5], [2, 4], [3, 5]]}], "meta": {"seed": 4202009, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.122449, "contourComplexity": 98, "connectedComponents": 1, "fillRatio": 0.111979, "difficultyScore": 0.646246, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 59, "strictValidation": true}, "imageAssets": {"target": "../images/voi-058/target.png", "shapes": {"S1": "../images/voi-058/shape_S1.png", "S2": "../images/voi-058/shape_S2.png", "S3": "../images/voi-058/shape_S3.png", "S4": "../images/voi-058/shape_S4.png"}}, "ID": "voi-058", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [2, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [2, 4]}]}, "legacy_answer": "S1 0 V1 [2,3]\nS2 0 V1 [3,2]\nS3 90 V2 [2,4]", "solutionText": "S1 0 V1 [2,3]\nS2 0 V1 [3,2]\nS3 90 V2 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-058\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-058/target.png", "shapes": {"S1": "images/voi-058/shape_S1.png", "S2": "images/voi-058/shape_S2.png", "S3": "images/voi-058/shape_S3.png", "S4": "images/voi-058/shape_S4.png"}}, "__sample_id__": "voi-058"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 5], [2, 5], [4, 3]]}, {"polygon": [[5, 2], [5, 4], [3, 2]]}, {"polygon": [[5, 5], [4, 5], [4, 3], [5, 3]]}], "meta": {"seed": 4202010, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 130, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 60, "strictValidation": true}, "imageAssets": {"target": "../images/voi-059/target.png", "shapes": {"S1": "../images/voi-059/shape_S1.png", "S2": "../images/voi-059/shape_S2.png", "S3": "../images/voi-059/shape_S3.png", "S4": "../images/voi-059/shape_S4.png"}}, "ID": "voi-059", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [4, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V3 [4,3]\nS2 270 V3 [3,2]\nS3 180 V3 [4,3]", "solutionText": "S1 180 V3 [4,3]\nS2 270 V3 [3,2]\nS3 180 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-059\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-059/target.png", "shapes": {"S1": "images/voi-059/shape_S1.png", "S2": "images/voi-059/shape_S2.png", "S3": "images/voi-059/shape_S3.png", "S4": "images/voi-059/shape_S4.png"}}, "__sample_id__": "voi-059"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [5, 4], [5, 6], [3, 6]]}, {"polygon": [[5, 3], [5, 5], [4, 5], [4, 3]]}, {"polygon": [[3, 4], [3, 2], [4, 2], [4, 4]]}], "meta": {"seed": 4202011, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.166667, "difficultyScore": 0.506667, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 61, "strictValidation": true}, "imageAssets": {"target": "../images/voi-060/target.png", "shapes": {"S1": "../images/voi-060/shape_S1.png", "S2": "../images/voi-060/shape_S2.png", "S3": "../images/voi-060/shape_S3.png", "S4": "../images/voi-060/shape_S4.png"}}, "ID": "voi-060", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 6]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [4, 3]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [3, 4]}]}, "legacy_answer": "S1 0 V3 [5,6]\nS3 270 V4 [4,3]\nS4 90 V1 [3,4]", "solutionText": "S1 0 V3 [5,6]\nS3 270 V4 [4,3]\nS4 90 V1 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-060\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-060/target.png", "shapes": {"S1": "images/voi-060/shape_S1.png", "S2": "images/voi-060/shape_S2.png", "S3": "images/voi-060/shape_S3.png", "S4": "images/voi-060/shape_S4.png"}}, "__sample_id__": "voi-060"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [3, 3], [4, 3], [4, 4]]}, {"polygon": [[4, 5], [2, 5], [2, 3], [4, 3]]}, {"polygon": [[6, 5], [4, 5], [4, 3], [6, 3]]}], "meta": {"seed": 4202012, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 62, "strictValidation": true}, "imageAssets": {"target": "../images/voi-061/target.png", "shapes": {"S1": "../images/voi-061/shape_S1.png", "S2": "../images/voi-061/shape_S2.png", "S3": "../images/voi-061/shape_S3.png", "S4": "../images/voi-061/shape_S4.png"}}, "ID": "voi-061", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 3]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [2, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 90 V2 [3,3]\nS3 180 V3 [2,3]\nS4 180 V2 [4,5]", "solutionText": "S1 90 V2 [3,3]\nS3 180 V3 [2,3]\nS4 180 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-061\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-061/target.png", "shapes": {"S1": "images/voi-061/shape_S1.png", "S2": "images/voi-061/shape_S2.png", "S3": "images/voi-061/shape_S3.png", "S4": "images/voi-061/shape_S4.png"}}, "__sample_id__": "voi-061"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}, {"polygon": [[1, 1], [3, 1], [3, 2], [1, 2]]}, {"polygon": [[3, 4], [3, 2], [5, 4]]}], "meta": {"seed": 4202013, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 63, "strictValidation": true}, "imageAssets": {"target": "../images/voi-062/target.png", "shapes": {"S1": "../images/voi-062/shape_S1.png", "S2": "../images/voi-062/shape_S2.png", "S3": "../images/voi-062/shape_S3.png", "S4": "../images/voi-062/shape_S4.png"}}, "ID": "voi-062", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [5, 1]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [3, 2]}]}, "legacy_answer": "S1 90 V3 [5,1]\nS2 0 V3 [3,2]\nS3 90 V2 [3,2]", "solutionText": "S1 90 V3 [5,1]\nS2 0 V3 [3,2]\nS3 90 V2 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-062\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-062/target.png", "shapes": {"S1": "images/voi-062/shape_S1.png", "S2": "images/voi-062/shape_S2.png", "S3": "images/voi-062/shape_S3.png", "S4": "images/voi-062/shape_S4.png"}}, "__sample_id__": "voi-062"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 2], [4, 4], [2, 2]]}, {"polygon": [[6, 2], [6, 3], [4, 3], [4, 2]]}, {"polygon": [[3, 2], [3, 4], [2, 4], [2, 2]]}], "meta": {"seed": 4202014, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.381191, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 64, "strictValidation": true}, "imageAssets": {"target": "../images/voi-063/target.png", "shapes": {"S1": "../images/voi-063/shape_S1.png", "S2": "../images/voi-063/shape_S2.png", "S3": "../images/voi-063/shape_S3.png", "S4": "../images/voi-063/shape_S4.png"}}, "ID": "voi-063", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [4, 2]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [4, 3]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [2, 2]}]}, "legacy_answer": "S2 270 V1 [4,2]\nS3 270 V3 [4,3]\nS4 270 V4 [2,2]", "solutionText": "S2 270 V1 [4,2]\nS3 270 V3 [4,3]\nS4 270 V4 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-063\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-063/target.png", "shapes": {"S1": "images/voi-063/shape_S1.png", "S2": "images/voi-063/shape_S2.png", "S3": "images/voi-063/shape_S3.png", "S4": "images/voi-063/shape_S4.png"}}, "__sample_id__": "voi-063"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 0], [4, 0], [4, 2], [2, 2]]}, {"polygon": [[4, 3], [4, 5], [2, 5], [2, 3]]}, {"polygon": [[4, 2], [4, 4], [2, 2]]}], "meta": {"seed": 4202015, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 65, "strictValidation": true}, "imageAssets": {"target": "../images/voi-064/target.png", "shapes": {"S1": "../images/voi-064/shape_S1.png", "S2": "../images/voi-064/shape_S2.png", "S3": "../images/voi-064/shape_S3.png", "S4": "../images/voi-064/shape_S4.png"}}, "ID": "voi-064", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 2]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [2, 3]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V4 [2,2]\nS3 270 V4 [2,3]\nS4 270 V2 [4,4]", "solutionText": "S1 0 V4 [2,2]\nS3 270 V4 [2,3]\nS4 270 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-064\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-064/target.png", "shapes": {"S1": "images/voi-064/shape_S1.png", "S2": "images/voi-064/shape_S2.png", "S3": "images/voi-064/shape_S3.png", "S4": "images/voi-064/shape_S4.png"}}, "__sample_id__": "voi-064"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 1], [4, 1], [4, 3]]}, {"polygon": [[2, 3], [2, 2], [3, 2], [3, 3]]}, {"polygon": [[2, 4], [2, 2], [4, 4]]}], "meta": {"seed": 4202016, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.111111, "difficultyScore": 0.457284, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 66, "strictValidation": true}, "imageAssets": {"target": "../images/voi-065/target.png", "shapes": {"S1": "../images/voi-065/shape_S1.png", "S2": "../images/voi-065/shape_S2.png", "S3": "../images/voi-065/shape_S3.png", "S4": "../images/voi-065/shape_S4.png"}}, "ID": "voi-065", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [4, 3]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [3, 2]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 4]}]}, "legacy_answer": "S2 90 V4 [4,3]\nS3 90 V3 [3,2]\nS4 90 V3 [4,4]", "solutionText": "S2 90 V4 [4,3]\nS3 90 V3 [3,2]\nS4 90 V3 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-065\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-065/target.png", "shapes": {"S1": "images/voi-065/shape_S1.png", "S2": "images/voi-065/shape_S2.png", "S3": "images/voi-065/shape_S3.png", "S4": "images/voi-065/shape_S4.png"}}, "__sample_id__": "voi-065"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [3, 3], [3, 1], [5, 1]]}, {"polygon": [[4, 2], [6, 2], [6, 4], [4, 4]]}, {"polygon": [[4, 5], [2, 5], [4, 3]]}], "meta": {"seed": 4202017, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.198758, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.223958, "difficultyScore": 0.187114, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 67, "strictValidation": true}, "imageAssets": {"target": "../images/voi-066/target.png", "shapes": {"S1": "../images/voi-066/shape_S1.png", "S2": "../images/voi-066/shape_S2.png", "S3": "../images/voi-066/shape_S3.png", "S4": "../images/voi-066/shape_S4.png"}}, "ID": "voi-066", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 1]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V3 [3,1]\nS2 0 V4 [4,4]\nS3 180 V3 [4,3]", "solutionText": "S1 180 V3 [3,1]\nS2 0 V4 [4,4]\nS3 180 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-066\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-066/target.png", "shapes": {"S1": "images/voi-066/shape_S1.png", "S2": "images/voi-066/shape_S2.png", "S3": "images/voi-066/shape_S3.png", "S4": "images/voi-066/shape_S4.png"}}, "__sample_id__": "voi-066"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [2, 5], [2, 4], [3, 4]]}, {"polygon": [[3, 4], [5, 4], [5, 6], [3, 6]]}, {"polygon": [[1, 4], [3, 4], [3, 6], [1, 6]]}], "meta": {"seed": 4202018, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 68, "strictValidation": true}, "imageAssets": {"target": "../images/voi-067/target.png", "shapes": {"S1": "../images/voi-067/shape_S1.png", "S2": "../images/voi-067/shape_S2.png", "S3": "../images/voi-067/shape_S3.png", "S4": "../images/voi-067/shape_S4.png"}}, "ID": "voi-067", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [2, 4]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [3, 4]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [1, 6]}]}, "legacy_answer": "S1 180 V3 [2,4]\nS3 0 V1 [3,4]\nS4 0 V4 [1,6]", "solutionText": "S1 180 V3 [2,4]\nS3 0 V1 [3,4]\nS4 0 V4 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-067\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-067/target.png", "shapes": {"S1": "images/voi-067/shape_S1.png", "S2": "images/voi-067/shape_S2.png", "S3": "images/voi-067/shape_S3.png", "S4": "images/voi-067/shape_S4.png"}}, "__sample_id__": "voi-067"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 6], [3, 6], [5, 4]]}, {"polygon": [[4, 5], [2, 5], [4, 3]]}, {"polygon": [[6, 5], [4, 5], [4, 3], [6, 3]]}], "meta": {"seed": 4202019, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.130769, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.196181, "difficultyScore": 0.444562, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 69, "strictValidation": true}, "imageAssets": {"target": "../images/voi-068/target.png", "shapes": {"S1": "../images/voi-068/shape_S1.png", "S2": "../images/voi-068/shape_S2.png", "S3": "../images/voi-068/shape_S3.png", "S4": "../images/voi-068/shape_S4.png"}}, "ID": "voi-068", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 6]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 5]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V1 [5,6]\nS2 180 V2 [2,5]\nS4 180 V3 [4,3]", "solutionText": "S1 180 V1 [5,6]\nS2 180 V2 [2,5]\nS4 180 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-068\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-068/target.png", "shapes": {"S1": "images/voi-068/shape_S1.png", "S2": "images/voi-068/shape_S2.png", "S3": "images/voi-068/shape_S3.png", "S4": "images/voi-068/shape_S4.png"}}, "__sample_id__": "voi-068"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [2, 3], [3, 3], [3, 4]]}, {"polygon": [[1, 3], [2, 3], [1, 4]]}, {"polygon": [[0, 3], [2, 3], [2, 5], [0, 5]]}], "meta": {"seed": 4202020, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.19209, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.124132, "difficultyScore": 0.360098, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 70, "strictValidation": true}, "imageAssets": {"target": "../images/voi-069/target.png", "shapes": {"S1": "../images/voi-069/shape_S1.png", "S2": "../images/voi-069/shape_S2.png", "S3": "../images/voi-069/shape_S3.png", "S4": "../images/voi-069/shape_S4.png"}}, "ID": "voi-069", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [2, 3]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 3]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [2, 5]}]}, "legacy_answer": "S1 90 V2 [2,3]\nS3 0 V1 [1,3]\nS4 0 V3 [2,5]", "solutionText": "S1 90 V2 [2,3]\nS3 0 V1 [1,3]\nS4 0 V3 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-069\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-069/target.png", "shapes": {"S1": "images/voi-069/shape_S1.png", "S2": "images/voi-069/shape_S2.png", "S3": "images/voi-069/shape_S3.png", "S4": "images/voi-069/shape_S4.png"}}, "__sample_id__": "voi-069"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 4], [1, 4], [2, 3]]}, {"polygon": [[4, 3], [2, 3], [2, 1], [4, 1]]}, {"polygon": [[2, 4], [0, 4], [2, 2]]}], "meta": {"seed": 4202021, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 100, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 71, "strictValidation": true}, "imageAssets": {"target": "../images/voi-070/target.png", "shapes": {"S1": "../images/voi-070/shape_S1.png", "S2": "../images/voi-070/shape_S2.png", "S3": "../images/voi-070/shape_S3.png", "S4": "../images/voi-070/shape_S4.png"}}, "ID": "voi-070", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [1, 4]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [0, 4]}]}, "legacy_answer": "S2 180 V2 [1,4]\nS3 180 V1 [4,3]\nS4 180 V2 [0,4]", "solutionText": "S2 180 V2 [1,4]\nS3 180 V1 [4,3]\nS4 180 V2 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-070\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-070/target.png", "shapes": {"S1": "images/voi-070/shape_S1.png", "S2": "images/voi-070/shape_S2.png", "S3": "images/voi-070/shape_S3.png", "S4": "images/voi-070/shape_S4.png"}}, "__sample_id__": "voi-070"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[0, 4], [0, 2], [2, 4]]}, {"polygon": [[2, 2], [0, 2], [0, 0], [2, 0]]}], "meta": {"seed": 4202022, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 73, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 72, "strictValidation": true}, "imageAssets": {"target": "../images/voi-071/target.png", "shapes": {"S1": "../images/voi-071/shape_S1.png", "S2": "../images/voi-071/shape_S2.png", "S3": "../images/voi-071/shape_S3.png", "S4": "../images/voi-071/shape_S4.png"}}, "ID": "voi-071", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [2, 4]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [0, 2]}]}, "legacy_answer": "S1 270 V2 [3,4]\nS2 90 V3 [2,4]\nS3 180 V2 [0,2]", "solutionText": "S1 270 V2 [3,4]\nS2 90 V3 [2,4]\nS3 180 V2 [0,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-071\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-071/target.png", "shapes": {"S1": "images/voi-071/shape_S1.png", "S2": "images/voi-071/shape_S2.png", "S3": "images/voi-071/shape_S3.png", "S4": "images/voi-071/shape_S4.png"}}, "__sample_id__": "voi-071"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 6], [0, 6], [2, 4]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}, {"polygon": [[2, 2], [3, 2], [2, 3]]}], "meta": {"seed": 4202023, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 73, "strictValidation": true}, "imageAssets": {"target": "../images/voi-072/target.png", "shapes": {"S1": "../images/voi-072/shape_S1.png", "S2": "../images/voi-072/shape_S2.png", "S3": "../images/voi-072/shape_S3.png", "S4": "../images/voi-072/shape_S4.png"}}, "ID": "voi-072", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [0, 6]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [3, 4]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [2, 2]}]}, "legacy_answer": "S1 180 V2 [0,6]\nS2 90 V4 [3,4]\nS3 0 V1 [2,2]", "solutionText": "S1 180 V2 [0,6]\nS2 90 V4 [3,4]\nS3 0 V1 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-072\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-072/target.png", "shapes": {"S1": "images/voi-072/shape_S1.png", "S2": "images/voi-072/shape_S2.png", "S3": "images/voi-072/shape_S3.png", "S4": "images/voi-072/shape_S4.png"}}, "__sample_id__": "voi-072"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 3], [3, 3], [3, 4], [2, 4]]}, {"polygon": [[1, 0], [3, 0], [3, 2], [1, 2]]}, {"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}], "meta": {"seed": 4202024, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 74, "strictValidation": true}, "imageAssets": {"target": "../images/voi-073/target.png", "shapes": {"S1": "../images/voi-073/shape_S1.png", "S2": "../images/voi-073/shape_S2.png", "S3": "../images/voi-073/shape_S3.png", "S4": "../images/voi-073/shape_S4.png"}}, "ID": "voi-073", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [3, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [1, 2]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V2 [3,3]\nS3 0 V4 [1,2]\nS4 90 V4 [4,4]", "solutionText": "S1 0 V2 [3,3]\nS3 0 V4 [1,2]\nS4 90 V4 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-073\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-073/target.png", "shapes": {"S1": "images/voi-073/shape_S1.png", "S2": "images/voi-073/shape_S2.png", "S3": "images/voi-073/shape_S3.png", "S4": "images/voi-073/shape_S4.png"}}, "__sample_id__": "voi-073"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 2], [4, 2], [4, 0], [6, 0]]}, {"polygon": [[4, 1], [4, 3], [2, 3], [2, 1]]}, {"polygon": [[3, 3], [3, 2], [4, 3]]}], "meta": {"seed": 4202025, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.207465, "difficultyScore": 0.446901, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 75, "strictValidation": true}, "imageAssets": {"target": "../images/voi-074/target.png", "shapes": {"S1": "../images/voi-074/shape_S1.png", "S2": "../images/voi-074/shape_S2.png", "S3": "../images/voi-074/shape_S3.png", "S4": "../images/voi-074/shape_S4.png"}}, "ID": "voi-074", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [6, 0]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [2, 1]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S2 180 V4 [6,0]\nS3 270 V4 [2,1]\nS4 90 V1 [3,3]", "solutionText": "S2 180 V4 [6,0]\nS3 270 V4 [2,1]\nS4 90 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-074\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-074/target.png", "shapes": {"S1": "images/voi-074/shape_S1.png", "S2": "images/voi-074/shape_S2.png", "S3": "images/voi-074/shape_S3.png", "S4": "images/voi-074/shape_S4.png"}}, "__sample_id__": "voi-074"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[4, 4], [4, 5], [2, 5], [2, 4]]}, {"polygon": [[2, 2], [4, 2], [2, 4]]}, {"polygon": [[1, 2], [3, 2], [1, 4]]}], "meta": {"seed": 4202026, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 76, "strictValidation": true}, "imageAssets": {"target": "../images/voi-075/target.png", "shapes": {"S1": "../images/voi-075/shape_S1.png", "S2": "../images/voi-075/shape_S2.png", "S3": "../images/voi-075/shape_S3.png", "S4": "../images/voi-075/shape_S4.png"}}, "ID": "voi-075", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [2, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 2]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 2]}]}, "legacy_answer": "S1 270 V4 [2,4]\nS2 0 V1 [2,2]\nS3 0 V1 [1,2]", "solutionText": "S1 270 V4 [2,4]\nS2 0 V1 [2,2]\nS3 0 V1 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-075\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-075/target.png", "shapes": {"S1": "images/voi-075/shape_S1.png", "S2": "images/voi-075/shape_S2.png", "S3": "images/voi-075/shape_S3.png", "S4": "images/voi-075/shape_S4.png"}}, "__sample_id__": "voi-075"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [2, 3], [4, 5]]}, {"polygon": [[3, 3], [1, 3], [3, 1]]}, {"polygon": [[4, 5], [3, 5], [3, 3], [4, 3]]}], "meta": {"seed": 4202027, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 77, "strictValidation": true}, "imageAssets": {"target": "../images/voi-076/target.png", "shapes": {"S1": "../images/voi-076/shape_S1.png", "S2": "../images/voi-076/shape_S2.png", "S3": "../images/voi-076/shape_S3.png", "S4": "../images/voi-076/shape_S4.png"}}, "ID": "voi-076", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [2, 3]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [3, 3]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [3, 3]}]}, "legacy_answer": "S1 90 V2 [2,3]\nS3 180 V1 [3,3]\nS4 180 V3 [3,3]", "solutionText": "S1 90 V2 [2,3]\nS3 180 V1 [3,3]\nS4 180 V3 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-076\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-076/target.png", "shapes": {"S1": "images/voi-076/shape_S1.png", "S2": "images/voi-076/shape_S2.png", "S3": "images/voi-076/shape_S3.png", "S4": "images/voi-076/shape_S4.png"}}, "__sample_id__": "voi-076"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [1, 5], [1, 3], [3, 3]]}, {"polygon": [[4, 2], [3, 2], [3, 1], [4, 1]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}], "meta": {"seed": 4202028, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 78, "strictValidation": true}, "imageAssets": {"target": "../images/voi-077/target.png", "shapes": {"S1": "../images/voi-077/shape_S1.png", "S2": "../images/voi-077/shape_S2.png", "S3": "../images/voi-077/shape_S3.png", "S4": "../images/voi-077/shape_S4.png"}}, "ID": "voi-077", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 5]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 2]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 1]}]}, "legacy_answer": "S2 180 V1 [3,5]\nS3 180 V1 [4,2]\nS4 0 V2 [4,1]", "solutionText": "S2 180 V1 [3,5]\nS3 180 V1 [4,2]\nS4 0 V2 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-077\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-077/target.png", "shapes": {"S1": "images/voi-077/shape_S1.png", "S2": "images/voi-077/shape_S2.png", "S3": "images/voi-077/shape_S3.png", "S4": "images/voi-077/shape_S4.png"}}, "__sample_id__": "voi-077"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 1], [3, 1], [3, 3], [1, 3]]}, {"polygon": [[1, 4], [1, 2], [3, 4]]}, {"polygon": [[3, 4], [3, 3], [4, 3], [4, 4]]}], "meta": {"seed": 4202029, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.150442, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.166667, "difficultyScore": 0.424897, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 79, "strictValidation": true}, "imageAssets": {"target": "../images/voi-078/target.png", "shapes": {"S1": "../images/voi-078/shape_S1.png", "S2": "../images/voi-078/shape_S2.png", "S3": "../images/voi-078/shape_S3.png", "S4": "../images/voi-078/shape_S4.png"}}, "ID": "voi-078", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 3]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 4]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V3 [3,3]\nS2 90 V1 [1,4]\nS3 90 V4 [4,4]", "solutionText": "S1 0 V3 [3,3]\nS2 90 V1 [1,4]\nS3 90 V4 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-078\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-078/target.png", "shapes": {"S1": "images/voi-078/shape_S1.png", "S2": "images/voi-078/shape_S2.png", "S3": "images/voi-078/shape_S3.png", "S4": "images/voi-078/shape_S4.png"}}, "__sample_id__": "voi-078"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 2], [2, 2], [1, 3]]}, {"polygon": [[5, 2], [5, 4], [3, 2]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}], "meta": {"seed": 4202030, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 100, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 80, "strictValidation": true}, "imageAssets": {"target": "../images/voi-079/target.png", "shapes": {"S1": "../images/voi-079/shape_S1.png", "S2": "../images/voi-079/shape_S2.png", "S3": "../images/voi-079/shape_S3.png", "S4": "../images/voi-079/shape_S4.png"}}, "ID": "voi-079", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 2]}]}, "legacy_answer": "S2 0 V1 [1,2]\nS3 270 V2 [5,4]\nS4 90 V2 [1,2]", "solutionText": "S2 0 V1 [1,2]\nS3 270 V2 [5,4]\nS4 90 V2 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-079\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-079/target.png", "shapes": {"S1": "images/voi-079/shape_S1.png", "S2": "images/voi-079/shape_S2.png", "S3": "images/voi-079/shape_S3.png", "S4": "images/voi-079/shape_S4.png"}}, "__sample_id__": "voi-079"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [4, 2], [6, 2], [6, 4]]}, {"polygon": [[5, 0], [5, 2], [3, 0]]}, {"polygon": [[4, 0], [4, 2], [3, 2], [3, 0]]}], "meta": {"seed": 4202031, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 81, "strictValidation": true}, "imageAssets": {"target": "../images/voi-080/target.png", "shapes": {"S1": "../images/voi-080/shape_S1.png", "S2": "../images/voi-080/shape_S2.png", "S3": "../images/voi-080/shape_S3.png", "S4": "../images/voi-080/shape_S4.png"}}, "ID": "voi-080", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [4, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [5, 2]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 0]}]}, "legacy_answer": "S1 90 V1 [4,4]\nS3 270 V2 [5,2]\nS4 270 V4 [3,0]", "solutionText": "S1 90 V1 [4,4]\nS3 270 V2 [5,2]\nS4 270 V4 [3,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-080\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-080/target.png", "shapes": {"S1": "images/voi-080/shape_S1.png", "S2": "images/voi-080/shape_S2.png", "S3": "images/voi-080/shape_S3.png", "S4": "images/voi-080/shape_S4.png"}}, "__sample_id__": "voi-080"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 1], [2, 1], [0, 3]]}, {"polygon": [[0, 2], [2, 2], [0, 4]]}, {"polygon": [[2, 0], [4, 0], [2, 2]]}], "meta": {"seed": 4202032, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.171717, "contourComplexity": 198, "connectedComponents": 1, "fillRatio": 0.142361, "difficultyScore": 0.388409, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 82, "strictValidation": true}, "imageAssets": {"target": "../images/voi-081/target.png", "shapes": {"S1": "../images/voi-081/shape_S1.png", "S2": "../images/voi-081/shape_S2.png", "S3": "../images/voi-081/shape_S3.png", "S4": "../images/voi-081/shape_S4.png"}}, "ID": "voi-081", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [0, 3]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [2, 2]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 0]}]}, "legacy_answer": "S1 0 V3 [0,3]\nS2 0 V2 [2,2]\nS4 0 V2 [4,0]", "solutionText": "S1 0 V3 [0,3]\nS2 0 V2 [2,2]\nS4 0 V2 [4,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-081\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-081/target.png", "shapes": {"S1": "images/voi-081/shape_S1.png", "S2": "images/voi-081/shape_S2.png", "S3": "images/voi-081/shape_S3.png", "S4": "images/voi-081/shape_S4.png"}}, "__sample_id__": "voi-081"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [3, 4], [5, 6]]}, {"polygon": [[4, 3], [3, 3], [4, 2]]}, {"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}], "meta": {"seed": 4202033, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 83, "strictValidation": true}, "imageAssets": {"target": "../images/voi-082/target.png", "shapes": {"S1": "../images/voi-082/shape_S1.png", "S2": "../images/voi-082/shape_S2.png", "S3": "../images/voi-082/shape_S3.png", "S4": "../images/voi-082/shape_S4.png"}}, "ID": "voi-082", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 6]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S2 90 V1 [3,6]\nS3 180 V3 [4,2]\nS4 90 V1 [2,4]", "solutionText": "S2 90 V1 [3,6]\nS3 180 V3 [4,2]\nS4 90 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-082\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-082/target.png", "shapes": {"S1": "images/voi-082/shape_S1.png", "S2": "images/voi-082/shape_S2.png", "S3": "images/voi-082/shape_S3.png", "S4": "images/voi-082/shape_S4.png"}}, "__sample_id__": "voi-082"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 1], [5, 3], [3, 1]]}, {"polygon": [[4, 1], [4, 3], [2, 1]]}, {"polygon": [[1, 1], [3, 1], [1, 3]]}], "meta": {"seed": 4202034, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.262626, "contourComplexity": 190, "connectedComponents": 1, "fillRatio": 0.126736, "difficultyScore": 0.637033, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 84, "strictValidation": true}, "imageAssets": {"target": "../images/voi-083/target.png", "shapes": {"S1": "../images/voi-083/shape_S1.png", "S2": "../images/voi-083/shape_S2.png", "S3": "../images/voi-083/shape_S3.png", "S4": "../images/voi-083/shape_S4.png"}}, "ID": "voi-083", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 3]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 3]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [3, 1]}]}, "legacy_answer": "S1 270 V2 [5,3]\nS3 270 V2 [4,3]\nS4 0 V2 [3,1]", "solutionText": "S1 270 V2 [5,3]\nS3 270 V2 [4,3]\nS4 0 V2 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-083\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-083/target.png", "shapes": {"S1": "images/voi-083/shape_S1.png", "S2": "images/voi-083/shape_S2.png", "S3": "images/voi-083/shape_S3.png", "S4": "images/voi-083/shape_S4.png"}}, "__sample_id__": "voi-083"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 5], [1, 3], [3, 5]]}, {"polygon": [[4, 5], [2, 5], [4, 3]]}, {"polygon": [[4, 2], [4, 4], [2, 2]]}], "meta": {"seed": 4202035, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 190, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.351477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 85, "strictValidation": true}, "imageAssets": {"target": "../images/voi-084/target.png", "shapes": {"S1": "../images/voi-084/shape_S1.png", "S2": "../images/voi-084/shape_S2.png", "S3": "../images/voi-084/shape_S3.png", "S4": "../images/voi-084/shape_S4.png"}}, "ID": "voi-084", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [1, 5]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 5]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 90 V1 [1,5]\nS2 180 V2 [2,5]\nS3 270 V2 [4,4]", "solutionText": "S1 90 V1 [1,5]\nS2 180 V2 [2,5]\nS3 270 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-084\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-084/target.png", "shapes": {"S1": "images/voi-084/shape_S1.png", "S2": "images/voi-084/shape_S2.png", "S3": "images/voi-084/shape_S3.png", "S4": "images/voi-084/shape_S4.png"}}, "__sample_id__": "voi-084"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 3], [0, 1], [1, 1], [1, 3]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}, {"polygon": [[3, 2], [3, 3], [2, 2]]}], "meta": {"seed": 4202036, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 86, "strictValidation": true}, "imageAssets": {"target": "../images/voi-085/target.png", "shapes": {"S1": "../images/voi-085/shape_S1.png", "S2": "../images/voi-085/shape_S2.png", "S3": "../images/voi-085/shape_S3.png", "S4": "../images/voi-085/shape_S4.png"}}, "ID": "voi-085", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [1, 1]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [1, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [3, 3]}]}, "legacy_answer": "S1 90 V3 [1,1]\nS2 90 V2 [1,2]\nS3 270 V2 [3,3]", "solutionText": "S1 90 V3 [1,1]\nS2 90 V2 [1,2]\nS3 270 V2 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-085\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-085/target.png", "shapes": {"S1": "images/voi-085/shape_S1.png", "S2": "images/voi-085/shape_S2.png", "S3": "images/voi-085/shape_S3.png", "S4": "images/voi-085/shape_S4.png"}}, "__sample_id__": "voi-085"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 3], [2, 2], [3, 3]]}, {"polygon": [[0, 4], [0, 3], [1, 4]]}, {"polygon": [[0, 2], [2, 2], [2, 4], [0, 4]]}], "meta": {"seed": 4202037, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 68, "connectedComponents": 1, "fillRatio": 0.111111, "difficultyScore": 0.457284, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 87, "strictValidation": true}, "imageAssets": {"target": "../images/voi-086/target.png", "shapes": {"S1": "../images/voi-086/shape_S1.png", "S2": "../images/voi-086/shape_S2.png", "S3": "../images/voi-086/shape_S3.png", "S4": "../images/voi-086/shape_S4.png"}}, "ID": "voi-086", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [2, 3]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [0, 4]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [2, 4]}]}, "legacy_answer": "S1 90 V1 [2,3]\nS2 90 V1 [0,4]\nS3 0 V3 [2,4]", "solutionText": "S1 90 V1 [2,3]\nS2 90 V1 [0,4]\nS3 0 V3 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-086\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-086/target.png", "shapes": {"S1": "images/voi-086/shape_S1.png", "S2": "images/voi-086/shape_S2.png", "S3": "images/voi-086/shape_S3.png", "S4": "images/voi-086/shape_S4.png"}}, "__sample_id__": "voi-086"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}, {"polygon": [[4, 2], [3, 2], [4, 1]]}, {"polygon": [[3, 5], [1, 5], [3, 3]]}], "meta": {"seed": 4202038, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 88, "strictValidation": true}, "imageAssets": {"target": "../images/voi-087/target.png", "shapes": {"S1": "../images/voi-087/shape_S1.png", "S2": "../images/voi-087/shape_S2.png", "S3": "../images/voi-087/shape_S3.png", "S4": "../images/voi-087/shape_S4.png"}}, "ID": "voi-087", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [4, 1]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 2]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [3, 3]}]}, "legacy_answer": "S2 0 V2 [4,1]\nS3 180 V1 [4,2]\nS4 180 V3 [3,3]", "solutionText": "S2 0 V2 [4,1]\nS3 180 V1 [4,2]\nS4 180 V3 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-087\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-087/target.png", "shapes": {"S1": "images/voi-087/shape_S1.png", "S2": "images/voi-087/shape_S2.png", "S3": "images/voi-087/shape_S3.png", "S4": "images/voi-087/shape_S4.png"}}, "__sample_id__": "voi-087"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 3], [4, 1], [6, 1], [6, 3]]}, {"polygon": [[3, 4], [3, 2], [5, 2], [5, 4]]}, {"polygon": [[4, 2], [2, 2], [4, 0]]}], "meta": {"seed": 4202039, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.198758, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.223958, "difficultyScore": 0.187114, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 89, "strictValidation": true}, "imageAssets": {"target": "../images/voi-088/target.png", "shapes": {"S1": "../images/voi-088/shape_S1.png", "S2": "../images/voi-088/shape_S2.png", "S3": "../images/voi-088/shape_S3.png", "S4": "../images/voi-088/shape_S4.png"}}, "ID": "voi-088", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 2]}]}, "legacy_answer": "S2 90 V4 [6,3]\nS3 90 V4 [5,4]\nS4 180 V1 [4,2]", "solutionText": "S2 90 V4 [6,3]\nS3 90 V4 [5,4]\nS4 180 V1 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-088\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-088/target.png", "shapes": {"S1": "images/voi-088/shape_S1.png", "S2": "images/voi-088/shape_S2.png", "S3": "images/voi-088/shape_S3.png", "S4": "images/voi-088/shape_S4.png"}}, "__sample_id__": "voi-088"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 2], [2, 4], [0, 4], [0, 2]]}, {"polygon": [[2, 2], [3, 2], [3, 3], [2, 3]]}, {"polygon": [[1, 5], [1, 3], [3, 3], [3, 5]]}], "meta": {"seed": 4202040, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 90, "strictValidation": true}, "imageAssets": {"target": "../images/voi-089/target.png", "shapes": {"S1": "../images/voi-089/shape_S1.png", "S2": "../images/voi-089/shape_S2.png", "S3": "../images/voi-089/shape_S3.png", "S4": "../images/voi-089/shape_S4.png"}}, "ID": "voi-089", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [2, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 2]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [3, 5]}]}, "legacy_answer": "S1 270 V2 [2,4]\nS2 0 V1 [2,2]\nS4 90 V4 [3,5]", "solutionText": "S1 270 V2 [2,4]\nS2 0 V1 [2,2]\nS4 90 V4 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-089\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-089/target.png", "shapes": {"S1": "images/voi-089/shape_S1.png", "S2": "images/voi-089/shape_S2.png", "S3": "images/voi-089/shape_S3.png", "S4": "images/voi-089/shape_S4.png"}}, "__sample_id__": "voi-089"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [4, 4], [4, 6], [3, 6]]}, {"polygon": [[3, 4], [1, 4], [1, 3], [3, 3]]}, {"polygon": [[2, 6], [2, 4], [4, 6]]}], "meta": {"seed": 4202041, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.381191, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 91, "strictValidation": true}, "imageAssets": {"target": "../images/voi-090/target.png", "shapes": {"S1": "../images/voi-090/shape_S1.png", "S2": "../images/voi-090/shape_S2.png", "S3": "../images/voi-090/shape_S3.png", "S4": "../images/voi-090/shape_S4.png"}}, "ID": "voi-090", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 4]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 4]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 6]}]}, "legacy_answer": "S1 0 V1 [3,4]\nS2 180 V1 [3,4]\nS3 90 V3 [4,6]", "solutionText": "S1 0 V1 [3,4]\nS2 180 V1 [3,4]\nS3 90 V3 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-090\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-090/target.png", "shapes": {"S1": "images/voi-090/shape_S1.png", "S2": "images/voi-090/shape_S2.png", "S3": "images/voi-090/shape_S3.png", "S4": "images/voi-090/shape_S4.png"}}, "__sample_id__": "voi-090"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 1], [2, 1], [2, 3], [0, 3]]}, {"polygon": [[4, 2], [4, 3], [2, 3], [2, 2]]}, {"polygon": [[2, 0], [2, 2], [0, 0]]}], "meta": {"seed": 4202042, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 92, "strictValidation": true}, "imageAssets": {"target": "../images/voi-091/target.png", "shapes": {"S1": "../images/voi-091/shape_S1.png", "S2": "../images/voi-091/shape_S2.png", "S3": "../images/voi-091/shape_S3.png", "S4": "../images/voi-091/shape_S4.png"}}, "ID": "voi-091", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [2, 1]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [2, 2]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [2, 0]}]}, "legacy_answer": "S1 0 V2 [2,1]\nS2 270 V4 [2,2]\nS4 270 V1 [2,0]", "solutionText": "S1 0 V2 [2,1]\nS2 270 V4 [2,2]\nS4 270 V1 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-091\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-091/target.png", "shapes": {"S1": "images/voi-091/shape_S1.png", "S2": "images/voi-091/shape_S2.png", "S3": "images/voi-091/shape_S3.png", "S4": "images/voi-091/shape_S4.png"}}, "__sample_id__": "voi-091"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [2, 4], [4, 2]]}, {"polygon": [[4, 2], [3, 2], [4, 1]]}, {"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}], "meta": {"seed": 4202043, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 103, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 93, "strictValidation": true}, "imageAssets": {"target": "../images/voi-092/target.png", "shapes": {"S1": "../images/voi-092/shape_S1.png", "S2": "../images/voi-092/shape_S2.png", "S3": "../images/voi-092/shape_S3.png", "S4": "../images/voi-092/shape_S4.png"}}, "ID": "voi-092", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [4, 2]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 2]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [1, 2]}]}, "legacy_answer": "S1 180 V3 [4,2]\nS3 180 V1 [4,2]\nS4 270 V4 [1,2]", "solutionText": "S1 180 V3 [4,2]\nS3 180 V1 [4,2]\nS4 270 V4 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-092\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-092/target.png", "shapes": {"S1": "images/voi-092/shape_S1.png", "S2": "images/voi-092/shape_S2.png", "S3": "images/voi-092/shape_S3.png", "S4": "images/voi-092/shape_S4.png"}}, "__sample_id__": "voi-092"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 2], [4, 2], [4, 1], [6, 1]]}, {"polygon": [[6, 3], [4, 3], [6, 1]]}, {"polygon": [[4, 2], [4, 4], [2, 2]]}], "meta": {"seed": 4202044, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 135, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 94, "strictValidation": true}, "imageAssets": {"target": "../images/voi-093/target.png", "shapes": {"S1": "../images/voi-093/shape_S1.png", "S2": "../images/voi-093/shape_S2.png", "S3": "../images/voi-093/shape_S3.png", "S4": "../images/voi-093/shape_S4.png"}}, "ID": "voi-093", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 3]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [2, 2]}]}, "legacy_answer": "S2 180 V1 [6,2]\nS3 180 V2 [4,3]\nS4 270 V3 [2,2]", "solutionText": "S2 180 V1 [6,2]\nS3 180 V2 [4,3]\nS4 270 V3 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-093\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-093/target.png", "shapes": {"S1": "images/voi-093/shape_S1.png", "S2": "images/voi-093/shape_S2.png", "S3": "images/voi-093/shape_S3.png", "S4": "images/voi-093/shape_S4.png"}}, "__sample_id__": "voi-093"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[2, 0], [4, 0], [4, 2], [2, 2]]}, {"polygon": [[1, 3], [1, 2], [3, 2], [3, 3]]}, {"polygon": [[1, 3], [1, 2], [2, 3]]}], "meta": {"seed": 4202045, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 95, "strictValidation": true}, "imageAssets": {"target": "../images/voi-094/target.png", "shapes": {"S1": "../images/voi-094/shape_S1.png", "S2": "../images/voi-094/shape_S2.png", "S3": "../images/voi-094/shape_S3.png", "S4": "../images/voi-094/shape_S4.png"}}, "ID": "voi-094", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 0]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [1, 2]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 2]}]}, "legacy_answer": "S1 0 V2 [4,0]\nS3 90 V2 [1,2]\nS4 90 V2 [1,2]", "solutionText": "S1 0 V2 [4,0]\nS3 90 V2 [1,2]\nS4 90 V2 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-094\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-094/target.png", "shapes": {"S1": "images/voi-094/shape_S1.png", "S2": "images/voi-094/shape_S2.png", "S3": "images/voi-094/shape_S3.png", "S4": "images/voi-094/shape_S4.png"}}, "__sample_id__": "voi-094"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 3], [4, 4], [3, 4], [3, 3]]}, {"polygon": [[3, 0], [5, 0], [5, 2], [3, 2]]}, {"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}], "meta": {"seed": 4202046, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 96, "strictValidation": true}, "imageAssets": {"target": "../images/voi-095/target.png", "shapes": {"S1": "../images/voi-095/shape_S1.png", "S2": "../images/voi-095/shape_S2.png", "S3": "../images/voi-095/shape_S3.png", "S4": "../images/voi-095/shape_S4.png"}}, "ID": "voi-095", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [3, 3]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 0]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S1 270 V4 [3,3]\nS2 0 V2 [5,0]\nS4 90 V1 [2,4]", "solutionText": "S1 270 V4 [3,3]\nS2 0 V2 [5,0]\nS4 90 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-095\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-095/target.png", "shapes": {"S1": "images/voi-095/shape_S1.png", "S2": "images/voi-095/shape_S2.png", "S3": "images/voi-095/shape_S3.png", "S4": "images/voi-095/shape_S4.png"}}, "__sample_id__": "voi-095"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 4], [2, 4], [4, 2]]}, {"polygon": [[3, 2], [3, 4], [2, 4], [2, 2]]}, {"polygon": [[2, 3], [2, 5], [0, 3]]}], "meta": {"seed": 4202047, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 97, "strictValidation": true}, "imageAssets": {"target": "../images/voi-096/target.png", "shapes": {"S1": "../images/voi-096/shape_S1.png", "S2": "../images/voi-096/shape_S2.png", "S3": "../images/voi-096/shape_S3.png", "S4": "../images/voi-096/shape_S4.png"}}, "ID": "voi-096", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [2, 3]}]}, "legacy_answer": "S2 180 V2 [2,4]\nS3 270 V2 [3,4]\nS4 270 V1 [2,3]", "solutionText": "S2 180 V2 [2,4]\nS3 270 V2 [3,4]\nS4 270 V1 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-096\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-096/target.png", "shapes": {"S1": "images/voi-096/shape_S1.png", "S2": "images/voi-096/shape_S2.png", "S3": "images/voi-096/shape_S3.png", "S4": "images/voi-096/shape_S4.png"}}, "__sample_id__": "voi-096"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 0], [6, 0], [6, 1], [4, 1]]}, {"polygon": [[4, 4], [4, 2], [5, 2], [5, 4]]}, {"polygon": [[6, 2], [4, 2], [6, 0]]}], "meta": {"seed": 4202048, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.381191, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 98, "strictValidation": true}, "imageAssets": {"target": "../images/voi-097/target.png", "shapes": {"S1": "../images/voi-097/shape_S1.png", "S2": "../images/voi-097/shape_S2.png", "S3": "../images/voi-097/shape_S3.png", "S4": "../images/voi-097/shape_S4.png"}}, "ID": "voi-097", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 0]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [4, 4]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S2 0 V2 [6,0]\nS3 90 V1 [4,4]\nS4 180 V2 [4,2]", "solutionText": "S2 0 V2 [6,0]\nS3 90 V1 [4,4]\nS4 180 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-097\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-097/target.png", "shapes": {"S1": "images/voi-097/shape_S1.png", "S2": "images/voi-097/shape_S2.png", "S3": "images/voi-097/shape_S3.png", "S4": "images/voi-097/shape_S4.png"}}, "__sample_id__": "voi-097"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 1], [2, 1], [2, 3], [0, 3]]}, {"polygon": [[1, 5], [1, 3], [3, 5]]}, {"polygon": [[2, 3], [4, 3], [4, 5], [2, 5]]}], "meta": {"seed": 4202049, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 99, "strictValidation": true}, "imageAssets": {"target": "../images/voi-098/target.png", "shapes": {"S1": "../images/voi-098/shape_S1.png", "S2": "../images/voi-098/shape_S2.png", "S3": "../images/voi-098/shape_S3.png", "S4": "../images/voi-098/shape_S4.png"}}, "ID": "voi-098", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [2, 3]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 5]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [2, 3]}]}, "legacy_answer": "S1 0 V3 [2,3]\nS2 90 V3 [3,5]\nS3 0 V1 [2,3]", "solutionText": "S1 0 V3 [2,3]\nS2 90 V3 [3,5]\nS3 0 V1 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-098\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-098/target.png", "shapes": {"S1": "images/voi-098/shape_S1.png", "S2": "images/voi-098/shape_S2.png", "S3": "images/voi-098/shape_S3.png", "S4": "images/voi-098/shape_S4.png"}}, "__sample_id__": "voi-098"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 4], [2, 3]]}, {"polygon": [[5, 6], [3, 6], [3, 4], [5, 4]]}, {"polygon": [[2, 4], [4, 4], [2, 6]]}], "meta": {"seed": 4202050, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 100, "strictValidation": true}, "imageAssets": {"target": "../images/voi-099/target.png", "shapes": {"S1": "../images/voi-099/shape_S1.png", "S2": "../images/voi-099/shape_S2.png", "S3": "../images/voi-099/shape_S3.png", "S4": "../images/voi-099/shape_S4.png"}}, "ID": "voi-099", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 3]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [5, 4]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 270 V3 [2,3]\nS3 180 V4 [5,4]\nS4 0 V2 [4,4]", "solutionText": "S1 270 V3 [2,3]\nS3 180 V4 [5,4]\nS4 0 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-099\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-099/target.png", "shapes": {"S1": "images/voi-099/shape_S1.png", "S2": "images/voi-099/shape_S2.png", "S3": "images/voi-099/shape_S3.png", "S4": "images/voi-099/shape_S4.png"}}, "__sample_id__": "voi-099"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [2, 2], [2, 0], [5, 0]]}, {"polygon": [[3, 1], [3, 0], [4, 0], [4, 1]]}, {"polygon": [[5, 1], [6, 1], [6, 3], [5, 3]]}], "meta": {"seed": 4203001, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 101, "strictValidation": true}, "imageAssets": {"target": "../images/voi-100/target.png", "shapes": {"S1": "../images/voi-100/shape_S1.png", "S2": "../images/voi-100/shape_S2.png", "S3": "../images/voi-100/shape_S3.png", "S4": "../images/voi-100/shape_S4.png"}}, "ID": "voi-100", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [2, 0]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 0]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 3]}]}, "legacy_answer": "S1 180 V3 [2,0]\nS3 90 V3 [4,0]\nS4 0 V4 [5,3]", "solutionText": "S1 180 V3 [2,0]\nS3 90 V3 [4,0]\nS4 0 V4 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-100\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-100/target.png", "shapes": {"S1": "images/voi-100/shape_S1.png", "S2": "images/voi-100/shape_S2.png", "S3": "images/voi-100/shape_S3.png", "S4": "images/voi-100/shape_S4.png"}}, "__sample_id__": "voi-100"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[6, 7], [5, 7], [5, 4], [6, 4]]}, {"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}], "meta": {"seed": 4203002, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.133333, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.560417, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 102, "strictValidation": true}, "imageAssets": {"target": "../images/voi-101/target.png", "shapes": {"S1": "../images/voi-101/shape_S1.png", "S2": "../images/voi-101/shape_S2.png", "S3": "../images/voi-101/shape_S3.png", "S4": "../images/voi-101/shape_S4.png"}}, "ID": "voi-101", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [8, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [5, 3]}]}, "legacy_answer": "S1 0 V3 [8,5]\nS3 180 V3 [5,4]\nS4 270 V1 [5,3]", "solutionText": "S1 0 V3 [8,5]\nS3 180 V3 [5,4]\nS4 270 V1 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-101\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-101/target.png", "shapes": {"S1": "images/voi-101/shape_S1.png", "S2": "images/voi-101/shape_S2.png", "S3": "images/voi-101/shape_S3.png", "S4": "images/voi-101/shape_S4.png"}}, "__sample_id__": "voi-101"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 8], [0, 6], [1, 6], [1, 8]]}, {"polygon": [[2, 8], [0, 8], [0, 7], [1, 7], [1, 5], [2, 5]]}, {"polygon": [[5, 7], [2, 7], [2, 5], [5, 5]]}], "meta": {"seed": 4203003, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 103, "strictValidation": true}, "imageAssets": {"target": "../images/voi-102/target.png", "shapes": {"S1": "../images/voi-102/shape_S1.png", "S2": "../images/voi-102/shape_S2.png", "S3": "../images/voi-102/shape_S3.png", "S4": "../images/voi-102/shape_S4.png"}}, "ID": "voi-102", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [0, 8]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 8]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [5, 7]}]}, "legacy_answer": "S1 90 V1 [0,8]\nS2 180 V2 [0,8]\nS4 180 V1 [5,7]", "solutionText": "S1 90 V1 [0,8]\nS2 180 V2 [0,8]\nS4 180 V1 [5,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-102\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-102/target.png", "shapes": {"S1": "images/voi-102/shape_S1.png", "S2": "images/voi-102/shape_S2.png", "S3": "images/voi-102/shape_S3.png", "S4": "images/voi-102/shape_S4.png"}}, "__sample_id__": "voi-102"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[3, 4], [3, 3], [6, 3], [6, 4]]}, {"polygon": [[2, 4], [2, 2], [3, 2], [3, 3], [5, 3], [5, 4]]}], "meta": {"seed": 4203004, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 104, "strictValidation": true}, "imageAssets": {"target": "../images/voi-103/target.png", "shapes": {"S1": "../images/voi-103/shape_S1.png", "S2": "../images/voi-103/shape_S2.png", "S3": "../images/voi-103/shape_S3.png", "S4": "../images/voi-103/shape_S4.png"}}, "ID": "voi-103", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 4]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [5, 4]}]}, "legacy_answer": "S1 270 V2 [5,6]\nS2 90 V4 [6,4]\nS4 90 V6 [5,4]", "solutionText": "S1 270 V2 [5,6]\nS2 90 V4 [6,4]\nS4 90 V6 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-103\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-103/target.png", "shapes": {"S1": "images/voi-103/shape_S1.png", "S2": "images/voi-103/shape_S2.png", "S3": "images/voi-103/shape_S3.png", "S4": "images/voi-103/shape_S4.png"}}, "__sample_id__": "voi-103"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 4], [1, 4], [1, 1], [2, 1]]}, {"polygon": [[2, 5], [2, 2], [4, 2], [4, 5]]}, {"polygon": [[3, 2], [3, 3], [2, 3], [2, 2]]}], "meta": {"seed": 4203005, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 105, "strictValidation": true}, "imageAssets": {"target": "../images/voi-104/target.png", "shapes": {"S1": "../images/voi-104/shape_S1.png", "S2": "../images/voi-104/shape_S2.png", "S3": "../images/voi-104/shape_S3.png", "S4": "../images/voi-104/shape_S4.png"}}, "ID": "voi-104", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 4]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [2, 3]}]}, "legacy_answer": "S1 180 V1 [2,4]\nS3 90 V4 [4,5]\nS4 270 V3 [2,3]", "solutionText": "S1 180 V1 [2,4]\nS3 90 V4 [4,5]\nS4 270 V3 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-104\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-104/target.png", "shapes": {"S1": "images/voi-104/shape_S1.png", "S2": "images/voi-104/shape_S2.png", "S3": "images/voi-104/shape_S3.png", "S4": "images/voi-104/shape_S4.png"}}, "__sample_id__": "voi-104"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 5], [3, 5], [3, 2], [4, 2]]}, {"polygon": [[4, 7], [3, 7], [3, 4], [4, 4]]}, {"polygon": [[3, 6], [1, 6], [1, 5], [2, 5], [2, 3], [3, 3]]}], "meta": {"seed": 4203006, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 106, "strictValidation": true}, "imageAssets": {"target": "../images/voi-105/target.png", "shapes": {"S1": "../images/voi-105/shape_S1.png", "S2": "../images/voi-105/shape_S2.png", "S3": "../images/voi-105/shape_S3.png", "S4": "../images/voi-105/shape_S4.png"}}, "ID": "voi-105", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [4, 2]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V5", "grid": [2, 3]}]}, "legacy_answer": "S1 180 V4 [4,2]\nS2 180 V4 [4,4]\nS3 180 V5 [2,3]", "solutionText": "S1 180 V4 [4,2]\nS2 180 V4 [4,4]\nS3 180 V5 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-105\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-105/target.png", "shapes": {"S1": "images/voi-105/shape_S1.png", "S2": "images/voi-105/shape_S2.png", "S3": "images/voi-105/shape_S3.png", "S4": "images/voi-105/shape_S4.png"}}, "__sample_id__": "voi-105"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [5, 4], [5, 6], [3, 6]]}, {"polygon": [[4, 5], [4, 6], [2, 6], [2, 5]]}, {"polygon": [[3, 5], [0, 5], [0, 4], [3, 4]]}], "meta": {"seed": 4203007, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 107, "strictValidation": true}, "imageAssets": {"target": "../images/voi-106/target.png", "shapes": {"S1": "../images/voi-106/shape_S1.png", "S2": "../images/voi-106/shape_S2.png", "S3": "../images/voi-106/shape_S3.png", "S4": "../images/voi-106/shape_S4.png"}}, "ID": "voi-106", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 6]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 6]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [0, 4]}]}, "legacy_answer": "S1 0 V4 [3,6]\nS3 270 V2 [4,6]\nS4 180 V3 [0,4]", "solutionText": "S1 0 V4 [3,6]\nS3 270 V2 [4,6]\nS4 180 V3 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-106\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-106/target.png", "shapes": {"S1": "images/voi-106/shape_S1.png", "S2": "images/voi-106/shape_S2.png", "S3": "images/voi-106/shape_S3.png", "S4": "images/voi-106/shape_S4.png"}}, "__sample_id__": "voi-106"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [2, 1], [4, 1], [4, 4]]}, {"polygon": [[3, 4], [5, 4], [5, 5], [4, 5], [4, 7], [3, 7]]}, {"polygon": [[5, 5], [5, 7], [3, 7], [3, 5]]}], "meta": {"seed": 4203008, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 108, "strictValidation": true}, "imageAssets": {"target": "../images/voi-107/target.png", "shapes": {"S1": "../images/voi-107/shape_S1.png", "S2": "../images/voi-107/shape_S2.png", "S3": "../images/voi-107/shape_S3.png", "S4": "../images/voi-107/shape_S4.png"}}, "ID": "voi-107", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [2, 1]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [5, 5]}]}, "legacy_answer": "S1 90 V2 [2,1]\nS2 0 V4 [4,5]\nS4 270 V1 [5,5]", "solutionText": "S1 90 V2 [2,1]\nS2 0 V4 [4,5]\nS4 270 V1 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-107\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-107/target.png", "shapes": {"S1": "images/voi-107/shape_S1.png", "S2": "images/voi-107/shape_S2.png", "S3": "images/voi-107/shape_S3.png", "S4": "images/voi-107/shape_S4.png"}}, "__sample_id__": "voi-107"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 6], [7, 6], [7, 8], [4, 8]]}, {"polygon": [[4, 7], [4, 8], [3, 8], [3, 7]]}, {"polygon": [[8, 8], [6, 8], [6, 7], [7, 7], [7, 5], [8, 5]]}], "meta": {"seed": 4203009, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 109, "strictValidation": true}, "imageAssets": {"target": "../images/voi-108/target.png", "shapes": {"S1": "../images/voi-108/shape_S1.png", "S2": "../images/voi-108/shape_S2.png", "S3": "../images/voi-108/shape_S3.png", "S4": "../images/voi-108/shape_S4.png"}}, "ID": "voi-108", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 8]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [3, 8]}, {"shape": "S3", "angle": 180, "vertex": "V5", "grid": [7, 5]}]}, "legacy_answer": "S1 0 V3 [7,8]\nS2 270 V3 [3,8]\nS3 180 V5 [7,5]", "solutionText": "S1 0 V3 [7,8]\nS2 270 V3 [3,8]\nS3 180 V5 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-108\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-108/target.png", "shapes": {"S1": "images/voi-108/shape_S1.png", "S2": "images/voi-108/shape_S2.png", "S3": "images/voi-108/shape_S3.png", "S4": "images/voi-108/shape_S4.png"}}, "__sample_id__": "voi-108"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 6], [8, 7], [5, 7], [5, 6]]}, {"polygon": [[6, 7], [3, 7], [4, 6], [6, 6]]}, {"polygon": [[4, 4], [7, 4], [7, 6], [4, 6]]}], "meta": {"seed": 4203010, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.173442, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.508381, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 110, "strictValidation": true}, "imageAssets": {"target": "../images/voi-109/target.png", "shapes": {"S1": "../images/voi-109/shape_S1.png", "S2": "../images/voi-109/shape_S2.png", "S3": "../images/voi-109/shape_S3.png", "S4": "../images/voi-109/shape_S4.png"}}, "ID": "voi-109", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [5, 7]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [6, 6]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 6]}]}, "legacy_answer": "S1 270 V3 [5,7]\nS2 180 V4 [6,6]\nS3 0 V4 [4,6]", "solutionText": "S1 270 V3 [5,7]\nS2 180 V4 [6,6]\nS3 0 V4 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-109\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-109/target.png", "shapes": {"S1": "images/voi-109/shape_S1.png", "S2": "images/voi-109/shape_S2.png", "S3": "images/voi-109/shape_S3.png", "S4": "images/voi-109/shape_S4.png"}}, "__sample_id__": "voi-109"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 6], [4, 6], [4, 8], [1, 8]]}, {"polygon": [[1, 6], [1, 3], [3, 3], [3, 6]]}, {"polygon": [[2, 5], [2, 3], [3, 3], [3, 5]]}], "meta": {"seed": 4203011, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 111, "strictValidation": true}, "imageAssets": {"target": "../images/voi-110/target.png", "shapes": {"S1": "../images/voi-110/shape_S1.png", "S2": "../images/voi-110/shape_S2.png", "S3": "../images/voi-110/shape_S3.png", "S4": "../images/voi-110/shape_S4.png"}}, "ID": "voi-110", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 6]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [1, 6]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 3]}]}, "legacy_answer": "S2 0 V1 [1,6]\nS3 90 V1 [1,6]\nS4 90 V2 [2,3]", "solutionText": "S2 0 V1 [1,6]\nS3 90 V1 [1,6]\nS4 90 V2 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-110\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-110/target.png", "shapes": {"S1": "images/voi-110/shape_S1.png", "S2": "images/voi-110/shape_S2.png", "S3": "images/voi-110/shape_S3.png", "S4": "images/voi-110/shape_S4.png"}}, "__sample_id__": "voi-110"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 4], [3, 4], [3, 6], [1, 6]]}, {"polygon": [[5, 5], [2, 5], [2, 3], [5, 3]]}, {"polygon": [[4, 8], [3, 8], [3, 5], [4, 5]]}], "meta": {"seed": 4203012, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.540865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 112, "strictValidation": true}, "imageAssets": {"target": "../images/voi-111/target.png", "shapes": {"S1": "../images/voi-111/shape_S1.png", "S2": "../images/voi-111/shape_S2.png", "S3": "../images/voi-111/shape_S3.png", "S4": "../images/voi-111/shape_S4.png"}}, "ID": "voi-111", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [1, 4]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [2, 3]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [3, 8]}]}, "legacy_answer": "S1 0 V1 [1,4]\nS2 180 V3 [2,3]\nS3 180 V2 [3,8]", "solutionText": "S1 0 V1 [1,4]\nS2 180 V3 [2,3]\nS3 180 V2 [3,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-111\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-111/target.png", "shapes": {"S1": "images/voi-111/shape_S1.png", "S2": "images/voi-111/shape_S2.png", "S3": "images/voi-111/shape_S3.png", "S4": "images/voi-111/shape_S4.png"}}, "__sample_id__": "voi-111"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [5, 5], [3, 5], [3, 2]]}, {"polygon": [[3, 6], [3, 3], [4, 3], [4, 6]]}, {"polygon": [[2, 3], [4, 3], [4, 5], [2, 5]]}], "meta": {"seed": 4203013, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 113, "strictValidation": true}, "imageAssets": {"target": "../images/voi-112/target.png", "shapes": {"S1": "../images/voi-112/shape_S1.png", "S2": "../images/voi-112/shape_S2.png", "S3": "../images/voi-112/shape_S3.png", "S4": "../images/voi-112/shape_S4.png"}}, "ID": "voi-112", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 5]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 6]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [4, 5]}]}, "legacy_answer": "S1 270 V2 [5,5]\nS2 90 V1 [3,6]\nS4 0 V3 [4,5]", "solutionText": "S1 270 V2 [5,5]\nS2 90 V1 [3,6]\nS4 0 V3 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-112\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-112/target.png", "shapes": {"S1": "images/voi-112/shape_S1.png", "S2": "images/voi-112/shape_S2.png", "S3": "images/voi-112/shape_S3.png", "S4": "images/voi-112/shape_S4.png"}}, "__sample_id__": "voi-112"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 0], [5, 0], [5, 1], [4, 1], [4, 3], [3, 3]]}, {"polygon": [[3, 2], [1, 2], [1, 1], [3, 1]]}, {"polygon": [[4, 2], [4, 0], [6, 0], [6, 2]]}], "meta": {"seed": 4203014, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 114, "strictValidation": true}, "imageAssets": {"target": "../images/voi-113/target.png", "shapes": {"S1": "../images/voi-113/shape_S1.png", "S2": "../images/voi-113/shape_S2.png", "S3": "../images/voi-113/shape_S3.png", "S4": "../images/voi-113/shape_S4.png"}}, "ID": "voi-113", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V6", "grid": [3, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [6, 2]}]}, "legacy_answer": "S1 0 V6 [3,3]\nS2 180 V1 [3,2]\nS3 90 V4 [6,2]", "solutionText": "S1 0 V6 [3,3]\nS2 180 V1 [3,2]\nS3 90 V4 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-113\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-113/target.png", "shapes": {"S1": "images/voi-113/shape_S1.png", "S2": "images/voi-113/shape_S2.png", "S3": "images/voi-113/shape_S3.png", "S4": "images/voi-113/shape_S4.png"}}, "__sample_id__": "voi-113"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 8], [2, 5], [3, 5], [3, 8]]}, {"polygon": [[2, 4], [5, 4], [5, 6], [2, 6]]}, {"polygon": [[3, 6], [1, 6], [1, 5], [3, 5]]}], "meta": {"seed": 4203015, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 115, "strictValidation": true}, "imageAssets": {"target": "../images/voi-114/target.png", "shapes": {"S1": "../images/voi-114/shape_S1.png", "S2": "../images/voi-114/shape_S2.png", "S3": "../images/voi-114/shape_S3.png", "S4": "../images/voi-114/shape_S4.png"}}, "ID": "voi-114", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 5]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [1, 5]}]}, "legacy_answer": "S2 90 V3 [3,5]\nS3 0 V4 [2,6]\nS4 180 V3 [1,5]", "solutionText": "S2 90 V3 [3,5]\nS3 0 V4 [2,6]\nS4 180 V3 [1,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-114\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-114/target.png", "shapes": {"S1": "images/voi-114/shape_S1.png", "S2": "images/voi-114/shape_S2.png", "S3": "images/voi-114/shape_S3.png", "S4": "images/voi-114/shape_S4.png"}}, "__sample_id__": "voi-114"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [5, 4], [5, 5], [4, 5], [4, 7], [3, 7]]}, {"polygon": [[6, 4], [6, 7], [4, 7], [4, 4]]}, {"polygon": [[2, 7], [4, 7], [4, 8], [2, 8]]}], "meta": {"seed": 4203016, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 116, "strictValidation": true}, "imageAssets": {"target": "../images/voi-115/target.png", "shapes": {"S1": "../images/voi-115/shape_S1.png", "S2": "../images/voi-115/shape_S2.png", "S3": "../images/voi-115/shape_S3.png", "S4": "../images/voi-115/shape_S4.png"}}, "ID": "voi-115", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [4, 5]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [4, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [2, 7]}]}, "legacy_answer": "S1 0 V4 [4,5]\nS3 270 V4 [4,4]\nS4 0 V1 [2,7]", "solutionText": "S1 0 V4 [4,5]\nS3 270 V4 [4,4]\nS4 0 V1 [2,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-115\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-115/target.png", "shapes": {"S1": "images/voi-115/shape_S1.png", "S2": "images/voi-115/shape_S2.png", "S3": "images/voi-115/shape_S3.png", "S4": "images/voi-115/shape_S4.png"}}, "__sample_id__": "voi-115"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [4, 3], [4, 4], [3, 4]]}, {"polygon": [[6, 4], [4, 4], [4, 2], [6, 2]]}, {"polygon": [[1, 2], [4, 2], [4, 4], [1, 4]]}], "meta": {"seed": 4203017, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 117, "strictValidation": true}, "imageAssets": {"target": "../images/voi-116/target.png", "shapes": {"S1": "../images/voi-116/shape_S1.png", "S2": "../images/voi-116/shape_S2.png", "S3": "../images/voi-116/shape_S3.png", "S4": "../images/voi-116/shape_S4.png"}}, "ID": "voi-116", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 3]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S1 0 V2 [4,3]\nS2 180 V3 [4,2]\nS4 0 V2 [4,2]", "solutionText": "S1 0 V2 [4,3]\nS2 180 V3 [4,2]\nS4 0 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-116\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-116/target.png", "shapes": {"S1": "images/voi-116/shape_S1.png", "S2": "images/voi-116/shape_S2.png", "S3": "images/voi-116/shape_S3.png", "S4": "images/voi-116/shape_S4.png"}}, "__sample_id__": "voi-116"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 2], [3, 2], [3, 1], [4, 1]]}, {"polygon": [[2, 3], [2, 1], [4, 1], [4, 3]]}, {"polygon": [[2, 4], [0, 4], [0, 3], [1, 3], [1, 1], [2, 1]]}], "meta": {"seed": 4203018, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 118, "strictValidation": true}, "imageAssets": {"target": "../images/voi-117/target.png", "shapes": {"S1": "../images/voi-117/shape_S1.png", "S2": "../images/voi-117/shape_S2.png", "S3": "../images/voi-117/shape_S3.png", "S4": "../images/voi-117/shape_S4.png"}}, "ID": "voi-117", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [4, 3]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S2 180 V2 [3,2]\nS3 90 V4 [4,3]\nS4 180 V1 [2,4]", "solutionText": "S2 180 V2 [3,2]\nS3 90 V4 [4,3]\nS4 180 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-117\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-117/target.png", "shapes": {"S1": "images/voi-117/shape_S1.png", "S2": "images/voi-117/shape_S2.png", "S3": "images/voi-117/shape_S3.png", "S4": "images/voi-117/shape_S4.png"}}, "__sample_id__": "voi-117"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 2], [4, 5], [2, 5], [2, 2]]}, {"polygon": [[3, 3], [3, 2], [4, 2], [4, 3]]}, {"polygon": [[0, 2], [2, 2], [2, 3], [0, 3]]}], "meta": {"seed": 4203019, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 119, "strictValidation": true}, "imageAssets": {"target": "../images/voi-118/target.png", "shapes": {"S1": "../images/voi-118/shape_S1.png", "S2": "../images/voi-118/shape_S2.png", "S3": "../images/voi-118/shape_S3.png", "S4": "../images/voi-118/shape_S4.png"}}, "ID": "voi-118", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [4, 5]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [4, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [0, 3]}]}, "legacy_answer": "S1 270 V2 [4,5]\nS2 90 V4 [4,3]\nS3 0 V4 [0,3]", "solutionText": "S1 270 V2 [4,5]\nS2 90 V4 [4,3]\nS3 0 V4 [0,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-118\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-118/target.png", "shapes": {"S1": "images/voi-118/shape_S1.png", "S2": "images/voi-118/shape_S2.png", "S3": "images/voi-118/shape_S3.png", "S4": "images/voi-118/shape_S4.png"}}, "__sample_id__": "voi-118"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [5, 6], [5, 5], [6, 5]]}, {"polygon": [[4, 7], [3, 7], [3, 5], [4, 5]]}, {"polygon": [[4, 5], [7, 5], [7, 7], [4, 7]]}], "meta": {"seed": 4203020, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 120, "strictValidation": true}, "imageAssets": {"target": "../images/voi-119/target.png", "shapes": {"S1": "../images/voi-119/shape_S1.png", "S2": "../images/voi-119/shape_S2.png", "S3": "../images/voi-119/shape_S3.png", "S4": "../images/voi-119/shape_S4.png"}}, "ID": "voi-119", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [5, 6]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 7]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 7]}]}, "legacy_answer": "S1 180 V2 [5,6]\nS2 180 V1 [4,7]\nS3 0 V4 [4,7]", "solutionText": "S1 180 V2 [5,6]\nS2 180 V1 [4,7]\nS3 0 V4 [4,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-119\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-119/target.png", "shapes": {"S1": "images/voi-119/shape_S1.png", "S2": "images/voi-119/shape_S2.png", "S3": "images/voi-119/shape_S3.png", "S4": "images/voi-119/shape_S4.png"}}, "__sample_id__": "voi-119"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 5], [0, 2], [2, 2], [2, 5]]}, {"polygon": [[0, 4], [0, 3], [1, 3], [1, 4]]}, {"polygon": [[1, 5], [3, 5], [3, 7], [1, 7]]}], "meta": {"seed": 4203021, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 121, "strictValidation": true}, "imageAssets": {"target": "../images/voi-120/target.png", "shapes": {"S1": "../images/voi-120/shape_S1.png", "S2": "../images/voi-120/shape_S2.png", "S3": "../images/voi-120/shape_S3.png", "S4": "../images/voi-120/shape_S4.png"}}, "ID": "voi-120", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [0, 2]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [1, 3]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [3, 5]}]}, "legacy_answer": "S1 90 V2 [0,2]\nS2 90 V3 [1,3]\nS4 0 V2 [3,5]", "solutionText": "S1 90 V2 [0,2]\nS2 90 V3 [1,3]\nS4 0 V2 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-120\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-120/target.png", "shapes": {"S1": "images/voi-120/shape_S1.png", "S2": "images/voi-120/shape_S2.png", "S3": "images/voi-120/shape_S3.png", "S4": "images/voi-120/shape_S4.png"}}, "__sample_id__": "voi-120"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [7, 5], [7, 7], [4, 7]]}, {"polygon": [[5, 3], [7, 3], [7, 4], [6, 4], [6, 6], [5, 6]]}, {"polygon": [[4, 4], [7, 4], [7, 5], [4, 5]]}], "meta": {"seed": 4203022, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 122, "strictValidation": true}, "imageAssets": {"target": "../images/voi-121/target.png", "shapes": {"S1": "../images/voi-121/shape_S1.png", "S2": "../images/voi-121/shape_S2.png", "S3": "../images/voi-121/shape_S3.png", "S4": "../images/voi-121/shape_S4.png"}}, "ID": "voi-121", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 7]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [7, 3]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 4]}]}, "legacy_answer": "S1 0 V3 [7,7]\nS2 0 V2 [7,3]\nS3 0 V2 [7,4]", "solutionText": "S1 0 V3 [7,7]\nS2 0 V2 [7,3]\nS3 0 V2 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-121\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-121/target.png", "shapes": {"S1": "images/voi-121/shape_S1.png", "S2": "images/voi-121/shape_S2.png", "S3": "images/voi-121/shape_S3.png", "S4": "images/voi-121/shape_S4.png"}}, "__sample_id__": "voi-121"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 1], [3, 4], [1, 4], [1, 1]]}, {"polygon": [[3, 5], [3, 2], [4, 2], [4, 5]]}, {"polygon": [[3, 3], [3, 6], [1, 6], [1, 3]]}], "meta": {"seed": 4203023, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.422917, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 123, "strictValidation": true}, "imageAssets": {"target": "../images/voi-122/target.png", "shapes": {"S1": "../images/voi-122/shape_S1.png", "S2": "../images/voi-122/shape_S2.png", "S3": "../images/voi-122/shape_S3.png", "S4": "../images/voi-122/shape_S4.png"}}, "ID": "voi-122", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [1, 4]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [1, 6]}]}, "legacy_answer": "S1 270 V3 [1,4]\nS3 90 V3 [4,2]\nS4 270 V3 [1,6]", "solutionText": "S1 270 V3 [1,4]\nS3 90 V3 [4,2]\nS4 270 V3 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-122\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-122/target.png", "shapes": {"S1": "images/voi-122/shape_S1.png", "S2": "images/voi-122/shape_S2.png", "S3": "images/voi-122/shape_S3.png", "S4": "images/voi-122/shape_S4.png"}}, "__sample_id__": "voi-122"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 1], [4, 4], [2, 4], [2, 1]]}, {"polygon": [[1, 4], [4, 4], [4, 5], [1, 5]]}, {"polygon": [[3, 4], [1, 4], [1, 3], [3, 3]]}], "meta": {"seed": 4203024, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 124, "strictValidation": true}, "imageAssets": {"target": "../images/voi-123/target.png", "shapes": {"S1": "../images/voi-123/shape_S1.png", "S2": "../images/voi-123/shape_S2.png", "S3": "../images/voi-123/shape_S3.png", "S4": "../images/voi-123/shape_S4.png"}}, "ID": "voi-123", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [4, 4]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [1, 5]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [3, 3]}]}, "legacy_answer": "S1 270 V2 [4,4]\nS2 0 V4 [1,5]\nS3 180 V4 [3,3]", "solutionText": "S1 270 V2 [4,4]\nS2 0 V4 [1,5]\nS3 180 V4 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-123\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-123/target.png", "shapes": {"S1": "images/voi-123/shape_S1.png", "S2": "images/voi-123/shape_S2.png", "S3": "images/voi-123/shape_S3.png", "S4": "images/voi-123/shape_S4.png"}}, "__sample_id__": "voi-123"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 4], [2, 1], [4, 1], [4, 4]]}, {"polygon": [[2, 1], [2, 3], [0, 3], [0, 1]]}, {"polygon": [[5, 4], [3, 4], [3, 3], [4, 3], [4, 1], [5, 1]]}], "meta": {"seed": 4203025, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.142857, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.553571, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 125, "strictValidation": true}, "imageAssets": {"target": "../images/voi-124/target.png", "shapes": {"S1": "../images/voi-124/shape_S1.png", "S2": "../images/voi-124/shape_S2.png", "S3": "../images/voi-124/shape_S3.png", "S4": "../images/voi-124/shape_S4.png"}}, "ID": "voi-124", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [4, 1]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [0, 1]}, {"shape": "S4", "angle": 180, "vertex": "V5", "grid": [4, 1]}]}, "legacy_answer": "S1 90 V3 [4,1]\nS2 270 V4 [0,1]\nS4 180 V5 [4,1]", "solutionText": "S1 90 V3 [4,1]\nS2 270 V4 [0,1]\nS4 180 V5 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-124\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-124/target.png", "shapes": {"S1": "images/voi-124/shape_S1.png", "S2": "images/voi-124/shape_S2.png", "S3": "images/voi-124/shape_S3.png", "S4": "images/voi-124/shape_S4.png"}}, "__sample_id__": "voi-124"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 8], [3, 5], [4, 6], [4, 8]]}, {"polygon": [[4, 6], [6, 6], [6, 8], [4, 8]]}, {"polygon": [[5, 4], [5, 7], [4, 6], [4, 4]]}], "meta": {"seed": 4203026, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.117241, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.781034, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 126, "strictValidation": true}, "imageAssets": {"target": "../images/voi-125/target.png", "shapes": {"S1": "../images/voi-125/shape_S1.png", "S2": "../images/voi-125/shape_S2.png", "S3": "../images/voi-125/shape_S3.png", "S4": "../images/voi-125/shape_S4.png"}}, "ID": "voi-125", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [4, 8]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 6]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [5, 4]}]}, "legacy_answer": "S1 90 V4 [4,8]\nS2 0 V2 [6,6]\nS3 270 V1 [5,4]", "solutionText": "S1 90 V4 [4,8]\nS2 0 V2 [6,6]\nS3 270 V1 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-125\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-125/target.png", "shapes": {"S1": "images/voi-125/shape_S1.png", "S2": "images/voi-125/shape_S2.png", "S3": "images/voi-125/shape_S3.png", "S4": "images/voi-125/shape_S4.png"}}, "__sample_id__": "voi-125"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 3], [1, 3], [1, 2]]}, {"polygon": [[4, 3], [1, 3], [1, 1], [4, 1]]}, {"polygon": [[7, 3], [4, 3], [4, 1], [7, 1]]}], "meta": {"seed": 4203027, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 127, "strictValidation": true}, "imageAssets": {"target": "../images/voi-126/target.png", "shapes": {"S1": "../images/voi-126/shape_S1.png", "S2": "../images/voi-126/shape_S2.png", "S3": "../images/voi-126/shape_S3.png", "S4": "../images/voi-126/shape_S4.png"}}, "ID": "voi-126", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [1, 3]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [7, 1]}]}, "legacy_answer": "S1 270 V1 [3,2]\nS3 180 V2 [1,3]\nS4 180 V4 [7,1]", "solutionText": "S1 270 V1 [3,2]\nS3 180 V2 [1,3]\nS4 180 V4 [7,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-126\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-126/target.png", "shapes": {"S1": "images/voi-126/shape_S1.png", "S2": "images/voi-126/shape_S2.png", "S3": "images/voi-126/shape_S3.png", "S4": "images/voi-126/shape_S4.png"}}, "__sample_id__": "voi-126"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 6], [3, 3], [4, 4], [4, 6]]}, {"polygon": [[3, 1], [3, 3], [2, 3], [2, 2], [0, 2], [0, 1]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}], "meta": {"seed": 4203028, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 128, "strictValidation": true}, "imageAssets": {"target": "../images/voi-127/target.png", "shapes": {"S1": "../images/voi-127/shape_S1.png", "S2": "../images/voi-127/shape_S2.png", "S3": "../images/voi-127/shape_S3.png", "S4": "../images/voi-127/shape_S4.png"}}, "ID": "voi-127", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [4, 6]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [2, 2]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S1 90 V4 [4,6]\nS2 270 V4 [2,2]\nS3 90 V3 [3,2]", "solutionText": "S1 90 V4 [4,6]\nS2 270 V4 [2,2]\nS3 90 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-127\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-127/target.png", "shapes": {"S1": "images/voi-127/shape_S1.png", "S2": "images/voi-127/shape_S2.png", "S3": "images/voi-127/shape_S3.png", "S4": "images/voi-127/shape_S4.png"}}, "__sample_id__": "voi-127"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 5], [2, 4], [2, 2]]}, {"polygon": [[3, 2], [0, 2], [0, 0], [3, 0]]}, {"polygon": [[1, 1], [2, 1], [2, 3], [1, 3]]}], "meta": {"seed": 4203029, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 43, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 129, "strictValidation": true}, "imageAssets": {"target": "../images/voi-128/target.png", "shapes": {"S1": "../images/voi-128/shape_S1.png", "S2": "../images/voi-128/shape_S2.png", "S3": "../images/voi-128/shape_S3.png", "S4": "../images/voi-128/shape_S4.png"}}, "ID": "voi-128", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 4]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 2]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [1, 1]}]}, "legacy_answer": "S1 270 V3 [2,4]\nS2 180 V2 [0,2]\nS4 0 V1 [1,1]", "solutionText": "S1 270 V3 [2,4]\nS2 180 V2 [0,2]\nS4 0 V1 [1,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-128\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-128/target.png", "shapes": {"S1": "images/voi-128/shape_S1.png", "S2": "images/voi-128/shape_S2.png", "S3": "images/voi-128/shape_S3.png", "S4": "images/voi-128/shape_S4.png"}}, "__sample_id__": "voi-128"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [4, 4], [3, 5]]}, {"polygon": [[4, 7], [4, 5], [5, 5], [5, 7]]}, {"polygon": [[4, 4], [4, 7], [2, 7], [2, 4]]}], "meta": {"seed": 4203030, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.768433, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 130, "strictValidation": true}, "imageAssets": {"target": "../images/voi-129/target.png", "shapes": {"S1": "../images/voi-129/shape_S1.png", "S2": "../images/voi-129/shape_S2.png", "S3": "../images/voi-129/shape_S3.png", "S4": "../images/voi-129/shape_S4.png"}}, "ID": "voi-129", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 5]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [4, 7]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V3 [3,5]\nS3 90 V1 [4,7]\nS4 270 V1 [4,4]", "solutionText": "S1 0 V3 [3,5]\nS3 90 V1 [4,7]\nS4 270 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-129\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-129/target.png", "shapes": {"S1": "images/voi-129/shape_S1.png", "S2": "images/voi-129/shape_S2.png", "S3": "images/voi-129/shape_S3.png", "S4": "images/voi-129/shape_S4.png"}}, "__sample_id__": "voi-129"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 1], [8, 1], [8, 3], [5, 3]]}, {"polygon": [[6, 3], [7, 3], [7, 4], [6, 4]]}, {"polygon": [[5, 3], [7, 3], [7, 5], [5, 5]]}], "meta": {"seed": 4203031, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 131, "strictValidation": true}, "imageAssets": {"target": "../images/voi-130/target.png", "shapes": {"S1": "../images/voi-130/shape_S1.png", "S2": "../images/voi-130/shape_S2.png", "S3": "../images/voi-130/shape_S3.png", "S4": "../images/voi-130/shape_S4.png"}}, "ID": "voi-130", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [5, 1]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 3]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 5]}]}, "legacy_answer": "S1 0 V1 [5,1]\nS3 0 V2 [7,3]\nS4 0 V4 [5,5]", "solutionText": "S1 0 V1 [5,1]\nS3 0 V2 [7,3]\nS4 0 V4 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-130\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-130/target.png", "shapes": {"S1": "images/voi-130/shape_S1.png", "S2": "images/voi-130/shape_S2.png", "S3": "images/voi-130/shape_S3.png", "S4": "images/voi-130/shape_S4.png"}}, "__sample_id__": "voi-130"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[2, 6], [4, 6], [4, 8], [2, 8]]}, {"polygon": [[1, 5], [2, 5], [2, 8], [1, 8]]}, {"polygon": [[3, 6], [3, 7], [2, 6]]}], "meta": {"seed": 4203032, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.141079, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.733536, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 132, "strictValidation": true}, "imageAssets": {"target": "../images/voi-131/target.png", "shapes": {"S1": "../images/voi-131/shape_S1.png", "S2": "../images/voi-131/shape_S2.png", "S3": "../images/voi-131/shape_S3.png", "S4": "../images/voi-131/shape_S4.png"}}, "ID": "voi-131", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [2, 6]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [2, 8]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 6]}]}, "legacy_answer": "S1 0 V1 [2,6]\nS2 0 V3 [2,8]\nS4 270 V1 [3,6]", "solutionText": "S1 0 V1 [2,6]\nS2 0 V3 [2,8]\nS4 270 V1 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-131\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-131/target.png", "shapes": {"S1": "images/voi-131/shape_S1.png", "S2": "images/voi-131/shape_S2.png", "S3": "images/voi-131/shape_S3.png", "S4": "images/voi-131/shape_S4.png"}}, "__sample_id__": "voi-131"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 3], [2, 5], [1, 5], [1, 3]]}, {"polygon": [[2, 7], [2, 4], [4, 4], [4, 7]]}, {"polygon": [[3, 6], [0, 6], [1, 5], [3, 5]]}], "meta": {"seed": 4203033, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 45, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 133, "strictValidation": true}, "imageAssets": {"target": "../images/voi-132/target.png", "shapes": {"S1": "../images/voi-132/shape_S1.png", "S2": "../images/voi-132/shape_S2.png", "S3": "../images/voi-132/shape_S3.png", "S4": "../images/voi-132/shape_S4.png"}}, "ID": "voi-132", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [1, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [4, 7]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [3, 5]}]}, "legacy_answer": "S1 270 V4 [1,3]\nS3 90 V4 [4,7]\nS4 180 V4 [3,5]", "solutionText": "S1 270 V4 [1,3]\nS3 90 V4 [4,7]\nS4 180 V4 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-132\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-132/target.png", "shapes": {"S1": "images/voi-132/shape_S1.png", "S2": "images/voi-132/shape_S2.png", "S3": "images/voi-132/shape_S3.png", "S4": "images/voi-132/shape_S4.png"}}, "__sample_id__": "voi-132"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 6], [0, 6], [0, 5], [1, 5], [1, 3], [2, 3]]}, {"polygon": [[3, 5], [2, 5], [2, 3], [3, 3]]}, {"polygon": [[0, 7], [0, 5], [1, 5], [1, 6], [3, 6], [3, 7]]}], "meta": {"seed": 4203034, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 134, "strictValidation": true}, "imageAssets": {"target": "../images/voi-133/target.png", "shapes": {"S1": "../images/voi-133/shape_S1.png", "S2": "../images/voi-133/shape_S2.png", "S3": "../images/voi-133/shape_S3.png", "S4": "../images/voi-133/shape_S4.png"}}, "ID": "voi-133", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 6]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [3, 5]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [0, 7]}]}, "legacy_answer": "S1 180 V1 [2,6]\nS3 180 V1 [3,5]\nS4 90 V1 [0,7]", "solutionText": "S1 180 V1 [2,6]\nS3 180 V1 [3,5]\nS4 90 V1 [0,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-133\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-133/target.png", "shapes": {"S1": "images/voi-133/shape_S1.png", "S2": "images/voi-133/shape_S2.png", "S3": "images/voi-133/shape_S3.png", "S4": "images/voi-133/shape_S4.png"}}, "__sample_id__": "voi-133"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 2], [4, 2], [4, 4], [1, 4]]}, {"polygon": [[2, 6], [0, 6], [0, 4], [2, 4]]}, {"polygon": [[2, 6], [2, 3], [4, 3], [4, 6]]}], "meta": {"seed": 4203035, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 135, "strictValidation": true}, "imageAssets": {"target": "../images/voi-134/target.png", "shapes": {"S1": "../images/voi-134/shape_S1.png", "S2": "../images/voi-134/shape_S2.png", "S3": "../images/voi-134/shape_S3.png", "S4": "../images/voi-134/shape_S4.png"}}, "ID": "voi-134", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [1, 2]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [2, 4]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 6]}]}, "legacy_answer": "S1 0 V1 [1,2]\nS2 180 V4 [2,4]\nS4 90 V1 [2,6]", "solutionText": "S1 0 V1 [1,2]\nS2 180 V4 [2,4]\nS4 90 V1 [2,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-134\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-134/target.png", "shapes": {"S1": "images/voi-134/shape_S1.png", "S2": "images/voi-134/shape_S2.png", "S3": "images/voi-134/shape_S3.png", "S4": "images/voi-134/shape_S4.png"}}, "__sample_id__": "voi-134"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 5], [5, 5], [5, 7], [3, 7]]}, {"polygon": [[4, 5], [3, 5], [3, 4], [4, 4]]}, {"polygon": [[4, 6], [4, 3], [6, 3], [6, 6]]}], "meta": {"seed": 4203036, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 136, "strictValidation": true}, "imageAssets": {"target": "../images/voi-135/target.png", "shapes": {"S1": "../images/voi-135/shape_S1.png", "S2": "../images/voi-135/shape_S2.png", "S3": "../images/voi-135/shape_S3.png", "S4": "../images/voi-135/shape_S4.png"}}, "ID": "voi-135", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 7]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [4, 4]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [4, 3]}]}, "legacy_answer": "S1 0 V3 [5,7]\nS2 180 V4 [4,4]\nS3 90 V2 [4,3]", "solutionText": "S1 0 V3 [5,7]\nS2 180 V4 [4,4]\nS3 90 V2 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-135\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-135/target.png", "shapes": {"S1": "images/voi-135/shape_S1.png", "S2": "images/voi-135/shape_S2.png", "S3": "images/voi-135/shape_S3.png", "S4": "images/voi-135/shape_S4.png"}}, "__sample_id__": "voi-135"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 7], [2, 7], [4, 5]]}, {"polygon": [[3, 6], [3, 3], [4, 3], [4, 6]]}, {"polygon": [[3, 6], [2, 6], [2, 3], [3, 3]]}], "meta": {"seed": 4203037, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.754118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 137, "strictValidation": true}, "imageAssets": {"target": "../images/voi-136/target.png", "shapes": {"S1": "../images/voi-136/shape_S1.png", "S2": "../images/voi-136/shape_S2.png", "S3": "../images/voi-136/shape_S3.png", "S4": "../images/voi-136/shape_S4.png"}}, "ID": "voi-136", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [2, 7]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [4, 6]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [2, 3]}]}, "legacy_answer": "S1 180 V2 [2,7]\nS2 90 V4 [4,6]\nS4 180 V3 [2,3]", "solutionText": "S1 180 V2 [2,7]\nS2 90 V4 [4,6]\nS4 180 V3 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-136\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-136/target.png", "shapes": {"S1": "images/voi-136/shape_S1.png", "S2": "images/voi-136/shape_S2.png", "S3": "images/voi-136/shape_S3.png", "S4": "images/voi-136/shape_S4.png"}}, "__sample_id__": "voi-136"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 3], [6, 3], [6, 4], [4, 4]]}, {"polygon": [[3, 2], [5, 2], [5, 4], [3, 4]]}, {"polygon": [[8, 3], [5, 3], [5, 2], [8, 2]]}], "meta": {"seed": 4203038, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 138, "strictValidation": true}, "imageAssets": {"target": "../images/voi-137/target.png", "shapes": {"S1": "../images/voi-137/shape_S1.png", "S2": "../images/voi-137/shape_S2.png", "S3": "../images/voi-137/shape_S3.png", "S4": "../images/voi-137/shape_S4.png"}}, "ID": "voi-137", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 3]}]}, "legacy_answer": "S1 0 V2 [6,3]\nS2 0 V1 [3,2]\nS4 180 V2 [5,3]", "solutionText": "S1 0 V2 [6,3]\nS2 0 V1 [3,2]\nS4 180 V2 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-137\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-137/target.png", "shapes": {"S1": "images/voi-137/shape_S1.png", "S2": "images/voi-137/shape_S2.png", "S3": "images/voi-137/shape_S3.png", "S4": "images/voi-137/shape_S4.png"}}, "__sample_id__": "voi-137"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 1], [7, 1], [7, 3], [4, 3]]}, {"polygon": [[3, 1], [5, 1], [5, 2], [3, 2]]}, {"polygon": [[4, 2], [4, 5], [3, 5], [3, 2]]}], "meta": {"seed": 4203039, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 139, "strictValidation": true}, "imageAssets": {"target": "../images/voi-138/target.png", "shapes": {"S1": "../images/voi-138/shape_S1.png", "S2": "../images/voi-138/shape_S2.png", "S3": "../images/voi-138/shape_S3.png", "S4": "../images/voi-138/shape_S4.png"}}, "ID": "voi-138", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [3, 2]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 0 V3 [7,3]\nS3 0 V4 [3,2]\nS4 270 V2 [4,5]", "solutionText": "S1 0 V3 [7,3]\nS3 0 V4 [3,2]\nS4 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-138\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-138/target.png", "shapes": {"S1": "images/voi-138/shape_S1.png", "S2": "images/voi-138/shape_S2.png", "S3": "images/voi-138/shape_S3.png", "S4": "images/voi-138/shape_S4.png"}}, "__sample_id__": "voi-138"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 8], [3, 8], [3, 7], [4, 7], [4, 5], [5, 5]]}, {"polygon": [[8, 4], [8, 6], [7, 6], [7, 5], [5, 5], [5, 4]]}, {"polygon": [[8, 6], [5, 6], [5, 5], [8, 5]]}], "meta": {"seed": 4203040, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 140, "strictValidation": true}, "imageAssets": {"target": "../images/voi-139/target.png", "shapes": {"S1": "../images/voi-139/shape_S1.png", "S2": "../images/voi-139/shape_S2.png", "S3": "../images/voi-139/shape_S3.png", "S4": "../images/voi-139/shape_S4.png"}}, "ID": "voi-139", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 8]}, {"shape": "S3", "angle": 270, "vertex": "V6", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [5, 5]}]}, "legacy_answer": "S2 180 V2 [3,8]\nS3 270 V6 [5,4]\nS4 180 V3 [5,5]", "solutionText": "S2 180 V2 [3,8]\nS3 270 V6 [5,4]\nS4 180 V3 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-139\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-139/target.png", "shapes": {"S1": "images/voi-139/shape_S1.png", "S2": "images/voi-139/shape_S2.png", "S3": "images/voi-139/shape_S3.png", "S4": "images/voi-139/shape_S4.png"}}, "__sample_id__": "voi-139"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 7], [5, 5], [6, 5], [6, 6], [8, 6], [8, 7]]}, {"polygon": [[7, 4], [4, 4], [5, 3], [7, 3]]}, {"polygon": [[5, 4], [7, 4], [7, 6], [5, 6]]}], "meta": {"seed": 4203041, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 141, "strictValidation": true}, "imageAssets": {"target": "../images/voi-140/target.png", "shapes": {"S1": "../images/voi-140/shape_S1.png", "S2": "../images/voi-140/shape_S2.png", "S3": "../images/voi-140/shape_S3.png", "S4": "../images/voi-140/shape_S4.png"}}, "ID": "voi-140", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [6, 5]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [5, 3]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 6]}]}, "legacy_answer": "S1 90 V3 [6,5]\nS2 180 V3 [5,3]\nS4 0 V4 [5,6]", "solutionText": "S1 90 V3 [6,5]\nS2 180 V3 [5,3]\nS4 0 V4 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-140\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-140/target.png", "shapes": {"S1": "images/voi-140/shape_S1.png", "S2": "images/voi-140/shape_S2.png", "S3": "images/voi-140/shape_S3.png", "S4": "images/voi-140/shape_S4.png"}}, "__sample_id__": "voi-140"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 3], [8, 3], [8, 4]]}, {"polygon": [[8, 4], [8, 6], [6, 4]]}, {"polygon": [[6, 5], [8, 5], [8, 7], [6, 7]]}], "meta": {"seed": 4203042, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.754118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 142, "strictValidation": true}, "imageAssets": {"target": "../images/voi-141/target.png", "shapes": {"S1": "../images/voi-141/shape_S1.png", "S2": "../images/voi-141/shape_S2.png", "S3": "../images/voi-141/shape_S3.png", "S4": "../images/voi-141/shape_S4.png"}}, "ID": "voi-141", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [6, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [6, 4]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [8, 5]}]}, "legacy_answer": "S1 90 V2 [6,3]\nS2 270 V3 [6,4]\nS3 0 V2 [8,5]", "solutionText": "S1 90 V2 [6,3]\nS2 270 V3 [6,4]\nS3 0 V2 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-141\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-141/target.png", "shapes": {"S1": "images/voi-141/shape_S1.png", "S2": "images/voi-141/shape_S2.png", "S3": "images/voi-141/shape_S3.png", "S4": "images/voi-141/shape_S4.png"}}, "__sample_id__": "voi-141"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 7], [4, 7], [4, 4]]}, {"polygon": [[3, 3], [6, 3], [5, 4], [3, 4]]}, {"polygon": [[5, 6], [5, 5], [6, 5], [6, 6]]}], "meta": {"seed": 4203043, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.425304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 143, "strictValidation": true}, "imageAssets": {"target": "../images/voi-142/target.png", "shapes": {"S1": "../images/voi-142/shape_S1.png", "S2": "../images/voi-142/shape_S2.png", "S3": "../images/voi-142/shape_S3.png", "S4": "../images/voi-142/shape_S4.png"}}, "ID": "voi-142", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [4, 4]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [3, 4]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S1 270 V4 [4,4]\nS2 0 V4 [3,4]\nS3 90 V3 [6,5]", "solutionText": "S1 270 V4 [4,4]\nS2 0 V4 [3,4]\nS3 90 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-142\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-142/target.png", "shapes": {"S1": "images/voi-142/shape_S1.png", "S2": "images/voi-142/shape_S2.png", "S3": "images/voi-142/shape_S3.png", "S4": "images/voi-142/shape_S4.png"}}, "__sample_id__": "voi-142"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[8, 4], [6, 4], [6, 3], [7, 3], [7, 1], [8, 1]]}, {"polygon": [[5, 4], [8, 4], [8, 6], [5, 6]]}, {"polygon": [[6, 5], [3, 5], [3, 3], [6, 3]]}], "meta": {"seed": 4203044, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.125, "contourComplexity": 13, "connectedComponents": 1, "fillRatio": 0.21875, "difficultyScore": 0.5625, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 144, "strictValidation": true}, "imageAssets": {"target": "../images/voi-143/target.png", "shapes": {"S1": "../images/voi-143/shape_S1.png", "S2": "../images/voi-143/shape_S2.png", "S3": "../images/voi-143/shape_S3.png", "S4": "../images/voi-143/shape_S4.png"}}, "ID": "voi-143", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V5", "grid": [7, 1]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [8, 6]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [6, 3]}]}, "legacy_answer": "S1 180 V5 [7,1]\nS2 0 V3 [8,6]\nS3 180 V4 [6,3]", "solutionText": "S1 180 V5 [7,1]\nS2 0 V3 [8,6]\nS3 180 V4 [6,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-143\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-143/target.png", "shapes": {"S1": "images/voi-143/shape_S1.png", "S2": "images/voi-143/shape_S2.png", "S3": "images/voi-143/shape_S3.png", "S4": "images/voi-143/shape_S4.png"}}, "__sample_id__": "voi-143"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [4, 1], [6, 1], [6, 4]]}, {"polygon": [[4, 0], [4, 2], [2, 2], [2, 0]]}, {"polygon": [[3, 3], [3, 2], [5, 2], [5, 3]]}], "meta": {"seed": 4203045, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 145, "strictValidation": true}, "imageAssets": {"target": "../images/voi-144/target.png", "shapes": {"S1": "../images/voi-144/shape_S1.png", "S2": "../images/voi-144/shape_S2.png", "S3": "../images/voi-144/shape_S3.png", "S4": "../images/voi-144/shape_S4.png"}}, "ID": "voi-144", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [4, 1]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [2, 2]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [5, 2]}]}, "legacy_answer": "S2 90 V2 [4,1]\nS3 270 V3 [2,2]\nS4 90 V3 [5,2]", "solutionText": "S2 90 V2 [4,1]\nS3 270 V3 [2,2]\nS4 90 V3 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-144\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-144/target.png", "shapes": {"S1": "images/voi-144/shape_S1.png", "S2": "images/voi-144/shape_S2.png", "S3": "images/voi-144/shape_S3.png", "S4": "images/voi-144/shape_S4.png"}}, "__sample_id__": "voi-144"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 3], [7, 3], [7, 5], [4, 5]]}, {"polygon": [[4, 4], [4, 6], [3, 6], [3, 5], [1, 5], [1, 4]]}, {"polygon": [[1, 6], [1, 5], [4, 5], [4, 6]]}], "meta": {"seed": 4203046, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.540865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 146, "strictValidation": true}, "imageAssets": {"target": "../images/voi-145/target.png", "shapes": {"S1": "../images/voi-145/shape_S1.png", "S2": "../images/voi-145/shape_S2.png", "S3": "../images/voi-145/shape_S3.png", "S4": "../images/voi-145/shape_S4.png"}}, "ID": "voi-145", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 5]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [3, 5]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [1, 6]}]}, "legacy_answer": "S1 0 V3 [7,5]\nS2 270 V4 [3,5]\nS3 90 V1 [1,6]", "solutionText": "S1 0 V3 [7,5]\nS2 270 V4 [3,5]\nS3 90 V1 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-145\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-145/target.png", "shapes": {"S1": "images/voi-145/shape_S1.png", "S2": "images/voi-145/shape_S2.png", "S3": "images/voi-145/shape_S3.png", "S4": "images/voi-145/shape_S4.png"}}, "__sample_id__": "voi-145"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 3], [6, 5], [5, 5], [5, 4], [3, 4], [3, 3]]}, {"polygon": [[6, 1], [8, 1], [8, 2], [7, 2], [7, 4], [6, 4]]}, {"polygon": [[5, 4], [7, 4], [7, 5], [5, 5]]}], "meta": {"seed": 4203047, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 147, "strictValidation": true}, "imageAssets": {"target": "../images/voi-146/target.png", "shapes": {"S1": "../images/voi-146/shape_S1.png", "S2": "../images/voi-146/shape_S2.png", "S3": "../images/voi-146/shape_S3.png", "S4": "../images/voi-146/shape_S4.png"}}, "ID": "voi-146", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [6, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [6, 1]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [7, 4]}]}, "legacy_answer": "S1 270 V1 [6,3]\nS2 0 V1 [6,1]\nS4 0 V2 [7,4]", "solutionText": "S1 270 V1 [6,3]\nS2 0 V1 [6,1]\nS4 0 V2 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-146\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-146/target.png", "shapes": {"S1": "images/voi-146/shape_S1.png", "S2": "images/voi-146/shape_S2.png", "S3": "images/voi-146/shape_S3.png", "S4": "images/voi-146/shape_S4.png"}}, "__sample_id__": "voi-146"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 2], [6, 2], [6, 3], [5, 3], [5, 5], [4, 5]]}, {"polygon": [[8, 4], [5, 4], [5, 2], [8, 2]]}, {"polygon": [[4, 3], [2, 3], [2, 2], [3, 2], [3, 0], [4, 0]]}], "meta": {"seed": 4203048, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.142857, "contourComplexity": 16, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.553571, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 148, "strictValidation": true}, "imageAssets": {"target": "../images/voi-147/target.png", "shapes": {"S1": "../images/voi-147/shape_S1.png", "S2": "../images/voi-147/shape_S2.png", "S3": "../images/voi-147/shape_S3.png", "S4": "../images/voi-147/shape_S4.png"}}, "ID": "voi-147", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 2]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [5, 2]}, {"shape": "S4", "angle": 180, "vertex": "V6", "grid": [4, 0]}]}, "legacy_answer": "S1 0 V2 [6,2]\nS2 180 V3 [5,2]\nS4 180 V6 [4,0]", "solutionText": "S1 0 V2 [6,2]\nS2 180 V3 [5,2]\nS4 180 V6 [4,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-147\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-147/target.png", "shapes": {"S1": "images/voi-147/shape_S1.png", "S2": "images/voi-147/shape_S2.png", "S3": "images/voi-147/shape_S3.png", "S4": "images/voi-147/shape_S4.png"}}, "__sample_id__": "voi-147"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [1, 6], [1, 5], [2, 5], [2, 3], [3, 3]]}, {"polygon": [[1, 1], [1, 4], [0, 4], [0, 1]]}, {"polygon": [[3, 2], [3, 5], [1, 5], [1, 2]]}], "meta": {"seed": 4203049, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 149, "strictValidation": true}, "imageAssets": {"target": "../images/voi-148/target.png", "shapes": {"S1": "../images/voi-148/shape_S1.png", "S2": "../images/voi-148/shape_S2.png", "S3": "../images/voi-148/shape_S3.png", "S4": "../images/voi-148/shape_S4.png"}}, "ID": "voi-148", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V6", "grid": [3, 3]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [0, 1]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [3, 5]}]}, "legacy_answer": "S1 180 V6 [3,3]\nS3 270 V4 [0,1]\nS4 270 V2 [3,5]", "solutionText": "S1 180 V6 [3,3]\nS3 270 V4 [0,1]\nS4 270 V2 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-148\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-148/target.png", "shapes": {"S1": "images/voi-148/shape_S1.png", "S2": "images/voi-148/shape_S2.png", "S3": "images/voi-148/shape_S3.png", "S4": "images/voi-148/shape_S4.png"}}, "__sample_id__": "voi-148"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 6], [4, 3], [6, 3], [6, 6]]}, {"polygon": [[7, 4], [5, 4], [5, 2], [7, 2]]}, {"polygon": [[5, 1], [7, 1], [7, 2], [6, 2], [6, 4], [5, 4]]}], "meta": {"seed": 4203050, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 150, "strictValidation": true}, "imageAssets": {"target": "../images/voi-149/target.png", "shapes": {"S1": "../images/voi-149/shape_S1.png", "S2": "../images/voi-149/shape_S2.png", "S3": "../images/voi-149/shape_S3.png", "S4": "../images/voi-149/shape_S4.png"}}, "ID": "voi-149", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [4, 6]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [7, 2]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [5, 1]}]}, "legacy_answer": "S1 90 V1 [4,6]\nS3 180 V4 [7,2]\nS4 0 V1 [5,1]", "solutionText": "S1 90 V1 [4,6]\nS3 180 V4 [7,2]\nS4 0 V1 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-149\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-149/target.png", "shapes": {"S1": "images/voi-149/shape_S1.png", "S2": "images/voi-149/shape_S2.png", "S3": "images/voi-149/shape_S3.png", "S4": "images/voi-149/shape_S4.png"}}, "__sample_id__": "voi-149"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 6], [2, 6], [3, 5], [5, 5]]}, {"polygon": [[4, 4], [7, 4], [7, 5], [4, 5]]}, {"polygon": [[7, 3], [7, 5], [6, 5], [6, 4], [4, 4], [4, 3]]}], "meta": {"seed": 4203051, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.425304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 151, "strictValidation": true}, "imageAssets": {"target": "../images/voi-150/target.png", "shapes": {"S1": "../images/voi-150/shape_S1.png", "S2": "../images/voi-150/shape_S2.png", "S3": "../images/voi-150/shape_S3.png", "S4": "../images/voi-150/shape_S4.png"}}, "ID": "voi-150", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 6]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 270, "vertex": "V6", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V1 [5,6]\nS2 0 V4 [4,5]\nS4 270 V6 [4,3]", "solutionText": "S1 180 V1 [5,6]\nS2 0 V4 [4,5]\nS4 270 V6 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-150\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-150/target.png", "shapes": {"S1": "images/voi-150/shape_S1.png", "S2": "images/voi-150/shape_S2.png", "S3": "images/voi-150/shape_S3.png", "S4": "images/voi-150/shape_S4.png"}}, "__sample_id__": "voi-150"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 0], [5, 3], [3, 3], [3, 0]]}, {"polygon": [[4, 2], [4, 0], [5, 0], [5, 1], [7, 1], [7, 2]]}, {"polygon": [[6, 5], [4, 5], [4, 4], [5, 4], [5, 2], [6, 2]]}], "meta": {"seed": 4203052, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 152, "strictValidation": true}, "imageAssets": {"target": "../images/voi-151/target.png", "shapes": {"S1": "../images/voi-151/shape_S1.png", "S2": "../images/voi-151/shape_S2.png", "S3": "../images/voi-151/shape_S3.png", "S4": "../images/voi-151/shape_S4.png"}}, "ID": "voi-151", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 0]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [5, 0]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [4, 4]}]}, "legacy_answer": "S1 270 V1 [5,0]\nS2 90 V3 [5,0]\nS4 180 V3 [4,4]", "solutionText": "S1 270 V1 [5,0]\nS2 90 V3 [5,0]\nS4 180 V3 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-151\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-151/target.png", "shapes": {"S1": "images/voi-151/shape_S1.png", "S2": "images/voi-151/shape_S2.png", "S3": "images/voi-151/shape_S3.png", "S4": "images/voi-151/shape_S4.png"}}, "__sample_id__": "voi-151"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 1], [8, 1], [8, 4]]}, {"polygon": [[5, 0], [7, 0], [7, 2], [5, 2]]}, {"polygon": [[7, 3], [5, 3], [7, 1]]}], "meta": {"seed": 4203053, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.331606, "contourComplexity": 78, "connectedComponents": 1, "fillRatio": 0.125977, "difficultyScore": 0.774472, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 153, "strictValidation": true}, "imageAssets": {"target": "../images/voi-152/target.png", "shapes": {"S1": "../images/voi-152/shape_S1.png", "S2": "../images/voi-152/shape_S2.png", "S3": "../images/voi-152/shape_S3.png", "S4": "../images/voi-152/shape_S4.png"}}, "ID": "voi-152", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [8, 1]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 0]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 3]}]}, "legacy_answer": "S1 90 V3 [8,1]\nS3 0 V2 [7,0]\nS4 180 V2 [5,3]", "solutionText": "S1 90 V3 [8,1]\nS3 0 V2 [7,0]\nS4 180 V2 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-152\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-152/target.png", "shapes": {"S1": "images/voi-152/shape_S1.png", "S2": "images/voi-152/shape_S2.png", "S3": "images/voi-152/shape_S3.png", "S4": "images/voi-152/shape_S4.png"}}, "__sample_id__": "voi-152"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 5], [1, 5], [1, 7], [0, 7]]}, {"polygon": [[2, 5], [2, 4], [3, 4], [3, 5]]}, {"polygon": [[1, 4], [4, 4], [4, 6], [1, 6]]}], "meta": {"seed": 4203054, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 154, "strictValidation": true}, "imageAssets": {"target": "../images/voi-153/target.png", "shapes": {"S1": "../images/voi-153/shape_S1.png", "S2": "../images/voi-153/shape_S2.png", "S3": "../images/voi-153/shape_S3.png", "S4": "../images/voi-153/shape_S4.png"}}, "ID": "voi-153", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [0, 7]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [2, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [1, 4]}]}, "legacy_answer": "S1 0 V4 [0,7]\nS3 90 V1 [2,5]\nS4 0 V1 [1,4]", "solutionText": "S1 0 V4 [0,7]\nS3 90 V1 [2,5]\nS4 0 V1 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-153\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-153/target.png", "shapes": {"S1": "images/voi-153/shape_S1.png", "S2": "images/voi-153/shape_S2.png", "S3": "images/voi-153/shape_S3.png", "S4": "images/voi-153/shape_S4.png"}}, "__sample_id__": "voi-153"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [5, 3], [5, 4], [3, 4]]}, {"polygon": [[5, 2], [8, 2], [8, 4], [5, 4]]}, {"polygon": [[8, 3], [8, 4], [7, 4], [7, 3]]}], "meta": {"seed": 4203055, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 155, "strictValidation": true}, "imageAssets": {"target": "../images/voi-154/target.png", "shapes": {"S1": "../images/voi-154/shape_S1.png", "S2": "../images/voi-154/shape_S2.png", "S3": "../images/voi-154/shape_S3.png", "S4": "../images/voi-154/shape_S4.png"}}, "ID": "voi-154", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [5, 2]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [7, 3]}]}, "legacy_answer": "S1 0 V1 [3,3]\nS2 0 V1 [5,2]\nS3 270 V4 [7,3]", "solutionText": "S1 0 V1 [3,3]\nS2 0 V1 [5,2]\nS3 270 V4 [7,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-154\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-154/target.png", "shapes": {"S1": "images/voi-154/shape_S1.png", "S2": "images/voi-154/shape_S2.png", "S3": "images/voi-154/shape_S3.png", "S4": "images/voi-154/shape_S4.png"}}, "__sample_id__": "voi-154"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 4], [1, 2], [2, 2], [2, 3], [4, 3], [4, 4]]}, {"polygon": [[5, 5], [3, 5], [5, 3]]}, {"polygon": [[4, 5], [4, 2], [6, 2], [6, 5]]}], "meta": {"seed": 4203056, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.253886, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.434294, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 156, "strictValidation": true}, "imageAssets": {"target": "../images/voi-155/target.png", "shapes": {"S1": "../images/voi-155/shape_S1.png", "S2": "../images/voi-155/shape_S2.png", "S3": "../images/voi-155/shape_S3.png", "S4": "../images/voi-155/shape_S4.png"}}, "ID": "voi-155", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V5", "grid": [4, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [5, 5]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [6, 5]}]}, "legacy_answer": "S1 90 V5 [4,3]\nS2 180 V1 [5,5]\nS3 90 V4 [6,5]", "solutionText": "S1 90 V5 [4,3]\nS2 180 V1 [5,5]\nS3 90 V4 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-155\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-155/target.png", "shapes": {"S1": "images/voi-155/shape_S1.png", "S2": "images/voi-155/shape_S2.png", "S3": "images/voi-155/shape_S3.png", "S4": "images/voi-155/shape_S4.png"}}, "__sample_id__": "voi-155"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [4, 7], [3, 7], [3, 6], [1, 6], [1, 5]]}, {"polygon": [[4, 6], [4, 4], [5, 4], [5, 6]]}, {"polygon": [[3, 3], [6, 3], [6, 5], [3, 5]]}], "meta": {"seed": 4203057, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 16, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 157, "strictValidation": true}, "imageAssets": {"target": "../images/voi-156/target.png", "shapes": {"S1": "../images/voi-156/shape_S1.png", "S2": "../images/voi-156/shape_S2.png", "S3": "../images/voi-156/shape_S3.png", "S4": "../images/voi-156/shape_S4.png"}}, "ID": "voi-156", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V5", "grid": [1, 6]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S1 270 V5 [1,6]\nS3 90 V3 [5,4]\nS4 0 V1 [3,3]", "solutionText": "S1 270 V5 [1,6]\nS3 90 V3 [5,4]\nS4 0 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-156\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-156/target.png", "shapes": {"S1": "images/voi-156/shape_S1.png", "S2": "images/voi-156/shape_S2.png", "S3": "images/voi-156/shape_S3.png", "S4": "images/voi-156/shape_S4.png"}}, "__sample_id__": "voi-156"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 3], [1, 3], [1, 1], [2, 1]]}, {"polygon": [[5, 2], [2, 2], [2, 0], [5, 0]]}, {"polygon": [[3, 1], [0, 1], [0, 0], [3, 0]]}], "meta": {"seed": 4203058, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 158, "strictValidation": true}, "imageAssets": {"target": "../images/voi-157/target.png", "shapes": {"S1": "../images/voi-157/shape_S1.png", "S2": "../images/voi-157/shape_S2.png", "S3": "../images/voi-157/shape_S3.png", "S4": "../images/voi-157/shape_S4.png"}}, "ID": "voi-157", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [2, 1]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [5, 0]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [3, 1]}]}, "legacy_answer": "S1 180 V4 [2,1]\nS2 180 V4 [5,0]\nS4 180 V1 [3,1]", "solutionText": "S1 180 V4 [2,1]\nS2 180 V4 [5,0]\nS4 180 V1 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-157\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-157/target.png", "shapes": {"S1": "images/voi-157/shape_S1.png", "S2": "images/voi-157/shape_S2.png", "S3": "images/voi-157/shape_S3.png", "S4": "images/voi-157/shape_S4.png"}}, "__sample_id__": "voi-157"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 6], [5, 6], [5, 5], [6, 5], [6, 3], [7, 3]]}, {"polygon": [[7, 7], [5, 7], [7, 5]]}, {"polygon": [[7, 0], [7, 3], [6, 3], [6, 0]]}], "meta": {"seed": 4203059, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.117241, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.781034, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 159, "strictValidation": true}, "imageAssets": {"target": "../images/voi-158/target.png", "shapes": {"S1": "../images/voi-158/shape_S1.png", "S2": "../images/voi-158/shape_S2.png", "S3": "../images/voi-158/shape_S3.png", "S4": "../images/voi-158/shape_S4.png"}}, "ID": "voi-158", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [5, 5]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [5, 7]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [7, 3]}]}, "legacy_answer": "S2 180 V3 [5,5]\nS3 180 V2 [5,7]\nS4 270 V2 [7,3]", "solutionText": "S2 180 V3 [5,5]\nS3 180 V2 [5,7]\nS4 270 V2 [7,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-158\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-158/target.png", "shapes": {"S1": "images/voi-158/shape_S1.png", "S2": "images/voi-158/shape_S2.png", "S3": "images/voi-158/shape_S3.png", "S4": "images/voi-158/shape_S4.png"}}, "__sample_id__": "voi-158"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [2, 4], [2, 2], [4, 2]]}, {"polygon": [[0, 3], [2, 3], [2, 5], [0, 5]]}, {"polygon": [[3, 4], [3, 6], [1, 6], [1, 4]]}], "meta": {"seed": 4203060, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 160, "strictValidation": true}, "imageAssets": {"target": "../images/voi-159/target.png", "shapes": {"S1": "../images/voi-159/shape_S1.png", "S2": "../images/voi-159/shape_S2.png", "S3": "../images/voi-159/shape_S3.png", "S4": "../images/voi-159/shape_S4.png"}}, "ID": "voi-159", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [4, 4]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [2, 3]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [3, 6]}]}, "legacy_answer": "S1 180 V1 [4,4]\nS2 0 V2 [2,3]\nS4 270 V2 [3,6]", "solutionText": "S1 180 V1 [4,4]\nS2 0 V2 [2,3]\nS4 270 V2 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-159\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-159/target.png", "shapes": {"S1": "images/voi-159/shape_S1.png", "S2": "images/voi-159/shape_S2.png", "S3": "images/voi-159/shape_S3.png", "S4": "images/voi-159/shape_S4.png"}}, "__sample_id__": "voi-159"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 5], [6, 5], [6, 7], [5, 7]]}, {"polygon": [[3, 3], [3, 6], [1, 6], [1, 3]]}, {"polygon": [[3, 5], [6, 5], [6, 7], [3, 7]]}], "meta": {"seed": 4203061, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 161, "strictValidation": true}, "imageAssets": {"target": "../images/voi-160/target.png", "shapes": {"S1": "../images/voi-160/shape_S1.png", "S2": "../images/voi-160/shape_S2.png", "S3": "../images/voi-160/shape_S3.png", "S4": "../images/voi-160/shape_S4.png"}}, "ID": "voi-160", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 5]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 6]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [6, 7]}]}, "legacy_answer": "S2 0 V2 [6,5]\nS3 270 V3 [1,6]\nS4 0 V3 [6,7]", "solutionText": "S2 0 V2 [6,5]\nS3 270 V3 [1,6]\nS4 0 V3 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-160\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-160/target.png", "shapes": {"S1": "images/voi-160/shape_S1.png", "S2": "images/voi-160/shape_S2.png", "S3": "images/voi-160/shape_S3.png", "S4": "images/voi-160/shape_S4.png"}}, "__sample_id__": "voi-160"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 2], [1, 1], [2, 2]]}, {"polygon": [[4, 1], [4, 2], [1, 2], [1, 1]]}, {"polygon": [[4, 0], [6, 0], [6, 1], [5, 1], [5, 3], [4, 3]]}], "meta": {"seed": 4203062, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.141079, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.733536, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 162, "strictValidation": true}, "imageAssets": {"target": "../images/voi-161/target.png", "shapes": {"S1": "../images/voi-161/shape_S1.png", "S2": "../images/voi-161/shape_S2.png", "S3": "../images/voi-161/shape_S3.png", "S4": "../images/voi-161/shape_S4.png"}}, "ID": "voi-161", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [1, 2]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 1]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [6, 1]}]}, "legacy_answer": "S1 90 V1 [1,2]\nS2 270 V4 [1,1]\nS3 0 V3 [6,1]", "solutionText": "S1 90 V1 [1,2]\nS2 270 V4 [1,1]\nS3 0 V3 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-161\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-161/target.png", "shapes": {"S1": "images/voi-161/shape_S1.png", "S2": "images/voi-161/shape_S2.png", "S3": "images/voi-161/shape_S3.png", "S4": "images/voi-161/shape_S4.png"}}, "__sample_id__": "voi-161"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 5], [5, 5], [5, 6], [2, 6]]}, {"polygon": [[2, 7], [5, 7], [5, 8], [2, 8]]}, {"polygon": [[2, 7], [2, 5], [3, 5], [3, 6], [5, 6], [5, 7]]}], "meta": {"seed": 4203063, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 163, "strictValidation": true}, "imageAssets": {"target": "../images/voi-162/target.png", "shapes": {"S1": "../images/voi-162/shape_S1.png", "S2": "../images/voi-162/shape_S2.png", "S3": "../images/voi-162/shape_S3.png", "S4": "../images/voi-162/shape_S4.png"}}, "ID": "voi-162", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 7]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [3, 6]}]}, "legacy_answer": "S1 0 V4 [2,6]\nS2 0 V1 [2,7]\nS4 90 V4 [3,6]", "solutionText": "S1 0 V4 [2,6]\nS2 0 V1 [2,7]\nS4 90 V4 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-162\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-162/target.png", "shapes": {"S1": "images/voi-162/shape_S1.png", "S2": "images/voi-162/shape_S2.png", "S3": "images/voi-162/shape_S3.png", "S4": "images/voi-162/shape_S4.png"}}, "__sample_id__": "voi-162"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[1, 5], [1, 3], [3, 3], [3, 5]]}, {"polygon": [[4, 2], [4, 3], [3, 2]]}, {"polygon": [[3, 4], [3, 2], [4, 2], [4, 3], [6, 3], [6, 4]]}], "meta": {"seed": 4203064, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.768433, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 164, "strictValidation": true}, "imageAssets": {"target": "../images/voi-163/target.png", "shapes": {"S1": "../images/voi-163/shape_S1.png", "S2": "../images/voi-163/shape_S2.png", "S3": "../images/voi-163/shape_S3.png", "S4": "../images/voi-163/shape_S4.png"}}, "ID": "voi-163", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [3, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S1 90 V3 [3,3]\nS2 270 V3 [3,2]\nS3 90 V3 [4,2]", "solutionText": "S1 90 V3 [3,3]\nS2 270 V3 [3,2]\nS3 90 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-163\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-163/target.png", "shapes": {"S1": "images/voi-163/shape_S1.png", "S2": "images/voi-163/shape_S2.png", "S3": "images/voi-163/shape_S3.png", "S4": "images/voi-163/shape_S4.png"}}, "__sample_id__": "voi-163"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 2], [4, 4], [2, 2]]}, {"polygon": [[4, 3], [4, 5], [3, 5], [3, 4], [1, 4], [1, 3]]}, {"polygon": [[4, 1], [4, 2], [1, 2], [1, 1]]}], "meta": {"seed": 4203065, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.117241, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.781034, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 165, "strictValidation": true}, "imageAssets": {"target": "../images/voi-164/target.png", "shapes": {"S1": "../images/voi-164/shape_S1.png", "S2": "../images/voi-164/shape_S2.png", "S3": "../images/voi-164/shape_S3.png", "S4": "../images/voi-164/shape_S4.png"}}, "ID": "voi-164", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 2]}, {"shape": "S2", "angle": 270, "vertex": "V5", "grid": [1, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S1 270 V3 [2,2]\nS2 270 V5 [1,4]\nS3 270 V2 [4,2]", "solutionText": "S1 270 V3 [2,2]\nS2 270 V5 [1,4]\nS3 270 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-164\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-164/target.png", "shapes": {"S1": "images/voi-164/shape_S1.png", "S2": "images/voi-164/shape_S2.png", "S3": "images/voi-164/shape_S3.png", "S4": "images/voi-164/shape_S4.png"}}, "__sample_id__": "voi-164"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 3], [5, 3], [5, 2], [6, 2], [6, 0], [7, 0]]}, {"polygon": [[5, 0], [5, 1], [2, 1], [2, 0]]}, {"polygon": [[6, 0], [6, 3], [5, 3], [5, 0]]}], "meta": {"seed": 4203067, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 166, "strictValidation": true}, "imageAssets": {"target": "../images/voi-165/target.png", "shapes": {"S1": "../images/voi-165/shape_S1.png", "S2": "../images/voi-165/shape_S2.png", "S3": "../images/voi-165/shape_S3.png", "S4": "../images/voi-165/shape_S4.png"}}, "ID": "voi-165", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 3]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [2, 0]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [6, 0]}]}, "legacy_answer": "S2 180 V1 [7,3]\nS3 270 V4 [2,0]\nS4 270 V1 [6,0]", "solutionText": "S2 180 V1 [7,3]\nS3 270 V4 [2,0]\nS4 270 V1 [6,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-165\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-165/target.png", "shapes": {"S1": "images/voi-165/shape_S1.png", "S2": "images/voi-165/shape_S2.png", "S3": "images/voi-165/shape_S3.png", "S4": "images/voi-165/shape_S4.png"}}, "__sample_id__": "voi-165"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 0], [6, 0], [6, 2], [3, 2]]}, {"polygon": [[2, 3], [2, 2], [5, 2], [5, 3]]}, {"polygon": [[5, 3], [5, 1], [6, 1], [6, 2], [8, 2], [8, 3]]}], "meta": {"seed": 4203068, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.540865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 167, "strictValidation": true}, "imageAssets": {"target": "../images/voi-166/target.png", "shapes": {"S1": "../images/voi-166/shape_S1.png", "S2": "../images/voi-166/shape_S2.png", "S3": "../images/voi-166/shape_S3.png", "S4": "../images/voi-166/shape_S4.png"}}, "ID": "voi-166", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [6, 2]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [2, 3]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [8, 3]}]}, "legacy_answer": "S1 0 V3 [6,2]\nS2 90 V1 [2,3]\nS4 90 V6 [8,3]", "solutionText": "S1 0 V3 [6,2]\nS2 90 V1 [2,3]\nS4 90 V6 [8,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-166\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-166/target.png", "shapes": {"S1": "images/voi-166/shape_S1.png", "S2": "images/voi-166/shape_S2.png", "S3": "images/voi-166/shape_S3.png", "S4": "images/voi-166/shape_S4.png"}}, "__sample_id__": "voi-166"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[6, 7], [3, 7], [3, 5], [6, 5]]}, {"polygon": [[6, 6], [6, 3], [7, 4], [7, 6]]}, {"polygon": [[8, 6], [8, 7], [5, 7], [5, 6]]}], "meta": {"seed": 4203069, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.173442, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.508381, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 168, "strictValidation": true}, "imageAssets": {"target": "../images/voi-167/target.png", "shapes": {"S1": "../images/voi-167/shape_S1.png", "S2": "../images/voi-167/shape_S2.png", "S3": "../images/voi-167/shape_S3.png", "S4": "../images/voi-167/shape_S4.png"}}, "ID": "voi-167", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [6, 7]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [7, 6]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [8, 6]}]}, "legacy_answer": "S1 180 V1 [6,7]\nS3 90 V4 [7,6]\nS4 270 V1 [8,6]", "solutionText": "S1 180 V1 [6,7]\nS3 90 V4 [7,6]\nS4 270 V1 [8,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-167\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-167/target.png", "shapes": {"S1": "images/voi-167/shape_S1.png", "S2": "images/voi-167/shape_S2.png", "S3": "images/voi-167/shape_S3.png", "S4": "images/voi-167/shape_S4.png"}}, "__sample_id__": "voi-167"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[1, 6], [1, 3], [3, 3], [3, 6]]}, {"polygon": [[2, 7], [2, 5], [4, 5], [4, 7]]}, {"polygon": [[4, 4], [4, 5], [3, 4]]}], "meta": {"seed": 4203070, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 169, "strictValidation": true}, "imageAssets": {"target": "../images/voi-168/target.png", "shapes": {"S1": "../images/voi-168/shape_S1.png", "S2": "../images/voi-168/shape_S2.png", "S3": "../images/voi-168/shape_S3.png", "S4": "../images/voi-168/shape_S4.png"}}, "ID": "voi-168", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 3]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [2, 5]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S2 90 V3 [3,3]\nS3 90 V2 [2,5]\nS4 270 V2 [4,5]", "solutionText": "S2 90 V3 [3,3]\nS3 90 V2 [2,5]\nS4 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-168\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-168/target.png", "shapes": {"S1": "images/voi-168/shape_S1.png", "S2": "images/voi-168/shape_S2.png", "S3": "images/voi-168/shape_S3.png", "S4": "images/voi-168/shape_S4.png"}}, "__sample_id__": "voi-168"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}, {"polygon": [[0, 3], [0, 1], [1, 1], [1, 2], [3, 2], [3, 3]]}, {"polygon": [[2, 5], [2, 3], [4, 3], [4, 5]]}], "meta": {"seed": 4203071, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 170, "strictValidation": true}, "imageAssets": {"target": "../images/voi-169/target.png", "shapes": {"S1": "../images/voi-169/shape_S1.png", "S2": "../images/voi-169/shape_S2.png", "S3": "../images/voi-169/shape_S3.png", "S4": "../images/voi-169/shape_S4.png"}}, "ID": "voi-169", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [0, 3]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 5]}]}, "legacy_answer": "S1 180 V3 [3,2]\nS3 90 V1 [0,3]\nS4 90 V1 [2,5]", "solutionText": "S1 180 V3 [3,2]\nS3 90 V1 [0,3]\nS4 90 V1 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-169\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-169/target.png", "shapes": {"S1": "images/voi-169/shape_S1.png", "S2": "images/voi-169/shape_S2.png", "S3": "images/voi-169/shape_S3.png", "S4": "images/voi-169/shape_S4.png"}}, "__sample_id__": "voi-169"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 4], [2, 4], [2, 3]]}, {"polygon": [[3, 0], [5, 0], [3, 2]]}, {"polygon": [[2, 5], [2, 2], [4, 2], [4, 5]]}], "meta": {"seed": 4203072, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.396538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 171, "strictValidation": true}, "imageAssets": {"target": "../images/voi-170/target.png", "shapes": {"S1": "../images/voi-170/shape_S1.png", "S2": "../images/voi-170/shape_S2.png", "S3": "../images/voi-170/shape_S3.png", "S4": "../images/voi-170/shape_S4.png"}}, "ID": "voi-170", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 4]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [5, 0]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 2]}]}, "legacy_answer": "S2 270 V3 [2,4]\nS3 0 V2 [5,0]\nS4 90 V2 [2,2]", "solutionText": "S2 270 V3 [2,4]\nS3 0 V2 [5,0]\nS4 90 V2 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-170\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-170/target.png", "shapes": {"S1": "images/voi-170/shape_S1.png", "S2": "images/voi-170/shape_S2.png", "S3": "images/voi-170/shape_S3.png", "S4": "images/voi-170/shape_S4.png"}}, "__sample_id__": "voi-170"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [6, 4], [6, 6], [4, 6]]}, {"polygon": [[4, 7], [4, 6], [5, 7]]}, {"polygon": [[4, 8], [4, 6], [6, 6], [6, 8]]}], "meta": {"seed": 4203073, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.768433, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 172, "strictValidation": true}, "imageAssets": {"target": "../images/voi-171/target.png", "shapes": {"S1": "../images/voi-171/shape_S1.png", "S2": "../images/voi-171/shape_S2.png", "S3": "../images/voi-171/shape_S3.png", "S4": "../images/voi-171/shape_S4.png"}}, "ID": "voi-171", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [6, 6]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [5, 7]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [6, 8]}]}, "legacy_answer": "S1 0 V3 [6,6]\nS2 90 V3 [5,7]\nS4 90 V4 [6,8]", "solutionText": "S1 0 V3 [6,6]\nS2 90 V3 [5,7]\nS4 90 V4 [6,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-171\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-171/target.png", "shapes": {"S1": "images/voi-171/shape_S1.png", "S2": "images/voi-171/shape_S2.png", "S3": "images/voi-171/shape_S3.png", "S4": "images/voi-171/shape_S4.png"}}, "__sample_id__": "voi-171"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 4], [5, 6], [4, 6], [4, 5], [2, 5], [2, 4]]}, {"polygon": [[4, 3], [4, 6], [2, 6], [2, 3]]}, {"polygon": [[0, 4], [3, 4], [3, 5], [0, 5]]}], "meta": {"seed": 4203074, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 173, "strictValidation": true}, "imageAssets": {"target": "../images/voi-172/target.png", "shapes": {"S1": "../images/voi-172/shape_S1.png", "S2": "../images/voi-172/shape_S2.png", "S3": "../images/voi-172/shape_S3.png", "S4": "../images/voi-172/shape_S4.png"}}, "ID": "voi-172", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V6", "grid": [2, 4]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 6]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [3, 4]}]}, "legacy_answer": "S1 270 V6 [2,4]\nS2 270 V3 [2,6]\nS3 0 V2 [3,4]", "solutionText": "S1 270 V6 [2,4]\nS2 270 V3 [2,6]\nS3 0 V2 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-172\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-172/target.png", "shapes": {"S1": "images/voi-172/shape_S1.png", "S2": "images/voi-172/shape_S2.png", "S3": "images/voi-172/shape_S3.png", "S4": "images/voi-172/shape_S4.png"}}, "__sample_id__": "voi-172"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 6], [2, 4], [4, 6]]}, {"polygon": [[2, 5], [2, 3], [4, 3], [4, 5]]}, {"polygon": [[2, 7], [2, 5], [3, 5], [3, 6], [5, 6], [5, 7]]}], "meta": {"seed": 4203075, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.304348, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.698641, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 174, "strictValidation": true}, "imageAssets": {"target": "../images/voi-173/target.png", "shapes": {"S1": "../images/voi-173/shape_S1.png", "S2": "../images/voi-173/shape_S2.png", "S3": "../images/voi-173/shape_S3.png", "S4": "../images/voi-173/shape_S4.png"}}, "ID": "voi-173", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [4, 6]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [2, 3]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 5]}]}, "legacy_answer": "S1 90 V3 [4,6]\nS3 90 V2 [2,3]\nS4 90 V2 [2,5]", "solutionText": "S1 90 V3 [4,6]\nS3 90 V2 [2,3]\nS4 90 V2 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-173\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-173/target.png", "shapes": {"S1": "images/voi-173/shape_S1.png", "S2": "images/voi-173/shape_S2.png", "S3": "images/voi-173/shape_S3.png", "S4": "images/voi-173/shape_S4.png"}}, "__sample_id__": "voi-173"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 2], [5, 2], [5, 3], [2, 3]]}, {"polygon": [[4, 6], [2, 6], [2, 5], [3, 5], [3, 3], [4, 3]]}, {"polygon": [[3, 3], [3, 6], [1, 6], [1, 3]]}], "meta": {"seed": 4203076, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.540865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 175, "strictValidation": true}, "imageAssets": {"target": "../images/voi-174/target.png", "shapes": {"S1": "../images/voi-174/shape_S1.png", "S2": "../images/voi-174/shape_S2.png", "S3": "../images/voi-174/shape_S3.png", "S4": "../images/voi-174/shape_S4.png"}}, "ID": "voi-174", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 2]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 6]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S2 0 V2 [5,2]\nS3 180 V1 [4,6]\nS4 270 V1 [3,3]", "solutionText": "S2 0 V2 [5,2]\nS3 180 V1 [4,6]\nS4 270 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-174\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-174/target.png", "shapes": {"S1": "images/voi-174/shape_S1.png", "S2": "images/voi-174/shape_S2.png", "S3": "images/voi-174/shape_S3.png", "S4": "images/voi-174/shape_S4.png"}}, "__sample_id__": "voi-174"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 3], [6, 3], [4, 5]]}, {"polygon": [[2, 4], [4, 4], [4, 6], [2, 6]]}, {"polygon": [[4, 3], [4, 5], [2, 3]]}], "meta": {"seed": 4203077, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.130769, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.75622, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 176, "strictValidation": true}, "imageAssets": {"target": "../images/voi-175/target.png", "shapes": {"S1": "../images/voi-175/shape_S1.png", "S2": "../images/voi-175/shape_S2.png", "S3": "../images/voi-175/shape_S3.png", "S4": "../images/voi-175/shape_S4.png"}}, "ID": "voi-175", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S2 0 V2 [6,3]\nS3 0 V4 [2,6]\nS4 270 V2 [4,5]", "solutionText": "S2 0 V2 [6,3]\nS3 0 V4 [2,6]\nS4 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-175\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-175/target.png", "shapes": {"S1": "images/voi-175/shape_S1.png", "S2": "images/voi-175/shape_S2.png", "S3": "images/voi-175/shape_S3.png", "S4": "images/voi-175/shape_S4.png"}}, "__sample_id__": "voi-175"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 6], [5, 5], [6, 5], [6, 6]]}, {"polygon": [[4, 6], [4, 3], [6, 3], [6, 6]]}, {"polygon": [[4, 4], [2, 4], [4, 2]]}], "meta": {"seed": 4203078, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.396538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 177, "strictValidation": true}, "imageAssets": {"target": "../images/voi-176/target.png", "shapes": {"S1": "../images/voi-176/shape_S1.png", "S2": "../images/voi-176/shape_S2.png", "S3": "../images/voi-176/shape_S3.png", "S4": "../images/voi-176/shape_S4.png"}}, "ID": "voi-176", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [5, 6]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 6]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S1 90 V1 [5,6]\nS2 90 V4 [6,6]\nS3 180 V3 [4,2]", "solutionText": "S1 90 V1 [5,6]\nS2 90 V4 [6,6]\nS3 180 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-176\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-176/target.png", "shapes": {"S1": "images/voi-176/shape_S1.png", "S2": "images/voi-176/shape_S2.png", "S3": "images/voi-176/shape_S3.png", "S4": "images/voi-176/shape_S4.png"}}, "__sample_id__": "voi-176"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}, {"polygon": [[5, 2], [2, 2], [3, 1], [5, 1]]}, {"polygon": [[5, 4], [3, 4], [3, 3], [4, 3], [4, 1], [5, 1]]}], "meta": {"seed": 4203079, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 178, "strictValidation": true}, "imageAssets": {"target": "../images/voi-177/target.png", "shapes": {"S1": "../images/voi-177/shape_S1.png", "S2": "../images/voi-177/shape_S2.png", "S3": "../images/voi-177/shape_S3.png", "S4": "../images/voi-177/shape_S4.png"}}, "ID": "voi-177", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [5, 1]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [4, 3]}]}, "legacy_answer": "S2 90 V4 [3,4]\nS3 180 V4 [5,1]\nS4 180 V4 [4,3]", "solutionText": "S2 90 V4 [3,4]\nS3 180 V4 [5,1]\nS4 180 V4 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-177\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-177/target.png", "shapes": {"S1": "images/voi-177/shape_S1.png", "S2": "images/voi-177/shape_S2.png", "S3": "images/voi-177/shape_S3.png", "S4": "images/voi-177/shape_S4.png"}}, "__sample_id__": "voi-177"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 3], [4, 0], [5, 0], [5, 3]]}, {"polygon": [[2, 0], [4, 0], [4, 1], [3, 1], [3, 3], [2, 3]]}, {"polygon": [[3, 3], [3, 0], [4, 0], [4, 3]]}], "meta": {"seed": 4203080, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 179, "strictValidation": true}, "imageAssets": {"target": "../images/voi-178/target.png", "shapes": {"S1": "../images/voi-178/shape_S1.png", "S2": "../images/voi-178/shape_S2.png", "S3": "../images/voi-178/shape_S3.png", "S4": "../images/voi-178/shape_S4.png"}}, "ID": "voi-178", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [4, 0]}, {"shape": "S3", "angle": 0, "vertex": "V5", "grid": [3, 3]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 0]}]}, "legacy_answer": "S2 90 V2 [4,0]\nS3 0 V5 [3,3]\nS4 90 V3 [4,0]", "solutionText": "S2 90 V2 [4,0]\nS3 0 V5 [3,3]\nS4 90 V3 [4,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-178\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-178/target.png", "shapes": {"S1": "images/voi-178/shape_S1.png", "S2": "images/voi-178/shape_S2.png", "S3": "images/voi-178/shape_S3.png", "S4": "images/voi-178/shape_S4.png"}}, "__sample_id__": "voi-178"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 6], [0, 3], [2, 3], [2, 6]]}, {"polygon": [[1, 6], [1, 5], [2, 5], [2, 6]]}, {"polygon": [[4, 4], [4, 6], [2, 4]]}], "meta": {"seed": 4203081, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.396538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 180, "strictValidation": true}, "imageAssets": {"target": "../images/voi-179/target.png", "shapes": {"S1": "../images/voi-179/shape_S1.png", "S2": "../images/voi-179/shape_S2.png", "S3": "../images/voi-179/shape_S3.png", "S4": "../images/voi-179/shape_S4.png"}}, "ID": "voi-179", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [0, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [2, 6]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S2 90 V2 [0,3]\nS3 90 V4 [2,6]\nS4 270 V1 [4,4]", "solutionText": "S2 90 V2 [0,3]\nS3 90 V4 [2,6]\nS4 270 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-179\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-179/target.png", "shapes": {"S1": "images/voi-179/shape_S1.png", "S2": "images/voi-179/shape_S2.png", "S3": "images/voi-179/shape_S3.png", "S4": "images/voi-179/shape_S4.png"}}, "__sample_id__": "voi-179"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[7, 1], [7, 4], [6, 4], [6, 1]]}, {"polygon": [[5, 1], [7, 1], [7, 2], [6, 2], [6, 4], [5, 4]]}, {"polygon": [[3, 2], [5, 2], [3, 4]]}], "meta": {"seed": 4203082, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.396538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 181, "strictValidation": true}, "imageAssets": {"target": "../images/voi-180/target.png", "shapes": {"S1": "../images/voi-180/shape_S1.png", "S2": "../images/voi-180/shape_S2.png", "S3": "../images/voi-180/shape_S3.png", "S4": "../images/voi-180/shape_S4.png"}}, "ID": "voi-180", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [6, 1]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [5, 1]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [5, 2]}]}, "legacy_answer": "S1 270 V4 [6,1]\nS3 0 V1 [5,1]\nS4 0 V2 [5,2]", "solutionText": "S1 270 V4 [6,1]\nS3 0 V1 [5,1]\nS4 0 V2 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-180\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-180/target.png", "shapes": {"S1": "images/voi-180/shape_S1.png", "S2": "images/voi-180/shape_S2.png", "S3": "images/voi-180/shape_S3.png", "S4": "images/voi-180/shape_S4.png"}}, "__sample_id__": "voi-180"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 7], [3, 7], [3, 6], [4, 6], [4, 4], [5, 4]]}, {"polygon": [[2, 7], [3, 7], [3, 8], [2, 8]]}, {"polygon": [[3, 5], [3, 8], [1, 8], [1, 5]]}], "meta": {"seed": 4203083, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 182, "strictValidation": true}, "imageAssets": {"target": "../images/voi-181/target.png", "shapes": {"S1": "../images/voi-181/shape_S1.png", "S2": "../images/voi-181/shape_S2.png", "S3": "../images/voi-181/shape_S3.png", "S4": "../images/voi-181/shape_S4.png"}}, "ID": "voi-181", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 7]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 7]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [1, 5]}]}, "legacy_answer": "S1 180 V1 [5,7]\nS2 0 V1 [2,7]\nS3 270 V4 [1,5]", "solutionText": "S1 180 V1 [5,7]\nS2 0 V1 [2,7]\nS3 270 V4 [1,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-181\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-181/target.png", "shapes": {"S1": "images/voi-181/shape_S1.png", "S2": "images/voi-181/shape_S2.png", "S3": "images/voi-181/shape_S3.png", "S4": "images/voi-181/shape_S4.png"}}, "__sample_id__": "voi-181"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 4], [6, 4], [6, 6], [4, 6]]}, {"polygon": [[7, 7], [6, 7], [6, 5], [7, 5]]}, {"polygon": [[7, 6], [7, 7], [4, 7], [4, 6]]}], "meta": {"seed": 4203084, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 183, "strictValidation": true}, "imageAssets": {"target": "../images/voi-182/target.png", "shapes": {"S1": "../images/voi-182/shape_S1.png", "S2": "../images/voi-182/shape_S2.png", "S3": "../images/voi-182/shape_S3.png", "S4": "../images/voi-182/shape_S4.png"}}, "ID": "voi-182", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [6, 5]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [7, 6]}]}, "legacy_answer": "S1 0 V1 [4,4]\nS3 180 V3 [6,5]\nS4 270 V1 [7,6]", "solutionText": "S1 0 V1 [4,4]\nS3 180 V3 [6,5]\nS4 270 V1 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-182\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-182/target.png", "shapes": {"S1": "images/voi-182/shape_S1.png", "S2": "images/voi-182/shape_S2.png", "S3": "images/voi-182/shape_S3.png", "S4": "images/voi-182/shape_S4.png"}}, "__sample_id__": "voi-182"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 4], [4, 4], [4, 6], [1, 6]]}, {"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}, {"polygon": [[1, 6], [1, 5], [2, 5], [2, 6]]}], "meta": {"seed": 4203085, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 184, "strictValidation": true}, "imageAssets": {"target": "../images/voi-183/target.png", "shapes": {"S1": "../images/voi-183/shape_S1.png", "S2": "../images/voi-183/shape_S2.png", "S3": "../images/voi-183/shape_S3.png", "S4": "../images/voi-183/shape_S4.png"}}, "ID": "voi-183", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 4]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [3, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [1, 6]}]}, "legacy_answer": "S1 0 V2 [4,4]\nS2 180 V3 [3,2]\nS4 90 V1 [1,6]", "solutionText": "S1 0 V2 [4,4]\nS2 180 V3 [3,2]\nS4 90 V1 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-183\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-183/target.png", "shapes": {"S1": "images/voi-183/shape_S1.png", "S2": "images/voi-183/shape_S2.png", "S3": "images/voi-183/shape_S3.png", "S4": "images/voi-183/shape_S4.png"}}, "__sample_id__": "voi-183"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 6], [5, 8], [4, 8], [4, 7], [2, 7], [2, 6]]}, {"polygon": [[5, 4], [6, 4], [6, 7], [5, 7]]}, {"polygon": [[6, 6], [3, 6], [3, 4], [6, 4]]}], "meta": {"seed": 4203086, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 185, "strictValidation": true}, "imageAssets": {"target": "../images/voi-184/target.png", "shapes": {"S1": "../images/voi-184/shape_S1.png", "S2": "../images/voi-184/shape_S2.png", "S3": "../images/voi-184/shape_S3.png", "S4": "../images/voi-184/shape_S4.png"}}, "ID": "voi-184", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 6]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [3, 6]}]}, "legacy_answer": "S1 270 V1 [5,6]\nS3 0 V1 [5,4]\nS4 180 V2 [3,6]", "solutionText": "S1 270 V1 [5,6]\nS3 0 V1 [5,4]\nS4 180 V2 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-184\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-184/target.png", "shapes": {"S1": "images/voi-184/shape_S1.png", "S2": "images/voi-184/shape_S2.png", "S3": "images/voi-184/shape_S3.png", "S4": "images/voi-184/shape_S4.png"}}, "__sample_id__": "voi-184"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [3, 3], [4, 3], [4, 5]]}, {"polygon": [[3, 5], [1, 5], [1, 4], [3, 4]]}, {"polygon": [[1, 2], [4, 2], [4, 4], [1, 4]]}], "meta": {"seed": 4203087, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 186, "strictValidation": true}, "imageAssets": {"target": "../images/voi-185/target.png", "shapes": {"S1": "../images/voi-185/shape_S1.png", "S2": "../images/voi-185/shape_S2.png", "S3": "../images/voi-185/shape_S3.png", "S4": "../images/voi-185/shape_S4.png"}}, "ID": "voi-185", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 5]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [1, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [1, 2]}]}, "legacy_answer": "S2 90 V1 [3,5]\nS3 180 V2 [1,5]\nS4 0 V1 [1,2]", "solutionText": "S2 90 V1 [3,5]\nS3 180 V2 [1,5]\nS4 0 V1 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-185\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-185/target.png", "shapes": {"S1": "images/voi-185/shape_S1.png", "S2": "images/voi-185/shape_S2.png", "S3": "images/voi-185/shape_S3.png", "S4": "images/voi-185/shape_S4.png"}}, "__sample_id__": "voi-185"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[7, 4], [5, 4], [5, 3], [6, 3], [6, 1], [7, 1]]}, {"polygon": [[4, 4], [4, 2], [6, 4]]}, {"polygon": [[6, 3], [5, 3], [5, 0], [6, 0]]}], "meta": {"seed": 4203088, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.117241, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.781034, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 187, "strictValidation": true}, "imageAssets": {"target": "../images/voi-186/target.png", "shapes": {"S1": "../images/voi-186/shape_S1.png", "S2": "../images/voi-186/shape_S2.png", "S3": "../images/voi-186/shape_S3.png", "S4": "../images/voi-186/shape_S4.png"}}, "ID": "voi-186", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 4]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 4]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [6, 0]}]}, "legacy_answer": "S2 180 V1 [7,4]\nS3 90 V3 [6,4]\nS4 180 V4 [6,0]", "solutionText": "S2 180 V1 [7,4]\nS3 90 V3 [6,4]\nS4 180 V4 [6,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-186\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-186/target.png", "shapes": {"S1": "images/voi-186/shape_S1.png", "S2": "images/voi-186/shape_S2.png", "S3": "images/voi-186/shape_S3.png", "S4": "images/voi-186/shape_S4.png"}}, "__sample_id__": "voi-186"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 6], [5, 6], [5, 4]]}, {"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}, {"polygon": [[6, 6], [6, 8], [4, 8], [4, 6]]}], "meta": {"seed": 4203089, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 188, "strictValidation": true}, "imageAssets": {"target": "../images/voi-187/target.png", "shapes": {"S1": "../images/voi-187/shape_S1.png", "S2": "../images/voi-187/shape_S2.png", "S3": "../images/voi-187/shape_S3.png", "S4": "../images/voi-187/shape_S4.png"}}, "ID": "voi-187", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 7]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [4, 6]}]}, "legacy_answer": "S1 270 V4 [5,4]\nS2 90 V1 [3,7]\nS4 270 V4 [4,6]", "solutionText": "S1 270 V4 [5,4]\nS2 90 V1 [3,7]\nS4 270 V4 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-187\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-187/target.png", "shapes": {"S1": "images/voi-187/shape_S1.png", "S2": "images/voi-187/shape_S2.png", "S3": "images/voi-187/shape_S3.png", "S4": "images/voi-187/shape_S4.png"}}, "__sample_id__": "voi-187"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [4, 3], [3, 4]]}, {"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}, {"polygon": [[5, 7], [4, 7], [4, 4], [5, 4]]}], "meta": {"seed": 4203090, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.141079, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.733536, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 189, "strictValidation": true}, "imageAssets": {"target": "../images/voi-188/target.png", "shapes": {"S1": "../images/voi-188/shape_S1.png", "S2": "../images/voi-188/shape_S2.png", "S3": "../images/voi-188/shape_S3.png", "S4": "../images/voi-188/shape_S4.png"}}, "ID": "voi-188", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 3]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V1 [3,3]\nS2 180 V2 [3,4]\nS3 180 V3 [4,4]", "solutionText": "S1 0 V1 [3,3]\nS2 180 V2 [3,4]\nS3 180 V3 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-188\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-188/target.png", "shapes": {"S1": "images/voi-188/shape_S1.png", "S2": "images/voi-188/shape_S2.png", "S3": "images/voi-188/shape_S3.png", "S4": "images/voi-188/shape_S4.png"}}, "__sample_id__": "voi-188"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 2], [4, 2], [4, 0], [7, 0]]}, {"polygon": [[6, 1], [4, 1], [4, 0], [6, 0]]}, {"polygon": [[5, 2], [8, 2], [8, 4], [5, 4]]}], "meta": {"seed": 4203091, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 190, "strictValidation": true}, "imageAssets": {"target": "../images/voi-189/target.png", "shapes": {"S1": "../images/voi-189/shape_S1.png", "S2": "../images/voi-189/shape_S2.png", "S3": "../images/voi-189/shape_S3.png", "S4": "../images/voi-189/shape_S4.png"}}, "ID": "voi-189", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 2]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 0]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [8, 2]}]}, "legacy_answer": "S2 180 V1 [7,2]\nS3 180 V3 [4,0]\nS4 0 V2 [8,2]", "solutionText": "S2 180 V1 [7,2]\nS3 180 V3 [4,0]\nS4 0 V2 [8,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-189\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-189/target.png", "shapes": {"S1": "images/voi-189/shape_S1.png", "S2": "images/voi-189/shape_S2.png", "S3": "images/voi-189/shape_S3.png", "S4": "images/voi-189/shape_S4.png"}}, "__sample_id__": "voi-189"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 5], [5, 4], [6, 4], [6, 5]]}, {"polygon": [[5, 0], [7, 0], [7, 2], [5, 2]]}, {"polygon": [[6, 2], [6, 5], [4, 5], [4, 2]]}], "meta": {"seed": 4203092, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 191, "strictValidation": true}, "imageAssets": {"target": "../images/voi-190/target.png", "shapes": {"S1": "../images/voi-190/shape_S1.png", "S2": "../images/voi-190/shape_S2.png", "S3": "../images/voi-190/shape_S3.png", "S4": "../images/voi-190/shape_S4.png"}}, "ID": "voi-190", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [5, 4]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 0]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [6, 2]}]}, "legacy_answer": "S2 90 V2 [5,4]\nS3 0 V2 [7,0]\nS4 270 V1 [6,2]", "solutionText": "S2 90 V2 [5,4]\nS3 0 V2 [7,0]\nS4 270 V1 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-190\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-190/target.png", "shapes": {"S1": "images/voi-190/shape_S1.png", "S2": "images/voi-190/shape_S2.png", "S3": "images/voi-190/shape_S3.png", "S4": "images/voi-190/shape_S4.png"}}, "__sample_id__": "voi-190"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 7], [7, 6], [8, 7]]}, {"polygon": [[6, 7], [6, 4], [8, 4], [8, 7]]}, {"polygon": [[5, 6], [8, 6], [8, 8], [5, 8]]}], "meta": {"seed": 4203093, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319202, "contourComplexity": 43, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.710206, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 192, "strictValidation": true}, "imageAssets": {"target": "../images/voi-191/target.png", "shapes": {"S1": "../images/voi-191/shape_S1.png", "S2": "../images/voi-191/shape_S2.png", "S3": "../images/voi-191/shape_S3.png", "S4": "../images/voi-191/shape_S4.png"}}, "ID": "voi-191", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [7, 7]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [6, 7]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 8]}]}, "legacy_answer": "S1 90 V1 [7,7]\nS2 90 V1 [6,7]\nS4 0 V4 [5,8]", "solutionText": "S1 90 V1 [7,7]\nS2 90 V1 [6,7]\nS4 0 V4 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-191\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-191/target.png", "shapes": {"S1": "images/voi-191/shape_S1.png", "S2": "images/voi-191/shape_S2.png", "S3": "images/voi-191/shape_S3.png", "S4": "images/voi-191/shape_S4.png"}}, "__sample_id__": "voi-191"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[4, 1], [4, 4], [3, 4], [3, 1]]}, {"polygon": [[3, 2], [3, 1], [6, 1], [6, 2]]}, {"polygon": [[4, 2], [1, 2], [2, 1], [4, 1]]}], "meta": {"seed": 4203094, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.433627, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 193, "strictValidation": true}, "imageAssets": {"target": "../images/voi-192/target.png", "shapes": {"S1": "../images/voi-192/shape_S1.png", "S2": "../images/voi-192/shape_S2.png", "S3": "../images/voi-192/shape_S3.png", "S4": "../images/voi-192/shape_S4.png"}}, "ID": "voi-192", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [3, 1]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 2]}]}, "legacy_answer": "S1 270 V3 [3,4]\nS2 90 V2 [3,1]\nS3 180 V1 [4,2]", "solutionText": "S1 270 V3 [3,4]\nS2 90 V2 [3,1]\nS3 180 V1 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-192\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-192/target.png", "shapes": {"S1": "images/voi-192/shape_S1.png", "S2": "images/voi-192/shape_S2.png", "S3": "images/voi-192/shape_S3.png", "S4": "images/voi-192/shape_S4.png"}}, "__sample_id__": "voi-192"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 4], [5, 5], [3, 5], [3, 4]]}, {"polygon": [[3, 5], [5, 5], [3, 7]]}, {"polygon": [[2, 7], [2, 5], [3, 5], [3, 6], [5, 6], [5, 7]]}], "meta": {"seed": 4203095, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.754118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 194, "strictValidation": true}, "imageAssets": {"target": "../images/voi-193/target.png", "shapes": {"S1": "../images/voi-193/shape_S1.png", "S2": "../images/voi-193/shape_S2.png", "S3": "../images/voi-193/shape_S3.png", "S4": "../images/voi-193/shape_S4.png"}}, "ID": "voi-193", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 4]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 5]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [3, 6]}]}, "legacy_answer": "S1 270 V1 [5,4]\nS2 0 V2 [5,5]\nS3 90 V4 [3,6]", "solutionText": "S1 270 V1 [5,4]\nS2 0 V2 [5,5]\nS3 90 V4 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-193\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-193/target.png", "shapes": {"S1": "images/voi-193/shape_S1.png", "S2": "images/voi-193/shape_S2.png", "S3": "images/voi-193/shape_S3.png", "S4": "images/voi-193/shape_S4.png"}}, "__sample_id__": "voi-193"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 0], [6, 0], [6, 1], [5, 1], [5, 3], [4, 3]]}, {"polygon": [[5, 3], [4, 3], [4, 2], [5, 2]]}, {"polygon": [[2, 0], [4, 0], [4, 2], [2, 2]]}], "meta": {"seed": 4203096, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 195, "strictValidation": true}, "imageAssets": {"target": "../images/voi-194/target.png", "shapes": {"S1": "../images/voi-194/shape_S1.png", "S2": "../images/voi-194/shape_S2.png", "S3": "../images/voi-194/shape_S3.png", "S4": "../images/voi-194/shape_S4.png"}}, "ID": "voi-194", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V5", "grid": [5, 3]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 0]}]}, "legacy_answer": "S2 0 V5 [5,3]\nS3 180 V3 [4,2]\nS4 0 V2 [4,0]", "solutionText": "S2 0 V5 [5,3]\nS3 180 V3 [4,2]\nS4 0 V2 [4,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-194\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-194/target.png", "shapes": {"S1": "images/voi-194/shape_S1.png", "S2": "images/voi-194/shape_S2.png", "S3": "images/voi-194/shape_S3.png", "S4": "images/voi-194/shape_S4.png"}}, "__sample_id__": "voi-194"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 5], [6, 7], [4, 5]]}, {"polygon": [[6, 6], [6, 8], [4, 8], [4, 6]]}, {"polygon": [[2, 6], [2, 5], [4, 5], [4, 6]]}], "meta": {"seed": 4203097, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.754118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 196, "strictValidation": true}, "imageAssets": {"target": "../images/voi-195/target.png", "shapes": {"S1": "../images/voi-195/shape_S1.png", "S2": "../images/voi-195/shape_S2.png", "S3": "../images/voi-195/shape_S3.png", "S4": "../images/voi-195/shape_S4.png"}}, "ID": "voi-195", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 7]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [6, 6]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [4, 6]}]}, "legacy_answer": "S2 270 V2 [6,7]\nS3 270 V1 [6,6]\nS4 90 V4 [4,6]", "solutionText": "S2 270 V2 [6,7]\nS3 270 V1 [6,6]\nS4 90 V4 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-195\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-195/target.png", "shapes": {"S1": "images/voi-195/shape_S1.png", "S2": "images/voi-195/shape_S2.png", "S3": "images/voi-195/shape_S3.png", "S4": "images/voi-195/shape_S4.png"}}, "__sample_id__": "voi-195"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 4], [5, 4], [5, 6], [2, 6]]}, {"polygon": [[2, 6], [2, 5], [3, 6]]}, {"polygon": [[5, 6], [5, 4], [6, 4], [6, 6]]}], "meta": {"seed": 4203098, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.768433, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 197, "strictValidation": true}, "imageAssets": {"target": "../images/voi-196/target.png", "shapes": {"S1": "../images/voi-196/shape_S1.png", "S2": "../images/voi-196/shape_S2.png", "S3": "../images/voi-196/shape_S3.png", "S4": "../images/voi-196/shape_S4.png"}}, "ID": "voi-196", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 6]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [2, 5]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [6, 6]}]}, "legacy_answer": "S1 0 V3 [5,6]\nS3 90 V2 [2,5]\nS4 90 V4 [6,6]", "solutionText": "S1 0 V3 [5,6]\nS3 90 V2 [2,5]\nS4 90 V4 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-196\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-196/target.png", "shapes": {"S1": "images/voi-196/shape_S1.png", "S2": "images/voi-196/shape_S2.png", "S3": "images/voi-196/shape_S3.png", "S4": "images/voi-196/shape_S4.png"}}, "__sample_id__": "voi-196"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [3, 6], [3, 4], [6, 4]]}, {"polygon": [[5, 6], [5, 7], [2, 7], [2, 6]]}, {"polygon": [[2, 6], [2, 5], [4, 5], [4, 6]]}], "meta": {"seed": 4203099, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 13, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 198, "strictValidation": true}, "imageAssets": {"target": "../images/voi-197/target.png", "shapes": {"S1": "../images/voi-197/shape_S1.png", "S2": "../images/voi-197/shape_S2.png", "S3": "../images/voi-197/shape_S3.png", "S4": "../images/voi-197/shape_S4.png"}}, "ID": "voi-197", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 4]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 7]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [2, 6]}]}, "legacy_answer": "S1 180 V3 [3,4]\nS2 270 V2 [5,7]\nS3 90 V1 [2,6]", "solutionText": "S1 180 V3 [3,4]\nS2 270 V2 [5,7]\nS3 90 V1 [2,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-197\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-197/target.png", "shapes": {"S1": "images/voi-197/shape_S1.png", "S2": "images/voi-197/shape_S2.png", "S3": "images/voi-197/shape_S3.png", "S4": "images/voi-197/shape_S4.png"}}, "__sample_id__": "voi-197"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 4], [0, 4], [2, 2]]}, {"polygon": [[4, 4], [3, 4], [3, 1], [4, 1]]}, {"polygon": [[2, 1], [4, 1], [4, 2], [3, 2], [3, 4], [2, 4]]}], "meta": {"seed": 4203100, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.396538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 199, "strictValidation": true}, "imageAssets": {"target": "../images/voi-198/target.png", "shapes": {"S1": "../images/voi-198/shape_S1.png", "S2": "../images/voi-198/shape_S2.png", "S3": "../images/voi-198/shape_S3.png", "S4": "../images/voi-198/shape_S4.png"}}, "ID": "voi-198", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [0, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [3, 1]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S1 180 V2 [0,4]\nS3 180 V3 [3,1]\nS4 0 V3 [4,2]", "solutionText": "S1 180 V2 [0,4]\nS3 180 V3 [3,1]\nS4 0 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-198\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-198/target.png", "shapes": {"S1": "images/voi-198/shape_S1.png", "S2": "images/voi-198/shape_S2.png", "S3": "images/voi-198/shape_S3.png", "S4": "images/voi-198/shape_S4.png"}}, "__sample_id__": "voi-198"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 4], [4, 4], [4, 1], [5, 1]]}, {"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}, {"polygon": [[6, 7], [4, 7], [4, 6], [5, 6], [5, 4], [6, 4]]}], "meta": {"seed": 4203101, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.540865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 200, "strictValidation": true}, "imageAssets": {"target": "../images/voi-199/target.png", "shapes": {"S1": "../images/voi-199/shape_S1.png", "S2": "../images/voi-199/shape_S2.png", "S3": "../images/voi-199/shape_S3.png", "S4": "../images/voi-199/shape_S4.png"}}, "ID": "voi-199", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 4]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [6, 7]}]}, "legacy_answer": "S1 180 V1 [5,4]\nS2 90 V3 [5,4]\nS4 180 V1 [6,7]", "solutionText": "S1 180 V1 [5,4]\nS2 90 V3 [5,4]\nS4 180 V1 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-199\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-199/target.png", "shapes": {"S1": "images/voi-199/shape_S1.png", "S2": "images/voi-199/shape_S2.png", "S3": "images/voi-199/shape_S3.png", "S4": "images/voi-199/shape_S4.png"}}, "__sample_id__": "voi-199"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 0], [6, 0], [6, 2], [3, 2]]}, {"polygon": [[4, 4], [2, 4], [2, 3], [3, 3], [3, 1], [4, 1]]}, {"polygon": [[2, 1], [4, 1], [4, 2], [3, 2], [3, 4], [2, 4]]}], "meta": {"seed": 4204001, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 201, "strictValidation": true}, "imageAssets": {"target": "../images/voi-200/target.png", "shapes": {"S1": "../images/voi-200/shape_S1.png", "S2": "../images/voi-200/shape_S2.png", "S3": "../images/voi-200/shape_S3.png", "S4": "../images/voi-200/shape_S4.png", "S5": "../images/voi-200/shape_S5.png"}}, "ID": "voi-200", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V6", "grid": [4, 1]}, {"shape": "S5", "angle": 0, "vertex": "V5", "grid": [3, 4]}]}, "legacy_answer": "S1 0 V4 [3,2]\nS3 180 V6 [4,1]\nS5 0 V5 [3,4]", "solutionText": "S1 0 V4 [3,2]\nS3 180 V6 [4,1]\nS5 0 V5 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-200\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-200/target.png", "shapes": {"S1": "images/voi-200/shape_S1.png", "S2": "images/voi-200/shape_S2.png", "S3": "images/voi-200/shape_S3.png", "S4": "images/voi-200/shape_S4.png", "S5": "images/voi-200/shape_S5.png"}}, "__sample_id__": "voi-200"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 2], [2, 2], [3, 1], [5, 1]]}, {"polygon": [[2, 0], [2, 3], [0, 3], [0, 0]]}, {"polygon": [[1, 2], [3, 2], [3, 3], [1, 3]]}], "meta": {"seed": 4204002, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.573755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 202, "strictValidation": true}, "imageAssets": {"target": "../images/voi-201/target.png", "shapes": {"S1": "../images/voi-201/shape_S1.png", "S2": "../images/voi-201/shape_S2.png", "S3": "../images/voi-201/shape_S3.png", "S4": "../images/voi-201/shape_S4.png", "S5": "../images/voi-201/shape_S5.png"}}, "ID": "voi-201", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [2, 2]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [0, 0]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V2 [2,2]\nS3 270 V4 [0,0]\nS4 0 V3 [3,3]", "solutionText": "S1 180 V2 [2,2]\nS3 270 V4 [0,0]\nS4 0 V3 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-201\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-201/target.png", "shapes": {"S1": "images/voi-201/shape_S1.png", "S2": "images/voi-201/shape_S2.png", "S3": "images/voi-201/shape_S3.png", "S4": "images/voi-201/shape_S4.png", "S5": "images/voi-201/shape_S5.png"}}, "__sample_id__": "voi-201"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 5], [2, 3], [3, 3], [3, 4], [5, 4], [5, 5]]}, {"polygon": [[5, 2], [5, 5], [3, 5], [3, 2]]}, {"polygon": [[4, 0], [6, 0], [6, 2], [4, 2]]}], "meta": {"seed": 4204003, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 203, "strictValidation": true}, "imageAssets": {"target": "../images/voi-202/target.png", "shapes": {"S1": "../images/voi-202/shape_S1.png", "S2": "../images/voi-202/shape_S2.png", "S3": "../images/voi-202/shape_S3.png", "S4": "../images/voi-202/shape_S4.png", "S5": "../images/voi-202/shape_S5.png"}}, "ID": "voi-202", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [2, 5]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [5, 2]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [6, 2]}]}, "legacy_answer": "S1 90 V1 [2,5]\nS2 270 V1 [5,2]\nS4 0 V3 [6,2]", "solutionText": "S1 90 V1 [2,5]\nS2 270 V1 [5,2]\nS4 0 V3 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-202\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-202/target.png", "shapes": {"S1": "images/voi-202/shape_S1.png", "S2": "images/voi-202/shape_S2.png", "S3": "images/voi-202/shape_S3.png", "S4": "images/voi-202/shape_S4.png", "S5": "images/voi-202/shape_S5.png"}}, "__sample_id__": "voi-202"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 5], [6, 2], [8, 2], [8, 5]]}, {"polygon": [[6, 6], [4, 6], [4, 5], [5, 5], [5, 3], [6, 3]]}, {"polygon": [[4, 6], [4, 5], [7, 5], [7, 6]]}], "meta": {"seed": 4204004, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 204, "strictValidation": true}, "imageAssets": {"target": "../images/voi-203/target.png", "shapes": {"S1": "../images/voi-203/shape_S1.png", "S2": "../images/voi-203/shape_S2.png", "S3": "../images/voi-203/shape_S3.png", "S4": "../images/voi-203/shape_S4.png", "S5": "../images/voi-203/shape_S5.png"}}, "ID": "voi-203", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [6, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S2 90 V1 [6,5]\nS3 180 V3 [4,5]\nS4 90 V1 [4,6]", "solutionText": "S2 90 V1 [6,5]\nS3 180 V3 [4,5]\nS4 90 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-203\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-203/target.png", "shapes": {"S1": "images/voi-203/shape_S1.png", "S2": "images/voi-203/shape_S2.png", "S3": "images/voi-203/shape_S3.png", "S4": "images/voi-203/shape_S4.png", "S5": "images/voi-203/shape_S5.png"}}, "__sample_id__": "voi-203"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 7], [3, 7], [4, 6]]}, {"polygon": [[1, 5], [4, 5], [4, 7], [1, 7]]}, {"polygon": [[3, 8], [3, 6], [4, 6], [4, 7], [6, 7], [6, 8]]}], "meta": {"seed": 4204005, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 41, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.573755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 205, "strictValidation": true}, "imageAssets": {"target": "../images/voi-204/target.png", "shapes": {"S1": "../images/voi-204/shape_S1.png", "S2": "../images/voi-204/shape_S2.png", "S3": "../images/voi-204/shape_S3.png", "S4": "../images/voi-204/shape_S4.png", "S5": "../images/voi-204/shape_S5.png"}}, "ID": "voi-204", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 7]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 5]}, {"shape": "S5", "angle": 90, "vertex": "V6", "grid": [6, 8]}]}, "legacy_answer": "S2 180 V1 [4,7]\nS3 0 V1 [1,5]\nS5 90 V6 [6,8]", "solutionText": "S2 180 V1 [4,7]\nS3 0 V1 [1,5]\nS5 90 V6 [6,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-204\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-204/target.png", "shapes": {"S1": "images/voi-204/shape_S1.png", "S2": "images/voi-204/shape_S2.png", "S3": "images/voi-204/shape_S3.png", "S4": "images/voi-204/shape_S4.png", "S5": "images/voi-204/shape_S5.png"}}, "__sample_id__": "voi-204"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [5, 6], [3, 8]]}, {"polygon": [[4, 3], [6, 3], [6, 4], [5, 4], [5, 6], [4, 6]]}, {"polygon": [[8, 5], [5, 5], [5, 3], [8, 3]]}], "meta": {"seed": 4204006, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.165803, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.157227, "difficultyScore": 0.622334, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 206, "strictValidation": true}, "imageAssets": {"target": "../images/voi-205/target.png", "shapes": {"S1": "../images/voi-205/shape_S1.png", "S2": "../images/voi-205/shape_S2.png", "S3": "../images/voi-205/shape_S3.png", "S4": "../images/voi-205/shape_S4.png", "S5": "../images/voi-205/shape_S5.png"}}, "ID": "voi-205", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 6]}, {"shape": "S3", "angle": 0, "vertex": "V5", "grid": [5, 6]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [8, 5]}]}, "legacy_answer": "S1 0 V2 [5,6]\nS3 0 V5 [5,6]\nS5 180 V1 [8,5]", "solutionText": "S1 0 V2 [5,6]\nS3 0 V5 [5,6]\nS5 180 V1 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-205\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-205/target.png", "shapes": {"S1": "images/voi-205/shape_S1.png", "S2": "images/voi-205/shape_S2.png", "S3": "images/voi-205/shape_S3.png", "S4": "images/voi-205/shape_S4.png", "S5": "images/voi-205/shape_S5.png"}}, "__sample_id__": "voi-205"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 7], [7, 7], [7, 6], [8, 6]]}, {"polygon": [[4, 5], [7, 5], [7, 7], [4, 7]]}, {"polygon": [[5, 4], [8, 4], [8, 6], [5, 6]]}], "meta": {"seed": 4204007, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 207, "strictValidation": true}, "imageAssets": {"target": "../images/voi-206/target.png", "shapes": {"S1": "../images/voi-206/shape_S1.png", "S2": "../images/voi-206/shape_S2.png", "S3": "../images/voi-206/shape_S3.png", "S4": "../images/voi-206/shape_S4.png", "S5": "../images/voi-206/shape_S5.png"}}, "ID": "voi-206", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [7, 6]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [4, 5]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [5, 6]}]}, "legacy_answer": "S2 180 V3 [7,6]\nS3 0 V1 [4,5]\nS5 0 V4 [5,6]", "solutionText": "S2 180 V3 [7,6]\nS3 0 V1 [4,5]\nS5 0 V4 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-206\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-206/target.png", "shapes": {"S1": "images/voi-206/shape_S1.png", "S2": "images/voi-206/shape_S2.png", "S3": "images/voi-206/shape_S3.png", "S4": "images/voi-206/shape_S4.png", "S5": "images/voi-206/shape_S5.png"}}, "__sample_id__": "voi-206"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 6], [3, 6], [3, 4], [6, 4]]}, {"polygon": [[6, 5], [6, 6], [5, 5]]}, {"polygon": [[6, 3], [6, 5], [4, 3]]}], "meta": {"seed": 4204008, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.247273, "contourComplexity": 100, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.408761, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 208, "strictValidation": true}, "imageAssets": {"target": "../images/voi-207/target.png", "shapes": {"S1": "../images/voi-207/shape_S1.png", "S2": "../images/voi-207/shape_S2.png", "S3": "../images/voi-207/shape_S3.png", "S4": "../images/voi-207/shape_S4.png", "S5": "../images/voi-207/shape_S5.png"}}, "ID": "voi-207", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [6, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [6, 6]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V4 [6,4]\nS3 270 V2 [6,6]\nS4 270 V3 [4,3]", "solutionText": "S1 180 V4 [6,4]\nS3 270 V2 [6,6]\nS4 270 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-207\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-207/target.png", "shapes": {"S1": "images/voi-207/shape_S1.png", "S2": "images/voi-207/shape_S2.png", "S3": "images/voi-207/shape_S3.png", "S4": "images/voi-207/shape_S4.png", "S5": "images/voi-207/shape_S5.png"}}, "__sample_id__": "voi-207"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 2], [1, 1], [3, 1], [3, 2]]}, {"polygon": [[2, 0], [4, 0], [4, 1], [3, 1], [3, 3], [2, 3]]}, {"polygon": [[2, 1], [5, 1], [4, 2], [2, 2]]}], "meta": {"seed": 4204009, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.458169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 209, "strictValidation": true}, "imageAssets": {"target": "../images/voi-208/target.png", "shapes": {"S1": "../images/voi-208/shape_S1.png", "S2": "../images/voi-208/shape_S2.png", "S3": "../images/voi-208/shape_S3.png", "S4": "../images/voi-208/shape_S4.png", "S5": "../images/voi-208/shape_S5.png"}}, "ID": "voi-208", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V4", "grid": [3, 2]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [4, 1]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [5, 1]}]}, "legacy_answer": "S3 90 V4 [3,2]\nS4 0 V3 [4,1]\nS5 0 V2 [5,1]", "solutionText": "S3 90 V4 [3,2]\nS4 0 V3 [4,1]\nS5 0 V2 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-208\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-208/target.png", "shapes": {"S1": "images/voi-208/shape_S1.png", "S2": "images/voi-208/shape_S2.png", "S3": "images/voi-208/shape_S3.png", "S4": "images/voi-208/shape_S4.png", "S5": "images/voi-208/shape_S5.png"}}, "__sample_id__": "voi-208"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [3, 5], [3, 8], [2, 8]]}, {"polygon": [[2, 3], [1, 3], [1, 2], [2, 2]]}, {"polygon": [[1, 5], [1, 2], [3, 2], [3, 5]]}], "meta": {"seed": 4204010, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 210, "strictValidation": true}, "imageAssets": {"target": "../images/voi-209/target.png", "shapes": {"S1": "../images/voi-209/shape_S1.png", "S2": "../images/voi-209/shape_S2.png", "S3": "../images/voi-209/shape_S3.png", "S4": "../images/voi-209/shape_S4.png", "S5": "../images/voi-209/shape_S5.png"}}, "ID": "voi-209", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [3, 8]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [2, 2]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S2 0 V3 [3,8]\nS4 180 V4 [2,2]\nS5 90 V3 [3,2]", "solutionText": "S2 0 V3 [3,8]\nS4 180 V4 [2,2]\nS5 90 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-209\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-209/target.png", "shapes": {"S1": "images/voi-209/shape_S1.png", "S2": "images/voi-209/shape_S2.png", "S3": "images/voi-209/shape_S3.png", "S4": "images/voi-209/shape_S4.png", "S5": "images/voi-209/shape_S5.png"}}, "__sample_id__": "voi-209"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[7, 8], [4, 8], [4, 6], [7, 6]]}, {"polygon": [[5, 4], [6, 4], [6, 6], [5, 6]]}, {"polygon": [[4, 6], [4, 4], [5, 4], [5, 5], [7, 5], [7, 6]]}], "meta": {"seed": 4204011, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.620833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 211, "strictValidation": true}, "imageAssets": {"target": "../images/voi-210/target.png", "shapes": {"S1": "../images/voi-210/shape_S1.png", "S2": "../images/voi-210/shape_S2.png", "S3": "../images/voi-210/shape_S3.png", "S4": "../images/voi-210/shape_S4.png", "S5": "../images/voi-210/shape_S5.png"}}, "ID": "voi-210", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [7, 6]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [6, 4]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [7, 6]}]}, "legacy_answer": "S1 180 V4 [7,6]\nS3 0 V2 [6,4]\nS4 90 V6 [7,6]", "solutionText": "S1 180 V4 [7,6]\nS3 0 V2 [6,4]\nS4 90 V6 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-210\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-210/target.png", "shapes": {"S1": "images/voi-210/shape_S1.png", "S2": "images/voi-210/shape_S2.png", "S3": "images/voi-210/shape_S3.png", "S4": "images/voi-210/shape_S4.png", "S5": "images/voi-210/shape_S5.png"}}, "__sample_id__": "voi-210"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 0], [5, 0], [4, 1], [2, 1]]}, {"polygon": [[3, 1], [3, 2], [1, 2], [1, 1]]}, {"polygon": [[3, 2], [3, 0], [4, 0], [4, 1], [6, 1], [6, 2]]}], "meta": {"seed": 4204012, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.458169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 212, "strictValidation": true}, "imageAssets": {"target": "../images/voi-211/target.png", "shapes": {"S1": "../images/voi-211/shape_S1.png", "S2": "../images/voi-211/shape_S2.png", "S3": "../images/voi-211/shape_S3.png", "S4": "../images/voi-211/shape_S4.png", "S5": "../images/voi-211/shape_S5.png"}}, "ID": "voi-211", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 1]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 1]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 0]}]}, "legacy_answer": "S1 0 V4 [2,1]\nS2 270 V4 [1,1]\nS3 90 V3 [4,0]", "solutionText": "S1 0 V4 [2,1]\nS2 270 V4 [1,1]\nS3 90 V3 [4,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-211\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-211/target.png", "shapes": {"S1": "images/voi-211/shape_S1.png", "S2": "images/voi-211/shape_S2.png", "S3": "images/voi-211/shape_S3.png", "S4": "images/voi-211/shape_S4.png", "S5": "images/voi-211/shape_S5.png"}}, "__sample_id__": "voi-211"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 0], [3, 3], [2, 2], [2, 0]]}, {"polygon": [[5, 0], [5, 3], [4, 3], [4, 0]]}, {"polygon": [[3, 0], [5, 0], [5, 1], [4, 1], [4, 3], [3, 3]]}], "meta": {"seed": 4204013, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 213, "strictValidation": true}, "imageAssets": {"target": "../images/voi-212/target.png", "shapes": {"S1": "../images/voi-212/shape_S1.png", "S2": "../images/voi-212/shape_S2.png", "S3": "../images/voi-212/shape_S3.png", "S4": "../images/voi-212/shape_S4.png", "S5": "../images/voi-212/shape_S5.png"}}, "ID": "voi-212", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 0]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [5, 0]}, {"shape": "S3", "angle": 0, "vertex": "V6", "grid": [3, 3]}]}, "legacy_answer": "S1 270 V1 [3,0]\nS2 270 V1 [5,0]\nS3 0 V6 [3,3]", "solutionText": "S1 270 V1 [3,0]\nS2 270 V1 [5,0]\nS3 0 V6 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-212\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-212/target.png", "shapes": {"S1": "images/voi-212/shape_S1.png", "S2": "images/voi-212/shape_S2.png", "S3": "images/voi-212/shape_S3.png", "S4": "images/voi-212/shape_S4.png", "S5": "images/voi-212/shape_S5.png"}}, "__sample_id__": "voi-212"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 4], [6, 7], [4, 7], [4, 4]]}, {"polygon": [[3, 4], [3, 6], [1, 6], [1, 4]]}, {"polygon": [[3, 7], [3, 5], [4, 5], [4, 6], [6, 6], [6, 7]]}], "meta": {"seed": 4204014, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 214, "strictValidation": true}, "imageAssets": {"target": "../images/voi-213/target.png", "shapes": {"S1": "../images/voi-213/shape_S1.png", "S2": "../images/voi-213/shape_S2.png", "S3": "../images/voi-213/shape_S3.png", "S4": "../images/voi-213/shape_S4.png", "S5": "../images/voi-213/shape_S5.png"}}, "ID": "voi-213", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [4, 4]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 6]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [4, 6]}]}, "legacy_answer": "S2 270 V4 [4,4]\nS3 270 V3 [1,6]\nS5 90 V4 [4,6]", "solutionText": "S2 270 V4 [4,4]\nS3 270 V3 [1,6]\nS5 90 V4 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-213\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-213/target.png", "shapes": {"S1": "images/voi-213/shape_S1.png", "S2": "images/voi-213/shape_S2.png", "S3": "images/voi-213/shape_S3.png", "S4": "images/voi-213/shape_S4.png", "S5": "images/voi-213/shape_S5.png"}}, "__sample_id__": "voi-213"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 6], [1, 6], [1, 4], [4, 4]]}, {"polygon": [[5, 5], [4, 5], [4, 2], [5, 2]]}, {"polygon": [[4, 6], [3, 6], [3, 5], [4, 5]]}], "meta": {"seed": 4204015, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 215, "strictValidation": true}, "imageAssets": {"target": "../images/voi-214/target.png", "shapes": {"S1": "../images/voi-214/shape_S1.png", "S2": "../images/voi-214/shape_S2.png", "S3": "../images/voi-214/shape_S3.png", "S4": "../images/voi-214/shape_S4.png", "S5": "../images/voi-214/shape_S5.png"}}, "ID": "voi-214", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S1 180 V4 [4,4]\nS3 180 V4 [5,2]\nS4 180 V1 [4,6]", "solutionText": "S1 180 V4 [4,4]\nS3 180 V4 [5,2]\nS4 180 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-214\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-214/target.png", "shapes": {"S1": "images/voi-214/shape_S1.png", "S2": "images/voi-214/shape_S2.png", "S3": "images/voi-214/shape_S3.png", "S4": "images/voi-214/shape_S4.png", "S5": "images/voi-214/shape_S5.png"}}, "__sample_id__": "voi-214"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 5], [1, 3]]}, {"polygon": [[3, 4], [3, 3], [5, 3], [5, 4]]}, {"polygon": [[3, 6], [1, 6], [1, 4], [3, 4]]}], "meta": {"seed": 4204016, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.854118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 216, "strictValidation": true}, "imageAssets": {"target": "../images/voi-215/target.png", "shapes": {"S1": "../images/voi-215/shape_S1.png", "S2": "../images/voi-215/shape_S2.png", "S3": "../images/voi-215/shape_S3.png", "S4": "../images/voi-215/shape_S4.png", "S5": "../images/voi-215/shape_S5.png"}}, "ID": "voi-215", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V3", "grid": [1, 3]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [5, 4]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [1, 6]}]}, "legacy_answer": "S2 270 V3 [1,3]\nS4 90 V4 [5,4]\nS5 180 V2 [1,6]", "solutionText": "S2 270 V3 [1,3]\nS4 90 V4 [5,4]\nS5 180 V2 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-215\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-215/target.png", "shapes": {"S1": "images/voi-215/shape_S1.png", "S2": "images/voi-215/shape_S2.png", "S3": "images/voi-215/shape_S3.png", "S4": "images/voi-215/shape_S4.png", "S5": "images/voi-215/shape_S5.png"}}, "__sample_id__": "voi-215"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [3, 3], [5, 3], [5, 5]]}, {"polygon": [[4, 3], [4, 4], [3, 4], [3, 3]]}, {"polygon": [[2, 8], [2, 5], [4, 5], [4, 8]]}], "meta": {"seed": 4204017, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 217, "strictValidation": true}, "imageAssets": {"target": "../images/voi-216/target.png", "shapes": {"S1": "../images/voi-216/shape_S1.png", "S2": "../images/voi-216/shape_S2.png", "S3": "../images/voi-216/shape_S3.png", "S4": "../images/voi-216/shape_S4.png", "S5": "../images/voi-216/shape_S5.png"}}, "ID": "voi-216", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 3]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [4, 3]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [4, 8]}]}, "legacy_answer": "S1 90 V2 [3,3]\nS4 270 V1 [4,3]\nS5 90 V4 [4,8]", "solutionText": "S1 90 V2 [3,3]\nS4 270 V1 [4,3]\nS5 90 V4 [4,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-216\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-216/target.png", "shapes": {"S1": "images/voi-216/shape_S1.png", "S2": "images/voi-216/shape_S2.png", "S3": "images/voi-216/shape_S3.png", "S4": "images/voi-216/shape_S4.png", "S5": "images/voi-216/shape_S5.png"}}, "__sample_id__": "voi-216"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 6], [2, 6], [2, 7], [0, 7]]}, {"polygon": [[1, 4], [4, 4], [4, 6], [1, 6]]}, {"polygon": [[4, 5], [4, 8], [2, 8], [2, 5]]}], "meta": {"seed": 4204018, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 218, "strictValidation": true}, "imageAssets": {"target": "../images/voi-217/target.png", "shapes": {"S1": "../images/voi-217/shape_S1.png", "S2": "../images/voi-217/shape_S2.png", "S3": "../images/voi-217/shape_S3.png", "S4": "../images/voi-217/shape_S4.png", "S5": "../images/voi-217/shape_S5.png"}}, "ID": "voi-217", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [0, 6]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [1, 6]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [2, 8]}]}, "legacy_answer": "S1 0 V1 [0,6]\nS2 0 V4 [1,6]\nS3 270 V3 [2,8]", "solutionText": "S1 0 V1 [0,6]\nS2 0 V4 [1,6]\nS3 270 V3 [2,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-217\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-217/target.png", "shapes": {"S1": "images/voi-217/shape_S1.png", "S2": "images/voi-217/shape_S2.png", "S3": "images/voi-217/shape_S3.png", "S4": "images/voi-217/shape_S4.png", "S5": "images/voi-217/shape_S5.png"}}, "__sample_id__": "voi-217"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 5], [7, 5], [7, 7], [5, 7]]}, {"polygon": [[6, 7], [6, 4], [8, 4], [8, 7]]}, {"polygon": [[5, 5], [5, 2], [6, 2], [6, 5]]}], "meta": {"seed": 4204019, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 219, "strictValidation": true}, "imageAssets": {"target": "../images/voi-218/target.png", "shapes": {"S1": "../images/voi-218/shape_S1.png", "S2": "../images/voi-218/shape_S2.png", "S3": "../images/voi-218/shape_S3.png", "S4": "../images/voi-218/shape_S4.png", "S5": "../images/voi-218/shape_S5.png"}}, "ID": "voi-218", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [7, 7]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [8, 4]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [6, 5]}]}, "legacy_answer": "S2 0 V3 [7,7]\nS3 90 V3 [8,4]\nS5 90 V4 [6,5]", "solutionText": "S2 0 V3 [7,7]\nS3 90 V3 [8,4]\nS5 90 V4 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-218\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-218/target.png", "shapes": {"S1": "images/voi-218/shape_S1.png", "S2": "images/voi-218/shape_S2.png", "S3": "images/voi-218/shape_S3.png", "S4": "images/voi-218/shape_S4.png", "S5": "images/voi-218/shape_S5.png"}}, "__sample_id__": "voi-218"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [4, 8], [3, 7], [3, 5]]}, {"polygon": [[0, 5], [3, 5], [3, 6], [0, 6]]}, {"polygon": [[1, 6], [4, 6], [4, 8], [1, 8]]}], "meta": {"seed": 4204020, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.265583, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.132324, "difficultyScore": 0.397682, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 220, "strictValidation": true}, "imageAssets": {"target": "../images/voi-219/target.png", "shapes": {"S1": "../images/voi-219/shape_S1.png", "S2": "../images/voi-219/shape_S2.png", "S3": "../images/voi-219/shape_S3.png", "S4": "../images/voi-219/shape_S4.png", "S5": "../images/voi-219/shape_S5.png"}}, "ID": "voi-219", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [4, 5]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [3, 6]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [1, 8]}]}, "legacy_answer": "S1 270 V1 [4,5]\nS2 0 V3 [3,6]\nS4 0 V4 [1,8]", "solutionText": "S1 270 V1 [4,5]\nS2 0 V3 [3,6]\nS4 0 V4 [1,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-219\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-219/target.png", "shapes": {"S1": "images/voi-219/shape_S1.png", "S2": "images/voi-219/shape_S2.png", "S3": "images/voi-219/shape_S3.png", "S4": "images/voi-219/shape_S4.png", "S5": "images/voi-219/shape_S5.png"}}, "__sample_id__": "voi-219"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 2], [7, 2], [7, 4], [4, 4]]}, {"polygon": [[5, 3], [3, 3], [3, 2], [5, 2]]}, {"polygon": [[1, 3], [4, 3], [3, 4], [1, 4]]}], "meta": {"seed": 4204021, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.573755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 221, "strictValidation": true}, "imageAssets": {"target": "../images/voi-220/target.png", "shapes": {"S1": "../images/voi-220/shape_S1.png", "S2": "../images/voi-220/shape_S2.png", "S3": "../images/voi-220/shape_S3.png", "S4": "../images/voi-220/shape_S4.png", "S5": "../images/voi-220/shape_S5.png"}}, "ID": "voi-220", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [4, 2]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [5, 3]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [4, 3]}]}, "legacy_answer": "S1 0 V1 [4,2]\nS2 180 V1 [5,3]\nS5 0 V2 [4,3]", "solutionText": "S1 0 V1 [4,2]\nS2 180 V1 [5,3]\nS5 0 V2 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-220\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-220/target.png", "shapes": {"S1": "images/voi-220/shape_S1.png", "S2": "images/voi-220/shape_S2.png", "S3": "images/voi-220/shape_S3.png", "S4": "images/voi-220/shape_S4.png", "S5": "images/voi-220/shape_S5.png"}}, "__sample_id__": "voi-220"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 3], [5, 3], [5, 2], [6, 2], [6, 0], [7, 0]]}, {"polygon": [[2, 1], [5, 1], [5, 3], [2, 3]]}, {"polygon": [[2, 0], [4, 0], [4, 1], [3, 1], [3, 3], [2, 3]]}], "meta": {"seed": 4204022, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 222, "strictValidation": true}, "imageAssets": {"target": "../images/voi-221/target.png", "shapes": {"S1": "../images/voi-221/shape_S1.png", "S2": "../images/voi-221/shape_S2.png", "S3": "../images/voi-221/shape_S3.png", "S4": "../images/voi-221/shape_S4.png", "S5": "../images/voi-221/shape_S5.png"}}, "ID": "voi-221", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [5, 2]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [5, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [3, 1]}]}, "legacy_answer": "S1 180 V3 [5,2]\nS2 0 V3 [5,3]\nS3 0 V4 [3,1]", "solutionText": "S1 180 V3 [5,2]\nS2 0 V3 [5,3]\nS3 0 V4 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-221\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-221/target.png", "shapes": {"S1": "images/voi-221/shape_S1.png", "S2": "images/voi-221/shape_S2.png", "S3": "images/voi-221/shape_S3.png", "S4": "images/voi-221/shape_S4.png", "S5": "images/voi-221/shape_S5.png"}}, "__sample_id__": "voi-221"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 3], [6, 3], [6, 4], [5, 4], [5, 6], [4, 6]]}, {"polygon": [[7, 2], [7, 4], [5, 4], [5, 2]]}, {"polygon": [[4, 0], [6, 0], [6, 1], [5, 1], [5, 3], [4, 3]]}], "meta": {"seed": 4204023, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.620833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 223, "strictValidation": true}, "imageAssets": {"target": "../images/voi-222/target.png", "shapes": {"S1": "../images/voi-222/shape_S1.png", "S2": "../images/voi-222/shape_S2.png", "S3": "../images/voi-222/shape_S3.png", "S4": "../images/voi-222/shape_S4.png", "S5": "../images/voi-222/shape_S5.png"}}, "ID": "voi-222", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 3]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [7, 2]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [6, 1]}]}, "legacy_answer": "S1 0 V2 [6,3]\nS3 270 V1 [7,2]\nS4 0 V3 [6,1]", "solutionText": "S1 0 V2 [6,3]\nS3 270 V1 [7,2]\nS4 0 V3 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-222\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-222/target.png", "shapes": {"S1": "images/voi-222/shape_S1.png", "S2": "images/voi-222/shape_S2.png", "S3": "images/voi-222/shape_S3.png", "S4": "images/voi-222/shape_S4.png", "S5": "images/voi-222/shape_S5.png"}}, "__sample_id__": "voi-222"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 5], [3, 5], [3, 6], [2, 6], [2, 8], [1, 8]]}, {"polygon": [[2, 5], [5, 5], [5, 7], [2, 7]]}, {"polygon": [[3, 8], [1, 8], [1, 7], [3, 7]]}], "meta": {"seed": 4204024, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.683333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 224, "strictValidation": true}, "imageAssets": {"target": "../images/voi-223/target.png", "shapes": {"S1": "../images/voi-223/shape_S1.png", "S2": "../images/voi-223/shape_S2.png", "S3": "../images/voi-223/shape_S3.png", "S4": "../images/voi-223/shape_S4.png", "S5": "../images/voi-223/shape_S5.png"}}, "ID": "voi-223", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [2, 7]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [3, 7]}]}, "legacy_answer": "S1 0 V4 [2,6]\nS3 0 V4 [2,7]\nS5 180 V4 [3,7]", "solutionText": "S1 0 V4 [2,6]\nS3 0 V4 [2,7]\nS5 180 V4 [3,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-223\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-223/target.png", "shapes": {"S1": "images/voi-223/shape_S1.png", "S2": "images/voi-223/shape_S2.png", "S3": "images/voi-223/shape_S3.png", "S4": "images/voi-223/shape_S4.png", "S5": "images/voi-223/shape_S5.png"}}, "__sample_id__": "voi-223"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 5], [7, 5], [6, 6], [4, 6]]}, {"polygon": [[8, 7], [5, 7], [5, 5], [8, 5]]}, {"polygon": [[4, 8], [4, 6], [5, 6], [5, 8]]}], "meta": {"seed": 4204025, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.290801, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.529806, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 225, "strictValidation": true}, "imageAssets": {"target": "../images/voi-224/target.png", "shapes": {"S1": "../images/voi-224/shape_S1.png", "S2": "../images/voi-224/shape_S2.png", "S3": "../images/voi-224/shape_S3.png", "S4": "../images/voi-224/shape_S4.png", "S5": "../images/voi-224/shape_S5.png"}}, "ID": "voi-224", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [4, 5]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [8, 7]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [4, 6]}]}, "legacy_answer": "S1 0 V1 [4,5]\nS4 180 V1 [8,7]\nS5 90 V2 [4,6]", "solutionText": "S1 0 V1 [4,5]\nS4 180 V1 [8,7]\nS5 90 V2 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-224\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-224/target.png", "shapes": {"S1": "images/voi-224/shape_S1.png", "S2": "images/voi-224/shape_S2.png", "S3": "images/voi-224/shape_S3.png", "S4": "images/voi-224/shape_S4.png", "S5": "images/voi-224/shape_S5.png"}}, "__sample_id__": "voi-224"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [4, 5], [5, 5], [5, 7]]}, {"polygon": [[3, 4], [3, 7], [1, 7], [1, 4]]}, {"polygon": [[3, 8], [3, 5], [5, 5], [5, 8]]}], "meta": {"seed": 4204026, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 226, "strictValidation": true}, "imageAssets": {"target": "../images/voi-225/target.png", "shapes": {"S1": "../images/voi-225/shape_S1.png", "S2": "../images/voi-225/shape_S2.png", "S3": "../images/voi-225/shape_S3.png", "S4": "../images/voi-225/shape_S4.png", "S5": "../images/voi-225/shape_S5.png"}}, "ID": "voi-225", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V3", "grid": [5, 5]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [3, 7]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [5, 8]}]}, "legacy_answer": "S3 90 V3 [5,5]\nS4 270 V2 [3,7]\nS5 90 V4 [5,8]", "solutionText": "S3 90 V3 [5,5]\nS4 270 V2 [3,7]\nS5 90 V4 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-225\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-225/target.png", "shapes": {"S1": "images/voi-225/shape_S1.png", "S2": "images/voi-225/shape_S2.png", "S3": "images/voi-225/shape_S3.png", "S4": "images/voi-225/shape_S4.png", "S5": "images/voi-225/shape_S5.png"}}, "__sample_id__": "voi-225"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [1, 4], [1, 2], [4, 2]]}, {"polygon": [[2, 4], [2, 7], [0, 7], [0, 4]]}, {"polygon": [[2, 3], [4, 3], [4, 5], [2, 5]]}], "meta": {"seed": 4204027, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.225, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 227, "strictValidation": true}, "imageAssets": {"target": "../images/voi-226/target.png", "shapes": {"S1": "../images/voi-226/shape_S1.png", "S2": "../images/voi-226/shape_S2.png", "S3": "../images/voi-226/shape_S3.png", "S4": "../images/voi-226/shape_S4.png", "S5": "../images/voi-226/shape_S5.png"}}, "ID": "voi-226", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [1, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [2, 7]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V3 [1,2]\nS3 270 V2 [2,7]\nS5 0 V2 [4,3]", "solutionText": "S1 180 V3 [1,2]\nS3 270 V2 [2,7]\nS5 0 V2 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-226\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-226/target.png", "shapes": {"S1": "images/voi-226/shape_S1.png", "S2": "images/voi-226/shape_S2.png", "S3": "images/voi-226/shape_S3.png", "S4": "images/voi-226/shape_S4.png", "S5": "images/voi-226/shape_S5.png"}}, "__sample_id__": "voi-226"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [4, 7], [3, 7], [3, 6], [1, 6], [1, 5]]}, {"polygon": [[3, 4], [3, 6], [2, 6], [2, 5], [0, 5], [0, 4]]}, {"polygon": [[4, 2], [4, 5], [3, 5], [3, 2]]}], "meta": {"seed": 4204028, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 228, "strictValidation": true}, "imageAssets": {"target": "../images/voi-227/target.png", "shapes": {"S1": "../images/voi-227/shape_S1.png", "S2": "../images/voi-227/shape_S2.png", "S3": "../images/voi-227/shape_S3.png", "S4": "../images/voi-227/shape_S4.png", "S5": "../images/voi-227/shape_S5.png"}}, "ID": "voi-227", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [4, 5]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 6]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 270 V1 [4,5]\nS2 270 V3 [2,6]\nS4 270 V2 [4,5]", "solutionText": "S1 270 V1 [4,5]\nS2 270 V3 [2,6]\nS4 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-227\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-227/target.png", "shapes": {"S1": "images/voi-227/shape_S1.png", "S2": "images/voi-227/shape_S2.png", "S3": "images/voi-227/shape_S3.png", "S4": "images/voi-227/shape_S4.png", "S5": "images/voi-227/shape_S5.png"}}, "__sample_id__": "voi-227"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 3], [4, 2], [5, 2], [5, 3]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[1, 1], [3, 1], [3, 2], [2, 2], [2, 4], [1, 4]]}], "meta": {"seed": 4204029, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 229, "strictValidation": true}, "imageAssets": {"target": "../images/voi-228/target.png", "shapes": {"S1": "../images/voi-228/shape_S1.png", "S2": "../images/voi-228/shape_S2.png", "S3": "../images/voi-228/shape_S3.png", "S4": "../images/voi-228/shape_S4.png", "S5": "../images/voi-228/shape_S5.png"}}, "ID": "voi-228", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [4, 2]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 1]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [1, 1]}]}, "legacy_answer": "S1 90 V2 [4,2]\nS4 270 V4 [3,1]\nS5 0 V1 [1,1]", "solutionText": "S1 90 V2 [4,2]\nS4 270 V4 [3,1]\nS5 0 V1 [1,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-228\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-228/target.png", "shapes": {"S1": "images/voi-228/shape_S1.png", "S2": "images/voi-228/shape_S2.png", "S3": "images/voi-228/shape_S3.png", "S4": "images/voi-228/shape_S4.png", "S5": "images/voi-228/shape_S5.png"}}, "__sample_id__": "voi-228"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 6], [6, 8], [5, 8], [5, 7], [3, 7], [3, 6]]}, {"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[6, 8], [4, 8], [4, 7], [5, 7], [5, 5], [6, 5]]}], "meta": {"seed": 4204030, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 230, "strictValidation": true}, "imageAssets": {"target": "../images/voi-229/target.png", "shapes": {"S1": "../images/voi-229/shape_S1.png", "S2": "../images/voi-229/shape_S2.png", "S3": "../images/voi-229/shape_S3.png", "S4": "../images/voi-229/shape_S4.png", "S5": "../images/voi-229/shape_S5.png"}}, "ID": "voi-229", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V2", "grid": [6, 8]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [5, 7]}]}, "legacy_answer": "S3 270 V2 [6,8]\nS4 270 V2 [5,6]\nS5 180 V4 [5,7]", "solutionText": "S3 270 V2 [6,8]\nS4 270 V2 [5,6]\nS5 180 V4 [5,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-229\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-229/target.png", "shapes": {"S1": "images/voi-229/shape_S1.png", "S2": "images/voi-229/shape_S2.png", "S3": "images/voi-229/shape_S3.png", "S4": "images/voi-229/shape_S4.png", "S5": "images/voi-229/shape_S5.png"}}, "__sample_id__": "voi-229"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 8], [5, 5], [7, 5], [7, 8]]}, {"polygon": [[5, 7], [3, 7], [3, 6], [4, 6], [4, 4], [5, 4]]}, {"polygon": [[6, 7], [6, 8], [5, 8], [5, 7]]}], "meta": {"seed": 4204031, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 231, "strictValidation": true}, "imageAssets": {"target": "../images/voi-230/target.png", "shapes": {"S1": "../images/voi-230/shape_S1.png", "S2": "../images/voi-230/shape_S2.png", "S3": "../images/voi-230/shape_S3.png", "S4": "../images/voi-230/shape_S4.png", "S5": "../images/voi-230/shape_S5.png"}}, "ID": "voi-230", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [7, 8]}, {"shape": "S3", "angle": 180, "vertex": "V5", "grid": [4, 4]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [6, 8]}]}, "legacy_answer": "S1 90 V4 [7,8]\nS3 180 V5 [4,4]\nS5 270 V2 [6,8]", "solutionText": "S1 90 V4 [7,8]\nS3 180 V5 [4,4]\nS5 270 V2 [6,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-230\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-230/target.png", "shapes": {"S1": "images/voi-230/shape_S1.png", "S2": "images/voi-230/shape_S2.png", "S3": "images/voi-230/shape_S3.png", "S4": "images/voi-230/shape_S4.png", "S5": "images/voi-230/shape_S5.png"}}, "__sample_id__": "voi-230"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[6, 4], [5, 4], [5, 3], [6, 3]]}, {"polygon": [[4, 4], [4, 1], [6, 1], [6, 4]]}, {"polygon": [[6, 6], [5, 6], [5, 3], [6, 3]]}], "meta": {"seed": 4204032, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 232, "strictValidation": true}, "imageAssets": {"target": "../images/voi-231/target.png", "shapes": {"S1": "../images/voi-231/shape_S1.png", "S2": "../images/voi-231/shape_S2.png", "S3": "../images/voi-231/shape_S3.png", "S4": "../images/voi-231/shape_S4.png", "S5": "../images/voi-231/shape_S5.png"}}, "ID": "voi-231", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [6, 1]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [6, 6]}]}, "legacy_answer": "S2 180 V2 [5,4]\nS4 90 V3 [6,1]\nS5 180 V1 [6,6]", "solutionText": "S2 180 V2 [5,4]\nS4 90 V3 [6,1]\nS5 180 V1 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-231\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-231/target.png", "shapes": {"S1": "images/voi-231/shape_S1.png", "S2": "images/voi-231/shape_S2.png", "S3": "images/voi-231/shape_S3.png", "S4": "images/voi-231/shape_S4.png", "S5": "images/voi-231/shape_S5.png"}}, "__sample_id__": "voi-231"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 3], [7, 3], [7, 4], [4, 4]]}, {"polygon": [[6, 7], [6, 4], [7, 5], [7, 7]]}, {"polygon": [[4, 6], [4, 3], [6, 3], [6, 6]]}], "meta": {"seed": 4204033, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.346883, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.752182, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 233, "strictValidation": true}, "imageAssets": {"target": "../images/voi-232/target.png", "shapes": {"S1": "../images/voi-232/shape_S1.png", "S2": "../images/voi-232/shape_S2.png", "S3": "../images/voi-232/shape_S3.png", "S4": "../images/voi-232/shape_S4.png", "S5": "../images/voi-232/shape_S5.png"}}, "ID": "voi-232", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [7, 3]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [7, 5]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S1 0 V2 [7,3]\nS2 90 V3 [7,5]\nS3 90 V1 [4,6]", "solutionText": "S1 0 V2 [7,3]\nS2 90 V3 [7,5]\nS3 90 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-232\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-232/target.png", "shapes": {"S1": "images/voi-232/shape_S1.png", "S2": "images/voi-232/shape_S2.png", "S3": "images/voi-232/shape_S3.png", "S4": "images/voi-232/shape_S4.png", "S5": "images/voi-232/shape_S5.png"}}, "__sample_id__": "voi-232"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [6, 5], [6, 7], [3, 7]]}, {"polygon": [[6, 7], [4, 7], [4, 6], [6, 6]]}, {"polygon": [[8, 3], [8, 6], [6, 6], [6, 3]]}], "meta": {"seed": 4204034, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 234, "strictValidation": true}, "imageAssets": {"target": "../images/voi-233/target.png", "shapes": {"S1": "../images/voi-233/shape_S1.png", "S2": "../images/voi-233/shape_S2.png", "S3": "../images/voi-233/shape_S3.png", "S4": "../images/voi-233/shape_S4.png", "S5": "../images/voi-233/shape_S5.png"}}, "ID": "voi-233", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 7]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 7]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [8, 3]}]}, "legacy_answer": "S1 0 V4 [3,7]\nS3 180 V2 [4,7]\nS5 270 V1 [8,3]", "solutionText": "S1 0 V4 [3,7]\nS3 180 V2 [4,7]\nS5 270 V1 [8,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-233\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-233/target.png", "shapes": {"S1": "images/voi-233/shape_S1.png", "S2": "images/voi-233/shape_S2.png", "S3": "images/voi-233/shape_S3.png", "S4": "images/voi-233/shape_S4.png", "S5": "images/voi-233/shape_S5.png"}}, "__sample_id__": "voi-233"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 5], [7, 5], [7, 7], [5, 7]]}, {"polygon": [[2, 5], [5, 5], [5, 6], [2, 6]]}, {"polygon": [[2, 7], [2, 5], [3, 5], [3, 6], [5, 6], [5, 7]]}], "meta": {"seed": 4204035, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 235, "strictValidation": true}, "imageAssets": {"target": "../images/voi-234/target.png", "shapes": {"S1": "../images/voi-234/shape_S1.png", "S2": "../images/voi-234/shape_S2.png", "S3": "../images/voi-234/shape_S3.png", "S4": "../images/voi-234/shape_S4.png", "S5": "../images/voi-234/shape_S5.png"}}, "ID": "voi-234", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [7, 5]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [3, 6]}]}, "legacy_answer": "S1 0 V2 [7,5]\nS2 0 V4 [2,6]\nS3 90 V4 [3,6]", "solutionText": "S1 0 V2 [7,5]\nS2 0 V4 [2,6]\nS3 90 V4 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-234\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-234/target.png", "shapes": {"S1": "images/voi-234/shape_S1.png", "S2": "images/voi-234/shape_S2.png", "S3": "images/voi-234/shape_S3.png", "S4": "images/voi-234/shape_S4.png", "S5": "images/voi-234/shape_S5.png"}}, "__sample_id__": "voi-234"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 7], [1, 4], [3, 4], [3, 7]]}, {"polygon": [[0, 6], [1, 6], [1, 7], [0, 7]]}, {"polygon": [[2, 5], [2, 6], [0, 6], [0, 5]]}], "meta": {"seed": 4204036, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 236, "strictValidation": true}, "imageAssets": {"target": "../images/voi-235/target.png", "shapes": {"S1": "../images/voi-235/shape_S1.png", "S2": "../images/voi-235/shape_S2.png", "S3": "../images/voi-235/shape_S3.png", "S4": "../images/voi-235/shape_S4.png", "S5": "../images/voi-235/shape_S5.png"}}, "ID": "voi-235", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [0, 6]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [2, 5]}]}, "legacy_answer": "S2 90 V3 [3,4]\nS4 0 V1 [0,6]\nS5 270 V1 [2,5]", "solutionText": "S2 90 V3 [3,4]\nS4 0 V1 [0,6]\nS5 270 V1 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-235\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-235/target.png", "shapes": {"S1": "images/voi-235/shape_S1.png", "S2": "images/voi-235/shape_S2.png", "S3": "images/voi-235/shape_S3.png", "S4": "images/voi-235/shape_S4.png", "S5": "images/voi-235/shape_S5.png"}}, "__sample_id__": "voi-235"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 3], [5, 3], [5, 2], [6, 2]]}, {"polygon": [[7, 1], [7, 2], [4, 2], [4, 1]]}, {"polygon": [[5, 5], [5, 2], [7, 2], [7, 5]]}], "meta": {"seed": 4204037, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 237, "strictValidation": true}, "imageAssets": {"target": "../images/voi-236/target.png", "shapes": {"S1": "../images/voi-236/shape_S1.png", "S2": "../images/voi-236/shape_S2.png", "S3": "../images/voi-236/shape_S3.png", "S4": "../images/voi-236/shape_S4.png", "S5": "../images/voi-236/shape_S5.png"}}, "ID": "voi-236", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [5, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [7, 2]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [5, 5]}]}, "legacy_answer": "S1 180 V3 [5,2]\nS3 270 V2 [7,2]\nS5 90 V1 [5,5]", "solutionText": "S1 180 V3 [5,2]\nS3 270 V2 [7,2]\nS5 90 V1 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-236\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-236/target.png", "shapes": {"S1": "images/voi-236/shape_S1.png", "S2": "images/voi-236/shape_S2.png", "S3": "images/voi-236/shape_S3.png", "S4": "images/voi-236/shape_S4.png", "S5": "images/voi-236/shape_S5.png"}}, "__sample_id__": "voi-236"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [3, 3], [4, 3], [4, 4]]}, {"polygon": [[7, 3], [7, 6], [6, 5], [6, 3]]}, {"polygon": [[3, 3], [6, 3], [6, 5], [3, 5]]}], "meta": {"seed": 4204038, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 238, "strictValidation": true}, "imageAssets": {"target": "../images/voi-237/target.png", "shapes": {"S1": "../images/voi-237/shape_S1.png", "S2": "../images/voi-237/shape_S2.png", "S3": "../images/voi-237/shape_S3.png", "S4": "../images/voi-237/shape_S4.png", "S5": "../images/voi-237/shape_S5.png"}}, "ID": "voi-237", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [4, 4]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [7, 6]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S1 90 V4 [4,4]\nS2 270 V2 [7,6]\nS3 0 V3 [6,5]", "solutionText": "S1 90 V4 [4,4]\nS2 270 V2 [7,6]\nS3 0 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-237\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-237/target.png", "shapes": {"S1": "images/voi-237/shape_S1.png", "S2": "images/voi-237/shape_S2.png", "S3": "images/voi-237/shape_S3.png", "S4": "images/voi-237/shape_S4.png", "S5": "images/voi-237/shape_S5.png"}}, "__sample_id__": "voi-237"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 2], [3, 2], [3, 1], [5, 1]]}, {"polygon": [[0, 0], [3, 0], [3, 2], [0, 2]]}, {"polygon": [[0, 2], [0, 1], [1, 1], [1, 2]]}], "meta": {"seed": 4204039, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 239, "strictValidation": true}, "imageAssets": {"target": "../images/voi-238/target.png", "shapes": {"S1": "../images/voi-238/shape_S1.png", "S2": "../images/voi-238/shape_S2.png", "S3": "../images/voi-238/shape_S3.png", "S4": "../images/voi-238/shape_S4.png", "S5": "../images/voi-238/shape_S5.png"}}, "ID": "voi-238", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 1]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [3, 2]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [1, 1]}]}, "legacy_answer": "S1 180 V3 [3,1]\nS2 0 V3 [3,2]\nS5 90 V3 [1,1]", "solutionText": "S1 180 V3 [3,1]\nS2 0 V3 [3,2]\nS5 90 V3 [1,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-238\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-238/target.png", "shapes": {"S1": "images/voi-238/shape_S1.png", "S2": "images/voi-238/shape_S2.png", "S3": "images/voi-238/shape_S3.png", "S4": "images/voi-238/shape_S4.png", "S5": "images/voi-238/shape_S5.png"}}, "__sample_id__": "voi-238"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[2, 6], [1, 6], [1, 3], [2, 3]]}, {"polygon": [[2, 5], [2, 3], [3, 3], [3, 4], [5, 4], [5, 5]]}, {"polygon": [[2, 3], [2, 4], [1, 3]]}], "meta": {"seed": 4204040, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.141079, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.833536, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 240, "strictValidation": true}, "imageAssets": {"target": "../images/voi-239/target.png", "shapes": {"S1": "../images/voi-239/shape_S1.png", "S2": "../images/voi-239/shape_S2.png", "S3": "../images/voi-239/shape_S3.png", "S4": "../images/voi-239/shape_S4.png", "S5": "../images/voi-239/shape_S5.png"}}, "ID": "voi-239", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [2, 3]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [5, 5]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [2, 3]}]}, "legacy_answer": "S2 180 V4 [2,3]\nS4 90 V6 [5,5]\nS5 270 V1 [2,3]", "solutionText": "S2 180 V4 [2,3]\nS4 90 V6 [5,5]\nS5 270 V1 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-239\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-239/target.png", "shapes": {"S1": "images/voi-239/shape_S1.png", "S2": "images/voi-239/shape_S2.png", "S3": "images/voi-239/shape_S3.png", "S4": "images/voi-239/shape_S4.png", "S5": "images/voi-239/shape_S5.png"}}, "__sample_id__": "voi-239"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 4], [1, 4], [1, 5], [0, 5]]}, {"polygon": [[3, 7], [1, 7], [1, 6], [2, 6], [2, 4], [3, 4]]}, {"polygon": [[0, 6], [0, 4], [2, 4], [2, 6]]}], "meta": {"seed": 4204041, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 241, "strictValidation": true}, "imageAssets": {"target": "../images/voi-240/target.png", "shapes": {"S1": "../images/voi-240/shape_S1.png", "S2": "../images/voi-240/shape_S2.png", "S3": "../images/voi-240/shape_S3.png", "S4": "../images/voi-240/shape_S4.png", "S5": "../images/voi-240/shape_S5.png"}}, "ID": "voi-240", "answer": {"placements": [{"shape": "S3", "angle": 0, "vertex": "V4", "grid": [0, 5]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [1, 7]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [2, 4]}]}, "legacy_answer": "S3 0 V4 [0,5]\nS4 180 V2 [1,7]\nS5 90 V3 [2,4]", "solutionText": "S3 0 V4 [0,5]\nS4 180 V2 [1,7]\nS5 90 V3 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-240\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-240/target.png", "shapes": {"S1": "images/voi-240/shape_S1.png", "S2": "images/voi-240/shape_S2.png", "S3": "images/voi-240/shape_S3.png", "S4": "images/voi-240/shape_S4.png", "S5": "images/voi-240/shape_S5.png"}}, "__sample_id__": "voi-240"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[4, 2], [4, 5], [3, 5], [3, 2]]}, {"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[4, 1], [5, 1], [4, 2]]}], "meta": {"seed": 4204042, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.141079, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.833536, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 242, "strictValidation": true}, "imageAssets": {"target": "../images/voi-241/target.png", "shapes": {"S1": "../images/voi-241/shape_S1.png", "S2": "../images/voi-241/shape_S2.png", "S3": "../images/voi-241/shape_S3.png", "S4": "../images/voi-241/shape_S4.png", "S5": "../images/voi-241/shape_S5.png"}}, "ID": "voi-241", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V3", "grid": [3, 5]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [4, 3]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S3 270 V3 [3,5]\nS4 270 V3 [4,3]\nS5 0 V3 [4,2]", "solutionText": "S3 270 V3 [3,5]\nS4 270 V3 [4,3]\nS5 0 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-241\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-241/target.png", "shapes": {"S1": "images/voi-241/shape_S1.png", "S2": "images/voi-241/shape_S2.png", "S3": "images/voi-241/shape_S3.png", "S4": "images/voi-241/shape_S4.png", "S5": "images/voi-241/shape_S5.png"}}, "__sample_id__": "voi-241"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 0], [4, 0], [4, 2], [1, 2]]}, {"polygon": [[6, 1], [6, 2], [4, 2], [4, 1]]}, {"polygon": [[6, 1], [3, 1], [3, 0], [6, 0]]}], "meta": {"seed": 4204043, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 243, "strictValidation": true}, "imageAssets": {"target": "../images/voi-242/target.png", "shapes": {"S1": "../images/voi-242/shape_S1.png", "S2": "../images/voi-242/shape_S2.png", "S3": "../images/voi-242/shape_S3.png", "S4": "../images/voi-242/shape_S4.png", "S5": "../images/voi-242/shape_S5.png"}}, "ID": "voi-242", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [4, 2]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [6, 2]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [6, 1]}]}, "legacy_answer": "S1 0 V3 [4,2]\nS3 270 V2 [6,2]\nS4 180 V1 [6,1]", "solutionText": "S1 0 V3 [4,2]\nS3 270 V2 [6,2]\nS4 180 V1 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-242\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-242/target.png", "shapes": {"S1": "images/voi-242/shape_S1.png", "S2": "images/voi-242/shape_S2.png", "S3": "images/voi-242/shape_S3.png", "S4": "images/voi-242/shape_S4.png", "S5": "images/voi-242/shape_S5.png"}}, "__sample_id__": "voi-242"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 7], [4, 5], [6, 5], [6, 7]]}, {"polygon": [[1, 7], [1, 4], [3, 4], [3, 7]]}, {"polygon": [[3, 7], [3, 5], [4, 5], [4, 6], [6, 6], [6, 7]]}], "meta": {"seed": 4204044, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 244, "strictValidation": true}, "imageAssets": {"target": "../images/voi-243/target.png", "shapes": {"S1": "../images/voi-243/shape_S1.png", "S2": "../images/voi-243/shape_S2.png", "S3": "../images/voi-243/shape_S3.png", "S4": "../images/voi-243/shape_S4.png", "S5": "../images/voi-243/shape_S5.png"}}, "ID": "voi-243", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 7]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [3, 7]}, {"shape": "S5", "angle": 90, "vertex": "V5", "grid": [6, 6]}]}, "legacy_answer": "S2 90 V4 [6,7]\nS4 90 V4 [3,7]\nS5 90 V5 [6,6]", "solutionText": "S2 90 V4 [6,7]\nS4 90 V4 [3,7]\nS5 90 V5 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-243\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-243/target.png", "shapes": {"S1": "images/voi-243/shape_S1.png", "S2": "images/voi-243/shape_S2.png", "S3": "images/voi-243/shape_S3.png", "S4": "images/voi-243/shape_S4.png", "S5": "images/voi-243/shape_S5.png"}}, "__sample_id__": "voi-243"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 2], [7, 2], [7, 4], [6, 4]]}, {"polygon": [[3, 2], [6, 2], [5, 3], [3, 3]]}, {"polygon": [[4, 3], [7, 3], [7, 5], [4, 5]]}], "meta": {"seed": 4204045, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.573755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 245, "strictValidation": true}, "imageAssets": {"target": "../images/voi-244/target.png", "shapes": {"S1": "../images/voi-244/shape_S1.png", "S2": "../images/voi-244/shape_S2.png", "S3": "../images/voi-244/shape_S3.png", "S4": "../images/voi-244/shape_S4.png", "S5": "../images/voi-244/shape_S5.png"}}, "ID": "voi-244", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [6, 4]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 2]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [7, 5]}]}, "legacy_answer": "S1 0 V4 [6,4]\nS2 0 V2 [6,2]\nS5 0 V3 [7,5]", "solutionText": "S1 0 V4 [6,4]\nS2 0 V2 [6,2]\nS5 0 V3 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-244\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-244/target.png", "shapes": {"S1": "images/voi-244/shape_S1.png", "S2": "images/voi-244/shape_S2.png", "S3": "images/voi-244/shape_S3.png", "S4": "images/voi-244/shape_S4.png", "S5": "images/voi-244/shape_S5.png"}}, "__sample_id__": "voi-244"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [7, 4], [7, 6], [4, 6]]}, {"polygon": [[7, 2], [7, 5], [5, 5], [5, 2]]}, {"polygon": [[8, 5], [6, 5], [6, 4], [8, 4]]}], "meta": {"seed": 4204046, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 246, "strictValidation": true}, "imageAssets": {"target": "../images/voi-245/target.png", "shapes": {"S1": "../images/voi-245/shape_S1.png", "S2": "../images/voi-245/shape_S2.png", "S3": "../images/voi-245/shape_S3.png", "S4": "../images/voi-245/shape_S4.png", "S5": "../images/voi-245/shape_S5.png"}}, "ID": "voi-245", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [4, 4]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [5, 5]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [8, 5]}]}, "legacy_answer": "S2 0 V1 [4,4]\nS3 270 V3 [5,5]\nS4 180 V1 [8,5]", "solutionText": "S2 0 V1 [4,4]\nS3 270 V3 [5,5]\nS4 180 V1 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-245\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-245/target.png", "shapes": {"S1": "images/voi-245/shape_S1.png", "S2": "images/voi-245/shape_S2.png", "S3": "images/voi-245/shape_S3.png", "S4": "images/voi-245/shape_S4.png", "S5": "images/voi-245/shape_S5.png"}}, "__sample_id__": "voi-245"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 5], [6, 7], [4, 7], [4, 5]]}, {"polygon": [[6, 4], [6, 6], [5, 6], [5, 5], [3, 5], [3, 4]]}, {"polygon": [[6, 7], [6, 8], [4, 8], [4, 7]]}], "meta": {"seed": 4204047, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 247, "strictValidation": true}, "imageAssets": {"target": "../images/voi-246/target.png", "shapes": {"S1": "../images/voi-246/shape_S1.png", "S2": "../images/voi-246/shape_S2.png", "S3": "../images/voi-246/shape_S3.png", "S4": "../images/voi-246/shape_S4.png", "S5": "../images/voi-246/shape_S5.png"}}, "ID": "voi-246", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 7]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [5, 6]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [4, 8]}]}, "legacy_answer": "S2 270 V2 [6,7]\nS3 270 V3 [5,6]\nS5 270 V3 [4,8]", "solutionText": "S2 270 V2 [6,7]\nS3 270 V3 [5,6]\nS5 270 V3 [4,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-246\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-246/target.png", "shapes": {"S1": "images/voi-246/shape_S1.png", "S2": "images/voi-246/shape_S2.png", "S3": "images/voi-246/shape_S3.png", "S4": "images/voi-246/shape_S4.png", "S5": "images/voi-246/shape_S5.png"}}, "__sample_id__": "voi-246"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 3], [1, 1], [3, 3]]}, {"polygon": [[3, 5], [0, 5], [0, 3], [3, 3]]}, {"polygon": [[2, 4], [2, 1], [4, 1], [4, 4]]}], "meta": {"seed": 4204048, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.217778, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.385139, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 248, "strictValidation": true}, "imageAssets": {"target": "../images/voi-247/target.png", "shapes": {"S1": "../images/voi-247/shape_S1.png", "S2": "../images/voi-247/shape_S2.png", "S3": "../images/voi-247/shape_S3.png", "S4": "../images/voi-247/shape_S4.png", "S5": "../images/voi-247/shape_S5.png"}}, "ID": "voi-247", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [3, 3]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 5]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 1]}]}, "legacy_answer": "S1 90 V3 [3,3]\nS2 180 V2 [0,5]\nS4 90 V3 [4,1]", "solutionText": "S1 90 V3 [3,3]\nS2 180 V2 [0,5]\nS4 90 V3 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-247\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-247/target.png", "shapes": {"S1": "images/voi-247/shape_S1.png", "S2": "images/voi-247/shape_S2.png", "S3": "images/voi-247/shape_S3.png", "S4": "images/voi-247/shape_S4.png", "S5": "images/voi-247/shape_S5.png"}}, "__sample_id__": "voi-247"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 5], [6, 5], [6, 4], [7, 4]]}, {"polygon": [[8, 5], [8, 6], [5, 6], [5, 5]]}, {"polygon": [[7, 5], [4, 5], [4, 3], [7, 3]]}], "meta": {"seed": 4204049, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 249, "strictValidation": true}, "imageAssets": {"target": "../images/voi-248/target.png", "shapes": {"S1": "../images/voi-248/shape_S1.png", "S2": "../images/voi-248/shape_S2.png", "S3": "../images/voi-248/shape_S3.png", "S4": "../images/voi-248/shape_S4.png", "S5": "../images/voi-248/shape_S5.png"}}, "ID": "voi-248", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [6, 5]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [5, 6]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S2 180 V2 [6,5]\nS3 270 V3 [5,6]\nS5 180 V2 [4,5]", "solutionText": "S2 180 V2 [6,5]\nS3 270 V3 [5,6]\nS5 180 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-248\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-248/target.png", "shapes": {"S1": "images/voi-248/shape_S1.png", "S2": "images/voi-248/shape_S2.png", "S3": "images/voi-248/shape_S3.png", "S4": "images/voi-248/shape_S4.png", "S5": "images/voi-248/shape_S5.png"}}, "__sample_id__": "voi-248"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [4, 4], [2, 6]]}, {"polygon": [[5, 6], [2, 6], [2, 4], [5, 4]]}, {"polygon": [[4, 2], [7, 2], [7, 4], [4, 4]]}], "meta": {"seed": 4204050, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.293333, "contourComplexity": 68, "connectedComponents": 1, "fillRatio": 0.155273, "difficultyScore": 0.462786, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 250, "strictValidation": true}, "imageAssets": {"target": "../images/voi-249/target.png", "shapes": {"S1": "../images/voi-249/shape_S1.png", "S2": "../images/voi-249/shape_S2.png", "S3": "../images/voi-249/shape_S3.png", "S4": "../images/voi-249/shape_S4.png", "S5": "../images/voi-249/shape_S5.png"}}, "ID": "voi-249", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [2, 4]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [4, 4]}]}, "legacy_answer": "S2 0 V2 [4,4]\nS3 180 V3 [2,4]\nS5 0 V4 [4,4]", "solutionText": "S2 0 V2 [4,4]\nS3 180 V3 [2,4]\nS5 0 V4 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-249\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-249/target.png", "shapes": {"S1": "images/voi-249/shape_S1.png", "S2": "images/voi-249/shape_S2.png", "S3": "images/voi-249/shape_S3.png", "S4": "images/voi-249/shape_S4.png", "S5": "images/voi-249/shape_S5.png"}}, "__sample_id__": "voi-249"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 6], [1, 6], [1, 4], [3, 4]]}, {"polygon": [[3, 3], [3, 5], [2, 5], [2, 4], [0, 4], [0, 3]]}, {"polygon": [[2, 8], [2, 6], [4, 6], [4, 8]]}], "meta": {"seed": 4204051, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.620833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 251, "strictValidation": true}, "imageAssets": {"target": "../images/voi-250/target.png", "shapes": {"S1": "../images/voi-250/shape_S1.png", "S2": "../images/voi-250/shape_S2.png", "S3": "../images/voi-250/shape_S3.png", "S4": "../images/voi-250/shape_S4.png", "S5": "../images/voi-250/shape_S5.png"}}, "ID": "voi-250", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [1, 4]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [2, 4]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 6]}]}, "legacy_answer": "S1 180 V3 [1,4]\nS3 270 V4 [2,4]\nS4 90 V3 [4,6]", "solutionText": "S1 180 V3 [1,4]\nS3 270 V4 [2,4]\nS4 90 V3 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-250\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-250/target.png", "shapes": {"S1": "images/voi-250/shape_S1.png", "S2": "images/voi-250/shape_S2.png", "S3": "images/voi-250/shape_S3.png", "S4": "images/voi-250/shape_S4.png", "S5": "images/voi-250/shape_S5.png"}}, "__sample_id__": "voi-250"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 5], [3, 5], [4, 4], [6, 4]]}, {"polygon": [[2, 3], [3, 3], [3, 6], [2, 6]]}, {"polygon": [[2, 5], [5, 5], [5, 7], [2, 7]]}], "meta": {"seed": 4204052, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.173442, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.608381, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 252, "strictValidation": true}, "imageAssets": {"target": "../images/voi-251/target.png", "shapes": {"S1": "../images/voi-251/shape_S1.png", "S2": "../images/voi-251/shape_S2.png", "S3": "../images/voi-251/shape_S3.png", "S4": "../images/voi-251/shape_S4.png", "S5": "../images/voi-251/shape_S5.png"}}, "ID": "voi-251", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V2", "grid": [3, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [2, 3]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [2, 7]}]}, "legacy_answer": "S3 180 V2 [3,5]\nS4 0 V1 [2,3]\nS5 0 V4 [2,7]", "solutionText": "S3 180 V2 [3,5]\nS4 0 V1 [2,3]\nS5 0 V4 [2,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-251\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-251/target.png", "shapes": {"S1": "images/voi-251/shape_S1.png", "S2": "images/voi-251/shape_S2.png", "S3": "images/voi-251/shape_S3.png", "S4": "images/voi-251/shape_S4.png", "S5": "images/voi-251/shape_S5.png"}}, "__sample_id__": "voi-251"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 6], [0, 4], [2, 4], [2, 6]]}, {"polygon": [[0, 5], [1, 5], [1, 7], [0, 7]]}, {"polygon": [[4, 7], [1, 7], [1, 6], [4, 6]]}], "meta": {"seed": 4204053, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 253, "strictValidation": true}, "imageAssets": {"target": "../images/voi-252/target.png", "shapes": {"S1": "../images/voi-252/shape_S1.png", "S2": "../images/voi-252/shape_S2.png", "S3": "../images/voi-252/shape_S3.png", "S4": "../images/voi-252/shape_S4.png", "S5": "../images/voi-252/shape_S5.png"}}, "ID": "voi-252", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V2", "grid": [0, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [0, 5]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [1, 6]}]}, "legacy_answer": "S3 90 V2 [0,4]\nS4 0 V1 [0,5]\nS5 180 V3 [1,6]", "solutionText": "S3 90 V2 [0,4]\nS4 0 V1 [0,5]\nS5 180 V3 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-252\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-252/target.png", "shapes": {"S1": "images/voi-252/shape_S1.png", "S2": "images/voi-252/shape_S2.png", "S3": "images/voi-252/shape_S3.png", "S4": "images/voi-252/shape_S4.png", "S5": "images/voi-252/shape_S5.png"}}, "__sample_id__": "voi-252"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 3], [5, 3], [5, 5], [2, 5]]}, {"polygon": [[1, 6], [1, 3], [3, 3], [3, 6]]}, {"polygon": [[3, 6], [3, 5], [6, 5], [6, 6]]}], "meta": {"seed": 4204054, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.322917, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 254, "strictValidation": true}, "imageAssets": {"target": "../images/voi-253/target.png", "shapes": {"S1": "../images/voi-253/shape_S1.png", "S2": "../images/voi-253/shape_S2.png", "S3": "../images/voi-253/shape_S3.png", "S4": "../images/voi-253/shape_S4.png", "S5": "../images/voi-253/shape_S5.png"}}, "ID": "voi-253", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [2, 3]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [3, 3]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S1 0 V1 [2,3]\nS3 90 V3 [3,3]\nS4 90 V3 [6,5]", "solutionText": "S1 0 V1 [2,3]\nS3 90 V3 [3,3]\nS4 90 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-253\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-253/target.png", "shapes": {"S1": "images/voi-253/shape_S1.png", "S2": "images/voi-253/shape_S2.png", "S3": "images/voi-253/shape_S3.png", "S4": "images/voi-253/shape_S4.png", "S5": "images/voi-253/shape_S5.png"}}, "__sample_id__": "voi-253"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 4], [2, 4], [2, 2], [5, 2]]}, {"polygon": [[5, 1], [6, 1], [6, 4], [5, 4]]}, {"polygon": [[6, 1], [6, 3], [5, 3], [5, 2], [3, 2], [3, 1]]}], "meta": {"seed": 4204055, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 255, "strictValidation": true}, "imageAssets": {"target": "../images/voi-254/target.png", "shapes": {"S1": "../images/voi-254/shape_S1.png", "S2": "../images/voi-254/shape_S2.png", "S3": "../images/voi-254/shape_S3.png", "S4": "../images/voi-254/shape_S4.png", "S5": "../images/voi-254/shape_S5.png"}}, "ID": "voi-254", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 4]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 1]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [6, 1]}]}, "legacy_answer": "S1 180 V1 [5,4]\nS2 0 V2 [6,1]\nS3 270 V1 [6,1]", "solutionText": "S1 180 V1 [5,4]\nS2 0 V2 [6,1]\nS3 270 V1 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-254\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-254/target.png", "shapes": {"S1": "images/voi-254/shape_S1.png", "S2": "images/voi-254/shape_S2.png", "S3": "images/voi-254/shape_S3.png", "S4": "images/voi-254/shape_S4.png", "S5": "images/voi-254/shape_S5.png"}}, "__sample_id__": "voi-254"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 3], [3, 3], [3, 5], [0, 5]]}, {"polygon": [[0, 3], [0, 1], [2, 1], [2, 3]]}, {"polygon": [[2, 4], [2, 1], [3, 2], [3, 4]]}], "meta": {"seed": 4204056, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.159601, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.632494, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 256, "strictValidation": true}, "imageAssets": {"target": "../images/voi-255/target.png", "shapes": {"S1": "../images/voi-255/shape_S1.png", "S2": "../images/voi-255/shape_S2.png", "S3": "../images/voi-255/shape_S3.png", "S4": "../images/voi-255/shape_S4.png", "S5": "../images/voi-255/shape_S5.png"}}, "ID": "voi-255", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 5]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [2, 1]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [3, 4]}]}, "legacy_answer": "S1 0 V3 [3,5]\nS2 90 V3 [2,1]\nS5 90 V4 [3,4]", "solutionText": "S1 0 V3 [3,5]\nS2 90 V3 [2,1]\nS5 90 V4 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-255\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-255/target.png", "shapes": {"S1": "images/voi-255/shape_S1.png", "S2": "images/voi-255/shape_S2.png", "S3": "images/voi-255/shape_S3.png", "S4": "images/voi-255/shape_S4.png", "S5": "images/voi-255/shape_S5.png"}}, "__sample_id__": "voi-255"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 3], [5, 3], [5, 2], [7, 2]]}, {"polygon": [[3, 3], [6, 3], [6, 4], [3, 4]]}, {"polygon": [[6, 5], [6, 2], [8, 2], [8, 5]]}], "meta": {"seed": 4204057, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 257, "strictValidation": true}, "imageAssets": {"target": "../images/voi-256/target.png", "shapes": {"S1": "../images/voi-256/shape_S1.png", "S2": "../images/voi-256/shape_S2.png", "S3": "../images/voi-256/shape_S3.png", "S4": "../images/voi-256/shape_S4.png", "S5": "../images/voi-256/shape_S5.png"}}, "ID": "voi-256", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [7, 2]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [3, 4]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [8, 2]}]}, "legacy_answer": "S2 180 V4 [7,2]\nS4 0 V4 [3,4]\nS5 90 V3 [8,2]", "solutionText": "S2 180 V4 [7,2]\nS4 0 V4 [3,4]\nS5 90 V3 [8,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-256\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-256/target.png", "shapes": {"S1": "images/voi-256/shape_S1.png", "S2": "images/voi-256/shape_S2.png", "S3": "images/voi-256/shape_S3.png", "S4": "images/voi-256/shape_S4.png", "S5": "images/voi-256/shape_S5.png"}}, "__sample_id__": "voi-256"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 3], [4, 3], [4, 5], [2, 5]]}, {"polygon": [[1, 5], [1, 3], [3, 5]]}, {"polygon": [[0, 2], [2, 2], [0, 4]]}], "meta": {"seed": 4204058, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.130769, "contourComplexity": 132, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.85622, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 258, "strictValidation": true}, "imageAssets": {"target": "../images/voi-257/target.png", "shapes": {"S1": "../images/voi-257/shape_S1.png", "S2": "../images/voi-257/shape_S2.png", "S3": "../images/voi-257/shape_S3.png", "S4": "../images/voi-257/shape_S4.png", "S5": "../images/voi-257/shape_S5.png"}}, "ID": "voi-257", "answer": {"placements": [{"shape": "S3", "angle": 0, "vertex": "V3", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [1, 5]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [0, 4]}]}, "legacy_answer": "S3 0 V3 [4,5]\nS4 90 V1 [1,5]\nS5 0 V3 [0,4]", "solutionText": "S3 0 V3 [4,5]\nS4 90 V1 [1,5]\nS5 0 V3 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-257\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-257/target.png", "shapes": {"S1": "images/voi-257/shape_S1.png", "S2": "images/voi-257/shape_S2.png", "S3": "images/voi-257/shape_S3.png", "S4": "images/voi-257/shape_S4.png", "S5": "images/voi-257/shape_S5.png"}}, "__sample_id__": "voi-257"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 3], [7, 5], [6, 5], [6, 3]]}, {"polygon": [[6, 4], [6, 2], [8, 2], [8, 4]]}, {"polygon": [[7, 7], [7, 4], [8, 5], [8, 7]]}], "meta": {"seed": 4204059, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.458169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 259, "strictValidation": true}, "imageAssets": {"target": "../images/voi-258/target.png", "shapes": {"S1": "../images/voi-258/shape_S1.png", "S2": "../images/voi-258/shape_S2.png", "S3": "../images/voi-258/shape_S3.png", "S4": "../images/voi-258/shape_S4.png", "S5": "../images/voi-258/shape_S5.png"}}, "ID": "voi-258", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V3", "grid": [6, 5]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [8, 4]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [7, 7]}]}, "legacy_answer": "S2 270 V3 [6,5]\nS3 90 V4 [8,4]\nS5 90 V1 [7,7]", "solutionText": "S2 270 V3 [6,5]\nS3 90 V4 [8,4]\nS5 90 V1 [7,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-258\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-258/target.png", "shapes": {"S1": "images/voi-258/shape_S1.png", "S2": "images/voi-258/shape_S2.png", "S3": "images/voi-258/shape_S3.png", "S4": "images/voi-258/shape_S4.png", "S5": "images/voi-258/shape_S5.png"}}, "__sample_id__": "voi-258"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[7, 5], [7, 7], [6, 7], [6, 6], [4, 6], [4, 5]]}, {"polygon": [[7, 6], [7, 7], [4, 7], [4, 6]]}, {"polygon": [[8, 6], [8, 8], [6, 8], [6, 6]]}], "meta": {"seed": 4204060, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 260, "strictValidation": true}, "imageAssets": {"target": "../images/voi-259/target.png", "shapes": {"S1": "../images/voi-259/shape_S1.png", "S2": "../images/voi-259/shape_S2.png", "S3": "../images/voi-259/shape_S3.png", "S4": "../images/voi-259/shape_S4.png", "S5": "../images/voi-259/shape_S5.png"}}, "ID": "voi-259", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V6", "grid": [4, 5]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [7, 7]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [6, 6]}]}, "legacy_answer": "S1 270 V6 [4,5]\nS3 270 V2 [7,7]\nS4 270 V4 [6,6]", "solutionText": "S1 270 V6 [4,5]\nS3 270 V2 [7,7]\nS4 270 V4 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-259\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-259/target.png", "shapes": {"S1": "images/voi-259/shape_S1.png", "S2": "images/voi-259/shape_S2.png", "S3": "images/voi-259/shape_S3.png", "S4": "images/voi-259/shape_S4.png", "S5": "images/voi-259/shape_S5.png"}}, "__sample_id__": "voi-259"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [3, 3], [4, 3], [4, 4]]}, {"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[6, 3], [6, 6], [5, 5], [5, 3]]}], "meta": {"seed": 4204061, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 261, "strictValidation": true}, "imageAssets": {"target": "../images/voi-260/target.png", "shapes": {"S1": "../images/voi-260/shape_S1.png", "S2": "../images/voi-260/shape_S2.png", "S3": "../images/voi-260/shape_S3.png", "S4": "../images/voi-260/shape_S4.png", "S5": "../images/voi-260/shape_S5.png"}}, "ID": "voi-260", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 3]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [5, 3]}]}, "legacy_answer": "S2 90 V3 [4,3]\nS3 270 V2 [5,6]\nS5 270 V4 [5,3]", "solutionText": "S2 90 V3 [4,3]\nS3 270 V2 [5,6]\nS5 270 V4 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-260\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-260/target.png", "shapes": {"S1": "images/voi-260/shape_S1.png", "S2": "images/voi-260/shape_S2.png", "S3": "images/voi-260/shape_S3.png", "S4": "images/voi-260/shape_S4.png", "S5": "images/voi-260/shape_S5.png"}}, "__sample_id__": "voi-260"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [6, 3], [8, 3], [8, 6]]}, {"polygon": [[7, 5], [6, 5], [6, 3], [7, 3]]}, {"polygon": [[8, 8], [5, 8], [5, 6], [8, 6]]}], "meta": {"seed": 4204062, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 262, "strictValidation": true}, "imageAssets": {"target": "../images/voi-261/target.png", "shapes": {"S1": "../images/voi-261/shape_S1.png", "S2": "../images/voi-261/shape_S2.png", "S3": "../images/voi-261/shape_S3.png", "S4": "../images/voi-261/shape_S4.png", "S5": "../images/voi-261/shape_S5.png"}}, "ID": "voi-261", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [8, 6]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [6, 3]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [8, 8]}]}, "legacy_answer": "S1 90 V4 [8,6]\nS4 180 V3 [6,3]\nS5 180 V1 [8,8]", "solutionText": "S1 90 V4 [8,6]\nS4 180 V3 [6,3]\nS5 180 V1 [8,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-261\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-261/target.png", "shapes": {"S1": "images/voi-261/shape_S1.png", "S2": "images/voi-261/shape_S2.png", "S3": "images/voi-261/shape_S3.png", "S4": "images/voi-261/shape_S4.png", "S5": "images/voi-261/shape_S5.png"}}, "__sample_id__": "voi-261"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 3], [3, 5], [1, 5], [1, 3]]}, {"polygon": [[2, 3], [2, 0], [4, 0], [4, 3]]}, {"polygon": [[4, 5], [3, 5], [3, 2], [4, 2]]}], "meta": {"seed": 4204063, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.640865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 263, "strictValidation": true}, "imageAssets": {"target": "../images/voi-262/target.png", "shapes": {"S1": "../images/voi-262/shape_S1.png", "S2": "../images/voi-262/shape_S2.png", "S3": "../images/voi-262/shape_S3.png", "S4": "../images/voi-262/shape_S4.png", "S5": "../images/voi-262/shape_S5.png"}}, "ID": "voi-262", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [1, 3]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 0]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 5]}]}, "legacy_answer": "S1 270 V4 [1,3]\nS2 90 V3 [4,0]\nS3 180 V1 [4,5]", "solutionText": "S1 270 V4 [1,3]\nS2 90 V3 [4,0]\nS3 180 V1 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-262\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-262/target.png", "shapes": {"S1": "images/voi-262/shape_S1.png", "S2": "images/voi-262/shape_S2.png", "S3": "images/voi-262/shape_S3.png", "S4": "images/voi-262/shape_S4.png", "S5": "images/voi-262/shape_S5.png"}}, "__sample_id__": "voi-262"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 6], [0, 3], [2, 3], [2, 6]]}, {"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}, {"polygon": [[2, 7], [0, 7], [0, 6], [1, 6], [1, 4], [2, 4]]}], "meta": {"seed": 4204064, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 264, "strictValidation": true}, "imageAssets": {"target": "../images/voi-263/target.png", "shapes": {"S1": "../images/voi-263/shape_S1.png", "S2": "../images/voi-263/shape_S2.png", "S3": "../images/voi-263/shape_S3.png", "S4": "../images/voi-263/shape_S4.png", "S5": "../images/voi-263/shape_S5.png"}}, "ID": "voi-263", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [2, 3]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [2, 4]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [0, 6]}]}, "legacy_answer": "S1 90 V3 [2,3]\nS3 90 V1 [2,4]\nS4 180 V3 [0,6]", "solutionText": "S1 90 V3 [2,3]\nS3 90 V1 [2,4]\nS4 180 V3 [0,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-263\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-263/target.png", "shapes": {"S1": "images/voi-263/shape_S1.png", "S2": "images/voi-263/shape_S2.png", "S3": "images/voi-263/shape_S3.png", "S4": "images/voi-263/shape_S4.png", "S5": "images/voi-263/shape_S5.png"}}, "__sample_id__": "voi-263"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 5], [3, 5], [5, 3]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[6, 1], [6, 3], [4, 1]]}], "meta": {"seed": 4204065, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 136, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.510494, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 265, "strictValidation": true}, "imageAssets": {"target": "../images/voi-264/target.png", "shapes": {"S1": "../images/voi-264/shape_S1.png", "S2": "../images/voi-264/shape_S2.png", "S3": "../images/voi-264/shape_S3.png", "S4": "../images/voi-264/shape_S4.png", "S5": "../images/voi-264/shape_S5.png"}}, "ID": "voi-264", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [5, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [3, 4]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [6, 1]}]}, "legacy_answer": "S1 180 V3 [5,3]\nS2 270 V3 [3,4]\nS5 270 V1 [6,1]", "solutionText": "S1 180 V3 [5,3]\nS2 270 V3 [3,4]\nS5 270 V1 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-264\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-264/target.png", "shapes": {"S1": "images/voi-264/shape_S1.png", "S2": "images/voi-264/shape_S2.png", "S3": "images/voi-264/shape_S3.png", "S4": "images/voi-264/shape_S4.png", "S5": "images/voi-264/shape_S5.png"}}, "__sample_id__": "voi-264"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [5, 4], [5, 5], [4, 5], [4, 7], [3, 7]]}, {"polygon": [[7, 4], [5, 4], [5, 3], [7, 3]]}, {"polygon": [[4, 4], [7, 4], [7, 6], [4, 6]]}], "meta": {"seed": 4204066, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.620833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 266, "strictValidation": true}, "imageAssets": {"target": "../images/voi-265/target.png", "shapes": {"S1": "../images/voi-265/shape_S1.png", "S2": "../images/voi-265/shape_S2.png", "S3": "../images/voi-265/shape_S3.png", "S4": "../images/voi-265/shape_S4.png", "S5": "../images/voi-265/shape_S5.png"}}, "ID": "voi-265", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 4]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [7, 4]}]}, "legacy_answer": "S1 0 V2 [5,4]\nS4 180 V2 [5,4]\nS5 0 V2 [7,4]", "solutionText": "S1 0 V2 [5,4]\nS4 180 V2 [5,4]\nS5 0 V2 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-265\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-265/target.png", "shapes": {"S1": "images/voi-265/shape_S1.png", "S2": "images/voi-265/shape_S2.png", "S3": "images/voi-265/shape_S3.png", "S4": "images/voi-265/shape_S4.png", "S5": "images/voi-265/shape_S5.png"}}, "__sample_id__": "voi-265"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 0], [5, 1], [4, 1], [4, 0]]}, {"polygon": [[6, 3], [4, 3], [4, 2], [5, 2], [5, 0], [6, 0]]}, {"polygon": [[5, 2], [3, 2], [3, 0], [5, 0]]}], "meta": {"seed": 4204067, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 267, "strictValidation": true}, "imageAssets": {"target": "../images/voi-266/target.png", "shapes": {"S1": "../images/voi-266/shape_S1.png", "S2": "../images/voi-266/shape_S2.png", "S3": "../images/voi-266/shape_S3.png", "S4": "../images/voi-266/shape_S4.png", "S5": "../images/voi-266/shape_S5.png"}}, "ID": "voi-266", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V1", "grid": [5, 0]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [5, 0]}]}, "legacy_answer": "S3 270 V1 [5,0]\nS4 180 V4 [5,2]\nS5 180 V4 [5,0]", "solutionText": "S3 270 V1 [5,0]\nS4 180 V4 [5,2]\nS5 180 V4 [5,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-266\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-266/target.png", "shapes": {"S1": "images/voi-266/shape_S1.png", "S2": "images/voi-266/shape_S2.png", "S3": "images/voi-266/shape_S3.png", "S4": "images/voi-266/shape_S4.png", "S5": "images/voi-266/shape_S5.png"}}, "__sample_id__": "voi-266"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[6, 5], [5, 5], [5, 4], [6, 4]]}, {"polygon": [[5, 3], [5, 1], [6, 1], [6, 2], [8, 2], [8, 3]]}], "meta": {"seed": 4204068, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 268, "strictValidation": true}, "imageAssets": {"target": "../images/voi-267/target.png", "shapes": {"S1": "../images/voi-267/shape_S1.png", "S2": "../images/voi-267/shape_S2.png", "S3": "../images/voi-267/shape_S3.png", "S4": "../images/voi-267/shape_S4.png", "S5": "../images/voi-267/shape_S5.png"}}, "ID": "voi-267", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [8, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 5]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [6, 2]}]}, "legacy_answer": "S1 0 V2 [8,3]\nS2 180 V1 [6,5]\nS5 90 V4 [6,2]", "solutionText": "S1 0 V2 [8,3]\nS2 180 V1 [6,5]\nS5 90 V4 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-267\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-267/target.png", "shapes": {"S1": "images/voi-267/shape_S1.png", "S2": "images/voi-267/shape_S2.png", "S3": "images/voi-267/shape_S3.png", "S4": "images/voi-267/shape_S4.png", "S5": "images/voi-267/shape_S5.png"}}, "__sample_id__": "voi-267"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 5], [4, 5], [4, 3], [7, 3]]}, {"polygon": [[8, 3], [6, 3], [6, 2], [8, 2]]}, {"polygon": [[6, 1], [6, 4], [4, 4], [4, 1]]}], "meta": {"seed": 4204069, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 269, "strictValidation": true}, "imageAssets": {"target": "../images/voi-268/target.png", "shapes": {"S1": "../images/voi-268/shape_S1.png", "S2": "../images/voi-268/shape_S2.png", "S3": "../images/voi-268/shape_S3.png", "S4": "../images/voi-268/shape_S4.png", "S5": "../images/voi-268/shape_S5.png"}}, "ID": "voi-268", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [4, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [8, 3]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S1 180 V3 [4,3]\nS2 180 V1 [8,3]\nS5 270 V2 [6,4]", "solutionText": "S1 180 V3 [4,3]\nS2 180 V1 [8,3]\nS5 270 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-268\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-268/target.png", "shapes": {"S1": "images/voi-268/shape_S1.png", "S2": "images/voi-268/shape_S2.png", "S3": "images/voi-268/shape_S3.png", "S4": "images/voi-268/shape_S4.png", "S5": "images/voi-268/shape_S5.png"}}, "__sample_id__": "voi-268"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 2], [5, 2], [5, 3], [4, 3], [4, 5], [3, 5]]}, {"polygon": [[3, 4], [3, 3], [5, 3], [5, 4]]}, {"polygon": [[2, 5], [2, 2], [3, 2], [3, 5]]}], "meta": {"seed": 4204070, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 270, "strictValidation": true}, "imageAssets": {"target": "../images/voi-269/target.png", "shapes": {"S1": "../images/voi-269/shape_S1.png", "S2": "../images/voi-269/shape_S2.png", "S3": "../images/voi-269/shape_S3.png", "S4": "../images/voi-269/shape_S4.png", "S5": "../images/voi-269/shape_S5.png"}}, "ID": "voi-269", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [4, 3]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [5, 3]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [2, 2]}]}, "legacy_answer": "S1 0 V4 [4,3]\nS4 90 V3 [5,3]\nS5 90 V2 [2,2]", "solutionText": "S1 0 V4 [4,3]\nS4 90 V3 [5,3]\nS5 90 V2 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-269\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-269/target.png", "shapes": {"S1": "images/voi-269/shape_S1.png", "S2": "images/voi-269/shape_S2.png", "S3": "images/voi-269/shape_S3.png", "S4": "images/voi-269/shape_S4.png", "S5": "images/voi-269/shape_S5.png"}}, "__sample_id__": "voi-269"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [4, 1], [5, 1], [5, 4]]}, {"polygon": [[3, 1], [5, 1], [5, 2], [4, 2], [4, 4], [3, 4]]}, {"polygon": [[6, 5], [5, 5], [5, 2], [6, 2]]}], "meta": {"seed": 4204071, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 271, "strictValidation": true}, "imageAssets": {"target": "../images/voi-270/target.png", "shapes": {"S1": "../images/voi-270/shape_S1.png", "S2": "../images/voi-270/shape_S2.png", "S3": "../images/voi-270/shape_S3.png", "S4": "../images/voi-270/shape_S4.png", "S5": "../images/voi-270/shape_S5.png"}}, "ID": "voi-270", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [5, 1]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [4, 2]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [5, 2]}]}, "legacy_answer": "S1 90 V3 [5,1]\nS2 0 V4 [4,2]\nS4 180 V3 [5,2]", "solutionText": "S1 90 V3 [5,1]\nS2 0 V4 [4,2]\nS4 180 V3 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-270\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-270/target.png", "shapes": {"S1": "images/voi-270/shape_S1.png", "S2": "images/voi-270/shape_S2.png", "S3": "images/voi-270/shape_S3.png", "S4": "images/voi-270/shape_S4.png", "S5": "images/voi-270/shape_S5.png"}}, "__sample_id__": "voi-270"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 8], [3, 5], [5, 5], [5, 8]]}, {"polygon": [[7, 4], [7, 5], [6, 5], [6, 4]]}, {"polygon": [[4, 4], [7, 4], [7, 5], [4, 5]]}], "meta": {"seed": 4204072, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 272, "strictValidation": true}, "imageAssets": {"target": "../images/voi-271/target.png", "shapes": {"S1": "../images/voi-271/shape_S1.png", "S2": "../images/voi-271/shape_S2.png", "S3": "../images/voi-271/shape_S3.png", "S4": "../images/voi-271/shape_S4.png", "S5": "../images/voi-271/shape_S5.png"}}, "ID": "voi-271", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [5, 8]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [6, 4]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S1 90 V4 [5,8]\nS2 270 V4 [6,4]\nS3 0 V1 [4,4]", "solutionText": "S1 90 V4 [5,8]\nS2 270 V4 [6,4]\nS3 0 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-271\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-271/target.png", "shapes": {"S1": "images/voi-271/shape_S1.png", "S2": "images/voi-271/shape_S2.png", "S3": "images/voi-271/shape_S3.png", "S4": "images/voi-271/shape_S4.png", "S5": "images/voi-271/shape_S5.png"}}, "__sample_id__": "voi-271"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[0, 8], [0, 5], [2, 5], [2, 8]]}, {"polygon": [[3, 6], [3, 8], [1, 6]]}, {"polygon": [[1, 8], [0, 8], [1, 7]]}], "meta": {"seed": 4204073, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.247273, "contourComplexity": 104, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.408761, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 273, "strictValidation": true}, "imageAssets": {"target": "../images/voi-272/target.png", "shapes": {"S1": "../images/voi-272/shape_S1.png", "S2": "../images/voi-272/shape_S2.png", "S3": "../images/voi-272/shape_S3.png", "S4": "../images/voi-272/shape_S4.png", "S5": "../images/voi-272/shape_S5.png"}}, "ID": "voi-272", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [2, 8]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 6]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [0, 8]}]}, "legacy_answer": "S1 90 V4 [2,8]\nS3 270 V3 [1,6]\nS5 180 V2 [0,8]", "solutionText": "S1 90 V4 [2,8]\nS3 270 V3 [1,6]\nS5 180 V2 [0,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-272\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-272/target.png", "shapes": {"S1": "images/voi-272/shape_S1.png", "S2": "images/voi-272/shape_S2.png", "S3": "images/voi-272/shape_S3.png", "S4": "images/voi-272/shape_S4.png", "S5": "images/voi-272/shape_S5.png"}}, "__sample_id__": "voi-272"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[1, 5], [1, 3], [2, 3], [2, 5]]}, {"polygon": [[4, 2], [4, 4], [3, 4], [3, 3], [1, 3], [1, 2]]}, {"polygon": [[4, 4], [4, 5], [1, 5], [1, 4]]}], "meta": {"seed": 4204074, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 274, "strictValidation": true}, "imageAssets": {"target": "../images/voi-273/target.png", "shapes": {"S1": "../images/voi-273/shape_S1.png", "S2": "../images/voi-273/shape_S2.png", "S3": "../images/voi-273/shape_S3.png", "S4": "../images/voi-273/shape_S4.png", "S5": "../images/voi-273/shape_S5.png"}}, "ID": "voi-273", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V3", "grid": [2, 3]}, {"shape": "S4", "angle": 270, "vertex": "V6", "grid": [1, 2]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S3 90 V3 [2,3]\nS4 270 V6 [1,2]\nS5 270 V1 [4,4]", "solutionText": "S3 90 V3 [2,3]\nS4 270 V6 [1,2]\nS5 270 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-273\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-273/target.png", "shapes": {"S1": "images/voi-273/shape_S1.png", "S2": "images/voi-273/shape_S2.png", "S3": "images/voi-273/shape_S3.png", "S4": "images/voi-273/shape_S4.png", "S5": "images/voi-273/shape_S5.png"}}, "__sample_id__": "voi-273"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [6, 5], [6, 6], [5, 6], [5, 8], [4, 8]]}, {"polygon": [[3, 4], [5, 4], [5, 5], [4, 5], [4, 7], [3, 7]]}, {"polygon": [[2, 8], [2, 6], [4, 6], [4, 8]]}], "meta": {"seed": 4204075, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.620833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 275, "strictValidation": true}, "imageAssets": {"target": "../images/voi-274/target.png", "shapes": {"S1": "../images/voi-274/shape_S1.png", "S2": "../images/voi-274/shape_S2.png", "S3": "../images/voi-274/shape_S3.png", "S4": "../images/voi-274/shape_S4.png", "S5": "../images/voi-274/shape_S5.png"}}, "ID": "voi-274", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [5, 6]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 6]}]}, "legacy_answer": "S1 0 V4 [5,6]\nS3 0 V4 [4,5]\nS4 90 V2 [2,6]", "solutionText": "S1 0 V4 [5,6]\nS3 0 V4 [4,5]\nS4 90 V2 [2,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-274\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-274/target.png", "shapes": {"S1": "images/voi-274/shape_S1.png", "S2": "images/voi-274/shape_S2.png", "S3": "images/voi-274/shape_S3.png", "S4": "images/voi-274/shape_S4.png", "S5": "images/voi-274/shape_S5.png"}}, "__sample_id__": "voi-274"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [1, 7], [2, 6], [4, 6]]}, {"polygon": [[3, 6], [1, 6], [1, 4], [3, 4]]}, {"polygon": [[5, 4], [5, 7], [3, 7], [3, 4]]}], "meta": {"seed": 4204076, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.159601, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.632494, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 276, "strictValidation": true}, "imageAssets": {"target": "../images/voi-275/target.png", "shapes": {"S1": "../images/voi-275/shape_S1.png", "S2": "../images/voi-275/shape_S2.png", "S3": "../images/voi-275/shape_S3.png", "S4": "../images/voi-275/shape_S4.png", "S5": "../images/voi-275/shape_S5.png"}}, "ID": "voi-275", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [4, 6]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [1, 6]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [5, 4]}]}, "legacy_answer": "S2 180 V4 [4,6]\nS4 180 V2 [1,6]\nS5 270 V1 [5,4]", "solutionText": "S2 180 V4 [4,6]\nS4 180 V2 [1,6]\nS5 270 V1 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-275\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-275/target.png", "shapes": {"S1": "images/voi-275/shape_S1.png", "S2": "images/voi-275/shape_S2.png", "S3": "images/voi-275/shape_S3.png", "S4": "images/voi-275/shape_S4.png", "S5": "images/voi-275/shape_S5.png"}}, "__sample_id__": "voi-275"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 3], [7, 3], [7, 4], [6, 4], [6, 6], [5, 6]]}, {"polygon": [[6, 7], [5, 7], [5, 5], [6, 5]]}, {"polygon": [[6, 7], [6, 4], [7, 4], [7, 7]]}], "meta": {"seed": 4204077, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 277, "strictValidation": true}, "imageAssets": {"target": "../images/voi-276/target.png", "shapes": {"S1": "../images/voi-276/shape_S1.png", "S2": "../images/voi-276/shape_S2.png", "S3": "../images/voi-276/shape_S3.png", "S4": "../images/voi-276/shape_S4.png", "S5": "../images/voi-276/shape_S5.png"}}, "ID": "voi-276", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [7, 3]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [6, 5]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [7, 4]}]}, "legacy_answer": "S2 0 V2 [7,3]\nS3 180 V4 [6,5]\nS5 90 V3 [7,4]", "solutionText": "S2 0 V2 [7,3]\nS3 180 V4 [6,5]\nS5 90 V3 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-276\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-276/target.png", "shapes": {"S1": "images/voi-276/shape_S1.png", "S2": "images/voi-276/shape_S2.png", "S3": "images/voi-276/shape_S3.png", "S4": "images/voi-276/shape_S4.png", "S5": "images/voi-276/shape_S5.png"}}, "__sample_id__": "voi-276"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 2], [7, 2], [7, 4], [5, 4]]}, {"polygon": [[3, 2], [6, 2], [5, 3], [3, 3]]}, {"polygon": [[5, 5], [3, 5], [5, 3]]}], "meta": {"seed": 4204078, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.123636, "contourComplexity": 104, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.870103, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 278, "strictValidation": true}, "imageAssets": {"target": "../images/voi-277/target.png", "shapes": {"S1": "../images/voi-277/shape_S1.png", "S2": "../images/voi-277/shape_S2.png", "S3": "../images/voi-277/shape_S3.png", "S4": "../images/voi-277/shape_S4.png", "S5": "../images/voi-277/shape_S5.png"}}, "ID": "voi-277", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [3, 5]}]}, "legacy_answer": "S1 0 V3 [7,4]\nS2 0 V1 [3,2]\nS5 180 V2 [3,5]", "solutionText": "S1 0 V3 [7,4]\nS2 0 V1 [3,2]\nS5 180 V2 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-277\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-277/target.png", "shapes": {"S1": "images/voi-277/shape_S1.png", "S2": "images/voi-277/shape_S2.png", "S3": "images/voi-277/shape_S3.png", "S4": "images/voi-277/shape_S4.png", "S5": "images/voi-277/shape_S5.png"}}, "__sample_id__": "voi-277"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[5, 4], [5, 2], [7, 4]]}, {"polygon": [[5, 4], [3, 4], [3, 3], [4, 3], [4, 1], [5, 1]]}, {"polygon": [[7, 1], [7, 2], [4, 2], [4, 1]]}], "meta": {"seed": 4204079, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.496538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 279, "strictValidation": true}, "imageAssets": {"target": "../images/voi-278/target.png", "shapes": {"S1": "../images/voi-278/shape_S1.png", "S2": "../images/voi-278/shape_S2.png", "S3": "../images/voi-278/shape_S3.png", "S4": "../images/voi-278/shape_S4.png", "S5": "../images/voi-278/shape_S5.png"}}, "ID": "voi-278", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [7, 4]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S2 90 V3 [7,4]\nS3 180 V2 [3,4]\nS5 270 V3 [4,2]", "solutionText": "S2 90 V3 [7,4]\nS3 180 V2 [3,4]\nS5 270 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-278\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-278/target.png", "shapes": {"S1": "images/voi-278/shape_S1.png", "S2": "images/voi-278/shape_S2.png", "S3": "images/voi-278/shape_S3.png", "S4": "images/voi-278/shape_S4.png", "S5": "images/voi-278/shape_S5.png"}}, "__sample_id__": "voi-278"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 1], [7, 2], [4, 2], [4, 1]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}, {"polygon": [[5, 2], [4, 2], [5, 1]]}], "meta": {"seed": 4204080, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 280, "strictValidation": true}, "imageAssets": {"target": "../images/voi-279/target.png", "shapes": {"S1": "../images/voi-279/shape_S1.png", "S2": "../images/voi-279/shape_S2.png", "S3": "../images/voi-279/shape_S3.png", "S4": "../images/voi-279/shape_S4.png", "S5": "../images/voi-279/shape_S5.png"}}, "ID": "voi-279", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [4, 1]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 4]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S1 270 V4 [4,1]\nS2 90 V1 [3,4]\nS4 180 V2 [4,2]", "solutionText": "S1 270 V4 [4,1]\nS2 90 V1 [3,4]\nS4 180 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-279\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-279/target.png", "shapes": {"S1": "images/voi-279/shape_S1.png", "S2": "images/voi-279/shape_S2.png", "S3": "images/voi-279/shape_S3.png", "S4": "images/voi-279/shape_S4.png", "S5": "images/voi-279/shape_S5.png"}}, "__sample_id__": "voi-279"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 8], [3, 8], [3, 5], [4, 5]]}, {"polygon": [[2, 6], [3, 6], [3, 7], [2, 7]]}, {"polygon": [[2, 4], [5, 4], [5, 6], [2, 6]]}], "meta": {"seed": 4204081, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 281, "strictValidation": true}, "imageAssets": {"target": "../images/voi-280/target.png", "shapes": {"S1": "../images/voi-280/shape_S1.png", "S2": "../images/voi-280/shape_S2.png", "S3": "../images/voi-280/shape_S3.png", "S4": "../images/voi-280/shape_S4.png", "S5": "../images/voi-280/shape_S5.png"}}, "ID": "voi-280", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 5]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [2, 7]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S1 180 V3 [3,5]\nS3 0 V4 [2,7]\nS5 0 V3 [5,6]", "solutionText": "S1 180 V3 [3,5]\nS3 0 V4 [2,7]\nS5 0 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-280\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-280/target.png", "shapes": {"S1": "images/voi-280/shape_S1.png", "S2": "images/voi-280/shape_S2.png", "S3": "images/voi-280/shape_S3.png", "S4": "images/voi-280/shape_S4.png", "S5": "images/voi-280/shape_S5.png"}}, "__sample_id__": "voi-280"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 6], [2, 6], [2, 4], [5, 4]]}, {"polygon": [[3, 4], [0, 4], [0, 3], [3, 3]]}, {"polygon": [[2, 3], [2, 5], [0, 5], [0, 3]]}], "meta": {"seed": 4204082, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 282, "strictValidation": true}, "imageAssets": {"target": "../images/voi-281/target.png", "shapes": {"S1": "../images/voi-281/shape_S1.png", "S2": "../images/voi-281/shape_S2.png", "S3": "../images/voi-281/shape_S3.png", "S4": "../images/voi-281/shape_S4.png", "S5": "../images/voi-281/shape_S5.png"}}, "ID": "voi-281", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [2, 4]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [0, 3]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [2, 5]}]}, "legacy_answer": "S1 180 V3 [2,4]\nS2 180 V3 [0,3]\nS4 270 V2 [2,5]", "solutionText": "S1 180 V3 [2,4]\nS2 180 V3 [0,3]\nS4 270 V2 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-281\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-281/target.png", "shapes": {"S1": "images/voi-281/shape_S1.png", "S2": "images/voi-281/shape_S2.png", "S3": "images/voi-281/shape_S3.png", "S4": "images/voi-281/shape_S4.png", "S5": "images/voi-281/shape_S5.png"}}, "__sample_id__": "voi-281"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[7, 1], [7, 0], [8, 0], [8, 1]]}, {"polygon": [[5, 0], [8, 0], [8, 2], [5, 2]]}, {"polygon": [[8, 3], [5, 3], [6, 2], [8, 2]]}], "meta": {"seed": 4204083, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 283, "strictValidation": true}, "imageAssets": {"target": "../images/voi-282/target.png", "shapes": {"S1": "../images/voi-282/shape_S1.png", "S2": "../images/voi-282/shape_S2.png", "S3": "../images/voi-282/shape_S3.png", "S4": "../images/voi-282/shape_S4.png", "S5": "../images/voi-282/shape_S5.png"}}, "ID": "voi-282", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [8, 0]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [8, 0]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [8, 3]}]}, "legacy_answer": "S1 90 V3 [8,0]\nS2 0 V2 [8,0]\nS3 180 V1 [8,3]", "solutionText": "S1 90 V3 [8,0]\nS2 0 V2 [8,0]\nS3 180 V1 [8,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-282\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-282/target.png", "shapes": {"S1": "images/voi-282/shape_S1.png", "S2": "images/voi-282/shape_S2.png", "S3": "images/voi-282/shape_S3.png", "S4": "images/voi-282/shape_S4.png", "S5": "images/voi-282/shape_S5.png"}}, "__sample_id__": "voi-282"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 1], [3, 1], [3, 2], [2, 2]]}, {"polygon": [[5, 2], [2, 2], [2, 0], [5, 0]]}, {"polygon": [[2, 3], [2, 0], [3, 1], [3, 3]]}], "meta": {"seed": 4204084, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.321311, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.683097, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 284, "strictValidation": true}, "imageAssets": {"target": "../images/voi-283/target.png", "shapes": {"S1": "../images/voi-283/shape_S1.png", "S2": "../images/voi-283/shape_S2.png", "S3": "../images/voi-283/shape_S3.png", "S4": "../images/voi-283/shape_S4.png", "S5": "../images/voi-283/shape_S5.png"}}, "ID": "voi-283", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [3, 1]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [5, 2]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [3, 1]}]}, "legacy_answer": "S1 0 V2 [3,1]\nS3 180 V1 [5,2]\nS4 90 V3 [3,1]", "solutionText": "S1 0 V2 [3,1]\nS3 180 V1 [5,2]\nS4 90 V3 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-283\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-283/target.png", "shapes": {"S1": "images/voi-283/shape_S1.png", "S2": "images/voi-283/shape_S2.png", "S3": "images/voi-283/shape_S3.png", "S4": "images/voi-283/shape_S4.png", "S5": "images/voi-283/shape_S5.png"}}, "__sample_id__": "voi-283"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 8], [1, 8], [1, 6], [3, 6]]}, {"polygon": [[1, 5], [2, 5], [2, 8], [1, 8]]}, {"polygon": [[2, 3], [4, 3], [4, 4], [3, 4], [3, 6], [2, 6]]}], "meta": {"seed": 4204085, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.363636, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.835795, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 285, "strictValidation": true}, "imageAssets": {"target": "../images/voi-284/target.png", "shapes": {"S1": "../images/voi-284/shape_S1.png", "S2": "../images/voi-284/shape_S2.png", "S3": "../images/voi-284/shape_S3.png", "S4": "../images/voi-284/shape_S4.png", "S5": "../images/voi-284/shape_S5.png"}}, "ID": "voi-284", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 8]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 5]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [2, 3]}]}, "legacy_answer": "S1 180 V2 [1,8]\nS3 0 V1 [1,5]\nS5 0 V1 [2,3]", "solutionText": "S1 180 V2 [1,8]\nS3 0 V1 [1,5]\nS5 0 V1 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-284\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-284/target.png", "shapes": {"S1": "images/voi-284/shape_S1.png", "S2": "images/voi-284/shape_S2.png", "S3": "images/voi-284/shape_S3.png", "S4": "images/voi-284/shape_S4.png", "S5": "images/voi-284/shape_S5.png"}}, "__sample_id__": "voi-284"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}, {"polygon": [[3, 8], [2, 8], [2, 7], [3, 7]]}, {"polygon": [[5, 8], [2, 8], [2, 7], [5, 7]]}], "meta": {"seed": 4204086, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 4, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 286, "strictValidation": true}, "imageAssets": {"target": "../images/voi-285/target.png", "shapes": {"S1": "../images/voi-285/shape_S1.png", "S2": "../images/voi-285/shape_S2.png", "S3": "../images/voi-285/shape_S3.png", "S4": "../images/voi-285/shape_S4.png", "S5": "../images/voi-285/shape_S5.png"}}, "ID": "voi-285", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [5, 4]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [3, 7]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [2, 7]}]}, "legacy_answer": "S1 90 V3 [5,4]\nS2 180 V4 [3,7]\nS3 180 V3 [2,7]", "solutionText": "S1 90 V3 [5,4]\nS2 180 V4 [3,7]\nS3 180 V3 [2,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-285\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-285/target.png", "shapes": {"S1": "images/voi-285/shape_S1.png", "S2": "images/voi-285/shape_S2.png", "S3": "images/voi-285/shape_S3.png", "S4": "images/voi-285/shape_S4.png", "S5": "images/voi-285/shape_S5.png"}}, "__sample_id__": "voi-285"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 5], [2, 2], [4, 2], [4, 5]]}, {"polygon": [[3, 1], [3, 3], [2, 3], [2, 1]]}, {"polygon": [[5, 1], [5, 3], [3, 1]]}], "meta": {"seed": 4204087, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.198758, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.125977, "difficultyScore": 0.553016, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 287, "strictValidation": true}, "imageAssets": {"target": "../images/voi-286/target.png", "shapes": {"S1": "../images/voi-286/shape_S1.png", "S2": "../images/voi-286/shape_S2.png", "S3": "../images/voi-286/shape_S3.png", "S4": "../images/voi-286/shape_S4.png", "S5": "../images/voi-286/shape_S5.png"}}, "ID": "voi-286", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 1]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [5, 1]}]}, "legacy_answer": "S2 90 V3 [4,2]\nS4 270 V1 [3,1]\nS5 270 V1 [5,1]", "solutionText": "S2 90 V3 [4,2]\nS4 270 V1 [3,1]\nS5 270 V1 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-286\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-286/target.png", "shapes": {"S1": "images/voi-286/shape_S1.png", "S2": "images/voi-286/shape_S2.png", "S3": "images/voi-286/shape_S3.png", "S4": "images/voi-286/shape_S4.png", "S5": "images/voi-286/shape_S5.png"}}, "__sample_id__": "voi-286"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [7, 6], [7, 7], [6, 7]]}, {"polygon": [[5, 7], [5, 5], [7, 5], [7, 7]]}, {"polygon": [[8, 5], [6, 5], [6, 3], [8, 3]]}], "meta": {"seed": 4204088, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 288, "strictValidation": true}, "imageAssets": {"target": "../images/voi-287/target.png", "shapes": {"S1": "../images/voi-287/shape_S1.png", "S2": "../images/voi-287/shape_S2.png", "S3": "../images/voi-287/shape_S3.png", "S4": "../images/voi-287/shape_S4.png", "S5": "../images/voi-287/shape_S5.png"}}, "ID": "voi-287", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [6, 6]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [5, 7]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [8, 5]}]}, "legacy_answer": "S1 0 V1 [6,6]\nS3 90 V1 [5,7]\nS4 180 V1 [8,5]", "solutionText": "S1 0 V1 [6,6]\nS3 90 V1 [5,7]\nS4 180 V1 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-287\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-287/target.png", "shapes": {"S1": "images/voi-287/shape_S1.png", "S2": "images/voi-287/shape_S2.png", "S3": "images/voi-287/shape_S3.png", "S4": "images/voi-287/shape_S4.png", "S5": "images/voi-287/shape_S5.png"}}, "__sample_id__": "voi-287"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}, {"polygon": [[2, 5], [2, 3], [3, 3], [3, 4], [5, 4], [5, 5]]}, {"polygon": [[2, 0], [4, 0], [2, 2]]}], "meta": {"seed": 4204089, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.198758, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.125977, "difficultyScore": 0.553016, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 289, "strictValidation": true}, "imageAssets": {"target": "../images/voi-288/target.png", "shapes": {"S1": "../images/voi-288/shape_S1.png", "S2": "../images/voi-288/shape_S2.png", "S3": "../images/voi-288/shape_S3.png", "S4": "../images/voi-288/shape_S4.png", "S5": "../images/voi-288/shape_S5.png"}}, "ID": "voi-288", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V1", "grid": [2, 4]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [5, 5]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [2, 0]}]}, "legacy_answer": "S3 90 V1 [2,4]\nS4 90 V6 [5,5]\nS5 0 V1 [2,0]", "solutionText": "S3 90 V1 [2,4]\nS4 90 V6 [5,5]\nS5 0 V1 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-288\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-288/target.png", "shapes": {"S1": "images/voi-288/shape_S1.png", "S2": "images/voi-288/shape_S2.png", "S3": "images/voi-288/shape_S3.png", "S4": "images/voi-288/shape_S4.png", "S5": "images/voi-288/shape_S5.png"}}, "__sample_id__": "voi-288"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 1], [8, 1], [8, 4]]}, {"polygon": [[7, 1], [8, 1], [8, 3], [7, 3]]}, {"polygon": [[6, 4], [3, 4], [3, 2], [6, 2]]}], "meta": {"seed": 4204090, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.430357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 290, "strictValidation": true}, "imageAssets": {"target": "../images/voi-289/target.png", "shapes": {"S1": "../images/voi-289/shape_S1.png", "S2": "../images/voi-289/shape_S2.png", "S3": "../images/voi-289/shape_S3.png", "S4": "../images/voi-289/shape_S4.png", "S5": "../images/voi-289/shape_S5.png"}}, "ID": "voi-289", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [6, 1]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [7, 3]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [6, 2]}]}, "legacy_answer": "S1 90 V2 [6,1]\nS2 0 V4 [7,3]\nS5 180 V4 [6,2]", "solutionText": "S1 90 V2 [6,1]\nS2 0 V4 [7,3]\nS5 180 V4 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-289\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-289/target.png", "shapes": {"S1": "images/voi-289/shape_S1.png", "S2": "images/voi-289/shape_S2.png", "S3": "images/voi-289/shape_S3.png", "S4": "images/voi-289/shape_S4.png", "S5": "images/voi-289/shape_S5.png"}}, "__sample_id__": "voi-289"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 2], [5, 3], [2, 3], [2, 2]]}, {"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[3, 2], [3, 5], [2, 4], [2, 2]]}], "meta": {"seed": 4204091, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.173442, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.608381, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 291, "strictValidation": true}, "imageAssets": {"target": "../images/voi-290/target.png", "shapes": {"S1": "../images/voi-290/shape_S1.png", "S2": "../images/voi-290/shape_S2.png", "S3": "../images/voi-290/shape_S3.png", "S4": "../images/voi-290/shape_S4.png", "S5": "../images/voi-290/shape_S5.png"}}, "ID": "voi-290", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 3]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 3]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [2, 2]}]}, "legacy_answer": "S1 270 V2 [5,3]\nS4 270 V4 [3,3]\nS5 270 V4 [2,2]", "solutionText": "S1 270 V2 [5,3]\nS4 270 V4 [3,3]\nS5 270 V4 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-290\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-290/target.png", "shapes": {"S1": "images/voi-290/shape_S1.png", "S2": "images/voi-290/shape_S2.png", "S3": "images/voi-290/shape_S3.png", "S4": "images/voi-290/shape_S4.png", "S5": "images/voi-290/shape_S5.png"}}, "__sample_id__": "voi-290"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 1], [2, 4], [0, 4], [0, 1]]}, {"polygon": [[0, 8], [0, 5], [2, 5], [2, 8]]}, {"polygon": [[0, 4], [2, 4], [2, 5], [1, 5], [1, 7], [0, 7]]}], "meta": {"seed": 4204092, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.225, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 292, "strictValidation": true}, "imageAssets": {"target": "../images/voi-291/target.png", "shapes": {"S1": "../images/voi-291/shape_S1.png", "S2": "../images/voi-291/shape_S2.png", "S3": "../images/voi-291/shape_S3.png", "S4": "../images/voi-291/shape_S4.png", "S5": "../images/voi-291/shape_S5.png"}}, "ID": "voi-291", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [0, 1]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [0, 8]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [0, 4]}]}, "legacy_answer": "S1 270 V4 [0,1]\nS3 90 V1 [0,8]\nS4 0 V1 [0,4]", "solutionText": "S1 270 V4 [0,1]\nS3 90 V1 [0,8]\nS4 0 V1 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-291\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-291/target.png", "shapes": {"S1": "images/voi-291/shape_S1.png", "S2": "images/voi-291/shape_S2.png", "S3": "images/voi-291/shape_S3.png", "S4": "images/voi-291/shape_S4.png", "S5": "images/voi-291/shape_S5.png"}}, "__sample_id__": "voi-291"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 0], [3, 0], [3, 1], [2, 1]]}, {"polygon": [[2, 3], [2, 0], [4, 0], [4, 3]]}, {"polygon": [[6, 4], [3, 4], [3, 3], [6, 3]]}], "meta": {"seed": 4204093, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 293, "strictValidation": true}, "imageAssets": {"target": "../images/voi-292/target.png", "shapes": {"S1": "../images/voi-292/shape_S1.png", "S2": "../images/voi-292/shape_S2.png", "S3": "../images/voi-292/shape_S3.png", "S4": "../images/voi-292/shape_S4.png", "S5": "../images/voi-292/shape_S5.png"}}, "ID": "voi-292", "answer": {"placements": [{"shape": "S3", "angle": 0, "vertex": "V3", "grid": [3, 1]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [4, 3]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [6, 4]}]}, "legacy_answer": "S3 0 V3 [3,1]\nS4 90 V4 [4,3]\nS5 180 V1 [6,4]", "solutionText": "S3 0 V3 [3,1]\nS4 90 V4 [4,3]\nS5 180 V1 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-292\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-292/target.png", "shapes": {"S1": "images/voi-292/shape_S1.png", "S2": "images/voi-292/shape_S2.png", "S3": "images/voi-292/shape_S3.png", "S4": "images/voi-292/shape_S4.png", "S5": "images/voi-292/shape_S5.png"}}, "__sample_id__": "voi-292"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [3, 4], [3, 6], [2, 6]]}, {"polygon": [[1, 4], [3, 4], [1, 6]]}, {"polygon": [[3, 4], [5, 4], [5, 6], [3, 6]]}], "meta": {"seed": 4204094, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.854118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 294, "strictValidation": true}, "imageAssets": {"target": "../images/voi-293/target.png", "shapes": {"S1": "../images/voi-293/shape_S1.png", "S2": "../images/voi-293/shape_S2.png", "S3": "../images/voi-293/shape_S3.png", "S4": "../images/voi-293/shape_S4.png", "S5": "../images/voi-293/shape_S5.png"}}, "ID": "voi-293", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [3, 4]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S1 0 V4 [2,6]\nS3 0 V2 [3,4]\nS5 0 V3 [5,6]", "solutionText": "S1 0 V4 [2,6]\nS3 0 V2 [3,4]\nS5 0 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-293\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-293/target.png", "shapes": {"S1": "images/voi-293/shape_S1.png", "S2": "images/voi-293/shape_S2.png", "S3": "images/voi-293/shape_S3.png", "S4": "images/voi-293/shape_S4.png", "S5": "images/voi-293/shape_S5.png"}}, "__sample_id__": "voi-293"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 0], [8, 0], [8, 2], [5, 2]]}, {"polygon": [[6, 3], [6, 1], [8, 3]]}, {"polygon": [[6, 3], [3, 3], [3, 1], [6, 1]]}], "meta": {"seed": 4204095, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.217778, "contourComplexity": 73, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.385139, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 295, "strictValidation": true}, "imageAssets": {"target": "../images/voi-294/target.png", "shapes": {"S1": "../images/voi-294/shape_S1.png", "S2": "../images/voi-294/shape_S2.png", "S3": "../images/voi-294/shape_S3.png", "S4": "../images/voi-294/shape_S4.png", "S5": "../images/voi-294/shape_S5.png"}}, "ID": "voi-294", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V4", "grid": [5, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [6, 3]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [6, 1]}]}, "legacy_answer": "S2 0 V4 [5,2]\nS4 90 V1 [6,3]\nS5 180 V4 [6,1]", "solutionText": "S2 0 V4 [5,2]\nS4 90 V1 [6,3]\nS5 180 V4 [6,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-294\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-294/target.png", "shapes": {"S1": "images/voi-294/shape_S1.png", "S2": "images/voi-294/shape_S2.png", "S3": "images/voi-294/shape_S3.png", "S4": "images/voi-294/shape_S4.png", "S5": "images/voi-294/shape_S5.png"}}, "__sample_id__": "voi-294"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 7], [5, 7], [7, 5]]}, {"polygon": [[6, 6], [3, 6], [3, 4], [6, 4]]}, {"polygon": [[5, 4], [6, 4], [6, 5], [5, 5]]}], "meta": {"seed": 4204096, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.496538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 296, "strictValidation": true}, "imageAssets": {"target": "../images/voi-295/target.png", "shapes": {"S1": "../images/voi-295/shape_S1.png", "S2": "../images/voi-295/shape_S2.png", "S3": "../images/voi-295/shape_S3.png", "S4": "../images/voi-295/shape_S4.png", "S5": "../images/voi-295/shape_S5.png"}}, "ID": "voi-295", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [7, 5]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 6]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 5]}]}, "legacy_answer": "S1 180 V3 [7,5]\nS2 180 V1 [6,6]\nS4 0 V4 [5,5]", "solutionText": "S1 180 V3 [7,5]\nS2 180 V1 [6,6]\nS4 0 V4 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-295\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-295/target.png", "shapes": {"S1": "images/voi-295/shape_S1.png", "S2": "images/voi-295/shape_S2.png", "S3": "images/voi-295/shape_S3.png", "S4": "images/voi-295/shape_S4.png", "S5": "images/voi-295/shape_S5.png"}}, "__sample_id__": "voi-295"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 5], [5, 5], [5, 7], [2, 7]]}, {"polygon": [[2, 2], [4, 2], [4, 3], [3, 3], [3, 5], [2, 5]]}, {"polygon": [[4, 3], [3, 3], [3, 2], [4, 2]]}], "meta": {"seed": 4204097, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 297, "strictValidation": true}, "imageAssets": {"target": "../images/voi-296/target.png", "shapes": {"S1": "../images/voi-296/shape_S1.png", "S2": "../images/voi-296/shape_S2.png", "S3": "../images/voi-296/shape_S3.png", "S4": "../images/voi-296/shape_S4.png", "S5": "../images/voi-296/shape_S5.png"}}, "ID": "voi-296", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 5]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 2]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S2 0 V1 [2,5]\nS4 0 V2 [4,2]\nS5 180 V3 [3,2]", "solutionText": "S2 0 V1 [2,5]\nS4 0 V2 [4,2]\nS5 180 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-296\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-296/target.png", "shapes": {"S1": "images/voi-296/shape_S1.png", "S2": "images/voi-296/shape_S2.png", "S3": "images/voi-296/shape_S3.png", "S4": "images/voi-296/shape_S4.png", "S5": "images/voi-296/shape_S5.png"}}, "__sample_id__": "voi-296"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 2], [8, 3], [6, 3], [6, 2]]}, {"polygon": [[5, 3], [4, 3], [4, 2], [5, 2]]}, {"polygon": [[6, 2], [6, 5], [4, 5], [4, 2]]}], "meta": {"seed": 4204098, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 298, "strictValidation": true}, "imageAssets": {"target": "../images/voi-297/target.png", "shapes": {"S1": "../images/voi-297/shape_S1.png", "S2": "../images/voi-297/shape_S2.png", "S3": "../images/voi-297/shape_S3.png", "S4": "../images/voi-297/shape_S4.png", "S5": "../images/voi-297/shape_S5.png"}}, "ID": "voi-297", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V2", "grid": [8, 3]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [4, 2]}]}, "legacy_answer": "S3 270 V2 [8,3]\nS4 180 V4 [5,2]\nS5 270 V4 [4,2]", "solutionText": "S3 270 V2 [8,3]\nS4 180 V4 [5,2]\nS5 270 V4 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-297\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-297/target.png", "shapes": {"S1": "images/voi-297/shape_S1.png", "S2": "images/voi-297/shape_S2.png", "S3": "images/voi-297/shape_S3.png", "S4": "images/voi-297/shape_S4.png", "S5": "images/voi-297/shape_S5.png"}}, "__sample_id__": "voi-297"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 2], [2, 1], [5, 1], [5, 2]]}, {"polygon": [[3, 4], [3, 2], [5, 4]]}, {"polygon": [[5, 3], [2, 3], [3, 2], [5, 2]]}], "meta": {"seed": 4204099, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.139918, "contourComplexity": 104, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.836228, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 299, "strictValidation": true}, "imageAssets": {"target": "../images/voi-298/target.png", "shapes": {"S1": "../images/voi-298/shape_S1.png", "S2": "../images/voi-298/shape_S2.png", "S3": "../images/voi-298/shape_S3.png", "S4": "../images/voi-298/shape_S4.png", "S5": "../images/voi-298/shape_S5.png"}}, "ID": "voi-298", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [2, 2]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S1 90 V1 [2,2]\nS2 90 V2 [3,2]\nS3 180 V3 [3,2]", "solutionText": "S1 90 V1 [2,2]\nS2 90 V2 [3,2]\nS3 180 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-298\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-298/target.png", "shapes": {"S1": "images/voi-298/shape_S1.png", "S2": "images/voi-298/shape_S2.png", "S3": "images/voi-298/shape_S3.png", "S4": "images/voi-298/shape_S4.png", "S5": "images/voi-298/shape_S5.png"}}, "__sample_id__": "voi-298"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [4, 7], [2, 7], [2, 4]]}, {"polygon": [[1, 8], [1, 6], [3, 8]]}, {"polygon": [[3, 8], [3, 5], [5, 5], [5, 8]]}], "meta": {"seed": 4204100, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.157227, "difficultyScore": 0.423325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 300, "strictValidation": true}, "imageAssets": {"target": "../images/voi-299/target.png", "shapes": {"S1": "../images/voi-299/shape_S1.png", "S2": "../images/voi-299/shape_S2.png", "S3": "../images/voi-299/shape_S3.png", "S4": "../images/voi-299/shape_S4.png", "S5": "../images/voi-299/shape_S5.png"}}, "ID": "voi-299", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 7]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 6]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [5, 5]}]}, "legacy_answer": "S2 270 V3 [2,7]\nS4 90 V2 [1,6]\nS5 90 V3 [5,5]", "solutionText": "S2 270 V3 [2,7]\nS4 90 V2 [1,6]\nS5 90 V3 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-299\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-299/target.png", "shapes": {"S1": "images/voi-299/shape_S1.png", "S2": "images/voi-299/shape_S2.png", "S3": "images/voi-299/shape_S3.png", "S4": "images/voi-299/shape_S4.png", "S5": "images/voi-299/shape_S5.png"}}, "__sample_id__": "voi-299"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [5, 7], [5, 8], [4, 8]]}, {"polygon": [[5, 5], [5, 4], [6, 4], [6, 5]]}, {"polygon": [[5, 5], [4, 5], [5, 4]]}, {"polygon": [[6, 5], [6, 8], [4, 8], [4, 5]]}], "meta": {"seed": 4205001, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.558169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 301, "strictValidation": true}, "imageAssets": {"target": "../images/voi-300/target.png", "shapes": {"S1": "../images/voi-300/shape_S1.png", "S2": "../images/voi-300/shape_S2.png", "S3": "../images/voi-300/shape_S3.png", "S4": "../images/voi-300/shape_S4.png", "S5": "../images/voi-300/shape_S5.png", "S6": "../images/voi-300/shape_S6.png"}}, "ID": "voi-300", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [4, 7]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [5, 5]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [5, 4]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [4, 5]}]}, "legacy_answer": "S2 0 V1 [4,7]\nS4 90 V1 [5,5]\nS5 180 V3 [5,4]\nS6 270 V4 [4,5]", "solutionText": "S2 0 V1 [4,7]\nS4 90 V1 [5,5]\nS5 180 V3 [5,4]\nS6 270 V4 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-300\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-300/target.png", "shapes": {"S1": "images/voi-300/shape_S1.png", "S2": "images/voi-300/shape_S2.png", "S3": "images/voi-300/shape_S3.png", "S4": "images/voi-300/shape_S4.png", "S5": "images/voi-300/shape_S5.png", "S6": "images/voi-300/shape_S6.png"}}, "__sample_id__": "voi-300"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[7, 5], [6, 5], [6, 4], [7, 4]]}, {"polygon": [[5, 6], [5, 5], [6, 5], [6, 6]]}, {"polygon": [[5, 5], [6, 5], [6, 8], [5, 8]]}, {"polygon": [[6, 4], [6, 6], [5, 6], [5, 5], [3, 5], [3, 4]]}], "meta": {"seed": 4205002, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.592361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 302, "strictValidation": true}, "imageAssets": {"target": "../images/voi-301/target.png", "shapes": {"S1": "../images/voi-301/shape_S1.png", "S2": "../images/voi-301/shape_S2.png", "S3": "../images/voi-301/shape_S3.png", "S4": "../images/voi-301/shape_S4.png", "S5": "../images/voi-301/shape_S5.png", "S6": "../images/voi-301/shape_S6.png"}}, "ID": "voi-301", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [6, 5]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 5]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 8]}, {"shape": "S6", "angle": 270, "vertex": "V5", "grid": [3, 5]}]}, "legacy_answer": "S2 180 V2 [6,5]\nS3 90 V3 [6,5]\nS4 0 V4 [5,8]\nS6 270 V5 [3,5]", "solutionText": "S2 180 V2 [6,5]\nS3 90 V3 [6,5]\nS4 0 V4 [5,8]\nS6 270 V5 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-301\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-301/target.png", "shapes": {"S1": "images/voi-301/shape_S1.png", "S2": "images/voi-301/shape_S2.png", "S3": "images/voi-301/shape_S3.png", "S4": "images/voi-301/shape_S4.png", "S5": "images/voi-301/shape_S5.png", "S6": "images/voi-301/shape_S6.png"}}, "__sample_id__": "voi-301"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [7, 4], [7, 6], [4, 6]]}, {"polygon": [[3, 5], [0, 5], [1, 4], [3, 4]]}, {"polygon": [[7, 5], [5, 5], [5, 3], [7, 3]]}, {"polygon": [[2, 4], [2, 2], [3, 2], [3, 3], [5, 3], [5, 4]]}], "meta": {"seed": 4205003, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.241966, "contourComplexity": 46, "connectedComponents": 1, "fillRatio": 0.195801, "difficultyScore": 0.340535, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 303, "strictValidation": true}, "imageAssets": {"target": "../images/voi-302/target.png", "shapes": {"S1": "../images/voi-302/shape_S1.png", "S2": "../images/voi-302/shape_S2.png", "S3": "../images/voi-302/shape_S3.png", "S4": "../images/voi-302/shape_S4.png", "S5": "../images/voi-302/shape_S5.png", "S6": "../images/voi-302/shape_S6.png"}}, "ID": "voi-302", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [4, 6]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 5]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [7, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 2]}]}, "legacy_answer": "S1 0 V4 [4,6]\nS2 180 V2 [0,5]\nS3 180 V1 [7,5]\nS4 90 V2 [2,2]", "solutionText": "S1 0 V4 [4,6]\nS2 180 V2 [0,5]\nS3 180 V1 [7,5]\nS4 90 V2 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-302\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-302/target.png", "shapes": {"S1": "images/voi-302/shape_S1.png", "S2": "images/voi-302/shape_S2.png", "S3": "images/voi-302/shape_S3.png", "S4": "images/voi-302/shape_S4.png", "S5": "images/voi-302/shape_S5.png", "S6": "images/voi-302/shape_S6.png"}}, "__sample_id__": "voi-302"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [3, 4], [3, 2], [4, 2]]}, {"polygon": [[2, 5], [2, 4], [5, 4], [5, 5]]}, {"polygon": [[3, 4], [1, 4], [1, 3], [2, 3], [2, 1], [3, 1]]}, {"polygon": [[1, 3], [3, 3], [3, 4], [2, 4], [2, 6], [1, 6]]}], "meta": {"seed": 4205004, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.449519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 304, "strictValidation": true}, "imageAssets": {"target": "../images/voi-303/target.png", "shapes": {"S1": "../images/voi-303/shape_S1.png", "S2": "../images/voi-303/shape_S2.png", "S3": "../images/voi-303/shape_S3.png", "S4": "../images/voi-303/shape_S4.png", "S5": "../images/voi-303/shape_S5.png", "S6": "../images/voi-303/shape_S6.png"}}, "ID": "voi-303", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [2, 4]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [3, 4]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [1, 3]}]}, "legacy_answer": "S1 180 V2 [3,4]\nS2 90 V2 [2,4]\nS3 180 V1 [3,4]\nS5 0 V1 [1,3]", "solutionText": "S1 180 V2 [3,4]\nS2 90 V2 [2,4]\nS3 180 V1 [3,4]\nS5 0 V1 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-303\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-303/target.png", "shapes": {"S1": "images/voi-303/shape_S1.png", "S2": "images/voi-303/shape_S2.png", "S3": "images/voi-303/shape_S3.png", "S4": "images/voi-303/shape_S4.png", "S5": "images/voi-303/shape_S5.png", "S6": "images/voi-303/shape_S6.png"}}, "__sample_id__": "voi-303"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [4, 4], [5, 4], [5, 5]]}, {"polygon": [[0, 4], [0, 3], [3, 3], [3, 4]]}, {"polygon": [[0, 5], [0, 3], [1, 3], [1, 4], [3, 4], [3, 5]]}, {"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}], "meta": {"seed": 4205005, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.583333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 305, "strictValidation": true}, "imageAssets": {"target": "../images/voi-304/target.png", "shapes": {"S1": "../images/voi-304/shape_S1.png", "S2": "../images/voi-304/shape_S2.png", "S3": "../images/voi-304/shape_S3.png", "S4": "../images/voi-304/shape_S4.png", "S5": "../images/voi-304/shape_S5.png", "S6": "../images/voi-304/shape_S6.png"}}, "ID": "voi-304", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V1", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [0, 3]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [0, 3]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [5, 4]}]}, "legacy_answer": "S3 90 V1 [4,5]\nS4 90 V2 [0,3]\nS5 90 V2 [0,3]\nS6 270 V1 [5,4]", "solutionText": "S3 90 V1 [4,5]\nS4 90 V2 [0,3]\nS5 90 V2 [0,3]\nS6 270 V1 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-304\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-304/target.png", "shapes": {"S1": "images/voi-304/shape_S1.png", "S2": "images/voi-304/shape_S2.png", "S3": "images/voi-304/shape_S3.png", "S4": "images/voi-304/shape_S4.png", "S5": "images/voi-304/shape_S5.png", "S6": "images/voi-304/shape_S6.png"}}, "__sample_id__": "voi-304"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[1, 8], [1, 6], [3, 6], [3, 8]]}, {"polygon": [[0, 5], [3, 5], [3, 7], [0, 7]]}, {"polygon": [[2, 7], [2, 5], [3, 5], [3, 6], [5, 6], [5, 7]]}, {"polygon": [[2, 6], [2, 3], [4, 3], [4, 6]]}], "meta": {"seed": 4205006, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.3, "contourComplexity": 17, "connectedComponents": 1, "fillRatio": 0.21875, "difficultyScore": 0.2625, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 306, "strictValidation": true}, "imageAssets": {"target": "../images/voi-305/target.png", "shapes": {"S1": "../images/voi-305/shape_S1.png", "S2": "../images/voi-305/shape_S2.png", "S3": "../images/voi-305/shape_S3.png", "S4": "../images/voi-305/shape_S4.png", "S5": "../images/voi-305/shape_S5.png", "S6": "../images/voi-305/shape_S6.png"}}, "ID": "voi-305", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [0, 7]}, {"shape": "S3", "angle": 90, "vertex": "V6", "grid": [5, 7]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 6]}]}, "legacy_answer": "S1 90 V2 [1,6]\nS2 0 V4 [0,7]\nS3 90 V6 [5,7]\nS4 90 V1 [2,6]", "solutionText": "S1 90 V2 [1,6]\nS2 0 V4 [0,7]\nS3 90 V6 [5,7]\nS4 90 V1 [2,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-305\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-305/target.png", "shapes": {"S1": "images/voi-305/shape_S1.png", "S2": "images/voi-305/shape_S2.png", "S3": "images/voi-305/shape_S3.png", "S4": "images/voi-305/shape_S4.png", "S5": "images/voi-305/shape_S5.png", "S6": "images/voi-305/shape_S6.png"}}, "__sample_id__": "voi-305"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 8], [3, 6], [5, 6], [5, 8]]}, {"polygon": [[3, 2], [3, 4], [1, 2]]}, {"polygon": [[3, 4], [3, 7], [2, 7], [2, 4]]}, {"polygon": [[4, 7], [4, 8], [2, 8], [2, 7]]}], "meta": {"seed": 4205007, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.180791, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.141602, "difficultyScore": 0.693633, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 307, "strictValidation": true}, "imageAssets": {"target": "../images/voi-306/target.png", "shapes": {"S1": "../images/voi-306/shape_S1.png", "S2": "../images/voi-306/shape_S2.png", "S3": "../images/voi-306/shape_S3.png", "S4": "../images/voi-306/shape_S4.png", "S5": "../images/voi-306/shape_S5.png", "S6": "../images/voi-306/shape_S6.png"}}, "ID": "voi-306", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [3, 6]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 4]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [2, 8]}]}, "legacy_answer": "S2 90 V2 [3,6]\nS3 270 V2 [3,4]\nS4 270 V1 [3,4]\nS5 270 V3 [2,8]", "solutionText": "S2 90 V2 [3,6]\nS3 270 V2 [3,4]\nS4 270 V1 [3,4]\nS5 270 V3 [2,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-306\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-306/target.png", "shapes": {"S1": "images/voi-306/shape_S1.png", "S2": "images/voi-306/shape_S2.png", "S3": "images/voi-306/shape_S3.png", "S4": "images/voi-306/shape_S4.png", "S5": "images/voi-306/shape_S5.png", "S6": "images/voi-306/shape_S6.png"}}, "__sample_id__": "voi-306"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 0], [5, 3], [3, 3], [3, 0]]}, {"polygon": [[4, 0], [6, 0], [6, 1], [4, 1]]}, {"polygon": [[2, 3], [4, 3], [4, 5], [2, 5]]}, {"polygon": [[5, 3], [5, 0], [6, 0], [6, 3]]}], "meta": {"seed": 4205008, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.289583, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 308, "strictValidation": true}, "imageAssets": {"target": "../images/voi-307/target.png", "shapes": {"S1": "../images/voi-307/shape_S1.png", "S2": "../images/voi-307/shape_S2.png", "S3": "../images/voi-307/shape_S3.png", "S4": "../images/voi-307/shape_S4.png", "S5": "../images/voi-307/shape_S5.png", "S6": "../images/voi-307/shape_S6.png"}}, "ID": "voi-307", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 0]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [6, 1]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 3]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [6, 3]}]}, "legacy_answer": "S1 270 V1 [5,0]\nS3 0 V3 [6,1]\nS4 0 V2 [4,3]\nS5 90 V4 [6,3]", "solutionText": "S1 270 V1 [5,0]\nS3 0 V3 [6,1]\nS4 0 V2 [4,3]\nS5 90 V4 [6,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-307\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-307/target.png", "shapes": {"S1": "images/voi-307/shape_S1.png", "S2": "images/voi-307/shape_S2.png", "S3": "images/voi-307/shape_S3.png", "S4": "images/voi-307/shape_S4.png", "S5": "images/voi-307/shape_S5.png", "S6": "images/voi-307/shape_S6.png"}}, "__sample_id__": "voi-307"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 5], [3, 5], [3, 3], [5, 3]]}, {"polygon": [[2, 3], [4, 3], [2, 5]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}, {"polygon": [[2, 4], [0, 4], [0, 3], [2, 3]]}], "meta": {"seed": 4205009, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.157227, "difficultyScore": 0.323325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 309, "strictValidation": true}, "imageAssets": {"target": "../images/voi-308/target.png", "shapes": {"S1": "../images/voi-308/shape_S1.png", "S2": "../images/voi-308/shape_S2.png", "S3": "../images/voi-308/shape_S3.png", "S4": "../images/voi-308/shape_S4.png", "S5": "../images/voi-308/shape_S5.png", "S6": "../images/voi-308/shape_S6.png"}}, "ID": "voi-308", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [5, 3]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [4, 3]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [3, 4]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [0, 3]}]}, "legacy_answer": "S1 180 V4 [5,3]\nS3 0 V2 [4,3]\nS4 90 V1 [3,4]\nS5 180 V3 [0,3]", "solutionText": "S1 180 V4 [5,3]\nS3 0 V2 [4,3]\nS4 90 V1 [3,4]\nS5 180 V3 [0,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-308\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-308/target.png", "shapes": {"S1": "images/voi-308/shape_S1.png", "S2": "images/voi-308/shape_S2.png", "S3": "images/voi-308/shape_S3.png", "S4": "images/voi-308/shape_S4.png", "S5": "images/voi-308/shape_S5.png", "S6": "images/voi-308/shape_S6.png"}}, "__sample_id__": "voi-308"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[1, 3], [0, 3], [0, 1], [1, 1]]}, {"polygon": [[4, 3], [1, 3], [1, 1], [4, 1]]}, {"polygon": [[1, 2], [1, 1], [3, 1], [3, 2]]}, {"polygon": [[0, 5], [0, 3], [1, 3], [1, 4], [3, 4], [3, 5]]}], "meta": {"seed": 4205010, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 310, "strictValidation": true}, "imageAssets": {"target": "../images/voi-309/target.png", "shapes": {"S1": "../images/voi-309/shape_S1.png", "S2": "../images/voi-309/shape_S2.png", "S3": "../images/voi-309/shape_S3.png", "S4": "../images/voi-309/shape_S4.png", "S5": "../images/voi-309/shape_S5.png", "S6": "../images/voi-309/shape_S6.png"}}, "ID": "voi-309", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [0, 1]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [1, 1]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 1]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [1, 3]}]}, "legacy_answer": "S2 180 V3 [0,1]\nS3 180 V3 [1,1]\nS4 90 V2 [1,1]\nS6 90 V3 [1,3]", "solutionText": "S2 180 V3 [0,1]\nS3 180 V3 [1,1]\nS4 90 V2 [1,1]\nS6 90 V3 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-309\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-309/target.png", "shapes": {"S1": "images/voi-309/shape_S1.png", "S2": "images/voi-309/shape_S2.png", "S3": "images/voi-309/shape_S3.png", "S4": "images/voi-309/shape_S4.png", "S5": "images/voi-309/shape_S5.png", "S6": "images/voi-309/shape_S6.png"}}, "__sample_id__": "voi-309"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 1], [5, 1], [5, 3], [3, 3]]}, {"polygon": [[3, 5], [1, 5], [1, 4], [2, 4], [2, 2], [3, 2]]}, {"polygon": [[1, 4], [1, 2], [2, 2], [2, 3], [4, 3], [4, 4]]}, {"polygon": [[4, 4], [4, 5], [3, 4]]}], "meta": {"seed": 4205011, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.159601, "contourComplexity": 45, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.732494, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 311, "strictValidation": true}, "imageAssets": {"target": "../images/voi-310/target.png", "shapes": {"S1": "../images/voi-310/shape_S1.png", "S2": "../images/voi-310/shape_S2.png", "S3": "../images/voi-310/shape_S3.png", "S4": "../images/voi-310/shape_S4.png", "S5": "../images/voi-310/shape_S5.png", "S6": "../images/voi-310/shape_S6.png"}}, "ID": "voi-310", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 1]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [1, 4]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 2]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S1 0 V2 [5,1]\nS3 180 V3 [1,4]\nS4 90 V2 [1,2]\nS6 270 V1 [4,4]", "solutionText": "S1 0 V2 [5,1]\nS3 180 V3 [1,4]\nS4 90 V2 [1,2]\nS6 270 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-310\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-310/target.png", "shapes": {"S1": "images/voi-310/shape_S1.png", "S2": "images/voi-310/shape_S2.png", "S3": "images/voi-310/shape_S3.png", "S4": "images/voi-310/shape_S4.png", "S5": "images/voi-310/shape_S5.png", "S6": "images/voi-310/shape_S6.png"}}, "__sample_id__": "voi-310"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 2], [4, 5], [3, 4], [3, 2]]}, {"polygon": [[2, 7], [2, 4], [4, 4], [4, 7]]}, {"polygon": [[2, 1], [4, 1], [2, 3]]}, {"polygon": [[2, 4], [2, 1], [3, 2], [3, 4]]}], "meta": {"seed": 4205012, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.242857, "contourComplexity": 132, "connectedComponents": 1, "fillRatio": 0.155273, "difficultyScore": 0.418025, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 312, "strictValidation": true}, "imageAssets": {"target": "../images/voi-311/target.png", "shapes": {"S1": "../images/voi-311/shape_S1.png", "S2": "../images/voi-311/shape_S2.png", "S3": "../images/voi-311/shape_S3.png", "S4": "../images/voi-311/shape_S4.png", "S5": "../images/voi-311/shape_S5.png", "S6": "../images/voi-311/shape_S6.png"}}, "ID": "voi-311", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [3, 2]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [4, 7]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [2, 1]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [3, 4]}]}, "legacy_answer": "S1 270 V4 [3,2]\nS2 90 V4 [4,7]\nS3 0 V1 [2,1]\nS4 90 V4 [3,4]", "solutionText": "S1 270 V4 [3,2]\nS2 90 V4 [4,7]\nS3 0 V1 [2,1]\nS4 90 V4 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-311\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-311/target.png", "shapes": {"S1": "images/voi-311/shape_S1.png", "S2": "images/voi-311/shape_S2.png", "S3": "images/voi-311/shape_S3.png", "S4": "images/voi-311/shape_S4.png", "S5": "images/voi-311/shape_S5.png", "S6": "images/voi-311/shape_S6.png"}}, "__sample_id__": "voi-311"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[4, 4], [3, 4], [3, 2], [4, 2]]}, {"polygon": [[4, 4], [5, 4], [5, 6], [4, 6]]}, {"polygon": [[5, 5], [7, 5], [7, 6], [6, 6], [6, 8], [5, 8]]}], "meta": {"seed": 4205013, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 313, "strictValidation": true}, "imageAssets": {"target": "../images/voi-312/target.png", "shapes": {"S1": "../images/voi-312/shape_S1.png", "S2": "../images/voi-312/shape_S2.png", "S3": "../images/voi-312/shape_S3.png", "S4": "../images/voi-312/shape_S4.png", "S5": "../images/voi-312/shape_S5.png", "S6": "../images/voi-312/shape_S6.png"}}, "ID": "voi-312", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 1]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 6]}, {"shape": "S5", "angle": 0, "vertex": "V6", "grid": [5, 8]}]}, "legacy_answer": "S1 270 V1 [5,1]\nS2 180 V3 [3,2]\nS3 0 V4 [4,6]\nS5 0 V6 [5,8]", "solutionText": "S1 270 V1 [5,1]\nS2 180 V3 [3,2]\nS3 0 V4 [4,6]\nS5 0 V6 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-312\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-312/target.png", "shapes": {"S1": "images/voi-312/shape_S1.png", "S2": "images/voi-312/shape_S2.png", "S3": "images/voi-312/shape_S3.png", "S4": "images/voi-312/shape_S4.png", "S5": "images/voi-312/shape_S5.png", "S6": "images/voi-312/shape_S6.png"}}, "__sample_id__": "voi-312"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 7], [7, 6], [8, 6], [8, 7]]}, {"polygon": [[6, 8], [4, 8], [4, 6], [6, 6]]}, {"polygon": [[6, 5], [8, 5], [8, 7], [6, 7]]}, {"polygon": [[4, 4], [5, 4], [5, 6], [4, 6]]}], "meta": {"seed": 4205014, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.691477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 314, "strictValidation": true}, "imageAssets": {"target": "../images/voi-313/target.png", "shapes": {"S1": "../images/voi-313/shape_S1.png", "S2": "../images/voi-313/shape_S2.png", "S3": "../images/voi-313/shape_S3.png", "S4": "../images/voi-313/shape_S4.png", "S5": "../images/voi-313/shape_S5.png", "S6": "../images/voi-313/shape_S6.png"}}, "ID": "voi-313", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [8, 6]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 6]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [8, 7]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [4, 4]}]}, "legacy_answer": "S1 90 V3 [8,6]\nS3 180 V3 [4,6]\nS4 0 V3 [8,7]\nS5 0 V1 [4,4]", "solutionText": "S1 90 V3 [8,6]\nS3 180 V3 [4,6]\nS4 0 V3 [8,7]\nS5 0 V1 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-313\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-313/target.png", "shapes": {"S1": "images/voi-313/shape_S1.png", "S2": "images/voi-313/shape_S2.png", "S3": "images/voi-313/shape_S3.png", "S4": "images/voi-313/shape_S4.png", "S5": "images/voi-313/shape_S5.png", "S6": "images/voi-313/shape_S6.png"}}, "__sample_id__": "voi-313"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 2]]}, {"polygon": [[7, 3], [7, 4], [4, 4], [4, 3]]}, {"polygon": [[5, 4], [5, 6], [4, 6], [4, 5], [2, 5], [2, 4]]}, {"polygon": [[7, 3], [7, 6], [5, 6], [5, 3]]}], "meta": {"seed": 4205015, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.172852, "difficultyScore": 0.292056, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 315, "strictValidation": true}, "imageAssets": {"target": "../images/voi-314/target.png", "shapes": {"S1": "../images/voi-314/shape_S1.png", "S2": "../images/voi-314/shape_S2.png", "S3": "../images/voi-314/shape_S3.png", "S4": "../images/voi-314/shape_S4.png", "S5": "../images/voi-314/shape_S5.png", "S6": "../images/voi-314/shape_S6.png"}}, "ID": "voi-314", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [7, 3]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [4, 6]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [7, 6]}]}, "legacy_answer": "S1 270 V2 [3,4]\nS2 270 V1 [7,3]\nS4 270 V3 [4,6]\nS6 270 V2 [7,6]", "solutionText": "S1 270 V2 [3,4]\nS2 270 V1 [7,3]\nS4 270 V3 [4,6]\nS6 270 V2 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-314\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-314/target.png", "shapes": {"S1": "images/voi-314/shape_S1.png", "S2": "images/voi-314/shape_S2.png", "S3": "images/voi-314/shape_S3.png", "S4": "images/voi-314/shape_S4.png", "S5": "images/voi-314/shape_S5.png", "S6": "images/voi-314/shape_S6.png"}}, "__sample_id__": "voi-314"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [5, 5], [3, 5], [3, 2]]}, {"polygon": [[7, 4], [7, 5], [5, 5], [5, 4]]}, {"polygon": [[3, 3], [3, 0], [5, 0], [5, 3]]}, {"polygon": [[3, 3], [3, 2], [5, 2], [5, 3]]}], "meta": {"seed": 4205016, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 316, "strictValidation": true}, "imageAssets": {"target": "../images/voi-315/target.png", "shapes": {"S1": "../images/voi-315/shape_S1.png", "S2": "../images/voi-315/shape_S2.png", "S3": "../images/voi-315/shape_S3.png", "S4": "../images/voi-315/shape_S4.png", "S5": "../images/voi-315/shape_S5.png", "S6": "../images/voi-315/shape_S6.png"}}, "ID": "voi-315", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V3", "grid": [3, 5]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [5, 5]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [3, 0]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [3, 2]}]}, "legacy_answer": "S3 270 V3 [3,5]\nS4 270 V3 [5,5]\nS5 90 V2 [3,0]\nS6 90 V2 [3,2]", "solutionText": "S3 270 V3 [3,5]\nS4 270 V3 [5,5]\nS5 90 V2 [3,0]\nS6 90 V2 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-315\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-315/target.png", "shapes": {"S1": "images/voi-315/shape_S1.png", "S2": "images/voi-315/shape_S2.png", "S3": "images/voi-315/shape_S3.png", "S4": "images/voi-315/shape_S4.png", "S5": "images/voi-315/shape_S5.png", "S6": "images/voi-315/shape_S6.png"}}, "__sample_id__": "voi-315"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [4, 7], [2, 7], [2, 4]]}, {"polygon": [[3, 1], [4, 1], [4, 4], [3, 4]]}, {"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}, {"polygon": [[6, 3], [6, 5], [4, 5], [4, 3]]}], "meta": {"seed": 4205017, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.352574, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 317, "strictValidation": true}, "imageAssets": {"target": "../images/voi-316/target.png", "shapes": {"S1": "../images/voi-316/shape_S1.png", "S2": "../images/voi-316/shape_S2.png", "S3": "../images/voi-316/shape_S3.png", "S4": "../images/voi-316/shape_S4.png", "S5": "../images/voi-316/shape_S5.png", "S6": "../images/voi-316/shape_S6.png"}}, "ID": "voi-316", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [2, 4]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [3, 4]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [3, 1]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [4, 5]}]}, "legacy_answer": "S2 270 V4 [2,4]\nS3 0 V4 [3,4]\nS4 90 V2 [3,1]\nS6 270 V3 [4,5]", "solutionText": "S2 270 V4 [2,4]\nS3 0 V4 [3,4]\nS4 90 V2 [3,1]\nS6 270 V3 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-316\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-316/target.png", "shapes": {"S1": "images/voi-316/shape_S1.png", "S2": "images/voi-316/shape_S2.png", "S3": "images/voi-316/shape_S3.png", "S4": "images/voi-316/shape_S4.png", "S5": "images/voi-316/shape_S5.png", "S6": "images/voi-316/shape_S6.png"}}, "__sample_id__": "voi-316"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 5], [5, 5], [5, 6], [4, 6], [4, 8], [3, 8]]}, {"polygon": [[2, 4], [3, 4], [3, 6], [2, 6]]}, {"polygon": [[8, 6], [5, 6], [5, 4], [8, 4]]}, {"polygon": [[8, 4], [8, 6], [7, 6], [7, 4]]}], "meta": {"seed": 4205018, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 318, "strictValidation": true}, "imageAssets": {"target": "../images/voi-317/target.png", "shapes": {"S1": "../images/voi-317/shape_S1.png", "S2": "../images/voi-317/shape_S2.png", "S3": "../images/voi-317/shape_S3.png", "S4": "../images/voi-317/shape_S4.png", "S5": "../images/voi-317/shape_S5.png", "S6": "../images/voi-317/shape_S6.png"}}, "ID": "voi-317", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 5]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [5, 4]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [7, 6]}]}, "legacy_answer": "S1 0 V1 [3,5]\nS2 0 V2 [3,4]\nS3 180 V3 [5,4]\nS6 270 V3 [7,6]", "solutionText": "S1 0 V1 [3,5]\nS2 0 V2 [3,4]\nS3 180 V3 [5,4]\nS6 270 V3 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-317\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-317/target.png", "shapes": {"S1": "images/voi-317/shape_S1.png", "S2": "images/voi-317/shape_S2.png", "S3": "images/voi-317/shape_S3.png", "S4": "images/voi-317/shape_S4.png", "S5": "images/voi-317/shape_S5.png", "S6": "images/voi-317/shape_S6.png"}}, "__sample_id__": "voi-317"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 2], [6, 2], [6, 3], [3, 3]]}, {"polygon": [[7, 3], [7, 5], [6, 5], [6, 4], [4, 4], [4, 3]]}, {"polygon": [[3, 2], [5, 2], [3, 4]]}, {"polygon": [[7, 4], [7, 2], [8, 2], [8, 4]]}], "meta": {"seed": 4205019, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.276836, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.357345, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 319, "strictValidation": true}, "imageAssets": {"target": "../images/voi-318/target.png", "shapes": {"S1": "../images/voi-318/shape_S1.png", "S2": "../images/voi-318/shape_S2.png", "S3": "../images/voi-318/shape_S3.png", "S4": "../images/voi-318/shape_S4.png", "S5": "../images/voi-318/shape_S5.png", "S6": "../images/voi-318/shape_S6.png"}}, "ID": "voi-318", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [6, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [7, 2]}]}, "legacy_answer": "S1 0 V1 [3,2]\nS3 270 V3 [6,5]\nS4 0 V1 [3,2]\nS5 90 V2 [7,2]", "solutionText": "S1 0 V1 [3,2]\nS3 270 V3 [6,5]\nS4 0 V1 [3,2]\nS5 90 V2 [7,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-318\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-318/target.png", "shapes": {"S1": "images/voi-318/shape_S1.png", "S2": "images/voi-318/shape_S2.png", "S3": "images/voi-318/shape_S3.png", "S4": "images/voi-318/shape_S4.png", "S5": "images/voi-318/shape_S5.png", "S6": "images/voi-318/shape_S6.png"}}, "__sample_id__": "voi-318"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 8], [5, 5], [7, 5], [7, 8]]}, {"polygon": [[4, 4], [4, 6], [2, 6], [2, 4]]}, {"polygon": [[5, 8], [5, 6], [7, 8]]}, {"polygon": [[6, 5], [4, 5], [4, 4], [5, 4], [5, 2], [6, 2]]}], "meta": {"seed": 4205020, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.256809, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.186523, "difficultyScore": 0.299716, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 320, "strictValidation": true}, "imageAssets": {"target": "../images/voi-319/target.png", "shapes": {"S1": "../images/voi-319/shape_S1.png", "S2": "../images/voi-319/shape_S2.png", "S3": "../images/voi-319/shape_S3.png", "S4": "../images/voi-319/shape_S4.png", "S5": "../images/voi-319/shape_S5.png", "S6": "../images/voi-319/shape_S6.png"}}, "ID": "voi-319", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [7, 8]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [2, 4]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [5, 6]}, {"shape": "S6", "angle": 180, "vertex": "V5", "grid": [5, 2]}]}, "legacy_answer": "S1 90 V4 [7,8]\nS4 270 V4 [2,4]\nS5 90 V2 [5,6]\nS6 180 V5 [5,2]", "solutionText": "S1 90 V4 [7,8]\nS4 270 V4 [2,4]\nS5 90 V2 [5,6]\nS6 180 V5 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-319\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-319/target.png", "shapes": {"S1": "images/voi-319/shape_S1.png", "S2": "images/voi-319/shape_S2.png", "S3": "images/voi-319/shape_S3.png", "S4": "images/voi-319/shape_S4.png", "S5": "images/voi-319/shape_S5.png", "S6": "images/voi-319/shape_S6.png"}}, "__sample_id__": "voi-319"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[7, 2], [7, 4], [6, 4], [6, 2]]}, {"polygon": [[7, 6], [5, 6], [5, 4], [7, 4]]}, {"polygon": [[5, 5], [4, 5], [4, 3], [5, 3]]}], "meta": {"seed": 4205021, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 321, "strictValidation": true}, "imageAssets": {"target": "../images/voi-320/target.png", "shapes": {"S1": "../images/voi-320/shape_S1.png", "S2": "../images/voi-320/shape_S2.png", "S3": "../images/voi-320/shape_S3.png", "S4": "../images/voi-320/shape_S4.png", "S5": "../images/voi-320/shape_S5.png", "S6": "../images/voi-320/shape_S6.png"}}, "ID": "voi-320", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 6]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [7, 4]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [7, 4]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 270 V3 [3,6]\nS4 270 V2 [7,4]\nS5 180 V4 [7,4]\nS6 180 V2 [4,5]", "solutionText": "S1 270 V3 [3,6]\nS4 270 V2 [7,4]\nS5 180 V4 [7,4]\nS6 180 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-320\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-320/target.png", "shapes": {"S1": "images/voi-320/shape_S1.png", "S2": "images/voi-320/shape_S2.png", "S3": "images/voi-320/shape_S3.png", "S4": "images/voi-320/shape_S4.png", "S5": "images/voi-320/shape_S5.png", "S6": "images/voi-320/shape_S6.png"}}, "__sample_id__": "voi-320"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 6], [3, 6], [3, 4], [5, 4]]}, {"polygon": [[5, 3], [5, 5], [3, 3]]}, {"polygon": [[4, 5], [4, 3], [5, 3], [5, 4], [7, 4], [7, 5]]}, {"polygon": [[2, 6], [5, 6], [5, 8], [2, 8]]}], "meta": {"seed": 4205022, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.188477, "difficultyScore": 0.326938, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 322, "strictValidation": true}, "imageAssets": {"target": "../images/voi-321/target.png", "shapes": {"S1": "../images/voi-321/shape_S1.png", "S2": "../images/voi-321/shape_S2.png", "S3": "../images/voi-321/shape_S3.png", "S4": "../images/voi-321/shape_S4.png", "S5": "../images/voi-321/shape_S5.png", "S6": "../images/voi-321/shape_S6.png"}}, "ID": "voi-321", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [3, 6]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [3, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [5, 4]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [5, 8]}]}, "legacy_answer": "S1 180 V2 [3,6]\nS2 270 V3 [3,3]\nS3 90 V4 [5,4]\nS4 0 V3 [5,8]", "solutionText": "S1 180 V2 [3,6]\nS2 270 V3 [3,3]\nS3 90 V4 [5,4]\nS4 0 V3 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-321\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-321/target.png", "shapes": {"S1": "images/voi-321/shape_S1.png", "S2": "images/voi-321/shape_S2.png", "S3": "images/voi-321/shape_S3.png", "S4": "images/voi-321/shape_S4.png", "S5": "images/voi-321/shape_S5.png", "S6": "images/voi-321/shape_S6.png"}}, "__sample_id__": "voi-321"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 1], [4, 3], [3, 3], [3, 2], [1, 2], [1, 1]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[2, 2], [2, 5], [1, 4], [1, 2]]}, {"polygon": [[5, 5], [2, 5], [2, 4], [5, 4]]}], "meta": {"seed": 4205023, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.257545, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.180176, "difficultyScore": 0.309467, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 323, "strictValidation": true}, "imageAssets": {"target": "../images/voi-322/target.png", "shapes": {"S1": "../images/voi-322/shape_S1.png", "S2": "../images/voi-322/shape_S2.png", "S3": "../images/voi-322/shape_S3.png", "S4": "../images/voi-322/shape_S4.png", "S5": "../images/voi-322/shape_S5.png", "S6": "../images/voi-322/shape_S6.png"}}, "ID": "voi-322", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [4, 1]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [1, 4]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [5, 5]}]}, "legacy_answer": "S2 270 V1 [4,1]\nS3 270 V2 [5,4]\nS4 270 V3 [1,4]\nS6 180 V1 [5,5]", "solutionText": "S2 270 V1 [4,1]\nS3 270 V2 [5,4]\nS4 270 V3 [1,4]\nS6 180 V1 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-322\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-322/target.png", "shapes": {"S1": "images/voi-322/shape_S1.png", "S2": "images/voi-322/shape_S2.png", "S3": "images/voi-322/shape_S3.png", "S4": "images/voi-322/shape_S4.png", "S5": "images/voi-322/shape_S5.png", "S6": "images/voi-322/shape_S6.png"}}, "__sample_id__": "voi-322"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 5], [7, 5], [7, 7], [5, 7]]}, {"polygon": [[5, 3], [7, 3], [5, 5]]}, {"polygon": [[3, 5], [3, 2], [5, 2], [5, 5]]}, {"polygon": [[5, 2], [8, 2], [8, 4], [5, 4]]}], "meta": {"seed": 4205024, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.16955, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.234375, "difficultyScore": 0.553049, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 324, "strictValidation": true}, "imageAssets": {"target": "../images/voi-323/target.png", "shapes": {"S1": "../images/voi-323/shape_S1.png", "S2": "../images/voi-323/shape_S2.png", "S3": "../images/voi-323/shape_S3.png", "S4": "../images/voi-323/shape_S4.png", "S5": "../images/voi-323/shape_S5.png", "S6": "../images/voi-323/shape_S6.png"}}, "ID": "voi-323", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [5, 5]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [5, 3]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [5, 2]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [8, 2]}]}, "legacy_answer": "S2 0 V1 [5,5]\nS3 0 V1 [5,3]\nS5 90 V3 [5,2]\nS6 0 V2 [8,2]", "solutionText": "S2 0 V1 [5,5]\nS3 0 V1 [5,3]\nS5 90 V3 [5,2]\nS6 0 V2 [8,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-323\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-323/target.png", "shapes": {"S1": "images/voi-323/shape_S1.png", "S2": "images/voi-323/shape_S2.png", "S3": "images/voi-323/shape_S3.png", "S4": "images/voi-323/shape_S4.png", "S5": "images/voi-323/shape_S5.png", "S6": "images/voi-323/shape_S6.png"}}, "__sample_id__": "voi-323"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 6], [1, 6], [1, 4], [4, 4]]}, {"polygon": [[7, 7], [6, 7], [6, 4], [7, 4]]}, {"polygon": [[4, 5], [4, 7], [3, 7], [3, 5]]}, {"polygon": [[3, 6], [3, 4], [4, 4], [4, 5], [6, 5], [6, 6]]}], "meta": {"seed": 4205025, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.289583, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 325, "strictValidation": true}, "imageAssets": {"target": "../images/voi-324/target.png", "shapes": {"S1": "../images/voi-324/shape_S1.png", "S2": "../images/voi-324/shape_S2.png", "S3": "../images/voi-324/shape_S3.png", "S4": "../images/voi-324/shape_S4.png", "S5": "../images/voi-324/shape_S5.png", "S6": "../images/voi-324/shape_S6.png"}}, "ID": "voi-324", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 7]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 7]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [3, 6]}]}, "legacy_answer": "S1 180 V2 [1,6]\nS2 180 V1 [7,7]\nS3 270 V2 [4,7]\nS6 90 V1 [3,6]", "solutionText": "S1 180 V2 [1,6]\nS2 180 V1 [7,7]\nS3 270 V2 [4,7]\nS6 90 V1 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-324\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-324/target.png", "shapes": {"S1": "images/voi-324/shape_S1.png", "S2": "images/voi-324/shape_S2.png", "S3": "images/voi-324/shape_S3.png", "S4": "images/voi-324/shape_S4.png", "S5": "images/voi-324/shape_S5.png", "S6": "images/voi-324/shape_S6.png"}}, "__sample_id__": "voi-324"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 7], [6, 4], [7, 4], [7, 7]]}, {"polygon": [[5, 8], [3, 8], [3, 7], [4, 7], [4, 5], [5, 5]]}, {"polygon": [[7, 8], [5, 8], [5, 7], [6, 7], [6, 5], [7, 5]]}, {"polygon": [[6, 4], [6, 6], [5, 6], [5, 4]]}], "meta": {"seed": 4205026, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.449519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 326, "strictValidation": true}, "imageAssets": {"target": "../images/voi-325/target.png", "shapes": {"S1": "../images/voi-325/shape_S1.png", "S2": "../images/voi-325/shape_S2.png", "S3": "../images/voi-325/shape_S3.png", "S4": "../images/voi-325/shape_S4.png", "S5": "../images/voi-325/shape_S5.png", "S6": "../images/voi-325/shape_S6.png"}}, "ID": "voi-325", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [7, 4]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [5, 8]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [7, 8]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S1 90 V3 [7,4]\nS3 180 V1 [5,8]\nS4 180 V1 [7,8]\nS6 270 V3 [5,6]", "solutionText": "S1 90 V3 [7,4]\nS3 180 V1 [5,8]\nS4 180 V1 [7,8]\nS6 270 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-325\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-325/target.png", "shapes": {"S1": "images/voi-325/shape_S1.png", "S2": "images/voi-325/shape_S2.png", "S3": "images/voi-325/shape_S3.png", "S4": "images/voi-325/shape_S4.png", "S5": "images/voi-325/shape_S5.png", "S6": "images/voi-325/shape_S6.png"}}, "__sample_id__": "voi-325"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 5], [7, 5], [7, 6], [4, 6]]}, {"polygon": [[6, 5], [6, 8], [4, 8], [4, 5]]}, {"polygon": [[2, 6], [2, 4], [3, 4], [3, 5], [5, 5], [5, 6]]}, {"polygon": [[8, 8], [6, 8], [6, 7], [7, 7], [7, 5], [8, 5]]}], "meta": {"seed": 4205027, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 17, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.352574, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 327, "strictValidation": true}, "imageAssets": {"target": "../images/voi-326/target.png", "shapes": {"S1": "../images/voi-326/shape_S1.png", "S2": "../images/voi-326/shape_S2.png", "S3": "../images/voi-326/shape_S3.png", "S4": "../images/voi-326/shape_S4.png", "S5": "../images/voi-326/shape_S5.png", "S6": "../images/voi-326/shape_S6.png"}}, "ID": "voi-326", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [4, 5]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 8]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [3, 4]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [7, 7]}]}, "legacy_answer": "S1 0 V1 [4,5]\nS2 270 V2 [6,8]\nS3 90 V3 [3,4]\nS4 180 V4 [7,7]", "solutionText": "S1 0 V1 [4,5]\nS2 270 V2 [6,8]\nS3 90 V3 [3,4]\nS4 180 V4 [7,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-326\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-326/target.png", "shapes": {"S1": "images/voi-326/shape_S1.png", "S2": "images/voi-326/shape_S2.png", "S3": "images/voi-326/shape_S3.png", "S4": "images/voi-326/shape_S4.png", "S5": "images/voi-326/shape_S5.png", "S6": "images/voi-326/shape_S6.png"}}, "__sample_id__": "voi-326"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 3], [3, 3], [3, 2], [6, 2]]}, {"polygon": [[3, 8], [3, 5], [5, 5], [5, 8]]}, {"polygon": [[4, 5], [3, 5], [3, 3], [4, 3]]}, {"polygon": [[5, 6], [4, 6], [4, 5], [5, 5]]}], "meta": {"seed": 4205028, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.720833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 328, "strictValidation": true}, "imageAssets": {"target": "../images/voi-327/target.png", "shapes": {"S1": "../images/voi-327/shape_S1.png", "S2": "../images/voi-327/shape_S2.png", "S3": "../images/voi-327/shape_S3.png", "S4": "../images/voi-327/shape_S4.png", "S5": "../images/voi-327/shape_S5.png", "S6": "../images/voi-327/shape_S6.png"}}, "ID": "voi-327", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [3, 3]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [5, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [3, 3]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [4, 6]}]}, "legacy_answer": "S1 180 V2 [3,3]\nS2 90 V3 [5,5]\nS3 180 V3 [3,3]\nS5 180 V2 [4,6]", "solutionText": "S1 180 V2 [3,3]\nS2 90 V3 [5,5]\nS3 180 V3 [3,3]\nS5 180 V2 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-327\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-327/target.png", "shapes": {"S1": "images/voi-327/shape_S1.png", "S2": "images/voi-327/shape_S2.png", "S3": "images/voi-327/shape_S3.png", "S4": "images/voi-327/shape_S4.png", "S5": "images/voi-327/shape_S5.png", "S6": "images/voi-327/shape_S6.png"}}, "__sample_id__": "voi-327"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [5, 3], [3, 3], [3, 2]]}, {"polygon": [[4, 2], [4, 3], [1, 3], [1, 2]]}, {"polygon": [[4, 4], [3, 4], [3, 1], [4, 1]]}, {"polygon": [[4, 4], [4, 1], [6, 1], [6, 4]]}], "meta": {"seed": 4205029, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 13, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 329, "strictValidation": true}, "imageAssets": {"target": "../images/voi-328/target.png", "shapes": {"S1": "../images/voi-328/shape_S1.png", "S2": "../images/voi-328/shape_S2.png", "S3": "../images/voi-328/shape_S3.png", "S4": "../images/voi-328/shape_S4.png", "S5": "../images/voi-328/shape_S5.png", "S6": "../images/voi-328/shape_S6.png"}}, "ID": "voi-328", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [5, 2]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 3]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 4]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [4, 1]}]}, "legacy_answer": "S2 270 V1 [5,2]\nS3 270 V3 [1,3]\nS4 180 V1 [4,4]\nS5 90 V2 [4,1]", "solutionText": "S2 270 V1 [5,2]\nS3 270 V3 [1,3]\nS4 180 V1 [4,4]\nS5 90 V2 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-328\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-328/target.png", "shapes": {"S1": "images/voi-328/shape_S1.png", "S2": "images/voi-328/shape_S2.png", "S3": "images/voi-328/shape_S3.png", "S4": "images/voi-328/shape_S4.png", "S5": "images/voi-328/shape_S5.png", "S6": "images/voi-328/shape_S6.png"}}, "__sample_id__": "voi-328"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 6], [4, 6], [3, 7], [1, 7]]}, {"polygon": [[2, 6], [1, 6], [1, 4], [2, 4]]}, {"polygon": [[4, 3], [4, 6], [3, 5], [3, 3]]}, {"polygon": [[3, 4], [3, 5], [1, 5], [1, 4]]}], "meta": {"seed": 4205030, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.22069, "contourComplexity": 73, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.596538, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 330, "strictValidation": true}, "imageAssets": {"target": "../images/voi-329/target.png", "shapes": {"S1": "../images/voi-329/shape_S1.png", "S2": "../images/voi-329/shape_S2.png", "S3": "../images/voi-329/shape_S3.png", "S4": "../images/voi-329/shape_S4.png", "S5": "../images/voi-329/shape_S5.png", "S6": "../images/voi-329/shape_S6.png"}}, "ID": "voi-329", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [1, 6]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [2, 4]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 3]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [1, 4]}]}, "legacy_answer": "S1 0 V1 [1,6]\nS2 180 V4 [2,4]\nS4 270 V4 [3,3]\nS5 270 V4 [1,4]", "solutionText": "S1 0 V1 [1,6]\nS2 180 V4 [2,4]\nS4 270 V4 [3,3]\nS5 270 V4 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-329\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-329/target.png", "shapes": {"S1": "images/voi-329/shape_S1.png", "S2": "images/voi-329/shape_S2.png", "S3": "images/voi-329/shape_S3.png", "S4": "images/voi-329/shape_S4.png", "S5": "images/voi-329/shape_S5.png", "S6": "images/voi-329/shape_S6.png"}}, "__sample_id__": "voi-329"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 5], [4, 8], [2, 8], [2, 5]]}, {"polygon": [[3, 4], [6, 4], [5, 5], [3, 5]]}, {"polygon": [[4, 7], [4, 8], [1, 8], [1, 7]]}, {"polygon": [[1, 4], [2, 4], [2, 7], [1, 7]]}], "meta": {"seed": 4205031, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.271974, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 331, "strictValidation": true}, "imageAssets": {"target": "../images/voi-330/target.png", "shapes": {"S1": "../images/voi-330/shape_S1.png", "S2": "../images/voi-330/shape_S2.png", "S3": "../images/voi-330/shape_S3.png", "S4": "../images/voi-330/shape_S4.png", "S5": "../images/voi-330/shape_S5.png", "S6": "../images/voi-330/shape_S6.png"}}, "ID": "voi-330", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [4, 8]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [3, 5]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [4, 7]}, {"shape": "S6", "angle": 0, "vertex": "V1", "grid": [1, 4]}]}, "legacy_answer": "S2 270 V2 [4,8]\nS3 0 V4 [3,5]\nS5 270 V1 [4,7]\nS6 0 V1 [1,4]", "solutionText": "S2 270 V2 [4,8]\nS3 0 V4 [3,5]\nS5 270 V1 [4,7]\nS6 0 V1 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-330\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-330/target.png", "shapes": {"S1": "images/voi-330/shape_S1.png", "S2": "images/voi-330/shape_S2.png", "S3": "images/voi-330/shape_S3.png", "S4": "images/voi-330/shape_S4.png", "S5": "images/voi-330/shape_S5.png", "S6": "images/voi-330/shape_S6.png"}}, "__sample_id__": "voi-330"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [2, 2], [4, 4]]}, {"polygon": [[4, 2], [4, 3], [3, 2]]}, {"polygon": [[1, 0], [3, 0], [3, 2], [1, 2]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}], "meta": {"seed": 4205032, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.168734, "contourComplexity": 107, "connectedComponents": 1, "fillRatio": 0.163574, "difficultyScore": 0.697914, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 332, "strictValidation": true}, "imageAssets": {"target": "../images/voi-331/target.png", "shapes": {"S1": "../images/voi-331/shape_S1.png", "S2": "../images/voi-331/shape_S2.png", "S3": "../images/voi-331/shape_S3.png", "S4": "../images/voi-331/shape_S4.png", "S5": "../images/voi-331/shape_S5.png", "S6": "../images/voi-331/shape_S6.png"}}, "ID": "voi-331", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [2, 4]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [4, 3]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [1, 0]}, {"shape": "S6", "angle": 90, "vertex": "V4", "grid": [5, 4]}]}, "legacy_answer": "S1 90 V1 [2,4]\nS2 270 V2 [4,3]\nS4 0 V1 [1,0]\nS6 90 V4 [5,4]", "solutionText": "S1 90 V1 [2,4]\nS2 270 V2 [4,3]\nS4 0 V1 [1,0]\nS6 90 V4 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-331\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-331/target.png", "shapes": {"S1": "images/voi-331/shape_S1.png", "S2": "images/voi-331/shape_S2.png", "S3": "images/voi-331/shape_S3.png", "S4": "images/voi-331/shape_S4.png", "S5": "images/voi-331/shape_S5.png", "S6": "images/voi-331/shape_S6.png"}}, "__sample_id__": "voi-331"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 4], [2, 4], [0, 6]]}, {"polygon": [[5, 4], [5, 7], [3, 7], [3, 4]]}, {"polygon": [[2, 5], [2, 4], [5, 4], [5, 5]]}, {"polygon": [[3, 6], [0, 6], [0, 5], [3, 5]]}], "meta": {"seed": 4205033, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.36, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.65875, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 333, "strictValidation": true}, "imageAssets": {"target": "../images/voi-332/target.png", "shapes": {"S1": "../images/voi-332/shape_S1.png", "S2": "../images/voi-332/shape_S2.png", "S3": "../images/voi-332/shape_S3.png", "S4": "../images/voi-332/shape_S4.png", "S5": "../images/voi-332/shape_S5.png", "S6": "../images/voi-332/shape_S6.png"}}, "ID": "voi-332", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [0, 4]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 4]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [2, 4]}, {"shape": "S6", "angle": 180, "vertex": "V4", "grid": [3, 5]}]}, "legacy_answer": "S1 0 V1 [0,4]\nS4 270 V4 [3,4]\nS5 90 V2 [2,4]\nS6 180 V4 [3,5]", "solutionText": "S1 0 V1 [0,4]\nS4 270 V4 [3,4]\nS5 90 V2 [2,4]\nS6 180 V4 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-332\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-332/target.png", "shapes": {"S1": "images/voi-332/shape_S1.png", "S2": "images/voi-332/shape_S2.png", "S3": "images/voi-332/shape_S3.png", "S4": "images/voi-332/shape_S4.png", "S5": "images/voi-332/shape_S5.png", "S6": "images/voi-332/shape_S6.png"}}, "__sample_id__": "voi-332"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 4], [6, 4], [4, 6]]}, {"polygon": [[5, 4], [7, 4], [5, 6]]}, {"polygon": [[5, 6], [5, 4], [6, 4], [6, 5], [8, 5], [8, 6]]}, {"polygon": [[3, 7], [3, 6], [6, 6], [6, 7]]}], "meta": {"seed": 4205034, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275281, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.125977, "difficultyScore": 0.34917, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 334, "strictValidation": true}, "imageAssets": {"target": "../images/voi-333/target.png", "shapes": {"S1": "../images/voi-333/shape_S1.png", "S2": "../images/voi-333/shape_S2.png", "S3": "../images/voi-333/shape_S3.png", "S4": "../images/voi-333/shape_S4.png", "S5": "../images/voi-333/shape_S5.png", "S6": "../images/voi-333/shape_S6.png"}}, "ID": "voi-333", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 4]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [5, 6]}, {"shape": "S3", "angle": 90, "vertex": "V6", "grid": [8, 6]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [6, 7]}]}, "legacy_answer": "S1 0 V2 [6,4]\nS2 0 V3 [5,6]\nS3 90 V6 [8,6]\nS4 90 V4 [6,7]", "solutionText": "S1 0 V2 [6,4]\nS2 0 V3 [5,6]\nS3 90 V6 [8,6]\nS4 90 V4 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-333\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-333/target.png", "shapes": {"S1": "images/voi-333/shape_S1.png", "S2": "images/voi-333/shape_S2.png", "S3": "images/voi-333/shape_S3.png", "S4": "images/voi-333/shape_S4.png", "S5": "images/voi-333/shape_S5.png", "S6": "images/voi-333/shape_S6.png"}}, "__sample_id__": "voi-333"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 2], [2, 5], [1, 5], [1, 2]]}, {"polygon": [[1, 4], [1, 3], [3, 3], [3, 4]]}, {"polygon": [[2, 2], [5, 2], [5, 4], [2, 4]]}, {"polygon": [[0, 3], [2, 3], [2, 4], [1, 4], [1, 6], [0, 6]]}], "meta": {"seed": 4205035, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.289583, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 335, "strictValidation": true}, "imageAssets": {"target": "../images/voi-334/target.png", "shapes": {"S1": "../images/voi-334/shape_S1.png", "S2": "../images/voi-334/shape_S2.png", "S3": "../images/voi-334/shape_S3.png", "S4": "../images/voi-334/shape_S4.png", "S5": "../images/voi-334/shape_S5.png", "S6": "../images/voi-334/shape_S6.png"}}, "ID": "voi-334", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 2]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [1, 4]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [5, 4]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [1, 4]}]}, "legacy_answer": "S2 270 V4 [1,2]\nS3 90 V1 [1,4]\nS4 0 V3 [5,4]\nS5 0 V4 [1,4]", "solutionText": "S2 270 V4 [1,2]\nS3 90 V1 [1,4]\nS4 0 V3 [5,4]\nS5 0 V4 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-334\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-334/target.png", "shapes": {"S1": "images/voi-334/shape_S1.png", "S2": "images/voi-334/shape_S2.png", "S3": "images/voi-334/shape_S3.png", "S4": "images/voi-334/shape_S4.png", "S5": "images/voi-334/shape_S5.png", "S6": "images/voi-334/shape_S6.png"}}, "__sample_id__": "voi-334"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 1], [6, 1], [6, 3], [3, 3]]}, {"polygon": [[0, 5], [0, 2], [1, 2], [1, 5]]}, {"polygon": [[6, 3], [4, 3], [6, 1]]}, {"polygon": [[1, 3], [4, 3], [4, 4], [1, 4]]}], "meta": {"seed": 4205036, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.293333, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.155273, "difficultyScore": 0.362786, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 336, "strictValidation": true}, "imageAssets": {"target": "../images/voi-335/target.png", "shapes": {"S1": "../images/voi-335/shape_S1.png", "S2": "../images/voi-335/shape_S2.png", "S3": "../images/voi-335/shape_S3.png", "S4": "../images/voi-335/shape_S4.png", "S5": "../images/voi-335/shape_S5.png", "S6": "../images/voi-335/shape_S6.png"}}, "ID": "voi-335", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 3]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [1, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 3]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [1, 3]}]}, "legacy_answer": "S1 0 V4 [3,3]\nS2 90 V3 [1,2]\nS3 180 V2 [4,3]\nS5 0 V1 [1,3]", "solutionText": "S1 0 V4 [3,3]\nS2 90 V3 [1,2]\nS3 180 V2 [4,3]\nS5 0 V1 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-335\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-335/target.png", "shapes": {"S1": "images/voi-335/shape_S1.png", "S2": "images/voi-335/shape_S2.png", "S3": "images/voi-335/shape_S3.png", "S4": "images/voi-335/shape_S4.png", "S5": "images/voi-335/shape_S5.png", "S6": "images/voi-335/shape_S6.png"}}, "__sample_id__": "voi-335"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[1, 4], [4, 4], [4, 5], [1, 5]]}, {"polygon": [[5, 2], [5, 5], [4, 5], [4, 2]]}, {"polygon": [[2, 2], [5, 2], [5, 4], [2, 4]]}, {"polygon": [[0, 4], [1, 4], [0, 5]]}], "meta": {"seed": 4205037, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319202, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.510206, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 337, "strictValidation": true}, "imageAssets": {"target": "../images/voi-336/target.png", "shapes": {"S1": "../images/voi-336/shape_S1.png", "S2": "../images/voi-336/shape_S2.png", "S3": "../images/voi-336/shape_S3.png", "S4": "../images/voi-336/shape_S4.png", "S5": "../images/voi-336/shape_S5.png", "S6": "../images/voi-336/shape_S6.png"}}, "ID": "voi-336", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [1, 5]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [4, 5]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [5, 4]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [0, 5]}]}, "legacy_answer": "S1 0 V4 [1,5]\nS2 270 V3 [4,5]\nS4 0 V3 [5,4]\nS6 0 V3 [0,5]", "solutionText": "S1 0 V4 [1,5]\nS2 270 V3 [4,5]\nS4 0 V3 [5,4]\nS6 0 V3 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-336\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-336/target.png", "shapes": {"S1": "images/voi-336/shape_S1.png", "S2": "images/voi-336/shape_S2.png", "S3": "images/voi-336/shape_S3.png", "S4": "images/voi-336/shape_S4.png", "S5": "images/voi-336/shape_S5.png", "S6": "images/voi-336/shape_S6.png"}}, "__sample_id__": "voi-336"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 5], [4, 6], [2, 6], [2, 5]]}, {"polygon": [[1, 6], [1, 4], [3, 4], [3, 6]]}, {"polygon": [[4, 4], [2, 4], [4, 2]]}, {"polygon": [[2, 5], [3, 5], [3, 8], [2, 8]]}], "meta": {"seed": 4205038, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.180791, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.141602, "difficultyScore": 0.693633, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 338, "strictValidation": true}, "imageAssets": {"target": "../images/voi-337/target.png", "shapes": {"S1": "../images/voi-337/shape_S1.png", "S2": "../images/voi-337/shape_S2.png", "S3": "../images/voi-337/shape_S3.png", "S4": "../images/voi-337/shape_S4.png", "S5": "../images/voi-337/shape_S5.png", "S6": "../images/voi-337/shape_S6.png"}}, "ID": "voi-337", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 6]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [1, 6]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [2, 4]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [3, 8]}]}, "legacy_answer": "S1 270 V3 [2,6]\nS3 90 V1 [1,6]\nS4 180 V2 [2,4]\nS6 0 V3 [3,8]", "solutionText": "S1 270 V3 [2,6]\nS3 90 V1 [1,6]\nS4 180 V2 [2,4]\nS6 0 V3 [3,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-337\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-337/target.png", "shapes": {"S1": "images/voi-337/shape_S1.png", "S2": "images/voi-337/shape_S2.png", "S3": "images/voi-337/shape_S3.png", "S4": "images/voi-337/shape_S4.png", "S5": "images/voi-337/shape_S5.png", "S6": "images/voi-337/shape_S6.png"}}, "__sample_id__": "voi-337"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[2, 1], [3, 1], [3, 4], [2, 4]]}, {"polygon": [[4, 6], [2, 6], [2, 5], [4, 5]]}, {"polygon": [[1, 7], [1, 4], [3, 4], [3, 7]]}, {"polygon": [[4, 5], [4, 8], [3, 8], [3, 5]]}], "meta": {"seed": 4205039, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 339, "strictValidation": true}, "imageAssets": {"target": "../images/voi-338/target.png", "shapes": {"S1": "../images/voi-338/shape_S1.png", "S2": "../images/voi-338/shape_S2.png", "S3": "../images/voi-338/shape_S3.png", "S4": "../images/voi-338/shape_S4.png", "S5": "../images/voi-338/shape_S5.png", "S6": "../images/voi-338/shape_S6.png"}}, "ID": "voi-338", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V4", "grid": [2, 4]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 4]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [3, 5]}]}, "legacy_answer": "S2 0 V4 [2,4]\nS3 180 V4 [4,5]\nS4 90 V2 [1,4]\nS5 270 V4 [3,5]", "solutionText": "S2 0 V4 [2,4]\nS3 180 V4 [4,5]\nS4 90 V2 [1,4]\nS5 270 V4 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-338\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-338/target.png", "shapes": {"S1": "images/voi-338/shape_S1.png", "S2": "images/voi-338/shape_S2.png", "S3": "images/voi-338/shape_S3.png", "S4": "images/voi-338/shape_S4.png", "S5": "images/voi-338/shape_S5.png", "S6": "images/voi-338/shape_S6.png"}}, "__sample_id__": "voi-338"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 8], [5, 5], [7, 5], [7, 8]]}, {"polygon": [[6, 6], [4, 6], [6, 4]]}, {"polygon": [[6, 4], [7, 4], [6, 5]]}, {"polygon": [[4, 8], [4, 6], [6, 8]]}], "meta": {"seed": 4205040, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.28739, "contourComplexity": 169, "connectedComponents": 1, "fillRatio": 0.118652, "difficultyScore": 0.412255, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 340, "strictValidation": true}, "imageAssets": {"target": "../images/voi-339/target.png", "shapes": {"S1": "../images/voi-339/shape_S1.png", "S2": "../images/voi-339/shape_S2.png", "S3": "../images/voi-339/shape_S3.png", "S4": "../images/voi-339/shape_S4.png", "S5": "../images/voi-339/shape_S5.png", "S6": "../images/voi-339/shape_S6.png"}}, "ID": "voi-339", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [7, 5]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [6, 6]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [6, 4]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [4, 8]}]}, "legacy_answer": "S1 90 V3 [7,5]\nS3 180 V1 [6,6]\nS4 0 V1 [6,4]\nS5 90 V1 [4,8]", "solutionText": "S1 90 V3 [7,5]\nS3 180 V1 [6,6]\nS4 0 V1 [6,4]\nS5 90 V1 [4,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-339\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-339/target.png", "shapes": {"S1": "images/voi-339/shape_S1.png", "S2": "images/voi-339/shape_S2.png", "S3": "images/voi-339/shape_S3.png", "S4": "images/voi-339/shape_S4.png", "S5": "images/voi-339/shape_S5.png", "S6": "images/voi-339/shape_S6.png"}}, "__sample_id__": "voi-339"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[6, 3], [3, 3], [4, 2], [6, 2]]}, {"polygon": [[4, 4], [4, 5], [2, 5], [2, 4]]}, {"polygon": [[1, 3], [2, 3], [2, 4], [1, 4]]}, {"polygon": [[1, 4], [1, 3], [4, 3], [4, 4]]}], "meta": {"seed": 4205041, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.558169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 341, "strictValidation": true}, "imageAssets": {"target": "../images/voi-340/target.png", "shapes": {"S1": "../images/voi-340/shape_S1.png", "S2": "../images/voi-340/shape_S2.png", "S3": "../images/voi-340/shape_S3.png", "S4": "../images/voi-340/shape_S4.png", "S5": "../images/voi-340/shape_S5.png", "S6": "../images/voi-340/shape_S6.png"}}, "ID": "voi-340", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [6, 2]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [1, 3]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [1, 3]}]}, "legacy_answer": "S1 180 V4 [6,2]\nS2 270 V3 [2,5]\nS4 0 V1 [1,3]\nS6 90 V2 [1,3]", "solutionText": "S1 180 V4 [6,2]\nS2 270 V3 [2,5]\nS4 0 V1 [1,3]\nS6 90 V2 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-340\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-340/target.png", "shapes": {"S1": "images/voi-340/shape_S1.png", "S2": "images/voi-340/shape_S2.png", "S3": "images/voi-340/shape_S3.png", "S4": "images/voi-340/shape_S4.png", "S5": "images/voi-340/shape_S5.png", "S6": "images/voi-340/shape_S6.png"}}, "__sample_id__": "voi-340"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 5], [2, 5], [2, 4], [4, 4]]}, {"polygon": [[3, 4], [3, 7], [2, 6], [2, 4]]}, {"polygon": [[7, 4], [4, 4], [4, 3], [7, 3]]}, {"polygon": [[2, 3], [4, 3], [2, 5]]}], "meta": {"seed": 4205042, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.208469, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.118652, "difficultyScore": 0.628819, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 342, "strictValidation": true}, "imageAssets": {"target": "../images/voi-341/target.png", "shapes": {"S1": "../images/voi-341/shape_S1.png", "S2": "../images/voi-341/shape_S2.png", "S3": "../images/voi-341/shape_S3.png", "S4": "../images/voi-341/shape_S4.png", "S5": "../images/voi-341/shape_S5.png", "S6": "../images/voi-341/shape_S6.png"}}, "ID": "voi-341", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [2, 5]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [3, 4]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [7, 3]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [2, 5]}]}, "legacy_answer": "S1 180 V2 [2,5]\nS3 270 V1 [3,4]\nS5 180 V4 [7,3]\nS6 0 V3 [2,5]", "solutionText": "S1 180 V2 [2,5]\nS3 270 V1 [3,4]\nS5 180 V4 [7,3]\nS6 0 V3 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-341\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-341/target.png", "shapes": {"S1": "images/voi-341/shape_S1.png", "S2": "images/voi-341/shape_S2.png", "S3": "images/voi-341/shape_S3.png", "S4": "images/voi-341/shape_S4.png", "S5": "images/voi-341/shape_S5.png", "S6": "images/voi-341/shape_S6.png"}}, "__sample_id__": "voi-341"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 2], [0, 0], [1, 0], [1, 1], [3, 1], [3, 2]]}, {"polygon": [[5, 2], [2, 2], [3, 1], [5, 1]]}, {"polygon": [[4, 3], [2, 3], [2, 1], [4, 1]]}, {"polygon": [[6, 2], [6, 4], [4, 4], [4, 2]]}], "meta": {"seed": 4205043, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 48, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.271974, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 343, "strictValidation": true}, "imageAssets": {"target": "../images/voi-342/target.png", "shapes": {"S1": "../images/voi-342/shape_S1.png", "S2": "../images/voi-342/shape_S2.png", "S3": "../images/voi-342/shape_S3.png", "S4": "../images/voi-342/shape_S4.png", "S5": "../images/voi-342/shape_S5.png", "S6": "../images/voi-342/shape_S6.png"}}, "ID": "voi-342", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V6", "grid": [3, 2]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 1]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [2, 3]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [6, 2]}]}, "legacy_answer": "S1 90 V6 [3,2]\nS4 180 V4 [5,1]\nS5 180 V2 [2,3]\nS6 270 V1 [6,2]", "solutionText": "S1 90 V6 [3,2]\nS4 180 V4 [5,1]\nS5 180 V2 [2,3]\nS6 270 V1 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-342\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-342/target.png", "shapes": {"S1": "images/voi-342/shape_S1.png", "S2": "images/voi-342/shape_S2.png", "S3": "images/voi-342/shape_S3.png", "S4": "images/voi-342/shape_S4.png", "S5": "images/voi-342/shape_S5.png", "S6": "images/voi-342/shape_S6.png"}}, "__sample_id__": "voi-342"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 4], [4, 4], [4, 2], [5, 2]]}, {"polygon": [[6, 0], [6, 3], [4, 3], [4, 0]]}, {"polygon": [[4, 7], [4, 4], [5, 5], [5, 7]]}, {"polygon": [[6, 2], [6, 4], [5, 4], [5, 3], [3, 3], [3, 2]]}], "meta": {"seed": 4205044, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.271974, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 344, "strictValidation": true}, "imageAssets": {"target": "../images/voi-343/target.png", "shapes": {"S1": "../images/voi-343/shape_S1.png", "S2": "../images/voi-343/shape_S2.png", "S3": "../images/voi-343/shape_S3.png", "S4": "../images/voi-343/shape_S4.png", "S5": "../images/voi-343/shape_S5.png", "S6": "../images/voi-343/shape_S6.png"}}, "ID": "voi-343", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [4, 2]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [4, 3]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [4, 4]}, {"shape": "S6", "angle": 270, "vertex": "V6", "grid": [3, 2]}]}, "legacy_answer": "S1 180 V3 [4,2]\nS3 270 V3 [4,3]\nS5 90 V2 [4,4]\nS6 270 V6 [3,2]", "solutionText": "S1 180 V3 [4,2]\nS3 270 V3 [4,3]\nS5 90 V2 [4,4]\nS6 270 V6 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-343\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-343/target.png", "shapes": {"S1": "images/voi-343/shape_S1.png", "S2": "images/voi-343/shape_S2.png", "S3": "images/voi-343/shape_S3.png", "S4": "images/voi-343/shape_S4.png", "S5": "images/voi-343/shape_S5.png", "S6": "images/voi-343/shape_S6.png"}}, "__sample_id__": "voi-343"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 1], [0, 0], [3, 0], [3, 1]]}, {"polygon": [[4, 0], [4, 3], [3, 3], [3, 0]]}, {"polygon": [[2, 1], [2, 2], [1, 2], [1, 1]]}, {"polygon": [[1, 0], [1, 3], [0, 2], [0, 0]]}], "meta": {"seed": 4205045, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.625304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 345, "strictValidation": true}, "imageAssets": {"target": "../images/voi-344/target.png", "shapes": {"S1": "../images/voi-344/shape_S1.png", "S2": "../images/voi-344/shape_S2.png", "S3": "../images/voi-344/shape_S3.png", "S4": "../images/voi-344/shape_S4.png", "S5": "../images/voi-344/shape_S5.png", "S6": "../images/voi-344/shape_S6.png"}}, "ID": "voi-344", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [0, 0]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [3, 0]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [1, 2]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [0, 0]}]}, "legacy_answer": "S2 90 V2 [0,0]\nS3 270 V4 [3,0]\nS5 270 V3 [1,2]\nS6 270 V4 [0,0]", "solutionText": "S2 90 V2 [0,0]\nS3 270 V4 [3,0]\nS5 270 V3 [1,2]\nS6 270 V4 [0,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-344\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-344/target.png", "shapes": {"S1": "images/voi-344/shape_S1.png", "S2": "images/voi-344/shape_S2.png", "S3": "images/voi-344/shape_S3.png", "S4": "images/voi-344/shape_S4.png", "S5": "images/voi-344/shape_S5.png", "S6": "images/voi-344/shape_S6.png"}}, "__sample_id__": "voi-344"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 6], [1, 6], [2, 5], [4, 5]]}, {"polygon": [[4, 6], [4, 4], [6, 4], [6, 6]]}, {"polygon": [[7, 5], [4, 5], [4, 3], [7, 3]]}, {"polygon": [[3, 5], [3, 3], [4, 3], [4, 4], [6, 4], [6, 5]]}], "meta": {"seed": 4205046, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.241966, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.195801, "difficultyScore": 0.340535, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 346, "strictValidation": true}, "imageAssets": {"target": "../images/voi-345/target.png", "shapes": {"S1": "../images/voi-345/shape_S1.png", "S2": "../images/voi-345/shape_S2.png", "S3": "../images/voi-345/shape_S3.png", "S4": "../images/voi-345/shape_S4.png", "S5": "../images/voi-345/shape_S5.png", "S6": "../images/voi-345/shape_S6.png"}}, "ID": "voi-345", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [4, 6]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [7, 3]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [3, 5]}]}, "legacy_answer": "S1 180 V2 [1,6]\nS2 90 V1 [4,6]\nS3 180 V4 [7,3]\nS6 90 V1 [3,5]", "solutionText": "S1 180 V2 [1,6]\nS2 90 V1 [4,6]\nS3 180 V4 [7,3]\nS6 90 V1 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-345\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-345/target.png", "shapes": {"S1": "images/voi-345/shape_S1.png", "S2": "images/voi-345/shape_S2.png", "S3": "images/voi-345/shape_S3.png", "S4": "images/voi-345/shape_S4.png", "S5": "images/voi-345/shape_S5.png", "S6": "images/voi-345/shape_S6.png"}}, "__sample_id__": "voi-345"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 7], [6, 6], [7, 6], [7, 7]]}, {"polygon": [[6, 5], [6, 3], [8, 3], [8, 5]]}, {"polygon": [[5, 7], [5, 5], [7, 5], [7, 7]]}, {"polygon": [[4, 6], [7, 6], [7, 8], [4, 8]]}], "meta": {"seed": 4205047, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.289583, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 347, "strictValidation": true}, "imageAssets": {"target": "../images/voi-346/target.png", "shapes": {"S1": "../images/voi-346/shape_S1.png", "S2": "../images/voi-346/shape_S2.png", "S3": "../images/voi-346/shape_S3.png", "S4": "../images/voi-346/shape_S4.png", "S5": "../images/voi-346/shape_S5.png", "S6": "../images/voi-346/shape_S6.png"}}, "ID": "voi-346", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [7, 7]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [6, 5]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [5, 5]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S2 90 V4 [7,7]\nS3 90 V1 [6,5]\nS4 90 V2 [5,5]\nS5 0 V1 [4,6]", "solutionText": "S2 90 V4 [7,7]\nS3 90 V1 [6,5]\nS4 90 V2 [5,5]\nS5 0 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-346\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-346/target.png", "shapes": {"S1": "images/voi-346/shape_S1.png", "S2": "images/voi-346/shape_S2.png", "S3": "images/voi-346/shape_S3.png", "S4": "images/voi-346/shape_S4.png", "S5": "images/voi-346/shape_S5.png", "S6": "images/voi-346/shape_S6.png"}}, "__sample_id__": "voi-346"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[7, 3], [7, 0], [8, 0], [8, 3]]}, {"polygon": [[7, 5], [5, 5], [5, 4], [6, 4], [6, 2], [7, 2]]}, {"polygon": [[4, 2], [6, 2], [4, 4]]}, {"polygon": [[4, 4], [6, 4], [6, 5], [4, 5]]}], "meta": {"seed": 4205048, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.180791, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.141602, "difficultyScore": 0.693633, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 348, "strictValidation": true}, "imageAssets": {"target": "../images/voi-347/target.png", "shapes": {"S1": "../images/voi-347/shape_S1.png", "S2": "../images/voi-347/shape_S2.png", "S3": "../images/voi-347/shape_S3.png", "S4": "../images/voi-347/shape_S4.png", "S5": "../images/voi-347/shape_S5.png", "S6": "../images/voi-347/shape_S6.png"}}, "ID": "voi-347", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [7, 3]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [4, 4]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S1 90 V1 [7,3]\nS2 180 V3 [5,4]\nS4 0 V3 [4,4]\nS5 0 V2 [6,4]", "solutionText": "S1 90 V1 [7,3]\nS2 180 V3 [5,4]\nS4 0 V3 [4,4]\nS5 0 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-347\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-347/target.png", "shapes": {"S1": "images/voi-347/shape_S1.png", "S2": "images/voi-347/shape_S2.png", "S3": "images/voi-347/shape_S3.png", "S4": "images/voi-347/shape_S4.png", "S5": "images/voi-347/shape_S5.png", "S6": "images/voi-347/shape_S6.png"}}, "__sample_id__": "voi-347"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 2], [2, 2], [0, 4]]}, {"polygon": [[1, 6], [1, 5], [4, 5], [4, 6]]}, {"polygon": [[1, 6], [1, 3], [2, 4], [2, 6]]}, {"polygon": [[1, 8], [1, 5], [2, 6], [2, 8]]}], "meta": {"seed": 4205049, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.197531, "contourComplexity": 132, "connectedComponents": 1, "fillRatio": 0.126953, "difficultyScore": 0.65597, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 349, "strictValidation": true}, "imageAssets": {"target": "../images/voi-348/target.png", "shapes": {"S1": "../images/voi-348/shape_S1.png", "S2": "../images/voi-348/shape_S2.png", "S3": "../images/voi-348/shape_S3.png", "S4": "../images/voi-348/shape_S4.png", "S5": "../images/voi-348/shape_S5.png", "S6": "../images/voi-348/shape_S6.png"}}, "ID": "voi-348", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [2, 2]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [1, 5]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [1, 3]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [1, 8]}]}, "legacy_answer": "S1 0 V2 [2,2]\nS2 90 V2 [1,5]\nS5 90 V2 [1,3]\nS6 90 V1 [1,8]", "solutionText": "S1 0 V2 [2,2]\nS2 90 V2 [1,5]\nS5 90 V2 [1,3]\nS6 90 V1 [1,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-348\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-348/target.png", "shapes": {"S1": "images/voi-348/shape_S1.png", "S2": "images/voi-348/shape_S2.png", "S3": "images/voi-348/shape_S3.png", "S4": "images/voi-348/shape_S4.png", "S5": "images/voi-348/shape_S5.png", "S6": "images/voi-348/shape_S6.png"}}, "__sample_id__": "voi-348"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 7], [0, 7], [0, 5], [2, 5]]}, {"polygon": [[3, 3], [3, 5], [1, 5], [1, 3]]}, {"polygon": [[0, 7], [3, 7], [2, 8], [0, 8]]}, {"polygon": [[1, 4], [1, 6], [0, 6], [0, 4]]}], "meta": {"seed": 4205050, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.159601, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.732494, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 350, "strictValidation": true}, "imageAssets": {"target": "../images/voi-349/target.png", "shapes": {"S1": "../images/voi-349/shape_S1.png", "S2": "../images/voi-349/shape_S2.png", "S3": "../images/voi-349/shape_S3.png", "S4": "../images/voi-349/shape_S4.png", "S5": "../images/voi-349/shape_S5.png", "S6": "../images/voi-349/shape_S6.png"}}, "ID": "voi-349", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V1", "grid": [2, 7]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [1, 5]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [2, 8]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [0, 4]}]}, "legacy_answer": "S3 180 V1 [2,7]\nS4 270 V3 [1,5]\nS5 0 V3 [2,8]\nS6 270 V4 [0,4]", "solutionText": "S3 180 V1 [2,7]\nS4 270 V3 [1,5]\nS5 0 V3 [2,8]\nS6 270 V4 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-349\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-349/target.png", "shapes": {"S1": "images/voi-349/shape_S1.png", "S2": "images/voi-349/shape_S2.png", "S3": "images/voi-349/shape_S3.png", "S4": "images/voi-349/shape_S4.png", "S5": "images/voi-349/shape_S5.png", "S6": "images/voi-349/shape_S6.png"}}, "__sample_id__": "voi-349"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 1], [2, 0], [4, 0], [4, 1]]}, {"polygon": [[2, 4], [1, 4], [2, 3]]}, {"polygon": [[3, 3], [0, 3], [0, 1], [3, 1]]}, {"polygon": [[0, 0], [2, 0], [2, 2], [0, 2]]}], "meta": {"seed": 4205051, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319202, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.510206, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 351, "strictValidation": true}, "imageAssets": {"target": "../images/voi-350/target.png", "shapes": {"S1": "../images/voi-350/shape_S1.png", "S2": "../images/voi-350/shape_S2.png", "S3": "../images/voi-350/shape_S3.png", "S4": "../images/voi-350/shape_S4.png", "S5": "../images/voi-350/shape_S5.png", "S6": "../images/voi-350/shape_S6.png"}}, "ID": "voi-350", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [2, 1]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [2, 3]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [3, 3]}, {"shape": "S6", "angle": 0, "vertex": "V1", "grid": [0, 0]}]}, "legacy_answer": "S1 90 V1 [2,1]\nS4 180 V3 [2,3]\nS5 180 V1 [3,3]\nS6 0 V1 [0,0]", "solutionText": "S1 90 V1 [2,1]\nS4 180 V3 [2,3]\nS5 180 V1 [3,3]\nS6 0 V1 [0,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-350\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-350/target.png", "shapes": {"S1": "images/voi-350/shape_S1.png", "S2": "images/voi-350/shape_S2.png", "S3": "images/voi-350/shape_S3.png", "S4": "images/voi-350/shape_S4.png", "S5": "images/voi-350/shape_S5.png", "S6": "images/voi-350/shape_S6.png"}}, "__sample_id__": "voi-350"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 6], [1, 6], [1, 4], [4, 4]]}, {"polygon": [[1, 4], [1, 5], [0, 4]]}, {"polygon": [[3, 5], [3, 7], [2, 7], [2, 6], [0, 6], [0, 5]]}, {"polygon": [[1, 8], [1, 5], [2, 5], [2, 8]]}], "meta": {"seed": 4205052, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.295612, "contourComplexity": 46, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.384596, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 352, "strictValidation": true}, "imageAssets": {"target": "../images/voi-351/target.png", "shapes": {"S1": "../images/voi-351/shape_S1.png", "S2": "../images/voi-351/shape_S2.png", "S3": "../images/voi-351/shape_S3.png", "S4": "../images/voi-351/shape_S4.png", "S5": "../images/voi-351/shape_S5.png", "S6": "../images/voi-351/shape_S6.png"}}, "ID": "voi-351", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V4", "grid": [4, 4]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [1, 5]}, {"shape": "S5", "angle": 270, "vertex": "V6", "grid": [0, 5]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [1, 8]}]}, "legacy_answer": "S3 180 V4 [4,4]\nS4 270 V2 [1,5]\nS5 270 V6 [0,5]\nS6 90 V1 [1,8]", "solutionText": "S3 180 V4 [4,4]\nS4 270 V2 [1,5]\nS5 270 V6 [0,5]\nS6 90 V1 [1,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-351\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-351/target.png", "shapes": {"S1": "images/voi-351/shape_S1.png", "S2": "images/voi-351/shape_S2.png", "S3": "images/voi-351/shape_S3.png", "S4": "images/voi-351/shape_S4.png", "S5": "images/voi-351/shape_S5.png", "S6": "images/voi-351/shape_S6.png"}}, "__sample_id__": "voi-351"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[0, 1], [3, 1], [3, 2], [0, 2]]}, {"polygon": [[2, 4], [0, 4], [0, 2], [2, 2]]}, {"polygon": [[1, 6], [1, 3], [3, 3], [3, 6]]}, {"polygon": [[4, 3], [4, 5], [3, 5], [3, 4], [1, 4], [1, 3]]}], "meta": {"seed": 4205053, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.352574, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 353, "strictValidation": true}, "imageAssets": {"target": "../images/voi-352/target.png", "shapes": {"S1": "../images/voi-352/shape_S1.png", "S2": "../images/voi-352/shape_S2.png", "S3": "../images/voi-352/shape_S3.png", "S4": "../images/voi-352/shape_S4.png", "S5": "../images/voi-352/shape_S5.png", "S6": "../images/voi-352/shape_S6.png"}}, "ID": "voi-352", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 2]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 4]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [3, 6]}, {"shape": "S6", "angle": 270, "vertex": "V6", "grid": [1, 3]}]}, "legacy_answer": "S1 0 V3 [3,2]\nS2 180 V2 [0,4]\nS3 90 V4 [3,6]\nS6 270 V6 [1,3]", "solutionText": "S1 0 V3 [3,2]\nS2 180 V2 [0,4]\nS3 90 V4 [3,6]\nS6 270 V6 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-352\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-352/target.png", "shapes": {"S1": "images/voi-352/shape_S1.png", "S2": "images/voi-352/shape_S2.png", "S3": "images/voi-352/shape_S3.png", "S4": "images/voi-352/shape_S4.png", "S5": "images/voi-352/shape_S5.png", "S6": "images/voi-352/shape_S6.png"}}, "__sample_id__": "voi-352"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 3], [5, 3], [5, 5], [2, 5]]}, {"polygon": [[4, 6], [3, 6], [3, 3], [4, 3]]}, {"polygon": [[3, 2], [5, 2], [3, 4]]}, {"polygon": [[3, 5], [3, 4], [4, 5]]}], "meta": {"seed": 4205054, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.345013, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.118652, "difficultyScore": 0.642749, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 354, "strictValidation": true}, "imageAssets": {"target": "../images/voi-353/target.png", "shapes": {"S1": "../images/voi-353/shape_S1.png", "S2": "../images/voi-353/shape_S2.png", "S3": "../images/voi-353/shape_S3.png", "S4": "../images/voi-353/shape_S4.png", "S5": "../images/voi-353/shape_S5.png", "S6": "../images/voi-353/shape_S6.png"}}, "ID": "voi-353", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 5]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [3, 3]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [3, 4]}]}, "legacy_answer": "S1 0 V3 [5,5]\nS2 180 V3 [3,3]\nS4 0 V1 [3,2]\nS5 90 V2 [3,4]", "solutionText": "S1 0 V3 [5,5]\nS2 180 V3 [3,3]\nS4 0 V1 [3,2]\nS5 90 V2 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-353\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-353/target.png", "shapes": {"S1": "images/voi-353/shape_S1.png", "S2": "images/voi-353/shape_S2.png", "S3": "images/voi-353/shape_S3.png", "S4": "images/voi-353/shape_S4.png", "S5": "images/voi-353/shape_S5.png", "S6": "images/voi-353/shape_S6.png"}}, "__sample_id__": "voi-353"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 3], [7, 5], [5, 3]]}, {"polygon": [[5, 5], [8, 5], [8, 7], [5, 7]]}, {"polygon": [[7, 4], [8, 4], [8, 5], [7, 5]]}, {"polygon": [[5, 3], [7, 3], [7, 5], [5, 5]]}], "meta": {"seed": 4205055, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 68, "connectedComponents": 1, "fillRatio": 0.139648, "difficultyScore": 0.483861, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 355, "strictValidation": true}, "imageAssets": {"target": "../images/voi-354/target.png", "shapes": {"S1": "../images/voi-354/shape_S1.png", "S2": "../images/voi-354/shape_S2.png", "S3": "../images/voi-354/shape_S3.png", "S4": "../images/voi-354/shape_S4.png", "S5": "../images/voi-354/shape_S5.png", "S6": "../images/voi-354/shape_S6.png"}}, "ID": "voi-354", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [5, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [5, 5]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [8, 4]}, {"shape": "S6", "angle": 0, "vertex": "V4", "grid": [5, 5]}]}, "legacy_answer": "S1 270 V3 [5,3]\nS2 0 V1 [5,5]\nS3 0 V2 [8,4]\nS6 0 V4 [5,5]", "solutionText": "S1 270 V3 [5,3]\nS2 0 V1 [5,5]\nS3 0 V2 [8,4]\nS6 0 V4 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-354\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-354/target.png", "shapes": {"S1": "images/voi-354/shape_S1.png", "S2": "images/voi-354/shape_S2.png", "S3": "images/voi-354/shape_S3.png", "S4": "images/voi-354/shape_S4.png", "S5": "images/voi-354/shape_S5.png", "S6": "images/voi-354/shape_S6.png"}}, "__sample_id__": "voi-354"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 2], [5, 5], [4, 4], [4, 2]]}, {"polygon": [[7, 5], [7, 6], [6, 6], [6, 5]]}, {"polygon": [[5, 5], [5, 3], [7, 3], [7, 5]]}, {"polygon": [[7, 3], [7, 4], [6, 4], [6, 3]]}], "meta": {"seed": 4205056, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.558169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 356, "strictValidation": true}, "imageAssets": {"target": "../images/voi-355/target.png", "shapes": {"S1": "../images/voi-355/shape_S1.png", "S2": "../images/voi-355/shape_S2.png", "S3": "../images/voi-355/shape_S3.png", "S4": "../images/voi-355/shape_S4.png", "S5": "../images/voi-355/shape_S5.png", "S6": "../images/voi-355/shape_S6.png"}}, "ID": "voi-355", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V1", "grid": [5, 2]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [6, 5]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [7, 5]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [6, 3]}]}, "legacy_answer": "S3 270 V1 [5,2]\nS4 270 V4 [6,5]\nS5 90 V4 [7,5]\nS6 270 V4 [6,3]", "solutionText": "S3 270 V1 [5,2]\nS4 270 V4 [6,5]\nS5 90 V4 [7,5]\nS6 270 V4 [6,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-355\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-355/target.png", "shapes": {"S1": "images/voi-355/shape_S1.png", "S2": "images/voi-355/shape_S2.png", "S3": "images/voi-355/shape_S3.png", "S4": "images/voi-355/shape_S4.png", "S5": "images/voi-355/shape_S5.png", "S6": "images/voi-355/shape_S6.png"}}, "__sample_id__": "voi-355"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 3], [4, 1], [6, 1], [6, 3]]}, {"polygon": [[5, 3], [8, 3], [8, 4], [5, 4]]}, {"polygon": [[7, 2], [7, 5], [6, 5], [6, 2]]}, {"polygon": [[6, 1], [8, 1], [8, 2], [7, 2], [7, 4], [6, 4]]}], "meta": {"seed": 4205057, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.330357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 357, "strictValidation": true}, "imageAssets": {"target": "../images/voi-356/target.png", "shapes": {"S1": "../images/voi-356/shape_S1.png", "S2": "../images/voi-356/shape_S2.png", "S3": "../images/voi-356/shape_S3.png", "S4": "../images/voi-356/shape_S4.png", "S5": "../images/voi-356/shape_S5.png", "S6": "../images/voi-356/shape_S6.png"}}, "ID": "voi-356", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [6, 1]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [8, 4]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [7, 5]}, {"shape": "S6", "angle": 0, "vertex": "V6", "grid": [6, 4]}]}, "legacy_answer": "S1 90 V3 [6,1]\nS4 0 V3 [8,4]\nS5 270 V2 [7,5]\nS6 0 V6 [6,4]", "solutionText": "S1 90 V3 [6,1]\nS4 0 V3 [8,4]\nS5 270 V2 [7,5]\nS6 0 V6 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-356\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-356/target.png", "shapes": {"S1": "images/voi-356/shape_S1.png", "S2": "images/voi-356/shape_S2.png", "S3": "images/voi-356/shape_S3.png", "S4": "images/voi-356/shape_S4.png", "S5": "images/voi-356/shape_S5.png", "S6": "images/voi-356/shape_S6.png"}}, "__sample_id__": "voi-356"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 6], [2, 5], [3, 5], [3, 6]]}, {"polygon": [[4, 5], [4, 2], [5, 3], [5, 5]]}, {"polygon": [[1, 6], [1, 4], [3, 4], [3, 6]]}, {"polygon": [[2, 5], [5, 5], [4, 6], [2, 6]]}], "meta": {"seed": 4205058, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.198758, "contourComplexity": 68, "connectedComponents": 1, "fillRatio": 0.125977, "difficultyScore": 0.653016, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 358, "strictValidation": true}, "imageAssets": {"target": "../images/voi-357/target.png", "shapes": {"S1": "../images/voi-357/shape_S1.png", "S2": "../images/voi-357/shape_S2.png", "S3": "../images/voi-357/shape_S3.png", "S4": "../images/voi-357/shape_S4.png", "S5": "../images/voi-357/shape_S5.png", "S6": "../images/voi-357/shape_S6.png"}}, "ID": "voi-357", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [2, 5]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [4, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [1, 6]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [2, 5]}]}, "legacy_answer": "S1 90 V2 [2,5]\nS2 90 V2 [4,2]\nS4 90 V1 [1,6]\nS5 0 V1 [2,5]", "solutionText": "S1 90 V2 [2,5]\nS2 90 V2 [4,2]\nS4 90 V1 [1,6]\nS5 0 V1 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-357\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-357/target.png", "shapes": {"S1": "images/voi-357/shape_S1.png", "S2": "images/voi-357/shape_S2.png", "S3": "images/voi-357/shape_S3.png", "S4": "images/voi-357/shape_S4.png", "S5": "images/voi-357/shape_S5.png", "S6": "images/voi-357/shape_S6.png"}}, "__sample_id__": "voi-357"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[5, 3], [5, 5], [3, 3]]}, {"polygon": [[4, 3], [4, 1], [6, 3]]}, {"polygon": [[5, 3], [5, 0], [7, 0], [7, 3]]}, {"polygon": [[8, 4], [5, 4], [5, 2], [8, 2]]}], "meta": {"seed": 4205059, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.248062, "contourComplexity": 138, "connectedComponents": 1, "fillRatio": 0.189453, "difficultyScore": 0.328846, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 359, "strictValidation": true}, "imageAssets": {"target": "../images/voi-358/target.png", "shapes": {"S1": "../images/voi-358/shape_S1.png", "S2": "../images/voi-358/shape_S2.png", "S3": "../images/voi-358/shape_S3.png", "S4": "../images/voi-358/shape_S4.png", "S5": "../images/voi-358/shape_S5.png", "S6": "../images/voi-358/shape_S6.png"}}, "ID": "voi-358", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 5]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [4, 1]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [5, 0]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [8, 2]}]}, "legacy_answer": "S2 270 V2 [5,5]\nS3 90 V2 [4,1]\nS4 90 V2 [5,0]\nS5 180 V4 [8,2]", "solutionText": "S2 270 V2 [5,5]\nS3 90 V2 [4,1]\nS4 90 V2 [5,0]\nS5 180 V4 [8,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-358\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-358/target.png", "shapes": {"S1": "images/voi-358/shape_S1.png", "S2": "images/voi-358/shape_S2.png", "S3": "images/voi-358/shape_S3.png", "S4": "images/voi-358/shape_S4.png", "S5": "images/voi-358/shape_S5.png", "S6": "images/voi-358/shape_S6.png"}}, "__sample_id__": "voi-358"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 6], [1, 6], [1, 3]]}, {"polygon": [[2, 5], [2, 8], [0, 8], [0, 5]]}, {"polygon": [[0, 3], [0, 1], [2, 3]]}, {"polygon": [[2, 7], [1, 7], [1, 5], [2, 5]]}], "meta": {"seed": 4205060, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.188477, "difficultyScore": 0.326938, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 360, "strictValidation": true}, "imageAssets": {"target": "../images/voi-359/target.png", "shapes": {"S1": "../images/voi-359/shape_S1.png", "S2": "../images/voi-359/shape_S2.png", "S3": "../images/voi-359/shape_S3.png", "S4": "../images/voi-359/shape_S4.png", "S5": "../images/voi-359/shape_S5.png", "S6": "../images/voi-359/shape_S6.png"}}, "ID": "voi-359", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 3]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [0, 8]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [2, 3]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [1, 7]}]}, "legacy_answer": "S1 270 V1 [3,3]\nS3 270 V3 [0,8]\nS4 90 V3 [2,3]\nS5 180 V2 [1,7]", "solutionText": "S1 270 V1 [3,3]\nS3 270 V3 [0,8]\nS4 90 V3 [2,3]\nS5 180 V2 [1,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-359\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-359/target.png", "shapes": {"S1": "images/voi-359/shape_S1.png", "S2": "images/voi-359/shape_S2.png", "S3": "images/voi-359/shape_S3.png", "S4": "images/voi-359/shape_S4.png", "S5": "images/voi-359/shape_S5.png", "S6": "images/voi-359/shape_S6.png"}}, "__sample_id__": "voi-359"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 4], [2, 6], [0, 6], [0, 4]]}, {"polygon": [[4, 2], [4, 5], [2, 5], [2, 2]]}, {"polygon": [[5, 3], [5, 5], [3, 3]]}, {"polygon": [[5, 1], [5, 4], [4, 4], [4, 1]]}], "meta": {"seed": 4205061, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.20332, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.511722, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 361, "strictValidation": true}, "imageAssets": {"target": "../images/voi-360/target.png", "shapes": {"S1": "../images/voi-360/shape_S1.png", "S2": "../images/voi-360/shape_S2.png", "S3": "../images/voi-360/shape_S3.png", "S4": "../images/voi-360/shape_S4.png", "S5": "../images/voi-360/shape_S5.png", "S6": "../images/voi-360/shape_S6.png"}}, "ID": "voi-360", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [2, 4]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [2, 5]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [3, 3]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [4, 1]}]}, "legacy_answer": "S1 270 V1 [2,4]\nS4 270 V3 [2,5]\nS5 270 V3 [3,3]\nS6 270 V4 [4,1]", "solutionText": "S1 270 V1 [2,4]\nS4 270 V3 [2,5]\nS5 270 V3 [3,3]\nS6 270 V4 [4,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-360\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-360/target.png", "shapes": {"S1": "images/voi-360/shape_S1.png", "S2": "images/voi-360/shape_S2.png", "S3": "images/voi-360/shape_S3.png", "S4": "images/voi-360/shape_S4.png", "S5": "images/voi-360/shape_S5.png", "S6": "images/voi-360/shape_S6.png"}}, "__sample_id__": "voi-360"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 4], [5, 3], [5, 1]]}, {"polygon": [[6, 4], [3, 4], [3, 2], [6, 2]]}, {"polygon": [[6, 2], [6, 3], [5, 2]]}, {"polygon": [[4, 1], [4, 2], [3, 1]]}], "meta": {"seed": 4205062, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319218, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.572771, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 362, "strictValidation": true}, "imageAssets": {"target": "../images/voi-361/target.png", "shapes": {"S1": "../images/voi-361/shape_S1.png", "S2": "../images/voi-361/shape_S2.png", "S3": "../images/voi-361/shape_S3.png", "S4": "../images/voi-361/shape_S4.png", "S5": "../images/voi-361/shape_S5.png", "S6": "../images/voi-361/shape_S6.png"}}, "ID": "voi-361", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [5, 1]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [6, 2]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [6, 3]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S2 270 V4 [5,1]\nS3 180 V4 [6,2]\nS4 270 V2 [6,3]\nS5 270 V2 [4,2]", "solutionText": "S2 270 V4 [5,1]\nS3 180 V4 [6,2]\nS4 270 V2 [6,3]\nS5 270 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-361\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-361/target.png", "shapes": {"S1": "images/voi-361/shape_S1.png", "S2": "images/voi-361/shape_S2.png", "S3": "images/voi-361/shape_S3.png", "S4": "images/voi-361/shape_S4.png", "S5": "images/voi-361/shape_S5.png", "S6": "images/voi-361/shape_S6.png"}}, "__sample_id__": "voi-361"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 4], [6, 4], [6, 6], [4, 6]]}, {"polygon": [[5, 4], [8, 4], [7, 5], [5, 5]]}, {"polygon": [[5, 3], [6, 3], [6, 6], [5, 6]]}, {"polygon": [[8, 5], [8, 7], [7, 7], [7, 6], [5, 6], [5, 5]]}], "meta": {"seed": 4205063, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.295612, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.384596, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 363, "strictValidation": true}, "imageAssets": {"target": "../images/voi-362/target.png", "shapes": {"S1": "../images/voi-362/shape_S1.png", "S2": "../images/voi-362/shape_S2.png", "S3": "../images/voi-362/shape_S3.png", "S4": "../images/voi-362/shape_S4.png", "S5": "../images/voi-362/shape_S5.png", "S6": "../images/voi-362/shape_S6.png"}}, "ID": "voi-362", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [6, 6]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 5]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [5, 6]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [8, 7]}]}, "legacy_answer": "S2 0 V3 [6,6]\nS4 0 V4 [5,5]\nS5 0 V4 [5,6]\nS6 270 V2 [8,7]", "solutionText": "S2 0 V3 [6,6]\nS4 0 V4 [5,5]\nS5 0 V4 [5,6]\nS6 270 V2 [8,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-362\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-362/target.png", "shapes": {"S1": "images/voi-362/shape_S1.png", "S2": "images/voi-362/shape_S2.png", "S3": "images/voi-362/shape_S3.png", "S4": "images/voi-362/shape_S4.png", "S5": "images/voi-362/shape_S5.png", "S6": "images/voi-362/shape_S6.png"}}, "__sample_id__": "voi-362"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[7, 6], [5, 6], [7, 4]]}, {"polygon": [[5, 6], [3, 6], [3, 5], [4, 5], [4, 3], [5, 3]]}, {"polygon": [[5, 5], [2, 5], [2, 3], [5, 3]]}], "meta": {"seed": 4205064, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.280277, "contourComplexity": 79, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.214857, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 364, "strictValidation": true}, "imageAssets": {"target": "../images/voi-363/target.png", "shapes": {"S1": "../images/voi-363/shape_S1.png", "S2": "../images/voi-363/shape_S2.png", "S3": "../images/voi-363/shape_S3.png", "S4": "../images/voi-363/shape_S4.png", "S5": "../images/voi-363/shape_S5.png", "S6": "../images/voi-363/shape_S6.png"}}, "ID": "voi-363", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [8, 5]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [7, 6]}, {"shape": "S5", "angle": 180, "vertex": "V5", "grid": [4, 3]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [2, 3]}]}, "legacy_answer": "S2 0 V3 [8,5]\nS4 180 V1 [7,6]\nS5 180 V5 [4,3]\nS6 180 V3 [2,3]", "solutionText": "S2 0 V3 [8,5]\nS4 180 V1 [7,6]\nS5 180 V5 [4,3]\nS6 180 V3 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-363\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-363/target.png", "shapes": {"S1": "images/voi-363/shape_S1.png", "S2": "images/voi-363/shape_S2.png", "S3": "images/voi-363/shape_S3.png", "S4": "images/voi-363/shape_S4.png", "S5": "images/voi-363/shape_S5.png", "S6": "images/voi-363/shape_S6.png"}}, "__sample_id__": "voi-363"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 2], [4, 5], [3, 4], [3, 2]]}, {"polygon": [[5, 6], [5, 3], [6, 4], [6, 6]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[4, 2], [4, 4], [3, 4], [3, 3], [1, 3], [1, 2]]}], "meta": {"seed": 4205065, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.172852, "difficultyScore": 0.292056, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 365, "strictValidation": true}, "imageAssets": {"target": "../images/voi-364/target.png", "shapes": {"S1": "../images/voi-364/shape_S1.png", "S2": "../images/voi-364/shape_S2.png", "S3": "../images/voi-364/shape_S3.png", "S4": "../images/voi-364/shape_S4.png", "S5": "../images/voi-364/shape_S5.png", "S6": "../images/voi-364/shape_S6.png"}}, "ID": "voi-364", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [3, 2]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 4]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [3, 4]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [3, 4]}]}, "legacy_answer": "S2 270 V4 [3,2]\nS3 90 V3 [6,4]\nS5 270 V3 [3,4]\nS6 270 V3 [3,4]", "solutionText": "S2 270 V4 [3,2]\nS3 90 V3 [6,4]\nS5 270 V3 [3,4]\nS6 270 V3 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-364\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-364/target.png", "shapes": {"S1": "images/voi-364/shape_S1.png", "S2": "images/voi-364/shape_S2.png", "S3": "images/voi-364/shape_S3.png", "S4": "images/voi-364/shape_S4.png", "S5": "images/voi-364/shape_S5.png", "S6": "images/voi-364/shape_S6.png"}}, "__sample_id__": "voi-364"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [7, 4], [7, 6], [4, 6]]}, {"polygon": [[3, 6], [5, 6], [3, 8]]}, {"polygon": [[2, 7], [2, 6], [5, 6], [5, 7]]}, {"polygon": [[6, 8], [3, 8], [3, 6], [6, 6]]}], "meta": {"seed": 4205066, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.296703, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.311813, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 366, "strictValidation": true}, "imageAssets": {"target": "../images/voi-365/target.png", "shapes": {"S1": "../images/voi-365/shape_S1.png", "S2": "../images/voi-365/shape_S2.png", "S3": "../images/voi-365/shape_S3.png", "S4": "../images/voi-365/shape_S4.png", "S5": "../images/voi-365/shape_S5.png", "S6": "../images/voi-365/shape_S6.png"}}, "ID": "voi-365", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [7, 6]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [5, 6]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [5, 6]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [3, 6]}]}, "legacy_answer": "S2 0 V3 [7,6]\nS4 0 V2 [5,6]\nS5 90 V3 [5,6]\nS6 180 V3 [3,6]", "solutionText": "S2 0 V3 [7,6]\nS4 0 V2 [5,6]\nS5 90 V3 [5,6]\nS6 180 V3 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-365\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-365/target.png", "shapes": {"S1": "images/voi-365/shape_S1.png", "S2": "images/voi-365/shape_S2.png", "S3": "images/voi-365/shape_S3.png", "S4": "images/voi-365/shape_S4.png", "S5": "images/voi-365/shape_S5.png", "S6": "images/voi-365/shape_S6.png"}}, "__sample_id__": "voi-365"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [3, 5], [3, 2], [4, 2]]}, {"polygon": [[6, 3], [4, 3], [4, 1], [6, 1]]}, {"polygon": [[1, 4], [4, 4], [4, 5], [1, 5]]}, {"polygon": [[4, 4], [4, 5], [3, 4]]}], "meta": {"seed": 4205067, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.673755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 367, "strictValidation": true}, "imageAssets": {"target": "../images/voi-366/target.png", "shapes": {"S1": "../images/voi-366/shape_S1.png", "S2": "../images/voi-366/shape_S2.png", "S3": "../images/voi-366/shape_S3.png", "S4": "../images/voi-366/shape_S4.png", "S5": "../images/voi-366/shape_S5.png", "S6": "../images/voi-366/shape_S6.png"}}, "ID": "voi-366", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [4, 2]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [4, 1]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [1, 5]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [3, 4]}]}, "legacy_answer": "S1 180 V4 [4,2]\nS2 180 V3 [4,1]\nS3 0 V4 [1,5]\nS5 270 V3 [3,4]", "solutionText": "S1 180 V4 [4,2]\nS2 180 V3 [4,1]\nS3 0 V4 [1,5]\nS5 270 V3 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-366\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-366/target.png", "shapes": {"S1": "images/voi-366/shape_S1.png", "S2": "images/voi-366/shape_S2.png", "S3": "images/voi-366/shape_S3.png", "S4": "images/voi-366/shape_S4.png", "S5": "images/voi-366/shape_S5.png", "S6": "images/voi-366/shape_S6.png"}}, "__sample_id__": "voi-366"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[8, 1], [8, 2], [5, 2], [5, 1]]}, {"polygon": [[8, 5], [5, 5], [5, 3], [8, 3]]}, {"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}, {"polygon": [[3, 3], [3, 2], [6, 2], [6, 3]]}], "meta": {"seed": 4205068, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 368, "strictValidation": true}, "imageAssets": {"target": "../images/voi-367/target.png", "shapes": {"S1": "../images/voi-367/shape_S1.png", "S2": "../images/voi-367/shape_S2.png", "S3": "../images/voi-367/shape_S3.png", "S4": "../images/voi-367/shape_S4.png", "S5": "../images/voi-367/shape_S5.png", "S6": "../images/voi-367/shape_S6.png"}}, "ID": "voi-367", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 1]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [8, 5]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [3, 2]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S1 270 V4 [5,1]\nS4 180 V1 [8,5]\nS5 180 V3 [3,2]\nS6 90 V1 [3,3]", "solutionText": "S1 270 V4 [5,1]\nS4 180 V1 [8,5]\nS5 180 V3 [3,2]\nS6 90 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-367\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-367/target.png", "shapes": {"S1": "images/voi-367/shape_S1.png", "S2": "images/voi-367/shape_S2.png", "S3": "images/voi-367/shape_S3.png", "S4": "images/voi-367/shape_S4.png", "S5": "images/voi-367/shape_S5.png", "S6": "images/voi-367/shape_S6.png"}}, "__sample_id__": "voi-367"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 4], [5, 4], [7, 2]]}, {"polygon": [[6, 4], [6, 7], [4, 7], [4, 4]]}, {"polygon": [[5, 3], [5, 5], [4, 5], [4, 4], [2, 4], [2, 3]]}, {"polygon": [[5, 6], [5, 7], [4, 7], [4, 6]]}], "meta": {"seed": 4205069, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.30622, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.141602, "difficultyScore": 0.441677, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 369, "strictValidation": true}, "imageAssets": {"target": "../images/voi-368/target.png", "shapes": {"S1": "../images/voi-368/shape_S1.png", "S2": "../images/voi-368/shape_S2.png", "S3": "../images/voi-368/shape_S3.png", "S4": "../images/voi-368/shape_S4.png", "S5": "../images/voi-368/shape_S5.png", "S6": "../images/voi-368/shape_S6.png"}}, "ID": "voi-368", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [6, 7]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [4, 4]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [4, 6]}]}, "legacy_answer": "S3 180 V2 [5,4]\nS4 270 V2 [6,7]\nS5 270 V4 [4,4]\nS6 270 V4 [4,6]", "solutionText": "S3 180 V2 [5,4]\nS4 270 V2 [6,7]\nS5 270 V4 [4,4]\nS6 270 V4 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-368\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-368/target.png", "shapes": {"S1": "images/voi-368/shape_S1.png", "S2": "images/voi-368/shape_S2.png", "S3": "images/voi-368/shape_S3.png", "S4": "images/voi-368/shape_S4.png", "S5": "images/voi-368/shape_S5.png", "S6": "images/voi-368/shape_S6.png"}}, "__sample_id__": "voi-368"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [5, 6], [5, 7], [3, 7]]}, {"polygon": [[3, 4], [5, 4], [5, 5], [4, 5], [4, 7], [3, 7]]}, {"polygon": [[3, 8], [3, 6], [4, 6], [4, 7], [6, 7], [6, 8]]}, {"polygon": [[6, 6], [5, 6], [5, 4], [6, 4]]}], "meta": {"seed": 4205070, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.720833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 370, "strictValidation": true}, "imageAssets": {"target": "../images/voi-369/target.png", "shapes": {"S1": "../images/voi-369/shape_S1.png", "S2": "../images/voi-369/shape_S2.png", "S3": "../images/voi-369/shape_S3.png", "S4": "../images/voi-369/shape_S4.png", "S5": "../images/voi-369/shape_S5.png", "S6": "../images/voi-369/shape_S6.png"}}, "ID": "voi-369", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 6]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [5, 5]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 6]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [5, 4]}]}, "legacy_answer": "S1 0 V2 [5,6]\nS3 0 V3 [5,5]\nS4 90 V3 [4,6]\nS6 180 V3 [5,4]", "solutionText": "S1 0 V2 [5,6]\nS3 0 V3 [5,5]\nS4 90 V3 [4,6]\nS6 180 V3 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-369\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-369/target.png", "shapes": {"S1": "images/voi-369/shape_S1.png", "S2": "images/voi-369/shape_S2.png", "S3": "images/voi-369/shape_S3.png", "S4": "images/voi-369/shape_S4.png", "S5": "images/voi-369/shape_S5.png", "S6": "images/voi-369/shape_S6.png"}}, "__sample_id__": "voi-369"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [2, 3], [2, 1], [5, 1]]}, {"polygon": [[0, 2], [2, 2], [0, 4]]}, {"polygon": [[1, 2], [1, 1], [3, 1], [3, 2]]}, {"polygon": [[6, 3], [6, 4], [4, 4], [4, 3]]}], "meta": {"seed": 4205071, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.165803, "contourComplexity": 78, "connectedComponents": 1, "fillRatio": 0.157227, "difficultyScore": 0.722334, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 371, "strictValidation": true}, "imageAssets": {"target": "../images/voi-370/target.png", "shapes": {"S1": "../images/voi-370/shape_S1.png", "S2": "../images/voi-370/shape_S2.png", "S3": "../images/voi-370/shape_S3.png", "S4": "../images/voi-370/shape_S4.png", "S5": "../images/voi-370/shape_S5.png", "S6": "../images/voi-370/shape_S6.png"}}, "ID": "voi-370", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V4", "grid": [5, 1]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [0, 2]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [1, 2]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [4, 3]}]}, "legacy_answer": "S3 180 V4 [5,1]\nS4 0 V1 [0,2]\nS5 90 V1 [1,2]\nS6 270 V4 [4,3]", "solutionText": "S3 180 V4 [5,1]\nS4 0 V1 [0,2]\nS5 90 V1 [1,2]\nS6 270 V4 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-370\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-370/target.png", "shapes": {"S1": "images/voi-370/shape_S1.png", "S2": "images/voi-370/shape_S2.png", "S3": "images/voi-370/shape_S3.png", "S4": "images/voi-370/shape_S4.png", "S5": "images/voi-370/shape_S5.png", "S6": "images/voi-370/shape_S6.png"}}, "__sample_id__": "voi-370"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [0, 4], [0, 2], [3, 2]]}, {"polygon": [[1, 3], [1, 6], [0, 6], [0, 3]]}, {"polygon": [[3, 8], [1, 8], [1, 7], [2, 7], [2, 5], [3, 5]]}, {"polygon": [[3, 4], [3, 7], [1, 7], [1, 4]]}], "meta": {"seed": 4205072, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.203125, "difficultyScore": 0.356908, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 372, "strictValidation": true}, "imageAssets": {"target": "../images/voi-371/target.png", "shapes": {"S1": "../images/voi-371/shape_S1.png", "S2": "../images/voi-371/shape_S2.png", "S3": "../images/voi-371/shape_S3.png", "S4": "../images/voi-371/shape_S4.png", "S5": "../images/voi-371/shape_S5.png", "S6": "../images/voi-371/shape_S6.png"}}, "ID": "voi-371", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [3, 4]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 6]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [1, 7]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [1, 4]}]}, "legacy_answer": "S1 180 V1 [3,4]\nS2 270 V3 [0,6]\nS4 180 V3 [1,7]\nS5 270 V4 [1,4]", "solutionText": "S1 180 V1 [3,4]\nS2 270 V3 [0,6]\nS4 180 V3 [1,7]\nS5 270 V4 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-371\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-371/target.png", "shapes": {"S1": "images/voi-371/shape_S1.png", "S2": "images/voi-371/shape_S2.png", "S3": "images/voi-371/shape_S3.png", "S4": "images/voi-371/shape_S4.png", "S5": "images/voi-371/shape_S5.png", "S6": "images/voi-371/shape_S6.png"}}, "__sample_id__": "voi-371"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 5], [6, 5], [6, 7], [5, 7]]}, {"polygon": [[4, 5], [7, 5], [7, 6], [4, 6]]}, {"polygon": [[1, 7], [1, 5], [2, 5], [2, 6], [4, 6], [4, 7]]}, {"polygon": [[6, 7], [4, 7], [6, 5]]}], "meta": {"seed": 4205073, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.361582, "contourComplexity": 75, "connectedComponents": 1, "fillRatio": 0.110352, "difficultyScore": 0.725625, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 373, "strictValidation": true}, "imageAssets": {"target": "../images/voi-372/target.png", "shapes": {"S1": "../images/voi-372/shape_S1.png", "S2": "../images/voi-372/shape_S2.png", "S3": "../images/voi-372/shape_S3.png", "S4": "../images/voi-372/shape_S4.png", "S5": "../images/voi-372/shape_S5.png", "S6": "../images/voi-372/shape_S6.png"}}, "ID": "voi-372", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [5, 5]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 5]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [1, 5]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [6, 7]}]}, "legacy_answer": "S1 0 V1 [5,5]\nS3 0 V2 [7,5]\nS5 90 V2 [1,5]\nS6 180 V1 [6,7]", "solutionText": "S1 0 V1 [5,5]\nS3 0 V2 [7,5]\nS5 90 V2 [1,5]\nS6 180 V1 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-372\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-372/target.png", "shapes": {"S1": "images/voi-372/shape_S1.png", "S2": "images/voi-372/shape_S2.png", "S3": "images/voi-372/shape_S3.png", "S4": "images/voi-372/shape_S4.png", "S5": "images/voi-372/shape_S5.png", "S6": "images/voi-372/shape_S6.png"}}, "__sample_id__": "voi-372"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 0], [4, 0], [3, 1], [1, 1]]}, {"polygon": [[1, 4], [1, 3], [3, 3], [3, 4]]}, {"polygon": [[4, 0], [5, 0], [5, 3], [4, 3]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}], "meta": {"seed": 4205074, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.295612, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.148926, "difficultyScore": 0.384596, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 374, "strictValidation": true}, "imageAssets": {"target": "../images/voi-373/target.png", "shapes": {"S1": "../images/voi-373/shape_S1.png", "S2": "../images/voi-373/shape_S2.png", "S3": "../images/voi-373/shape_S3.png", "S4": "../images/voi-373/shape_S4.png", "S5": "../images/voi-373/shape_S5.png", "S6": "../images/voi-373/shape_S6.png"}}, "ID": "voi-373", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 0]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 4]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [4, 0]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [5, 1]}]}, "legacy_answer": "S1 0 V2 [4,0]\nS2 90 V1 [1,4]\nS3 0 V1 [4,0]\nS5 90 V3 [5,1]", "solutionText": "S1 0 V2 [4,0]\nS2 90 V1 [1,4]\nS3 0 V1 [4,0]\nS5 90 V3 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-373\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-373/target.png", "shapes": {"S1": "images/voi-373/shape_S1.png", "S2": "images/voi-373/shape_S2.png", "S3": "images/voi-373/shape_S3.png", "S4": "images/voi-373/shape_S4.png", "S5": "images/voi-373/shape_S5.png", "S6": "images/voi-373/shape_S6.png"}}, "__sample_id__": "voi-373"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[1, 3], [1, 0], [3, 0], [3, 3]]}, {"polygon": [[6, 2], [6, 4], [5, 4], [5, 3], [3, 3], [3, 2]]}, {"polygon": [[7, 5], [4, 5], [4, 3], [7, 3]]}, {"polygon": [[6, 3], [6, 4], [3, 4], [3, 3]]}], "meta": {"seed": 4205075, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.210526, "contourComplexity": 17, "connectedComponents": 1, "fillRatio": 0.234375, "difficultyScore": 0.389145, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 375, "strictValidation": true}, "imageAssets": {"target": "../images/voi-374/target.png", "shapes": {"S1": "../images/voi-374/shape_S1.png", "S2": "../images/voi-374/shape_S2.png", "S3": "../images/voi-374/shape_S3.png", "S4": "../images/voi-374/shape_S4.png", "S5": "../images/voi-374/shape_S5.png", "S6": "../images/voi-374/shape_S6.png"}}, "ID": "voi-374", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [1, 0]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [5, 3]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 5]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S1 90 V2 [1,0]\nS2 270 V4 [5,3]\nS3 180 V2 [4,5]\nS6 270 V2 [6,4]", "solutionText": "S1 90 V2 [1,0]\nS2 270 V4 [5,3]\nS3 180 V2 [4,5]\nS6 270 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-374\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-374/target.png", "shapes": {"S1": "images/voi-374/shape_S1.png", "S2": "images/voi-374/shape_S2.png", "S3": "images/voi-374/shape_S3.png", "S4": "images/voi-374/shape_S4.png", "S5": "images/voi-374/shape_S5.png", "S6": "images/voi-374/shape_S6.png"}}, "__sample_id__": "voi-374"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [6, 4], [6, 6], [3, 6]]}, {"polygon": [[3, 4], [5, 4], [5, 5], [3, 5]]}, {"polygon": [[3, 0], [5, 0], [5, 2], [3, 2]]}, {"polygon": [[6, 2], [6, 5], [4, 5], [4, 2]]}], "meta": {"seed": 4206001, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.12, "difficultyScore": 0.493333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 376, "strictValidation": true}, "imageAssets": {"target": "../images/voi-375/target.png", "shapes": {"S1": "../images/voi-375/shape_S1.png", "S2": "../images/voi-375/shape_S2.png", "S3": "../images/voi-375/shape_S3.png", "S4": "../images/voi-375/shape_S4.png", "S5": "../images/voi-375/shape_S5.png", "S6": "../images/voi-375/shape_S6.png"}}, "ID": "voi-375", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 4]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [3, 5]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [5, 2]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [4, 5]}]}, "legacy_answer": "S1 0 V2 [6,4]\nS2 0 V4 [3,5]\nS5 0 V3 [5,2]\nS6 270 V3 [4,5]", "solutionText": "S1 0 V2 [6,4]\nS2 0 V4 [3,5]\nS5 0 V3 [5,2]\nS6 270 V3 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-375\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-375/target.png", "shapes": {"S1": "images/voi-375/shape_S1.png", "S2": "images/voi-375/shape_S2.png", "S3": "images/voi-375/shape_S3.png", "S4": "images/voi-375/shape_S4.png", "S5": "images/voi-375/shape_S5.png", "S6": "images/voi-375/shape_S6.png"}}, "__sample_id__": "voi-375"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 7], [0, 5], [1, 5], [1, 6], [3, 6], [3, 7]]}, {"polygon": [[8, 3], [10, 3], [10, 4], [9, 4], [9, 6], [8, 6]]}, {"polygon": [[10, 3], [10, 4], [7, 4], [7, 3]]}, {"polygon": [[8, 4], [8, 2], [10, 2], [10, 4]]}], "meta": {"seed": 4206002, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 377, "strictValidation": true}, "imageAssets": {"target": "../images/voi-376/target.png", "shapes": {"S1": "../images/voi-376/shape_S1.png", "S2": "../images/voi-376/shape_S2.png", "S3": "../images/voi-376/shape_S3.png", "S4": "../images/voi-376/shape_S4.png", "S5": "../images/voi-376/shape_S5.png", "S6": "../images/voi-376/shape_S6.png"}}, "ID": "voi-376", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V5", "grid": [3, 6]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [10, 3]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [7, 4]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [10, 4]}]}, "legacy_answer": "S2 90 V5 [3,6]\nS3 0 V2 [10,3]\nS4 270 V3 [7,4]\nS5 90 V4 [10,4]", "solutionText": "S2 90 V5 [3,6]\nS3 0 V2 [10,3]\nS4 270 V3 [7,4]\nS5 90 V4 [10,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-376\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-376/target.png", "shapes": {"S1": "images/voi-376/shape_S1.png", "S2": "images/voi-376/shape_S2.png", "S3": "images/voi-376/shape_S3.png", "S4": "images/voi-376/shape_S4.png", "S5": "images/voi-376/shape_S5.png", "S6": "images/voi-376/shape_S6.png"}}, "__sample_id__": "voi-376"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [2, 7], [0, 7], [0, 5]]}, {"polygon": [[0, 6], [3, 6], [2, 7], [0, 7]]}, {"polygon": [[3, 2], [5, 2], [5, 4], [3, 4]]}, {"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}], "meta": {"seed": 4206003, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.241966, "contourComplexity": 42, "connectedComponents": 2, "fillRatio": 0.125312, "difficultyScore": 0.831511, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 378, "strictValidation": true}, "imageAssets": {"target": "../images/voi-377/target.png", "shapes": {"S1": "../images/voi-377/shape_S1.png", "S2": "../images/voi-377/shape_S2.png", "S3": "../images/voi-377/shape_S3.png", "S4": "../images/voi-377/shape_S4.png", "S5": "../images/voi-377/shape_S5.png", "S6": "../images/voi-377/shape_S6.png"}}, "ID": "voi-377", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [2, 5]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [0, 7]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [5, 2]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [3, 7]}]}, "legacy_answer": "S1 270 V1 [2,5]\nS2 0 V4 [0,7]\nS5 0 V2 [5,2]\nS6 90 V1 [3,7]", "solutionText": "S1 270 V1 [2,5]\nS2 0 V4 [0,7]\nS5 0 V2 [5,2]\nS6 90 V1 [3,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-377\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-377/target.png", "shapes": {"S1": "images/voi-377/shape_S1.png", "S2": "images/voi-377/shape_S2.png", "S3": "images/voi-377/shape_S3.png", "S4": "images/voi-377/shape_S4.png", "S5": "images/voi-377/shape_S5.png", "S6": "images/voi-377/shape_S6.png"}}, "__sample_id__": "voi-377"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 0], [9, 0], [7, 2]]}, {"polygon": [[7, 2], [9, 2], [9, 3], [7, 3]]}, {"polygon": [[4, 2], [7, 2], [7, 4], [4, 4]]}, {"polygon": [[7, 5], [5, 5], [5, 3], [7, 3]]}], "meta": {"seed": 4206004, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.710972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 379, "strictValidation": true}, "imageAssets": {"target": "../images/voi-378/target.png", "shapes": {"S1": "../images/voi-378/shape_S1.png", "S2": "../images/voi-378/shape_S2.png", "S3": "../images/voi-378/shape_S3.png", "S4": "../images/voi-378/shape_S4.png", "S5": "../images/voi-378/shape_S5.png", "S6": "../images/voi-378/shape_S6.png"}}, "ID": "voi-378", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [9, 0]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [7, 2]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [4, 2]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [7, 5]}]}, "legacy_answer": "S2 0 V2 [9,0]\nS3 0 V1 [7,2]\nS4 0 V1 [4,2]\nS5 180 V1 [7,5]", "solutionText": "S2 0 V2 [9,0]\nS3 0 V1 [7,2]\nS4 0 V1 [4,2]\nS5 180 V1 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-378\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-378/target.png", "shapes": {"S1": "images/voi-378/shape_S1.png", "S2": "images/voi-378/shape_S2.png", "S3": "images/voi-378/shape_S3.png", "S4": "images/voi-378/shape_S4.png", "S5": "images/voi-378/shape_S5.png", "S6": "images/voi-378/shape_S6.png"}}, "__sample_id__": "voi-378"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 5], [4, 4], [6, 4], [6, 5]]}, {"polygon": [[7, 5], [4, 5], [4, 3], [7, 3]]}, {"polygon": [[6, 8], [7, 8], [6, 9]]}, {"polygon": [[7, 6], [7, 3], [9, 3], [9, 6]]}], "meta": {"seed": 4206005, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 42, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 380, "strictValidation": true}, "imageAssets": {"target": "../images/voi-379/target.png", "shapes": {"S1": "../images/voi-379/shape_S1.png", "S2": "../images/voi-379/shape_S2.png", "S3": "../images/voi-379/shape_S3.png", "S4": "../images/voi-379/shape_S4.png", "S5": "../images/voi-379/shape_S5.png", "S6": "../images/voi-379/shape_S6.png"}}, "ID": "voi-379", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [4, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 3]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [6, 8]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [7, 6]}]}, "legacy_answer": "S2 90 V2 [4,4]\nS3 180 V3 [4,3]\nS4 0 V1 [6,8]\nS5 90 V1 [7,6]", "solutionText": "S2 90 V2 [4,4]\nS3 180 V3 [4,3]\nS4 0 V1 [6,8]\nS5 90 V1 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-379\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-379/target.png", "shapes": {"S1": "images/voi-379/shape_S1.png", "S2": "images/voi-379/shape_S2.png", "S3": "images/voi-379/shape_S3.png", "S4": "images/voi-379/shape_S4.png", "S5": "images/voi-379/shape_S5.png", "S6": "images/voi-379/shape_S6.png"}}, "__sample_id__": "voi-379"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 7], [7, 9], [5, 9], [5, 7]]}, {"polygon": [[5, 4], [7, 4], [7, 6], [5, 6]]}, {"polygon": [[3, 7], [3, 5], [5, 7]]}, {"polygon": [[7, 8], [5, 8], [5, 6], [7, 6]]}], "meta": {"seed": 4206006, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 72, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.710972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 381, "strictValidation": true}, "imageAssets": {"target": "../images/voi-380/target.png", "shapes": {"S1": "../images/voi-380/shape_S1.png", "S2": "../images/voi-380/shape_S2.png", "S3": "../images/voi-380/shape_S3.png", "S4": "../images/voi-380/shape_S4.png", "S5": "../images/voi-380/shape_S5.png", "S6": "../images/voi-380/shape_S6.png"}}, "ID": "voi-380", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 7]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [7, 6]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [3, 7]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S1 270 V4 [5,7]\nS2 0 V3 [7,6]\nS3 90 V1 [3,7]\nS4 180 V3 [5,6]", "solutionText": "S1 270 V4 [5,7]\nS2 0 V3 [7,6]\nS3 90 V1 [3,7]\nS4 180 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-380\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-380/target.png", "shapes": {"S1": "images/voi-380/shape_S1.png", "S2": "images/voi-380/shape_S2.png", "S3": "images/voi-380/shape_S3.png", "S4": "images/voi-380/shape_S4.png", "S5": "images/voi-380/shape_S5.png", "S6": "images/voi-380/shape_S6.png"}}, "__sample_id__": "voi-380"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 7], [4, 5], [5, 5], [5, 6], [7, 6], [7, 7]]}, {"polygon": [[6, 2], [6, 0], [8, 0], [8, 2]]}, {"polygon": [[8, 3], [6, 3], [6, 2], [7, 2], [7, 0], [8, 0]]}, {"polygon": [[3, 6], [3, 3], [4, 4], [4, 6]]}], "meta": {"seed": 4206007, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 46, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 382, "strictValidation": true}, "imageAssets": {"target": "../images/voi-381/target.png", "shapes": {"S1": "../images/voi-381/shape_S1.png", "S2": "../images/voi-381/shape_S2.png", "S3": "../images/voi-381/shape_S3.png", "S4": "../images/voi-381/shape_S4.png", "S5": "../images/voi-381/shape_S5.png", "S6": "../images/voi-381/shape_S6.png"}}, "ID": "voi-381", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [5, 5]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [6, 0]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [8, 3]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [4, 4]}]}, "legacy_answer": "S1 90 V3 [5,5]\nS2 90 V2 [6,0]\nS4 180 V1 [8,3]\nS6 90 V3 [4,4]", "solutionText": "S1 90 V3 [5,5]\nS2 90 V2 [6,0]\nS4 180 V1 [8,3]\nS6 90 V3 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-381\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-381/target.png", "shapes": {"S1": "images/voi-381/shape_S1.png", "S2": "images/voi-381/shape_S2.png", "S3": "images/voi-381/shape_S3.png", "S4": "images/voi-381/shape_S4.png", "S5": "images/voi-381/shape_S5.png", "S6": "images/voi-381/shape_S6.png"}}, "__sample_id__": "voi-381"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 6], [6, 8], [5, 8], [5, 7], [3, 7], [3, 6]]}, {"polygon": [[6, 9], [6, 6], [8, 6], [8, 9]]}, {"polygon": [[7, 4], [7, 6], [6, 6], [6, 5], [4, 5], [4, 4]]}, {"polygon": [[7, 8], [5, 8], [7, 6]]}], "meta": {"seed": 4206008, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.256809, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.119375, "difficultyScore": 0.784013, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 383, "strictValidation": true}, "imageAssets": {"target": "../images/voi-382/target.png", "shapes": {"S1": "../images/voi-382/shape_S1.png", "S2": "../images/voi-382/shape_S2.png", "S3": "../images/voi-382/shape_S3.png", "S4": "../images/voi-382/shape_S4.png", "S5": "../images/voi-382/shape_S5.png", "S6": "../images/voi-382/shape_S6.png"}}, "ID": "voi-382", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 8]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [8, 9]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [7, 6]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [5, 8]}]}, "legacy_answer": "S2 270 V2 [6,8]\nS4 90 V4 [8,9]\nS5 270 V2 [7,6]\nS6 180 V2 [5,8]", "solutionText": "S2 270 V2 [6,8]\nS4 90 V4 [8,9]\nS5 270 V2 [7,6]\nS6 180 V2 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-382\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-382/target.png", "shapes": {"S1": "images/voi-382/shape_S1.png", "S2": "images/voi-382/shape_S2.png", "S3": "images/voi-382/shape_S3.png", "S4": "images/voi-382/shape_S4.png", "S5": "images/voi-382/shape_S5.png", "S6": "images/voi-382/shape_S6.png"}}, "__sample_id__": "voi-382"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[0, 5], [0, 3], [1, 3], [1, 4], [3, 4], [3, 5]]}, {"polygon": [[2, 3], [2, 0], [4, 0], [4, 3]]}, {"polygon": [[3, 3], [6, 3], [6, 5], [3, 5]]}, {"polygon": [[7, 3], [7, 5], [6, 5], [6, 4], [4, 4], [4, 3]]}], "meta": {"seed": 4206009, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.16, "difficultyScore": 0.68, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 384, "strictValidation": true}, "imageAssets": {"target": "../images/voi-383/target.png", "shapes": {"S1": "../images/voi-383/shape_S1.png", "S2": "../images/voi-383/shape_S2.png", "S3": "../images/voi-383/shape_S3.png", "S4": "../images/voi-383/shape_S4.png", "S5": "../images/voi-383/shape_S5.png", "S6": "../images/voi-383/shape_S6.png"}}, "ID": "voi-383", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V5", "grid": [3, 4]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 0]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [6, 3]}, {"shape": "S6", "angle": 270, "vertex": "V6", "grid": [4, 3]}]}, "legacy_answer": "S2 90 V5 [3,4]\nS4 90 V2 [2,0]\nS5 0 V2 [6,3]\nS6 270 V6 [4,3]", "solutionText": "S2 90 V5 [3,4]\nS4 90 V2 [2,0]\nS5 0 V2 [6,3]\nS6 270 V6 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-383\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-383/target.png", "shapes": {"S1": "images/voi-383/shape_S1.png", "S2": "images/voi-383/shape_S2.png", "S3": "images/voi-383/shape_S3.png", "S4": "images/voi-383/shape_S4.png", "S5": "images/voi-383/shape_S5.png", "S6": "images/voi-383/shape_S6.png"}}, "__sample_id__": "voi-383"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 3], [2, 0], [3, 0], [3, 3]]}, {"polygon": [[6, 0], [6, 3], [4, 3], [4, 0]]}, {"polygon": [[5, 1], [6, 1], [6, 4], [5, 4]]}, {"polygon": [[4, 5], [4, 3], [5, 3], [5, 4], [7, 4], [7, 5]]}], "meta": {"seed": 4206010, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.81, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 385, "strictValidation": true}, "imageAssets": {"target": "../images/voi-384/target.png", "shapes": {"S1": "../images/voi-384/shape_S1.png", "S2": "../images/voi-384/shape_S2.png", "S3": "../images/voi-384/shape_S3.png", "S4": "../images/voi-384/shape_S4.png", "S5": "../images/voi-384/shape_S5.png", "S6": "../images/voi-384/shape_S6.png"}}, "ID": "voi-384", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [3, 0]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 3]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [6, 1]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [5, 3]}]}, "legacy_answer": "S1 90 V3 [3,0]\nS2 270 V2 [6,3]\nS4 0 V2 [6,1]\nS5 90 V3 [5,3]", "solutionText": "S1 90 V3 [3,0]\nS2 270 V2 [6,3]\nS4 0 V2 [6,1]\nS5 90 V3 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-384\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-384/target.png", "shapes": {"S1": "images/voi-384/shape_S1.png", "S2": "images/voi-384/shape_S2.png", "S3": "images/voi-384/shape_S3.png", "S4": "images/voi-384/shape_S4.png", "S5": "images/voi-384/shape_S5.png", "S6": "images/voi-384/shape_S6.png"}}, "__sample_id__": "voi-384"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[9, 6], [9, 8], [7, 6]]}, {"polygon": [[4, 2], [7, 2], [6, 3], [4, 3]]}, {"polygon": [[8, 10], [8, 8], [10, 8], [10, 10]]}, {"polygon": [[7, 6], [10, 6], [10, 8], [7, 8]]}], "meta": {"seed": 4206011, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.282655, "contourComplexity": 104, "connectedComponents": 2, "fillRatio": 0.104688, "difficultyScore": 0.710004, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 386, "strictValidation": true}, "imageAssets": {"target": "../images/voi-385/target.png", "shapes": {"S1": "../images/voi-385/shape_S1.png", "S2": "../images/voi-385/shape_S2.png", "S3": "../images/voi-385/shape_S3.png", "S4": "../images/voi-385/shape_S4.png", "S5": "../images/voi-385/shape_S5.png", "S6": "../images/voi-385/shape_S6.png"}}, "ID": "voi-385", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [9, 6]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 3]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [8, 10]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [7, 8]}]}, "legacy_answer": "S2 270 V1 [9,6]\nS3 0 V4 [4,3]\nS4 90 V1 [8,10]\nS5 0 V4 [7,8]", "solutionText": "S2 270 V1 [9,6]\nS3 0 V4 [4,3]\nS4 90 V1 [8,10]\nS5 0 V4 [7,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-385\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-385/target.png", "shapes": {"S1": "images/voi-385/shape_S1.png", "S2": "images/voi-385/shape_S2.png", "S3": "images/voi-385/shape_S3.png", "S4": "images/voi-385/shape_S4.png", "S5": "images/voi-385/shape_S5.png", "S6": "images/voi-385/shape_S6.png"}}, "__sample_id__": "voi-385"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 1], [4, 1], [2, 3]]}, {"polygon": [[3, 6], [3, 4], [4, 4], [4, 5], [6, 5], [6, 6]]}, {"polygon": [[5, 2], [5, 4], [3, 4], [3, 2]]}, {"polygon": [[4, 4], [6, 4], [6, 6], [4, 6]]}], "meta": {"seed": 4206012, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.100625, "difficultyScore": 0.460972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 387, "strictValidation": true}, "imageAssets": {"target": "../images/voi-386/target.png", "shapes": {"S1": "../images/voi-386/shape_S1.png", "S2": "../images/voi-386/shape_S2.png", "S3": "../images/voi-386/shape_S3.png", "S4": "../images/voi-386/shape_S4.png", "S5": "../images/voi-386/shape_S5.png", "S6": "../images/voi-386/shape_S6.png"}}, "ID": "voi-386", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 1]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [3, 6]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [5, 4]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S1 0 V2 [4,1]\nS4 90 V1 [3,6]\nS5 270 V2 [5,4]\nS6 0 V2 [6,4]", "solutionText": "S1 0 V2 [4,1]\nS4 90 V1 [3,6]\nS5 270 V2 [5,4]\nS6 0 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-386\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-386/target.png", "shapes": {"S1": "images/voi-386/shape_S1.png", "S2": "images/voi-386/shape_S2.png", "S3": "images/voi-386/shape_S3.png", "S4": "images/voi-386/shape_S4.png", "S5": "images/voi-386/shape_S5.png", "S6": "images/voi-386/shape_S6.png"}}, "__sample_id__": "voi-386"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 2], [4, 5], [3, 5], [3, 2]]}, {"polygon": [[4, 4], [6, 4], [4, 6]]}, {"polygon": [[6, 5], [6, 8], [4, 8], [4, 5]]}, {"polygon": [[3, 6], [5, 6], [5, 7], [4, 7], [4, 9], [3, 9]]}], "meta": {"seed": 4206013, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.20332, "contourComplexity": 78, "connectedComponents": 1, "fillRatio": 0.12, "difficultyScore": 0.746722, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 388, "strictValidation": true}, "imageAssets": {"target": "../images/voi-387/target.png", "shapes": {"S1": "../images/voi-387/shape_S1.png", "S2": "../images/voi-387/shape_S2.png", "S3": "../images/voi-387/shape_S3.png", "S4": "../images/voi-387/shape_S4.png", "S5": "../images/voi-387/shape_S5.png", "S6": "../images/voi-387/shape_S6.png"}}, "ID": "voi-387", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 5]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [6, 4]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [6, 8]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [3, 6]}]}, "legacy_answer": "S1 270 V3 [3,5]\nS3 0 V2 [6,4]\nS4 270 V2 [6,8]\nS5 0 V1 [3,6]", "solutionText": "S1 270 V3 [3,5]\nS3 0 V2 [6,4]\nS4 270 V2 [6,8]\nS5 0 V1 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-387\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-387/target.png", "shapes": {"S1": "images/voi-387/shape_S1.png", "S2": "images/voi-387/shape_S2.png", "S3": "images/voi-387/shape_S3.png", "S4": "images/voi-387/shape_S4.png", "S5": "images/voi-387/shape_S5.png", "S6": "images/voi-387/shape_S6.png"}}, "__sample_id__": "voi-387"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 5], [6, 5], [6, 6], [5, 6]]}, {"polygon": [[5, 4], [2, 4], [2, 2], [5, 2]]}, {"polygon": [[2, 1], [4, 1], [4, 2], [3, 2], [3, 4], [2, 4]]}, {"polygon": [[7, 1], [7, 4], [5, 4], [5, 1]]}], "meta": {"seed": 4206014, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.848824, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 389, "strictValidation": true}, "imageAssets": {"target": "../images/voi-388/target.png", "shapes": {"S1": "../images/voi-388/shape_S1.png", "S2": "../images/voi-388/shape_S2.png", "S3": "../images/voi-388/shape_S3.png", "S4": "../images/voi-388/shape_S4.png", "S5": "../images/voi-388/shape_S5.png", "S6": "../images/voi-388/shape_S6.png"}}, "ID": "voi-388", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [5, 5]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S5", "angle": 0, "vertex": "V5", "grid": [3, 4]}, {"shape": "S6", "angle": 270, "vertex": "V4", "grid": [5, 1]}]}, "legacy_answer": "S1 0 V1 [5,5]\nS4 180 V4 [5,2]\nS5 0 V5 [3,4]\nS6 270 V4 [5,1]", "solutionText": "S1 0 V1 [5,5]\nS4 180 V4 [5,2]\nS5 0 V5 [3,4]\nS6 270 V4 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-388\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-388/target.png", "shapes": {"S1": "images/voi-388/shape_S1.png", "S2": "images/voi-388/shape_S2.png", "S3": "images/voi-388/shape_S3.png", "S4": "images/voi-388/shape_S4.png", "S5": "images/voi-388/shape_S5.png", "S6": "images/voi-388/shape_S6.png"}}, "__sample_id__": "voi-388"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 4], [4, 5], [1, 5], [1, 4]]}, {"polygon": [[8, 9], [5, 9], [5, 7], [8, 7]]}, {"polygon": [[2, 3], [5, 3], [5, 5], [2, 5]]}, {"polygon": [[4, 8], [4, 5], [5, 6], [5, 8]]}], "meta": {"seed": 4206015, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.228164, "contourComplexity": 46, "connectedComponents": 2, "fillRatio": 0.135313, "difficultyScore": 0.866719, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 390, "strictValidation": true}, "imageAssets": {"target": "../images/voi-389/target.png", "shapes": {"S1": "../images/voi-389/shape_S1.png", "S2": "../images/voi-389/shape_S2.png", "S3": "../images/voi-389/shape_S3.png", "S4": "../images/voi-389/shape_S4.png", "S5": "../images/voi-389/shape_S5.png", "S6": "../images/voi-389/shape_S6.png"}}, "ID": "voi-389", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 5]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [8, 7]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [5, 3]}, {"shape": "S6", "angle": 90, "vertex": "V4", "grid": [5, 8]}]}, "legacy_answer": "S3 270 V2 [4,5]\nS4 180 V4 [8,7]\nS5 0 V2 [5,3]\nS6 90 V4 [5,8]", "solutionText": "S3 270 V2 [4,5]\nS4 180 V4 [8,7]\nS5 0 V2 [5,3]\nS6 90 V4 [5,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-389\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-389/target.png", "shapes": {"S1": "images/voi-389/shape_S1.png", "S2": "images/voi-389/shape_S2.png", "S3": "images/voi-389/shape_S3.png", "S4": "images/voi-389/shape_S4.png", "S5": "images/voi-389/shape_S5.png", "S6": "images/voi-389/shape_S6.png"}}, "__sample_id__": "voi-389"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 3], [4, 6], [2, 6], [2, 3]]}, {"polygon": [[4, 5], [4, 2], [5, 3], [5, 5]]}, {"polygon": [[3, 6], [2, 6], [2, 4], [3, 4]]}, {"polygon": [[10, 6], [8, 6], [8, 5], [9, 5], [9, 3], [10, 3]]}], "meta": {"seed": 4206016, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 46, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 391, "strictValidation": true}, "imageAssets": {"target": "../images/voi-390/target.png", "shapes": {"S1": "../images/voi-390/shape_S1.png", "S2": "../images/voi-390/shape_S2.png", "S3": "../images/voi-390/shape_S3.png", "S4": "../images/voi-390/shape_S4.png", "S5": "../images/voi-390/shape_S5.png", "S6": "../images/voi-390/shape_S6.png"}}, "ID": "voi-390", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [2, 3]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [4, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [2, 6]}, {"shape": "S5", "angle": 180, "vertex": "V5", "grid": [9, 3]}]}, "legacy_answer": "S1 270 V4 [2,3]\nS2 90 V2 [4,2]\nS3 180 V2 [2,6]\nS5 180 V5 [9,3]", "solutionText": "S1 270 V4 [2,3]\nS2 90 V2 [4,2]\nS3 180 V2 [2,6]\nS5 180 V5 [9,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-390\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-390/target.png", "shapes": {"S1": "images/voi-390/shape_S1.png", "S2": "images/voi-390/shape_S2.png", "S3": "images/voi-390/shape_S3.png", "S4": "images/voi-390/shape_S4.png", "S5": "images/voi-390/shape_S5.png", "S6": "images/voi-390/shape_S6.png"}}, "__sample_id__": "voi-390"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 3], [5, 3], [5, 2], [3, 2], [3, 1]]}, {"polygon": [[3, 3], [3, 4], [1, 4], [1, 3]]}, {"polygon": [[8, 1], [5, 1], [5, 0], [8, 0]]}, {"polygon": [[4, 4], [1, 4], [1, 2], [4, 2]]}], "meta": {"seed": 4206017, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 16, "connectedComponents": 1, "fillRatio": 0.11, "difficultyScore": 0.513333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 392, "strictValidation": true}, "imageAssets": {"target": "../images/voi-391/target.png", "shapes": {"S1": "../images/voi-391/shape_S1.png", "S2": "../images/voi-391/shape_S2.png", "S3": "../images/voi-391/shape_S3.png", "S4": "../images/voi-391/shape_S4.png", "S5": "../images/voi-391/shape_S5.png", "S6": "../images/voi-391/shape_S6.png"}}, "ID": "voi-391", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V6", "grid": [3, 1]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [1, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 1]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [4, 2]}]}, "legacy_answer": "S2 270 V6 [3,1]\nS3 270 V4 [1,3]\nS4 180 V2 [5,1]\nS5 180 V4 [4,2]", "solutionText": "S2 270 V6 [3,1]\nS3 270 V4 [1,3]\nS4 180 V2 [5,1]\nS5 180 V4 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-391\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-391/target.png", "shapes": {"S1": "images/voi-391/shape_S1.png", "S2": "images/voi-391/shape_S2.png", "S3": "images/voi-391/shape_S3.png", "S4": "images/voi-391/shape_S4.png", "S5": "images/voi-391/shape_S5.png", "S6": "images/voi-391/shape_S6.png"}}, "__sample_id__": "voi-391"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 4], [2, 4], [2, 3], [3, 3], [3, 1], [4, 1]]}, {"polygon": [[3, 10], [1, 10], [1, 9], [2, 9], [2, 7], [3, 7]]}, {"polygon": [[4, 0], [5, 0], [5, 3], [4, 3]]}, {"polygon": [[2, 3], [5, 3], [5, 4], [2, 4]]}], "meta": {"seed": 4206018, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 393, "strictValidation": true}, "imageAssets": {"target": "../images/voi-392/target.png", "shapes": {"S1": "../images/voi-392/shape_S1.png", "S2": "../images/voi-392/shape_S2.png", "S3": "../images/voi-392/shape_S3.png", "S4": "../images/voi-392/shape_S4.png", "S5": "../images/voi-392/shape_S5.png", "S6": "../images/voi-392/shape_S6.png"}}, "ID": "voi-392", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [4, 4]}, {"shape": "S2", "angle": 180, "vertex": "V6", "grid": [3, 7]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [4, 0]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [5, 4]}]}, "legacy_answer": "S1 180 V1 [4,4]\nS2 180 V6 [3,7]\nS3 0 V1 [4,0]\nS4 0 V3 [5,4]", "solutionText": "S1 180 V1 [4,4]\nS2 180 V6 [3,7]\nS3 0 V1 [4,0]\nS4 0 V3 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-392\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-392/target.png", "shapes": {"S1": "images/voi-392/shape_S1.png", "S2": "images/voi-392/shape_S2.png", "S3": "images/voi-392/shape_S3.png", "S4": "images/voi-392/shape_S4.png", "S5": "images/voi-392/shape_S5.png", "S6": "images/voi-392/shape_S6.png"}}, "__sample_id__": "voi-392"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[3, 8], [1, 8], [1, 7], [2, 7], [2, 5], [3, 5]]}, {"polygon": [[0, 7], [0, 6], [3, 6], [3, 7]]}, {"polygon": [[2, 9], [2, 6], [4, 6], [4, 9]]}, {"polygon": [[9, 8], [9, 9], [6, 9], [6, 8]]}], "meta": {"seed": 4206019, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 21, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.81, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 394, "strictValidation": true}, "imageAssets": {"target": "../images/voi-393/target.png", "shapes": {"S1": "../images/voi-393/shape_S1.png", "S2": "../images/voi-393/shape_S2.png", "S3": "../images/voi-393/shape_S3.png", "S4": "../images/voi-393/shape_S4.png", "S5": "../images/voi-393/shape_S5.png", "S6": "../images/voi-393/shape_S6.png"}}, "ID": "voi-393", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 8]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [0, 6]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [4, 9]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [6, 9]}]}, "legacy_answer": "S1 180 V2 [1,8]\nS4 90 V2 [0,6]\nS5 90 V4 [4,9]\nS6 270 V3 [6,9]", "solutionText": "S1 180 V2 [1,8]\nS4 90 V2 [0,6]\nS5 90 V4 [4,9]\nS6 270 V3 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-393\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-393/target.png", "shapes": {"S1": "images/voi-393/shape_S1.png", "S2": "images/voi-393/shape_S2.png", "S3": "images/voi-393/shape_S3.png", "S4": "images/voi-393/shape_S4.png", "S5": "images/voi-393/shape_S5.png", "S6": "images/voi-393/shape_S6.png"}}, "__sample_id__": "voi-393"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[8, 4], [8, 5], [6, 5], [6, 4]]}, {"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[8, 8], [8, 5], [10, 5], [10, 8]]}, {"polygon": [[4, 4], [5, 4], [4, 5]]}], "meta": {"seed": 4206020, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 395, "strictValidation": true}, "imageAssets": {"target": "../images/voi-394/target.png", "shapes": {"S1": "../images/voi-394/shape_S1.png", "S2": "../images/voi-394/shape_S2.png", "S3": "../images/voi-394/shape_S3.png", "S4": "../images/voi-394/shape_S4.png", "S5": "../images/voi-394/shape_S5.png", "S6": "../images/voi-394/shape_S6.png"}}, "ID": "voi-394", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [8, 4]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [5, 5]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [8, 5]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [5, 4]}]}, "legacy_answer": "S1 270 V1 [8,4]\nS2 0 V4 [5,5]\nS3 90 V2 [8,5]\nS5 0 V2 [5,4]", "solutionText": "S1 270 V1 [8,4]\nS2 0 V4 [5,5]\nS3 90 V2 [8,5]\nS5 0 V2 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-394\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-394/target.png", "shapes": {"S1": "images/voi-394/shape_S1.png", "S2": "images/voi-394/shape_S2.png", "S3": "images/voi-394/shape_S3.png", "S4": "images/voi-394/shape_S4.png", "S5": "images/voi-394/shape_S5.png", "S6": "images/voi-394/shape_S6.png"}}, "__sample_id__": "voi-394"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [1, 7], [1, 5], [4, 5]]}, {"polygon": [[7, 2], [7, 1], [8, 1], [8, 2]]}, {"polygon": [[4, 1], [4, 0], [6, 0], [6, 1]]}, {"polygon": [[4, 0], [7, 0], [7, 2], [4, 2]]}], "meta": {"seed": 4206021, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 396, "strictValidation": true}, "imageAssets": {"target": "../images/voi-395/target.png", "shapes": {"S1": "../images/voi-395/shape_S1.png", "S2": "../images/voi-395/shape_S2.png", "S3": "../images/voi-395/shape_S3.png", "S4": "../images/voi-395/shape_S4.png", "S5": "../images/voi-395/shape_S5.png", "S6": "../images/voi-395/shape_S6.png"}}, "ID": "voi-395", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [4, 5]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [8, 1]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [4, 1]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [7, 0]}]}, "legacy_answer": "S1 180 V4 [4,5]\nS2 90 V3 [8,1]\nS3 90 V1 [4,1]\nS6 0 V2 [7,0]", "solutionText": "S1 180 V4 [4,5]\nS2 90 V3 [8,1]\nS3 90 V1 [4,1]\nS6 0 V2 [7,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-395\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-395/target.png", "shapes": {"S1": "images/voi-395/shape_S1.png", "S2": "images/voi-395/shape_S2.png", "S3": "images/voi-395/shape_S3.png", "S4": "images/voi-395/shape_S4.png", "S5": "images/voi-395/shape_S5.png", "S6": "images/voi-395/shape_S6.png"}}, "__sample_id__": "voi-395"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 3], [8, 3], [8, 5], [7, 5]]}, {"polygon": [[6, 10], [4, 10], [4, 9], [5, 9], [5, 7], [6, 7]]}, {"polygon": [[10, 4], [8, 4], [10, 2]]}, {"polygon": [[6, 6], [6, 9], [4, 9], [4, 6]]}], "meta": {"seed": 4206022, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.710972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 397, "strictValidation": true}, "imageAssets": {"target": "../images/voi-396/target.png", "shapes": {"S1": "../images/voi-396/shape_S1.png", "S2": "../images/voi-396/shape_S2.png", "S3": "../images/voi-396/shape_S3.png", "S4": "../images/voi-396/shape_S4.png", "S5": "../images/voi-396/shape_S5.png", "S6": "../images/voi-396/shape_S6.png"}}, "ID": "voi-396", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [7, 5]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 10]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [10, 4]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [6, 9]}]}, "legacy_answer": "S1 0 V4 [7,5]\nS3 180 V2 [4,10]\nS5 180 V1 [10,4]\nS6 270 V2 [6,9]", "solutionText": "S1 0 V4 [7,5]\nS3 180 V2 [4,10]\nS5 180 V1 [10,4]\nS6 270 V2 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-396\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-396/target.png", "shapes": {"S1": "images/voi-396/shape_S1.png", "S2": "images/voi-396/shape_S2.png", "S3": "images/voi-396/shape_S3.png", "S4": "images/voi-396/shape_S4.png", "S5": "images/voi-396/shape_S5.png", "S6": "images/voi-396/shape_S6.png"}}, "__sample_id__": "voi-396"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 10], [1, 10], [2, 9]]}, {"polygon": [[3, 4], [0, 4], [0, 2], [3, 2]]}, {"polygon": [[1, 0], [3, 0], [1, 2]]}, {"polygon": [[4, 2], [1, 2], [1, 0], [4, 0]]}], "meta": {"seed": 4206023, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.282655, "contourComplexity": 104, "connectedComponents": 2, "fillRatio": 0.104688, "difficultyScore": 0.710004, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 398, "strictValidation": true}, "imageAssets": {"target": "../images/voi-397/target.png", "shapes": {"S1": "../images/voi-397/shape_S1.png", "S2": "../images/voi-397/shape_S2.png", "S3": "../images/voi-397/shape_S3.png", "S4": "../images/voi-397/shape_S4.png", "S5": "../images/voi-397/shape_S5.png", "S6": "../images/voi-397/shape_S6.png"}}, "ID": "voi-397", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 10]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [3, 2]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [3, 0]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [1, 2]}]}, "legacy_answer": "S1 180 V1 [2,10]\nS2 180 V4 [3,2]\nS3 0 V2 [3,0]\nS6 180 V2 [1,2]", "solutionText": "S1 180 V1 [2,10]\nS2 180 V4 [3,2]\nS3 0 V2 [3,0]\nS6 180 V2 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-397\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-397/target.png", "shapes": {"S1": "images/voi-397/shape_S1.png", "S2": "images/voi-397/shape_S2.png", "S3": "images/voi-397/shape_S3.png", "S4": "images/voi-397/shape_S4.png", "S5": "images/voi-397/shape_S5.png", "S6": "images/voi-397/shape_S6.png"}}, "__sample_id__": "voi-397"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 7], [8, 7], [8, 9], [5, 9]]}, {"polygon": [[7, 9], [4, 9], [4, 8], [7, 8]]}, {"polygon": [[3, 10], [3, 9], [6, 9], [6, 10]]}, {"polygon": [[1, 9], [1, 8], [4, 8], [4, 9]]}], "meta": {"seed": 4206024, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 399, "strictValidation": true}, "imageAssets": {"target": "../images/voi-398/target.png", "shapes": {"S1": "../images/voi-398/shape_S1.png", "S2": "../images/voi-398/shape_S2.png", "S3": "../images/voi-398/shape_S3.png", "S4": "../images/voi-398/shape_S4.png", "S5": "../images/voi-398/shape_S5.png", "S6": "../images/voi-398/shape_S6.png"}}, "ID": "voi-398", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [5, 9]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [7, 8]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 9]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 8]}]}, "legacy_answer": "S1 0 V4 [5,9]\nS2 180 V4 [7,8]\nS3 90 V3 [6,9]\nS4 90 V2 [1,8]", "solutionText": "S1 0 V4 [5,9]\nS2 180 V4 [7,8]\nS3 90 V3 [6,9]\nS4 90 V2 [1,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-398\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-398/target.png", "shapes": {"S1": "images/voi-398/shape_S1.png", "S2": "images/voi-398/shape_S2.png", "S3": "images/voi-398/shape_S3.png", "S4": "images/voi-398/shape_S4.png", "S5": "images/voi-398/shape_S5.png", "S6": "images/voi-398/shape_S6.png"}}, "__sample_id__": "voi-398"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 4], [6, 4], [6, 1], [7, 1]]}, {"polygon": [[5, 5], [4, 5], [4, 3], [5, 3]]}, {"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[6, 1], [9, 1], [9, 3], [6, 3]]}], "meta": {"seed": 4206025, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.352941, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.11, "difficultyScore": 0.591765, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 400, "strictValidation": true}, "imageAssets": {"target": "../images/voi-399/target.png", "shapes": {"S1": "../images/voi-399/shape_S1.png", "S2": "../images/voi-399/shape_S2.png", "S3": "../images/voi-399/shape_S3.png", "S4": "../images/voi-399/shape_S4.png", "S5": "../images/voi-399/shape_S5.png", "S6": "../images/voi-399/shape_S6.png"}}, "ID": "voi-399", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [7, 1]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 5]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [5, 3]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [9, 1]}]}, "legacy_answer": "S2 180 V4 [7,1]\nS3 180 V2 [4,5]\nS5 0 V1 [5,3]\nS6 0 V2 [9,1]", "solutionText": "S2 180 V4 [7,1]\nS3 180 V2 [4,5]\nS5 0 V1 [5,3]\nS6 0 V2 [9,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-399\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-399/target.png", "shapes": {"S1": "images/voi-399/shape_S1.png", "S2": "images/voi-399/shape_S2.png", "S3": "images/voi-399/shape_S3.png", "S4": "images/voi-399/shape_S4.png", "S5": "images/voi-399/shape_S5.png", "S6": "images/voi-399/shape_S6.png"}}, "__sample_id__": "voi-399"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 4], [6, 2], [8, 2], [8, 4]]}, {"polygon": [[4, 2], [4, 1], [7, 1], [7, 2]]}, {"polygon": [[9, 1], [9, 4], [7, 4], [7, 1]]}, {"polygon": [[4, 9], [4, 7], [6, 9]]}], "meta": {"seed": 4206026, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.110625, "difficultyScore": 0.766509, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 401, "strictValidation": true}, "imageAssets": {"target": "../images/voi-400/target.png", "shapes": {"S1": "../images/voi-400/shape_S1.png", "S2": "../images/voi-400/shape_S2.png", "S3": "../images/voi-400/shape_S3.png", "S4": "../images/voi-400/shape_S4.png", "S5": "../images/voi-400/shape_S5.png", "S6": "../images/voi-400/shape_S6.png"}}, "ID": "voi-400", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [6, 2]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [4, 1]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [9, 4]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [6, 9]}]}, "legacy_answer": "S1 90 V2 [6,2]\nS3 90 V2 [4,1]\nS4 270 V2 [9,4]\nS6 90 V3 [6,9]", "solutionText": "S1 90 V2 [6,2]\nS3 90 V2 [4,1]\nS4 270 V2 [9,4]\nS6 90 V3 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-400\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-400/target.png", "shapes": {"S1": "images/voi-400/shape_S1.png", "S2": "images/voi-400/shape_S2.png", "S3": "images/voi-400/shape_S3.png", "S4": "images/voi-400/shape_S4.png", "S5": "images/voi-400/shape_S5.png", "S6": "images/voi-400/shape_S6.png"}}, "__sample_id__": "voi-400"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 8], [7, 5], [9, 5], [9, 8]]}, {"polygon": [[6, 10], [4, 10], [4, 9], [5, 9], [5, 7], [6, 7]]}, {"polygon": [[8, 8], [5, 8], [5, 6], [8, 6]]}, {"polygon": [[7, 6], [8, 6], [8, 8], [7, 8]]}], "meta": {"seed": 4206027, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.743333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 402, "strictValidation": true}, "imageAssets": {"target": "../images/voi-401/target.png", "shapes": {"S1": "../images/voi-401/shape_S1.png", "S2": "../images/voi-401/shape_S2.png", "S3": "../images/voi-401/shape_S3.png", "S4": "../images/voi-401/shape_S4.png", "S5": "../images/voi-401/shape_S5.png", "S6": "../images/voi-401/shape_S6.png"}}, "ID": "voi-401", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [9, 8]}, {"shape": "S2", "angle": 180, "vertex": "V5", "grid": [5, 7]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [8, 6]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [8, 8]}]}, "legacy_answer": "S1 90 V4 [9,8]\nS2 180 V5 [5,7]\nS4 180 V4 [8,6]\nS6 0 V3 [8,8]", "solutionText": "S1 90 V4 [9,8]\nS2 180 V5 [5,7]\nS4 180 V4 [8,6]\nS6 0 V3 [8,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-401\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-401/target.png", "shapes": {"S1": "images/voi-401/shape_S1.png", "S2": "images/voi-401/shape_S2.png", "S3": "images/voi-401/shape_S3.png", "S4": "images/voi-401/shape_S4.png", "S5": "images/voi-401/shape_S5.png", "S6": "images/voi-401/shape_S6.png"}}, "__sample_id__": "voi-401"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 8], [3, 6], [4, 6], [4, 7], [6, 7], [6, 8]]}, {"polygon": [[3, 8], [4, 8], [4, 10], [3, 10]]}, {"polygon": [[1, 7], [1, 4], [2, 4], [2, 7]]}, {"polygon": [[6, 5], [6, 8], [4, 8], [4, 5]]}], "meta": {"seed": 4206028, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 403, "strictValidation": true}, "imageAssets": {"target": "../images/voi-402/target.png", "shapes": {"S1": "../images/voi-402/shape_S1.png", "S2": "../images/voi-402/shape_S2.png", "S3": "../images/voi-402/shape_S3.png", "S4": "../images/voi-402/shape_S4.png", "S5": "../images/voi-402/shape_S5.png", "S6": "../images/voi-402/shape_S6.png"}}, "ID": "voi-402", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V6", "grid": [6, 8]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 8]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [2, 4]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [6, 5]}]}, "legacy_answer": "S2 90 V6 [6,8]\nS4 0 V1 [3,8]\nS5 90 V3 [2,4]\nS6 270 V1 [6,5]", "solutionText": "S2 90 V6 [6,8]\nS4 0 V1 [3,8]\nS5 90 V3 [2,4]\nS6 270 V1 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-402\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-402/target.png", "shapes": {"S1": "images/voi-402/shape_S1.png", "S2": "images/voi-402/shape_S2.png", "S3": "images/voi-402/shape_S3.png", "S4": "images/voi-402/shape_S4.png", "S5": "images/voi-402/shape_S5.png", "S6": "images/voi-402/shape_S6.png"}}, "__sample_id__": "voi-402"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 6], [4, 6], [4, 5], [5, 5], [5, 3], [6, 3]]}, {"polygon": [[4, 6], [6, 6], [6, 8], [4, 8]]}, {"polygon": [[7, 2], [4, 2], [4, 1], [7, 1]]}, {"polygon": [[6, 2], [6, 5], [5, 5], [5, 2]]}], "meta": {"seed": 4206029, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 404, "strictValidation": true}, "imageAssets": {"target": "../images/voi-403/target.png", "shapes": {"S1": "../images/voi-403/shape_S1.png", "S2": "../images/voi-403/shape_S2.png", "S3": "../images/voi-403/shape_S3.png", "S4": "../images/voi-403/shape_S4.png", "S5": "../images/voi-403/shape_S5.png", "S6": "../images/voi-403/shape_S6.png"}}, "ID": "voi-403", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V6", "grid": [6, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 8]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [4, 2]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [5, 5]}]}, "legacy_answer": "S2 180 V6 [6,3]\nS3 0 V4 [4,8]\nS5 180 V2 [4,2]\nS6 270 V3 [5,5]", "solutionText": "S2 180 V6 [6,3]\nS3 0 V4 [4,8]\nS5 180 V2 [4,2]\nS6 270 V3 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-403\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-403/target.png", "shapes": {"S1": "images/voi-403/shape_S1.png", "S2": "images/voi-403/shape_S2.png", "S3": "images/voi-403/shape_S3.png", "S4": "images/voi-403/shape_S4.png", "S5": "images/voi-403/shape_S5.png", "S6": "images/voi-403/shape_S6.png"}}, "__sample_id__": "voi-403"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[9, 5], [8, 5], [8, 2], [9, 2]]}, {"polygon": [[7, 3], [9, 3], [9, 4], [8, 4], [8, 6], [7, 6]]}, {"polygon": [[7, 4], [7, 3], [10, 3], [10, 4]]}, {"polygon": [[5, 9], [3, 9], [3, 7], [5, 7]]}], "meta": {"seed": 4206030, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 405, "strictValidation": true}, "imageAssets": {"target": "../images/voi-404/target.png", "shapes": {"S1": "../images/voi-404/shape_S1.png", "S2": "../images/voi-404/shape_S2.png", "S3": "../images/voi-404/shape_S3.png", "S4": "../images/voi-404/shape_S4.png", "S5": "../images/voi-404/shape_S5.png", "S6": "../images/voi-404/shape_S6.png"}}, "ID": "voi-404", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [9, 5]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [9, 3]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [7, 4]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [3, 9]}]}, "legacy_answer": "S1 180 V1 [9,5]\nS2 0 V2 [9,3]\nS3 90 V1 [7,4]\nS5 180 V2 [3,9]", "solutionText": "S1 180 V1 [9,5]\nS2 0 V2 [9,3]\nS3 90 V1 [7,4]\nS5 180 V2 [3,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-404\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-404/target.png", "shapes": {"S1": "images/voi-404/shape_S1.png", "S2": "images/voi-404/shape_S2.png", "S3": "images/voi-404/shape_S3.png", "S4": "images/voi-404/shape_S4.png", "S5": "images/voi-404/shape_S5.png", "S6": "images/voi-404/shape_S6.png"}}, "__sample_id__": "voi-404"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 9], [7, 9], [6, 10], [4, 10]]}, {"polygon": [[6, 9], [6, 7], [7, 7], [7, 8], [9, 8], [9, 9]]}, {"polygon": [[7, 10], [7, 7], [9, 7], [9, 10]]}, {"polygon": [[1, 3], [3, 3], [3, 4], [1, 4]]}], "meta": {"seed": 4206031, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 46, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 406, "strictValidation": true}, "imageAssets": {"target": "../images/voi-405/target.png", "shapes": {"S1": "../images/voi-405/shape_S1.png", "S2": "../images/voi-405/shape_S2.png", "S3": "../images/voi-405/shape_S3.png", "S4": "../images/voi-405/shape_S4.png", "S5": "../images/voi-405/shape_S5.png", "S6": "../images/voi-405/shape_S6.png"}}, "ID": "voi-405", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [6, 10]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [6, 9]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [9, 10]}, {"shape": "S6", "angle": 0, "vertex": "V1", "grid": [1, 3]}]}, "legacy_answer": "S2 0 V3 [6,10]\nS3 90 V1 [6,9]\nS5 90 V4 [9,10]\nS6 0 V1 [1,3]", "solutionText": "S2 0 V3 [6,10]\nS3 90 V1 [6,9]\nS5 90 V4 [9,10]\nS6 0 V1 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-405\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-405/target.png", "shapes": {"S1": "images/voi-405/shape_S1.png", "S2": "images/voi-405/shape_S2.png", "S3": "images/voi-405/shape_S3.png", "S4": "images/voi-405/shape_S4.png", "S5": "images/voi-405/shape_S5.png", "S6": "images/voi-405/shape_S6.png"}}, "__sample_id__": "voi-405"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 6], [0, 4], [2, 6]]}, {"polygon": [[1, 7], [1, 5], [3, 7]]}, {"polygon": [[3, 0], [6, 0], [6, 2], [3, 2]]}, {"polygon": [[1, 5], [3, 5], [3, 7], [1, 7]]}], "meta": {"seed": 4206032, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.292035, "contourComplexity": 70, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.681858, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 407, "strictValidation": true}, "imageAssets": {"target": "../images/voi-406/target.png", "shapes": {"S1": "../images/voi-406/shape_S1.png", "S2": "../images/voi-406/shape_S2.png", "S3": "../images/voi-406/shape_S3.png", "S4": "../images/voi-406/shape_S4.png", "S5": "../images/voi-406/shape_S5.png", "S6": "../images/voi-406/shape_S6.png"}}, "ID": "voi-406", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [0, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 7]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 0]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [3, 7]}]}, "legacy_answer": "S1 90 V2 [0,4]\nS2 90 V1 [1,7]\nS4 0 V1 [3,0]\nS6 0 V3 [3,7]", "solutionText": "S1 90 V2 [0,4]\nS2 90 V1 [1,7]\nS4 0 V1 [3,0]\nS6 0 V3 [3,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-406\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-406/target.png", "shapes": {"S1": "images/voi-406/shape_S1.png", "S2": "images/voi-406/shape_S2.png", "S3": "images/voi-406/shape_S3.png", "S4": "images/voi-406/shape_S4.png", "S5": "images/voi-406/shape_S5.png", "S6": "images/voi-406/shape_S6.png"}}, "__sample_id__": "voi-406"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 4], [2, 7], [0, 7], [0, 4]]}, {"polygon": [[0, 3], [0, 0], [1, 1], [1, 3]]}, {"polygon": [[1, 7], [4, 7], [4, 9], [1, 9]]}, {"polygon": [[1, 5], [1, 8], [0, 7], [0, 5]]}], "meta": {"seed": 4206033, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.130625, "difficultyScore": 0.851021, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 408, "strictValidation": true}, "imageAssets": {"target": "../images/voi-407/target.png", "shapes": {"S1": "../images/voi-407/shape_S1.png", "S2": "../images/voi-407/shape_S2.png", "S3": "../images/voi-407/shape_S3.png", "S4": "../images/voi-407/shape_S4.png", "S5": "../images/voi-407/shape_S5.png", "S6": "../images/voi-407/shape_S6.png"}}, "ID": "voi-407", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [2, 7]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [1, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [1, 9]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [0, 7]}]}, "legacy_answer": "S1 270 V2 [2,7]\nS2 90 V4 [1,3]\nS3 0 V4 [1,9]\nS5 270 V3 [0,7]", "solutionText": "S1 270 V2 [2,7]\nS2 90 V4 [1,3]\nS3 0 V4 [1,9]\nS5 270 V3 [0,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-407\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-407/target.png", "shapes": {"S1": "images/voi-407/shape_S1.png", "S2": "images/voi-407/shape_S2.png", "S3": "images/voi-407/shape_S3.png", "S4": "images/voi-407/shape_S4.png", "S5": "images/voi-407/shape_S5.png", "S6": "images/voi-407/shape_S6.png"}}, "__sample_id__": "voi-407"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 3], [5, 3], [5, 2], [3, 2], [3, 1]]}, {"polygon": [[1, 6], [1, 3], [3, 3], [3, 6]]}, {"polygon": [[6, 1], [6, 4], [4, 4], [4, 1]]}, {"polygon": [[0, 1], [3, 1], [3, 3], [0, 3]]}], "meta": {"seed": 4206034, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.272727, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.16, "difficultyScore": 0.639091, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 409, "strictValidation": true}, "imageAssets": {"target": "../images/voi-408/target.png", "shapes": {"S1": "../images/voi-408/shape_S1.png", "S2": "../images/voi-408/shape_S2.png", "S3": "../images/voi-408/shape_S3.png", "S4": "../images/voi-408/shape_S4.png", "S5": "../images/voi-408/shape_S5.png", "S6": "../images/voi-408/shape_S6.png"}}, "ID": "voi-408", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 2]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [3, 6]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [4, 1]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [3, 3]}]}, "legacy_answer": "S1 270 V4 [5,2]\nS2 90 V4 [3,6]\nS5 270 V4 [4,1]\nS6 0 V3 [3,3]", "solutionText": "S1 270 V4 [5,2]\nS2 90 V4 [3,6]\nS5 270 V4 [4,1]\nS6 0 V3 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-408\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-408/target.png", "shapes": {"S1": "images/voi-408/shape_S1.png", "S2": "images/voi-408/shape_S2.png", "S3": "images/voi-408/shape_S3.png", "S4": "images/voi-408/shape_S4.png", "S5": "images/voi-408/shape_S5.png", "S6": "images/voi-408/shape_S6.png"}}, "__sample_id__": "voi-408"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [7, 2], [7, 3], [5, 3]]}, {"polygon": [[6, 1], [6, 0], [9, 0], [9, 1]]}, {"polygon": [[4, 1], [7, 1], [7, 3], [4, 3]]}, {"polygon": [[4, 4], [1, 4], [1, 2], [4, 2]]}], "meta": {"seed": 4206035, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.13, "difficultyScore": 0.598824, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 410, "strictValidation": true}, "imageAssets": {"target": "../images/voi-409/target.png", "shapes": {"S1": "../images/voi-409/shape_S1.png", "S2": "../images/voi-409/shape_S2.png", "S3": "../images/voi-409/shape_S3.png", "S4": "../images/voi-409/shape_S4.png", "S5": "../images/voi-409/shape_S5.png", "S6": "../images/voi-409/shape_S6.png"}}, "ID": "voi-409", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [5, 3]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [6, 1]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [7, 3]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [1, 2]}]}, "legacy_answer": "S1 0 V4 [5,3]\nS3 90 V1 [6,1]\nS4 0 V3 [7,3]\nS5 180 V3 [1,2]", "solutionText": "S1 0 V4 [5,3]\nS3 90 V1 [6,1]\nS4 0 V3 [7,3]\nS5 180 V3 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-409\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-409/target.png", "shapes": {"S1": "images/voi-409/shape_S1.png", "S2": "images/voi-409/shape_S2.png", "S3": "images/voi-409/shape_S3.png", "S4": "images/voi-409/shape_S4.png", "S5": "images/voi-409/shape_S5.png", "S6": "images/voi-409/shape_S6.png"}}, "__sample_id__": "voi-409"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 6], [2, 5], [2, 3]]}, {"polygon": [[4, 0], [6, 0], [6, 1], [5, 1], [5, 3], [4, 3]]}, {"polygon": [[2, 3], [4, 3], [2, 5]]}, {"polygon": [[3, 5], [0, 5], [0, 3], [3, 3]]}], "meta": {"seed": 4206036, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.27409, "contourComplexity": 106, "connectedComponents": 2, "fillRatio": 0.105938, "difficultyScore": 0.741765, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 411, "strictValidation": true}, "imageAssets": {"target": "../images/voi-410/target.png", "shapes": {"S1": "../images/voi-410/shape_S1.png", "S2": "../images/voi-410/shape_S2.png", "S3": "../images/voi-410/shape_S3.png", "S4": "../images/voi-410/shape_S4.png", "S5": "../images/voi-410/shape_S5.png", "S6": "../images/voi-410/shape_S6.png"}}, "ID": "voi-410", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [3, 3]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 1]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [2, 3]}, {"shape": "S6", "angle": 180, "vertex": "V4", "grid": [3, 3]}]}, "legacy_answer": "S2 270 V1 [3,3]\nS4 0 V4 [5,1]\nS5 0 V1 [2,3]\nS6 180 V4 [3,3]", "solutionText": "S2 270 V1 [3,3]\nS4 0 V4 [5,1]\nS5 0 V1 [2,3]\nS6 180 V4 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-410\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-410/target.png", "shapes": {"S1": "images/voi-410/shape_S1.png", "S2": "images/voi-410/shape_S2.png", "S3": "images/voi-410/shape_S3.png", "S4": "images/voi-410/shape_S4.png", "S5": "images/voi-410/shape_S5.png", "S6": "images/voi-410/shape_S6.png"}}, "__sample_id__": "voi-410"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 5], [4, 5], [4, 7], [1, 7]]}, {"polygon": [[5, 7], [3, 7], [3, 6], [4, 6], [4, 4], [5, 4]]}, {"polygon": [[4, 4], [4, 7], [3, 7], [3, 4]]}, {"polygon": [[0, 4], [2, 4], [2, 5], [0, 5]]}], "meta": {"seed": 4206037, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 15, "connectedComponents": 1, "fillRatio": 0.11, "difficultyScore": 0.513333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 412, "strictValidation": true}, "imageAssets": {"target": "../images/voi-411/target.png", "shapes": {"S1": "../images/voi-411/shape_S1.png", "S2": "../images/voi-411/shape_S2.png", "S3": "../images/voi-411/shape_S3.png", "S4": "../images/voi-411/shape_S4.png", "S5": "../images/voi-411/shape_S5.png", "S6": "../images/voi-411/shape_S6.png"}}, "ID": "voi-411", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [4, 5]}, {"shape": "S3", "angle": 180, "vertex": "V5", "grid": [4, 4]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [3, 7]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [0, 5]}]}, "legacy_answer": "S2 0 V2 [4,5]\nS3 180 V5 [4,4]\nS4 270 V3 [3,7]\nS5 0 V4 [0,5]", "solutionText": "S2 0 V2 [4,5]\nS3 180 V5 [4,4]\nS4 270 V3 [3,7]\nS5 0 V4 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-411\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-411/target.png", "shapes": {"S1": "images/voi-411/shape_S1.png", "S2": "images/voi-411/shape_S2.png", "S3": "images/voi-411/shape_S3.png", "S4": "images/voi-411/shape_S4.png", "S5": "images/voi-411/shape_S5.png", "S6": "images/voi-411/shape_S6.png"}}, "__sample_id__": "voi-411"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 6], [0, 6], [0, 4], [2, 4]]}, {"polygon": [[3, 8], [0, 8], [0, 6], [3, 6]]}, {"polygon": [[1, 6], [2, 6], [2, 9], [1, 9]]}, {"polygon": [[4, 10], [1, 10], [1, 8], [4, 8]]}], "meta": {"seed": 4206038, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.653158, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 413, "strictValidation": true}, "imageAssets": {"target": "../images/voi-412/target.png", "shapes": {"S1": "../images/voi-412/shape_S1.png", "S2": "../images/voi-412/shape_S2.png", "S3": "../images/voi-412/shape_S3.png", "S4": "../images/voi-412/shape_S4.png", "S5": "../images/voi-412/shape_S5.png", "S6": "../images/voi-412/shape_S6.png"}}, "ID": "voi-412", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [0, 6]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [0, 6]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [1, 9]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [1, 8]}]}, "legacy_answer": "S1 180 V2 [0,6]\nS2 180 V3 [0,6]\nS5 0 V4 [1,9]\nS6 180 V3 [1,8]", "solutionText": "S1 180 V2 [0,6]\nS2 180 V3 [0,6]\nS5 0 V4 [1,9]\nS6 180 V3 [1,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-412\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-412/target.png", "shapes": {"S1": "images/voi-412/shape_S1.png", "S2": "images/voi-412/shape_S2.png", "S3": "images/voi-412/shape_S3.png", "S4": "images/voi-412/shape_S4.png", "S5": "images/voi-412/shape_S5.png", "S6": "images/voi-412/shape_S6.png"}}, "__sample_id__": "voi-412"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 8], [4, 8], [4, 7], [5, 7], [5, 5], [6, 5]]}, {"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}, {"polygon": [[3, 3], [0, 3], [1, 2], [3, 2]]}, {"polygon": [[5, 5], [3, 5], [3, 4], [4, 4], [4, 2], [5, 2]]}], "meta": {"seed": 4206039, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 414, "strictValidation": true}, "imageAssets": {"target": "../images/voi-413/target.png", "shapes": {"S1": "../images/voi-413/shape_S1.png", "S2": "../images/voi-413/shape_S2.png", "S3": "../images/voi-413/shape_S3.png", "S4": "../images/voi-413/shape_S4.png", "S5": "../images/voi-413/shape_S5.png", "S6": "../images/voi-413/shape_S6.png"}}, "ID": "voi-413", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [6, 8]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [3, 2]}, {"shape": "S6", "angle": 180, "vertex": "V5", "grid": [4, 2]}]}, "legacy_answer": "S1 180 V1 [6,8]\nS2 180 V2 [3,4]\nS3 180 V4 [3,2]\nS6 180 V5 [4,2]", "solutionText": "S1 180 V1 [6,8]\nS2 180 V2 [3,4]\nS3 180 V4 [3,2]\nS6 180 V5 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-413\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-413/target.png", "shapes": {"S1": "images/voi-413/shape_S1.png", "S2": "images/voi-413/shape_S2.png", "S3": "images/voi-413/shape_S3.png", "S4": "images/voi-413/shape_S4.png", "S5": "images/voi-413/shape_S5.png", "S6": "images/voi-413/shape_S6.png"}}, "__sample_id__": "voi-413"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[9, 5], [9, 2], [10, 2], [10, 5]]}, {"polygon": [[6, 2], [9, 2], [9, 4], [6, 4]]}, {"polygon": [[4, 3], [4, 1], [5, 1], [5, 2], [7, 2], [7, 3]]}, {"polygon": [[8, 7], [8, 4], [10, 4], [10, 7]]}], "meta": {"seed": 4206040, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.210526, "contourComplexity": 18, "connectedComponents": 2, "fillRatio": 0.15, "difficultyScore": 0.907895, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 415, "strictValidation": true}, "imageAssets": {"target": "../images/voi-414/target.png", "shapes": {"S1": "../images/voi-414/shape_S1.png", "S2": "../images/voi-414/shape_S2.png", "S3": "../images/voi-414/shape_S3.png", "S4": "../images/voi-414/shape_S4.png", "S5": "../images/voi-414/shape_S5.png", "S6": "../images/voi-414/shape_S6.png"}}, "ID": "voi-414", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [9, 2]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [6, 2]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [7, 3]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [10, 4]}]}, "legacy_answer": "S1 90 V2 [9,2]\nS3 0 V1 [6,2]\nS4 90 V6 [7,3]\nS6 90 V3 [10,4]", "solutionText": "S1 90 V2 [9,2]\nS3 0 V1 [6,2]\nS4 90 V6 [7,3]\nS6 90 V3 [10,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-414\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-414/target.png", "shapes": {"S1": "images/voi-414/shape_S1.png", "S2": "images/voi-414/shape_S2.png", "S3": "images/voi-414/shape_S3.png", "S4": "images/voi-414/shape_S4.png", "S5": "images/voi-414/shape_S5.png", "S6": "images/voi-414/shape_S6.png"}}, "__sample_id__": "voi-414"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 6], [4, 4], [6, 4], [6, 6]]}, {"polygon": [[3, 9], [2, 9], [2, 6], [3, 6]]}, {"polygon": [[3, 6], [6, 6], [6, 8], [3, 8]]}, {"polygon": [[6, 6], [4, 6], [6, 4]]}], "meta": {"seed": 4206041, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.273859, "contourComplexity": 70, "connectedComponents": 2, "fillRatio": 0.109375, "difficultyScore": 0.735814, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 416, "strictValidation": true}, "imageAssets": {"target": "../images/voi-415/target.png", "shapes": {"S1": "../images/voi-415/shape_S1.png", "S2": "../images/voi-415/shape_S2.png", "S3": "../images/voi-415/shape_S3.png", "S4": "../images/voi-415/shape_S4.png", "S5": "../images/voi-415/shape_S5.png", "S6": "../images/voi-415/shape_S6.png"}}, "ID": "voi-415", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [6, 4]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [2, 6]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [6, 6]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [6, 6]}]}, "legacy_answer": "S2 90 V3 [6,4]\nS3 180 V3 [2,6]\nS4 0 V2 [6,6]\nS6 180 V1 [6,6]", "solutionText": "S2 90 V3 [6,4]\nS3 180 V3 [2,6]\nS4 0 V2 [6,6]\nS6 180 V1 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-415\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-415/target.png", "shapes": {"S1": "images/voi-415/shape_S1.png", "S2": "images/voi-415/shape_S2.png", "S3": "images/voi-415/shape_S3.png", "S4": "images/voi-415/shape_S4.png", "S5": "images/voi-415/shape_S5.png", "S6": "images/voi-415/shape_S6.png"}}, "__sample_id__": "voi-415"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}, {"polygon": [[4, 7], [4, 6], [6, 6], [6, 7]]}, {"polygon": [[3, 6], [6, 6], [6, 8], [3, 8]]}, {"polygon": [[2, 0], [2, 2], [1, 2], [1, 0]]}], "meta": {"seed": 4206042, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 417, "strictValidation": true}, "imageAssets": {"target": "../images/voi-416/target.png", "shapes": {"S1": "../images/voi-416/shape_S1.png", "S2": "../images/voi-416/shape_S2.png", "S3": "../images/voi-416/shape_S3.png", "S4": "../images/voi-416/shape_S4.png", "S5": "../images/voi-416/shape_S5.png", "S6": "../images/voi-416/shape_S6.png"}}, "ID": "voi-416", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 6]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [3, 8]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [1, 2]}]}, "legacy_answer": "S1 270 V2 [5,6]\nS3 90 V3 [6,6]\nS4 0 V4 [3,8]\nS5 270 V3 [1,2]", "solutionText": "S1 270 V2 [5,6]\nS3 90 V3 [6,6]\nS4 0 V4 [3,8]\nS5 270 V3 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-416\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-416/target.png", "shapes": {"S1": "images/voi-416/shape_S1.png", "S2": "images/voi-416/shape_S2.png", "S3": "images/voi-416/shape_S3.png", "S4": "images/voi-416/shape_S4.png", "S5": "images/voi-416/shape_S5.png", "S6": "images/voi-416/shape_S6.png"}}, "__sample_id__": "voi-416"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[6, 6], [5, 6], [5, 3], [6, 3]]}, {"polygon": [[5, 9], [4, 9], [4, 8], [5, 8]]}, {"polygon": [[5, 8], [3, 8], [3, 7], [4, 7], [4, 5], [5, 5]]}], "meta": {"seed": 4206043, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 418, "strictValidation": true}, "imageAssets": {"target": "../images/voi-417/target.png", "shapes": {"S1": "../images/voi-417/shape_S1.png", "S2": "../images/voi-417/shape_S2.png", "S3": "../images/voi-417/shape_S3.png", "S4": "../images/voi-417/shape_S4.png", "S5": "../images/voi-417/shape_S5.png", "S6": "../images/voi-417/shape_S6.png"}}, "ID": "voi-417", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [8, 5]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [5, 3]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [5, 8]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [3, 8]}]}, "legacy_answer": "S2 0 V3 [8,5]\nS4 180 V3 [5,3]\nS5 180 V4 [5,8]\nS6 180 V2 [3,8]", "solutionText": "S2 0 V3 [8,5]\nS4 180 V3 [5,3]\nS5 180 V4 [5,8]\nS6 180 V2 [3,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-417\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-417/target.png", "shapes": {"S1": "images/voi-417/shape_S1.png", "S2": "images/voi-417/shape_S2.png", "S3": "images/voi-417/shape_S3.png", "S4": "images/voi-417/shape_S4.png", "S5": "images/voi-417/shape_S5.png", "S6": "images/voi-417/shape_S6.png"}}, "__sample_id__": "voi-417"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 10], [1, 7], [2, 7], [2, 10]]}, {"polygon": [[3, 5], [3, 2], [5, 2], [5, 5]]}, {"polygon": [[2, 0], [5, 0], [5, 2], [2, 2]]}, {"polygon": [[4, 5], [4, 3], [5, 3], [5, 5]]}], "meta": {"seed": 4206044, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.848824, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 419, "strictValidation": true}, "imageAssets": {"target": "../images/voi-418/target.png", "shapes": {"S1": "../images/voi-418/shape_S1.png", "S2": "../images/voi-418/shape_S2.png", "S3": "../images/voi-418/shape_S3.png", "S4": "../images/voi-418/shape_S4.png", "S5": "../images/voi-418/shape_S5.png", "S6": "../images/voi-418/shape_S6.png"}}, "ID": "voi-418", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [2, 7]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 5]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [2, 2]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [4, 5]}]}, "legacy_answer": "S1 90 V3 [2,7]\nS2 90 V1 [3,5]\nS5 0 V4 [2,2]\nS6 90 V1 [4,5]", "solutionText": "S1 90 V3 [2,7]\nS2 90 V1 [3,5]\nS5 0 V4 [2,2]\nS6 90 V1 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-418\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-418/target.png", "shapes": {"S1": "images/voi-418/shape_S1.png", "S2": "images/voi-418/shape_S2.png", "S3": "images/voi-418/shape_S3.png", "S4": "images/voi-418/shape_S4.png", "S5": "images/voi-418/shape_S5.png", "S6": "images/voi-418/shape_S6.png"}}, "__sample_id__": "voi-418"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 3], [0, 3], [0, 1], [3, 1]]}, {"polygon": [[0, 7], [2, 7], [2, 9], [0, 9]]}, {"polygon": [[5, 0], [5, 3], [3, 3], [3, 0]]}, {"polygon": [[3, 0], [5, 0], [5, 1], [3, 1]]}], "meta": {"seed": 4206045, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 2, "fillRatio": 0.14, "difficultyScore": 0.881111, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 420, "strictValidation": true}, "imageAssets": {"target": "../images/voi-419/target.png", "shapes": {"S1": "../images/voi-419/shape_S1.png", "S2": "../images/voi-419/shape_S2.png", "S3": "../images/voi-419/shape_S3.png", "S4": "../images/voi-419/shape_S4.png", "S5": "../images/voi-419/shape_S5.png", "S6": "../images/voi-419/shape_S6.png"}}, "ID": "voi-419", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 3]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [2, 7]}, {"shape": "S5", "angle": 270, "vertex": "V3", "grid": [3, 3]}, {"shape": "S6", "angle": 0, "vertex": "V4", "grid": [3, 1]}]}, "legacy_answer": "S2 180 V2 [0,3]\nS3 0 V2 [2,7]\nS5 270 V3 [3,3]\nS6 0 V4 [3,1]", "solutionText": "S2 180 V2 [0,3]\nS3 0 V2 [2,7]\nS5 270 V3 [3,3]\nS6 0 V4 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-419\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-419/target.png", "shapes": {"S1": "images/voi-419/shape_S1.png", "S2": "images/voi-419/shape_S2.png", "S3": "images/voi-419/shape_S3.png", "S4": "images/voi-419/shape_S4.png", "S5": "images/voi-419/shape_S5.png", "S6": "images/voi-419/shape_S6.png"}}, "__sample_id__": "voi-419"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 7], [1, 7], [1, 9], [0, 9]]}, {"polygon": [[5, 5], [5, 8], [3, 8], [3, 5]]}, {"polygon": [[4, 7], [7, 7], [7, 9], [4, 9]]}, {"polygon": [[4, 8], [4, 6], [6, 8]]}], "meta": {"seed": 4206046, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.256809, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.119375, "difficultyScore": 0.784013, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 421, "strictValidation": true}, "imageAssets": {"target": "../images/voi-420/target.png", "shapes": {"S1": "../images/voi-420/shape_S1.png", "S2": "../images/voi-420/shape_S2.png", "S3": "../images/voi-420/shape_S3.png", "S4": "../images/voi-420/shape_S4.png", "S5": "../images/voi-420/shape_S5.png", "S6": "../images/voi-420/shape_S6.png"}}, "ID": "voi-420", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [0, 7]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 5]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [4, 9]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [4, 6]}]}, "legacy_answer": "S2 0 V1 [0,7]\nS4 270 V4 [3,5]\nS5 0 V4 [4,9]\nS6 90 V2 [4,6]", "solutionText": "S2 0 V1 [0,7]\nS4 270 V4 [3,5]\nS5 0 V4 [4,9]\nS6 90 V2 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-420\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-420/target.png", "shapes": {"S1": "images/voi-420/shape_S1.png", "S2": "images/voi-420/shape_S2.png", "S3": "images/voi-420/shape_S3.png", "S4": "images/voi-420/shape_S4.png", "S5": "images/voi-420/shape_S5.png", "S6": "images/voi-420/shape_S6.png"}}, "__sample_id__": "voi-420"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 9], [5, 7], [7, 7], [7, 9]]}, {"polygon": [[8, 5], [8, 7], [6, 7], [6, 5]]}, {"polygon": [[7, 6], [8, 6], [8, 9], [7, 9]]}, {"polygon": [[3, 8], [6, 8], [6, 9], [3, 9]]}], "meta": {"seed": 4206047, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 422, "strictValidation": true}, "imageAssets": {"target": "../images/voi-421/target.png", "shapes": {"S1": "../images/voi-421/shape_S1.png", "S2": "../images/voi-421/shape_S2.png", "S3": "../images/voi-421/shape_S3.png", "S4": "../images/voi-421/shape_S4.png", "S5": "../images/voi-421/shape_S5.png", "S6": "../images/voi-421/shape_S6.png"}}, "ID": "voi-421", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [7, 9]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [8, 5]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [7, 6]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [6, 8]}]}, "legacy_answer": "S2 90 V4 [7,9]\nS4 270 V1 [8,5]\nS5 0 V1 [7,6]\nS6 0 V2 [6,8]", "solutionText": "S2 90 V4 [7,9]\nS4 270 V1 [8,5]\nS5 0 V1 [7,6]\nS6 0 V2 [6,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-421\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-421/target.png", "shapes": {"S1": "images/voi-421/shape_S1.png", "S2": "images/voi-421/shape_S2.png", "S3": "images/voi-421/shape_S3.png", "S4": "images/voi-421/shape_S4.png", "S5": "images/voi-421/shape_S5.png", "S6": "images/voi-421/shape_S6.png"}}, "__sample_id__": "voi-421"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[10, 3], [9, 3], [9, 0], [10, 0]]}, {"polygon": [[5, 1], [8, 1], [8, 3], [5, 3]]}, {"polygon": [[9, 0], [9, 2], [7, 2], [7, 0]]}, {"polygon": [[9, 3], [6, 3], [7, 2], [9, 2]]}], "meta": {"seed": 4206048, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.325956, "contourComplexity": 42, "connectedComponents": 2, "fillRatio": 0.104688, "difficultyScore": 0.744448, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 423, "strictValidation": true}, "imageAssets": {"target": "../images/voi-422/target.png", "shapes": {"S1": "../images/voi-422/shape_S1.png", "S2": "../images/voi-422/shape_S2.png", "S3": "../images/voi-422/shape_S3.png", "S4": "../images/voi-422/shape_S4.png", "S5": "../images/voi-422/shape_S5.png", "S6": "../images/voi-422/shape_S6.png"}}, "ID": "voi-422", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [9, 0]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [8, 1]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [9, 2]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [7, 2]}]}, "legacy_answer": "S1 180 V3 [9,0]\nS3 0 V2 [8,1]\nS4 270 V2 [9,2]\nS6 180 V3 [7,2]", "solutionText": "S1 180 V3 [9,0]\nS3 0 V2 [8,1]\nS4 270 V2 [9,2]\nS6 180 V3 [7,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-422\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-422/target.png", "shapes": {"S1": "images/voi-422/shape_S1.png", "S2": "images/voi-422/shape_S2.png", "S3": "images/voi-422/shape_S3.png", "S4": "images/voi-422/shape_S4.png", "S5": "images/voi-422/shape_S5.png", "S6": "images/voi-422/shape_S6.png"}}, "__sample_id__": "voi-422"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 0], [2, 1], [0, 1], [0, 0]]}, {"polygon": [[6, 3], [4, 3], [6, 1]]}, {"polygon": [[3, 2], [0, 2], [0, 0], [3, 0]]}, {"polygon": [[6, 6], [4, 6], [4, 5], [5, 5], [5, 3], [6, 3]]}], "meta": {"seed": 4206049, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.710972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 424, "strictValidation": true}, "imageAssets": {"target": "../images/voi-423/target.png", "shapes": {"S1": "../images/voi-423/shape_S1.png", "S2": "../images/voi-423/shape_S2.png", "S3": "../images/voi-423/shape_S3.png", "S4": "../images/voi-423/shape_S4.png", "S5": "../images/voi-423/shape_S5.png", "S6": "../images/voi-423/shape_S6.png"}}, "ID": "voi-423", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [0, 0]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 3]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [0, 0]}, {"shape": "S5", "angle": 180, "vertex": "V4", "grid": [5, 5]}]}, "legacy_answer": "S1 270 V4 [0,0]\nS2 180 V1 [6,3]\nS4 180 V3 [0,0]\nS5 180 V4 [5,5]", "solutionText": "S1 270 V4 [0,0]\nS2 180 V1 [6,3]\nS4 180 V3 [0,0]\nS5 180 V4 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-423\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-423/target.png", "shapes": {"S1": "images/voi-423/shape_S1.png", "S2": "images/voi-423/shape_S2.png", "S3": "images/voi-423/shape_S3.png", "S4": "images/voi-423/shape_S4.png", "S5": "images/voi-423/shape_S5.png", "S6": "images/voi-423/shape_S6.png"}}, "__sample_id__": "voi-423"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 8], [0, 8], [2, 6]]}, {"polygon": [[3, 7], [3, 10], [2, 9], [2, 7]]}, {"polygon": [[3, 6], [3, 4], [4, 4], [4, 5], [6, 5], [6, 6]]}, {"polygon": [[7, 6], [4, 6], [4, 4], [7, 4]]}], "meta": {"seed": 4206050, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.27409, "contourComplexity": 108, "connectedComponents": 2, "fillRatio": 0.105938, "difficultyScore": 0.741765, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 425, "strictValidation": true}, "imageAssets": {"target": "../images/voi-424/target.png", "shapes": {"S1": "../images/voi-424/shape_S1.png", "S2": "../images/voi-424/shape_S2.png", "S3": "../images/voi-424/shape_S3.png", "S4": "../images/voi-424/shape_S4.png", "S5": "../images/voi-424/shape_S5.png", "S6": "../images/voi-424/shape_S6.png"}}, "ID": "voi-424", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [2, 8]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [3, 10]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [4, 5]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [7, 6]}]}, "legacy_answer": "S2 180 V1 [2,8]\nS4 270 V2 [3,10]\nS5 90 V4 [4,5]\nS6 180 V1 [7,6]", "solutionText": "S2 180 V1 [2,8]\nS4 270 V2 [3,10]\nS5 90 V4 [4,5]\nS6 180 V1 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-424\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-424/target.png", "shapes": {"S1": "images/voi-424/shape_S1.png", "S2": "images/voi-424/shape_S2.png", "S3": "images/voi-424/shape_S3.png", "S4": "images/voi-424/shape_S4.png", "S5": "images/voi-424/shape_S5.png", "S6": "images/voi-424/shape_S6.png"}}, "__sample_id__": "voi-424"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[9, 1], [10, 1], [10, 3], [9, 3]]}, {"polygon": [[6, 4], [7, 4], [7, 6], [6, 6]]}, {"polygon": [[6, 7], [6, 5], [8, 5], [8, 7]]}, {"polygon": [[9, 5], [6, 5], [6, 3], [9, 3]]}], "meta": {"seed": 4206051, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 426, "strictValidation": true}, "imageAssets": {"target": "../images/voi-425/target.png", "shapes": {"S1": "../images/voi-425/shape_S1.png", "S2": "../images/voi-425/shape_S2.png", "S3": "../images/voi-425/shape_S3.png", "S4": "../images/voi-425/shape_S4.png", "S5": "../images/voi-425/shape_S5.png", "S6": "../images/voi-425/shape_S6.png"}}, "ID": "voi-425", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [9, 1]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [7, 4]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [6, 5]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [9, 5]}]}, "legacy_answer": "S1 0 V1 [9,1]\nS4 0 V2 [7,4]\nS5 90 V2 [6,5]\nS6 180 V1 [9,5]", "solutionText": "S1 0 V1 [9,1]\nS4 0 V2 [7,4]\nS5 90 V2 [6,5]\nS6 180 V1 [9,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-425\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-425/target.png", "shapes": {"S1": "images/voi-425/shape_S1.png", "S2": "images/voi-425/shape_S2.png", "S3": "images/voi-425/shape_S3.png", "S4": "images/voi-425/shape_S4.png", "S5": "images/voi-425/shape_S5.png", "S6": "images/voi-425/shape_S6.png"}}, "__sample_id__": "voi-425"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 6], [1, 6], [1, 3], [2, 3]]}, {"polygon": [[6, 5], [6, 7], [5, 7], [5, 5]]}, {"polygon": [[0, 4], [1, 4], [1, 7], [0, 7]]}, {"polygon": [[7, 5], [7, 8], [5, 8], [5, 5]]}], "meta": {"seed": 4206052, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 427, "strictValidation": true}, "imageAssets": {"target": "../images/voi-426/target.png", "shapes": {"S1": "../images/voi-426/shape_S1.png", "S2": "../images/voi-426/shape_S2.png", "S3": "../images/voi-426/shape_S3.png", "S4": "../images/voi-426/shape_S4.png", "S5": "../images/voi-426/shape_S5.png", "S6": "../images/voi-426/shape_S6.png"}}, "ID": "voi-426", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 6]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 7]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [1, 7]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [7, 5]}]}, "legacy_answer": "S1 180 V1 [2,6]\nS2 270 V2 [6,7]\nS5 0 V3 [1,7]\nS6 270 V1 [7,5]", "solutionText": "S1 180 V1 [2,6]\nS2 270 V2 [6,7]\nS5 0 V3 [1,7]\nS6 270 V1 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-426\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-426/target.png", "shapes": {"S1": "images/voi-426/shape_S1.png", "S2": "images/voi-426/shape_S2.png", "S3": "images/voi-426/shape_S3.png", "S4": "images/voi-426/shape_S4.png", "S5": "images/voi-426/shape_S5.png", "S6": "images/voi-426/shape_S6.png"}}, "__sample_id__": "voi-426"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 3], [4, 3], [4, 4], [3, 4], [3, 6], [2, 6]]}, {"polygon": [[10, 6], [8, 6], [8, 5], [9, 5], [9, 3], [10, 3]]}, {"polygon": [[9, 2], [9, 5], [7, 5], [7, 2]]}, {"polygon": [[8, 2], [8, 4], [7, 4], [7, 2]]}], "meta": {"seed": 4206053, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.81, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 428, "strictValidation": true}, "imageAssets": {"target": "../images/voi-427/target.png", "shapes": {"S1": "../images/voi-427/shape_S1.png", "S2": "../images/voi-427/shape_S2.png", "S3": "../images/voi-427/shape_S3.png", "S4": "../images/voi-427/shape_S4.png", "S5": "../images/voi-427/shape_S5.png", "S6": "../images/voi-427/shape_S6.png"}}, "ID": "voi-427", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 4]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [10, 6]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [9, 2]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [8, 4]}]}, "legacy_answer": "S1 0 V4 [3,4]\nS2 180 V1 [10,6]\nS3 270 V1 [9,2]\nS5 270 V2 [8,4]", "solutionText": "S1 0 V4 [3,4]\nS2 180 V1 [10,6]\nS3 270 V1 [9,2]\nS5 270 V2 [8,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-427\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-427/target.png", "shapes": {"S1": "images/voi-427/shape_S1.png", "S2": "images/voi-427/shape_S2.png", "S3": "images/voi-427/shape_S3.png", "S4": "images/voi-427/shape_S4.png", "S5": "images/voi-427/shape_S5.png", "S6": "images/voi-427/shape_S6.png"}}, "__sample_id__": "voi-427"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 1], [6, 1], [6, 3], [5, 3]]}, {"polygon": [[8, 7], [6, 7], [6, 5], [8, 5]]}, {"polygon": [[8, 2], [8, 4], [6, 4], [6, 2]]}, {"polygon": [[6, 5], [6, 3], [8, 3], [8, 5]]}], "meta": {"seed": 4206054, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 429, "strictValidation": true}, "imageAssets": {"target": "../images/voi-428/target.png", "shapes": {"S1": "../images/voi-428/shape_S1.png", "S2": "../images/voi-428/shape_S2.png", "S3": "../images/voi-428/shape_S3.png", "S4": "../images/voi-428/shape_S4.png", "S5": "../images/voi-428/shape_S5.png", "S6": "../images/voi-428/shape_S6.png"}}, "ID": "voi-428", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [6, 1]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [6, 5]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [8, 2]}, {"shape": "S6", "angle": 90, "vertex": "V4", "grid": [8, 5]}]}, "legacy_answer": "S1 0 V2 [6,1]\nS2 180 V3 [6,5]\nS4 270 V1 [8,2]\nS6 90 V4 [8,5]", "solutionText": "S1 0 V2 [6,1]\nS2 180 V3 [6,5]\nS4 270 V1 [8,2]\nS6 90 V4 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-428\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-428/target.png", "shapes": {"S1": "images/voi-428/shape_S1.png", "S2": "images/voi-428/shape_S2.png", "S3": "images/voi-428/shape_S3.png", "S4": "images/voi-428/shape_S4.png", "S5": "images/voi-428/shape_S5.png", "S6": "images/voi-428/shape_S6.png"}}, "__sample_id__": "voi-428"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[7, 8], [4, 8], [4, 6], [7, 6]]}, {"polygon": [[5, 8], [2, 8], [2, 6], [5, 6]]}, {"polygon": [[5, 9], [4, 9], [4, 7], [5, 7]]}, {"polygon": [[2, 10], [0, 10], [2, 8]]}], "meta": {"seed": 4206055, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.120625, "difficultyScore": 0.812641, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 430, "strictValidation": true}, "imageAssets": {"target": "../images/voi-429/target.png", "shapes": {"S1": "../images/voi-429/shape_S1.png", "S2": "../images/voi-429/shape_S2.png", "S3": "../images/voi-429/shape_S3.png", "S4": "../images/voi-429/shape_S4.png", "S5": "../images/voi-429/shape_S5.png", "S6": "../images/voi-429/shape_S6.png"}}, "ID": "voi-429", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [7, 6]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [5, 6]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [5, 9]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [2, 8]}]}, "legacy_answer": "S1 180 V4 [7,6]\nS2 180 V4 [5,6]\nS4 180 V1 [5,9]\nS5 180 V3 [2,8]", "solutionText": "S1 180 V4 [7,6]\nS2 180 V4 [5,6]\nS4 180 V1 [5,9]\nS5 180 V3 [2,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-429\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-429/target.png", "shapes": {"S1": "images/voi-429/shape_S1.png", "S2": "images/voi-429/shape_S2.png", "S3": "images/voi-429/shape_S3.png", "S4": "images/voi-429/shape_S4.png", "S5": "images/voi-429/shape_S5.png", "S6": "images/voi-429/shape_S6.png"}}, "__sample_id__": "voi-429"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 1], [5, 0], [7, 0], [7, 1]]}, {"polygon": [[8, 2], [5, 2], [5, 0], [8, 0]]}, {"polygon": [[3, 2], [4, 2], [4, 3], [3, 3]]}, {"polygon": [[9, 4], [6, 4], [6, 2], [9, 2]]}], "meta": {"seed": 4206056, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 431, "strictValidation": true}, "imageAssets": {"target": "../images/voi-430/target.png", "shapes": {"S1": "../images/voi-430/shape_S1.png", "S2": "../images/voi-430/shape_S2.png", "S3": "../images/voi-430/shape_S3.png", "S4": "../images/voi-430/shape_S4.png", "S5": "../images/voi-430/shape_S5.png", "S6": "../images/voi-430/shape_S6.png"}}, "ID": "voi-430", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V2", "grid": [5, 0]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [8, 0]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [4, 3]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [9, 4]}]}, "legacy_answer": "S2 90 V2 [5,0]\nS3 180 V4 [8,0]\nS5 0 V3 [4,3]\nS6 180 V1 [9,4]", "solutionText": "S2 90 V2 [5,0]\nS3 180 V4 [8,0]\nS5 0 V3 [4,3]\nS6 180 V1 [9,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-430\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-430/target.png", "shapes": {"S1": "images/voi-430/shape_S1.png", "S2": "images/voi-430/shape_S2.png", "S3": "images/voi-430/shape_S3.png", "S4": "images/voi-430/shape_S4.png", "S5": "images/voi-430/shape_S5.png", "S6": "images/voi-430/shape_S6.png"}}, "__sample_id__": "voi-430"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 9], [0, 9], [0, 8], [1, 8], [1, 6], [2, 6]]}, {"polygon": [[9, 4], [9, 5], [8, 5], [8, 4]]}, {"polygon": [[3, 6], [3, 9], [2, 9], [2, 6]]}, {"polygon": [[0, 8], [0, 5], [2, 5], [2, 8]]}], "meta": {"seed": 4206057, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 432, "strictValidation": true}, "imageAssets": {"target": "../images/voi-431/target.png", "shapes": {"S1": "../images/voi-431/shape_S1.png", "S2": "../images/voi-431/shape_S2.png", "S3": "../images/voi-431/shape_S3.png", "S4": "../images/voi-431/shape_S4.png", "S5": "../images/voi-431/shape_S5.png", "S6": "../images/voi-431/shape_S6.png"}}, "ID": "voi-431", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V6", "grid": [2, 6]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [9, 5]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [2, 6]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [2, 5]}]}, "legacy_answer": "S1 180 V6 [2,6]\nS3 270 V2 [9,5]\nS5 270 V4 [2,6]\nS6 90 V3 [2,5]", "solutionText": "S1 180 V6 [2,6]\nS3 270 V2 [9,5]\nS5 270 V4 [2,6]\nS6 90 V3 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-431\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-431/target.png", "shapes": {"S1": "images/voi-431/shape_S1.png", "S2": "images/voi-431/shape_S2.png", "S3": "images/voi-431/shape_S3.png", "S4": "images/voi-431/shape_S4.png", "S5": "images/voi-431/shape_S5.png", "S6": "images/voi-431/shape_S6.png"}}, "__sample_id__": "voi-431"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 6], [3, 3], [5, 3], [5, 6]]}, {"polygon": [[5, 2], [5, 4], [4, 4], [4, 3], [2, 3], [2, 2]]}, {"polygon": [[10, 6], [7, 6], [7, 4], [10, 4]]}, {"polygon": [[7, 4], [9, 4], [9, 5], [7, 5]]}], "meta": {"seed": 4206058, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.743333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 433, "strictValidation": true}, "imageAssets": {"target": "../images/voi-432/target.png", "shapes": {"S1": "../images/voi-432/shape_S1.png", "S2": "../images/voi-432/shape_S2.png", "S3": "../images/voi-432/shape_S3.png", "S4": "../images/voi-432/shape_S4.png", "S5": "../images/voi-432/shape_S5.png", "S6": "../images/voi-432/shape_S6.png"}}, "ID": "voi-432", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 3]}, {"shape": "S3", "angle": 270, "vertex": "V6", "grid": [2, 2]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [10, 4]}, {"shape": "S6", "angle": 0, "vertex": "V1", "grid": [7, 4]}]}, "legacy_answer": "S1 90 V2 [3,3]\nS3 270 V6 [2,2]\nS4 180 V4 [10,4]\nS6 0 V1 [7,4]", "solutionText": "S1 90 V2 [3,3]\nS3 270 V6 [2,2]\nS4 180 V4 [10,4]\nS6 0 V1 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-432\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-432/target.png", "shapes": {"S1": "images/voi-432/shape_S1.png", "S2": "images/voi-432/shape_S2.png", "S3": "images/voi-432/shape_S3.png", "S4": "images/voi-432/shape_S4.png", "S5": "images/voi-432/shape_S5.png", "S6": "images/voi-432/shape_S6.png"}}, "__sample_id__": "voi-432"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 9], [5, 9], [5, 7], [6, 7]]}, {"polygon": [[7, 7], [5, 7], [5, 6], [6, 6], [6, 4], [7, 4]]}, {"polygon": [[6, 5], [7, 5], [7, 7], [6, 7]]}, {"polygon": [[3, 9], [3, 6], [5, 6], [5, 9]]}], "meta": {"seed": 4206059, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 434, "strictValidation": true}, "imageAssets": {"target": "../images/voi-433/target.png", "shapes": {"S1": "../images/voi-433/shape_S1.png", "S2": "../images/voi-433/shape_S2.png", "S3": "../images/voi-433/shape_S3.png", "S4": "../images/voi-433/shape_S4.png", "S5": "../images/voi-433/shape_S5.png", "S6": "../images/voi-433/shape_S6.png"}}, "ID": "voi-433", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [5, 9]}, {"shape": "S3", "angle": 180, "vertex": "V6", "grid": [7, 4]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [7, 7]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [5, 6]}]}, "legacy_answer": "S2 180 V2 [5,9]\nS3 180 V6 [7,4]\nS4 0 V3 [7,7]\nS6 90 V3 [5,6]", "solutionText": "S2 180 V2 [5,9]\nS3 180 V6 [7,4]\nS4 0 V3 [7,7]\nS6 90 V3 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-433\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-433/target.png", "shapes": {"S1": "images/voi-433/shape_S1.png", "S2": "images/voi-433/shape_S2.png", "S3": "images/voi-433/shape_S3.png", "S4": "images/voi-433/shape_S4.png", "S5": "images/voi-433/shape_S5.png", "S6": "images/voi-433/shape_S6.png"}}, "__sample_id__": "voi-433"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 4], [6, 6], [4, 4]]}, {"polygon": [[7, 3], [7, 5], [5, 5], [5, 3]]}, {"polygon": [[3, 2], [6, 2], [6, 4], [3, 4]]}, {"polygon": [[8, 1], [8, 3], [6, 3], [6, 1]]}], "meta": {"seed": 4206060, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.120625, "difficultyScore": 0.812641, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 435, "strictValidation": true}, "imageAssets": {"target": "../images/voi-434/target.png", "shapes": {"S1": "../images/voi-434/shape_S1.png", "S2": "../images/voi-434/shape_S2.png", "S3": "../images/voi-434/shape_S3.png", "S4": "../images/voi-434/shape_S4.png", "S5": "../images/voi-434/shape_S5.png", "S6": "../images/voi-434/shape_S6.png"}}, "ID": "voi-434", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [6, 4]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [5, 3]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [6, 2]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [8, 1]}]}, "legacy_answer": "S1 270 V1 [6,4]\nS2 270 V4 [5,3]\nS3 0 V2 [6,2]\nS4 270 V1 [8,1]", "solutionText": "S1 270 V1 [6,4]\nS2 270 V4 [5,3]\nS3 0 V2 [6,2]\nS4 270 V1 [8,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-434\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-434/target.png", "shapes": {"S1": "images/voi-434/shape_S1.png", "S2": "images/voi-434/shape_S2.png", "S3": "images/voi-434/shape_S3.png", "S4": "images/voi-434/shape_S4.png", "S5": "images/voi-434/shape_S5.png", "S6": "images/voi-434/shape_S6.png"}}, "__sample_id__": "voi-434"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 3], [6, 3], [6, 4], [5, 4], [5, 6], [4, 6]]}, {"polygon": [[4, 6], [4, 4], [6, 4], [6, 6]]}, {"polygon": [[3, 1], [5, 1], [5, 2], [4, 2], [4, 4], [3, 4]]}, {"polygon": [[0, 2], [3, 2], [2, 3], [0, 3]]}], "meta": {"seed": 4206061, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 1, "fillRatio": 0.105313, "difficultyScore": 0.4883, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 436, "strictValidation": true}, "imageAssets": {"target": "../images/voi-435/target.png", "shapes": {"S1": "../images/voi-435/shape_S1.png", "S2": "../images/voi-435/shape_S2.png", "S3": "../images/voi-435/shape_S3.png", "S4": "../images/voi-435/shape_S4.png", "S5": "../images/voi-435/shape_S5.png", "S6": "../images/voi-435/shape_S6.png"}}, "ID": "voi-435", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V5", "grid": [5, 6]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 6]}, {"shape": "S4", "angle": 0, "vertex": "V5", "grid": [4, 4]}, {"shape": "S6", "angle": 0, "vertex": "V2", "grid": [3, 2]}]}, "legacy_answer": "S1 0 V5 [5,6]\nS2 90 V4 [6,6]\nS4 0 V5 [4,4]\nS6 0 V2 [3,2]", "solutionText": "S1 0 V5 [5,6]\nS2 90 V4 [6,6]\nS4 0 V5 [4,4]\nS6 0 V2 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-435\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-435/target.png", "shapes": {"S1": "images/voi-435/shape_S1.png", "S2": "images/voi-435/shape_S2.png", "S3": "images/voi-435/shape_S3.png", "S4": "images/voi-435/shape_S4.png", "S5": "images/voi-435/shape_S5.png", "S6": "images/voi-435/shape_S6.png"}}, "__sample_id__": "voi-435"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[7, 1], [7, 4], [6, 4], [6, 1]]}, {"polygon": [[4, 5], [2, 5], [2, 4], [3, 4], [3, 2], [4, 2]]}, {"polygon": [[6, 3], [3, 3], [3, 1], [6, 1]]}, {"polygon": [[6, 4], [4, 4], [6, 2]]}], "meta": {"seed": 4206062, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.20332, "contourComplexity": 79, "connectedComponents": 1, "fillRatio": 0.12, "difficultyScore": 0.746722, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 437, "strictValidation": true}, "imageAssets": {"target": "../images/voi-436/target.png", "shapes": {"S1": "../images/voi-436/shape_S1.png", "S2": "../images/voi-436/shape_S2.png", "S3": "../images/voi-436/shape_S3.png", "S4": "../images/voi-436/shape_S4.png", "S5": "../images/voi-436/shape_S5.png", "S6": "../images/voi-436/shape_S6.png"}}, "ID": "voi-436", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [7, 1]}, {"shape": "S2", "angle": 180, "vertex": "V6", "grid": [4, 2]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [6, 1]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [6, 4]}]}, "legacy_answer": "S1 270 V1 [7,1]\nS2 180 V6 [4,2]\nS3 180 V4 [6,1]\nS6 180 V1 [6,4]", "solutionText": "S1 270 V1 [7,1]\nS2 180 V6 [4,2]\nS3 180 V4 [6,1]\nS6 180 V1 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-436\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-436/target.png", "shapes": {"S1": "images/voi-436/shape_S1.png", "S2": "images/voi-436/shape_S2.png", "S3": "images/voi-436/shape_S3.png", "S4": "images/voi-436/shape_S4.png", "S5": "images/voi-436/shape_S5.png", "S6": "images/voi-436/shape_S6.png"}}, "__sample_id__": "voi-436"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 6], [5, 6], [5, 8], [3, 8]]}, {"polygon": [[5, 6], [2, 6], [2, 5], [5, 5]]}, {"polygon": [[4, 8], [1, 8], [1, 6], [4, 6]]}, {"polygon": [[2, 4], [2, 7], [1, 7], [1, 4]]}], "meta": {"seed": 4206063, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.375, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.1, "difficultyScore": 0.7, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 438, "strictValidation": true}, "imageAssets": {"target": "../images/voi-437/target.png", "shapes": {"S1": "../images/voi-437/shape_S1.png", "S2": "../images/voi-437/shape_S2.png", "S3": "../images/voi-437/shape_S3.png", "S4": "../images/voi-437/shape_S4.png", "S5": "../images/voi-437/shape_S5.png", "S6": "../images/voi-437/shape_S6.png"}}, "ID": "voi-437", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 6]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [2, 6]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [4, 8]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [1, 7]}]}, "legacy_answer": "S1 0 V1 [3,6]\nS4 180 V2 [2,6]\nS5 180 V1 [4,8]\nS6 270 V3 [1,7]", "solutionText": "S1 0 V1 [3,6]\nS4 180 V2 [2,6]\nS5 180 V1 [4,8]\nS6 270 V3 [1,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-437\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-437/target.png", "shapes": {"S1": "images/voi-437/shape_S1.png", "S2": "images/voi-437/shape_S2.png", "S3": "images/voi-437/shape_S3.png", "S4": "images/voi-437/shape_S4.png", "S5": "images/voi-437/shape_S5.png", "S6": "images/voi-437/shape_S6.png"}}, "__sample_id__": "voi-437"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 2], [6, 2], [6, 4], [5, 4]]}, {"polygon": [[4, 7], [4, 4], [5, 4], [5, 7]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[3, 5], [3, 2], [4, 2], [4, 5]]}], "meta": {"seed": 4206064, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.1, "difficultyScore": 0.457143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 439, "strictValidation": true}, "imageAssets": {"target": "../images/voi-438/target.png", "shapes": {"S1": "../images/voi-438/shape_S1.png", "S2": "../images/voi-438/shape_S2.png", "S3": "../images/voi-438/shape_S3.png", "S4": "../images/voi-438/shape_S4.png", "S5": "../images/voi-438/shape_S5.png", "S6": "../images/voi-438/shape_S6.png"}}, "ID": "voi-438", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 2]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [5, 7]}, {"shape": "S5", "angle": 270, "vertex": "V1", "grid": [5, 1]}, {"shape": "S6", "angle": 90, "vertex": "V4", "grid": [4, 5]}]}, "legacy_answer": "S2 0 V2 [6,2]\nS4 90 V4 [5,7]\nS5 270 V1 [5,1]\nS6 90 V4 [4,5]", "solutionText": "S2 0 V2 [6,2]\nS4 90 V4 [5,7]\nS5 270 V1 [5,1]\nS6 90 V4 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-438\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-438/target.png", "shapes": {"S1": "images/voi-438/shape_S1.png", "S2": "images/voi-438/shape_S2.png", "S3": "images/voi-438/shape_S3.png", "S4": "images/voi-438/shape_S4.png", "S5": "images/voi-438/shape_S5.png", "S6": "images/voi-438/shape_S6.png"}}, "__sample_id__": "voi-438"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 7], [8, 9], [7, 9], [7, 7]]}, {"polygon": [[7, 9], [6, 9], [6, 6], [7, 6]]}, {"polygon": [[5, 8], [5, 6], [7, 6], [7, 8]]}, {"polygon": [[7, 6], [4, 6], [4, 4], [7, 4]]}], "meta": {"seed": 4206065, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 440, "strictValidation": true}, "imageAssets": {"target": "../images/voi-439/target.png", "shapes": {"S1": "../images/voi-439/shape_S1.png", "S2": "../images/voi-439/shape_S2.png", "S3": "../images/voi-439/shape_S3.png", "S4": "../images/voi-439/shape_S4.png", "S5": "../images/voi-439/shape_S5.png", "S6": "../images/voi-439/shape_S6.png"}}, "ID": "voi-439", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [8, 7]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 9]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [5, 8]}, {"shape": "S6", "angle": 180, "vertex": "V4", "grid": [7, 4]}]}, "legacy_answer": "S1 270 V1 [8,7]\nS2 180 V1 [7,9]\nS5 90 V1 [5,8]\nS6 180 V4 [7,4]", "solutionText": "S1 270 V1 [8,7]\nS2 180 V1 [7,9]\nS5 90 V1 [5,8]\nS6 180 V4 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-439\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-439/target.png", "shapes": {"S1": "images/voi-439/shape_S1.png", "S2": "images/voi-439/shape_S2.png", "S3": "images/voi-439/shape_S3.png", "S4": "images/voi-439/shape_S4.png", "S5": "images/voi-439/shape_S5.png", "S6": "images/voi-439/shape_S6.png"}}, "__sample_id__": "voi-439"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [5, 5], [4, 5], [4, 4], [2, 4], [2, 3]]}, {"polygon": [[0, 3], [0, 1], [1, 1], [1, 2], [3, 2], [3, 3]]}, {"polygon": [[4, 3], [4, 6], [2, 6], [2, 3]]}, {"polygon": [[2, 3], [2, 5], [0, 5], [0, 3]]}], "meta": {"seed": 4206066, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 16, "connectedComponents": 1, "fillRatio": 0.14, "difficultyScore": 0.631111, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 441, "strictValidation": true}, "imageAssets": {"target": "../images/voi-440/target.png", "shapes": {"S1": "../images/voi-440/shape_S1.png", "S2": "../images/voi-440/shape_S2.png", "S3": "../images/voi-440/shape_S3.png", "S4": "../images/voi-440/shape_S4.png", "S5": "../images/voi-440/shape_S5.png", "S6": "../images/voi-440/shape_S6.png"}}, "ID": "voi-440", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 5]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [0, 1]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [4, 3]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [0, 5]}]}, "legacy_answer": "S1 270 V2 [5,5]\nS3 90 V2 [0,1]\nS4 270 V1 [4,3]\nS6 270 V3 [0,5]", "solutionText": "S1 270 V2 [5,5]\nS3 90 V2 [0,1]\nS4 270 V1 [4,3]\nS6 270 V3 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-440\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-440/target.png", "shapes": {"S1": "images/voi-440/shape_S1.png", "S2": "images/voi-440/shape_S2.png", "S3": "images/voi-440/shape_S3.png", "S4": "images/voi-440/shape_S4.png", "S5": "images/voi-440/shape_S5.png", "S6": "images/voi-440/shape_S6.png"}}, "__sample_id__": "voi-440"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 6], [2, 3], [3, 3], [3, 6]]}, {"polygon": [[5, 0], [8, 0], [8, 2], [5, 2]]}, {"polygon": [[7, 2], [7, 0], [8, 0], [8, 1], [10, 1], [10, 2]]}, {"polygon": [[7, 0], [10, 0], [10, 1], [7, 1]]}], "meta": {"seed": 4206067, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.81, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 442, "strictValidation": true}, "imageAssets": {"target": "../images/voi-441/target.png", "shapes": {"S1": "../images/voi-441/shape_S1.png", "S2": "../images/voi-441/shape_S2.png", "S3": "../images/voi-441/shape_S3.png", "S4": "../images/voi-441/shape_S4.png", "S5": "../images/voi-441/shape_S5.png", "S6": "../images/voi-441/shape_S6.png"}}, "ID": "voi-441", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [3, 6]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [5, 2]}, {"shape": "S3", "angle": 90, "vertex": "V6", "grid": [10, 2]}, {"shape": "S6", "angle": 0, "vertex": "V4", "grid": [7, 1]}]}, "legacy_answer": "S1 90 V4 [3,6]\nS2 0 V4 [5,2]\nS3 90 V6 [10,2]\nS6 0 V4 [7,1]", "solutionText": "S1 90 V4 [3,6]\nS2 0 V4 [5,2]\nS3 90 V6 [10,2]\nS6 0 V4 [7,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-441\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-441/target.png", "shapes": {"S1": "images/voi-441/shape_S1.png", "S2": "images/voi-441/shape_S2.png", "S3": "images/voi-441/shape_S3.png", "S4": "images/voi-441/shape_S4.png", "S5": "images/voi-441/shape_S5.png", "S6": "images/voi-441/shape_S6.png"}}, "__sample_id__": "voi-441"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 8], [0, 5], [2, 5], [2, 8]]}, {"polygon": [[2, 5], [4, 5], [4, 7], [2, 7]]}, {"polygon": [[0, 8], [0, 6], [2, 8]]}, {"polygon": [[7, 4], [7, 6], [5, 6], [5, 4]]}], "meta": {"seed": 4206068, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.256809, "contourComplexity": 72, "connectedComponents": 2, "fillRatio": 0.119375, "difficultyScore": 0.784013, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 443, "strictValidation": true}, "imageAssets": {"target": "../images/voi-442/target.png", "shapes": {"S1": "../images/voi-442/shape_S1.png", "S2": "../images/voi-442/shape_S2.png", "S3": "../images/voi-442/shape_S3.png", "S4": "../images/voi-442/shape_S4.png", "S5": "../images/voi-442/shape_S5.png", "S6": "../images/voi-442/shape_S6.png"}}, "ID": "voi-442", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [0, 5]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 5]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [0, 8]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [7, 6]}]}, "legacy_answer": "S1 90 V2 [0,5]\nS4 0 V2 [4,5]\nS5 90 V1 [0,8]\nS6 270 V2 [7,6]", "solutionText": "S1 90 V2 [0,5]\nS4 0 V2 [4,5]\nS5 90 V1 [0,8]\nS6 270 V2 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-442\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-442/target.png", "shapes": {"S1": "images/voi-442/shape_S1.png", "S2": "images/voi-442/shape_S2.png", "S3": "images/voi-442/shape_S3.png", "S4": "images/voi-442/shape_S4.png", "S5": "images/voi-442/shape_S5.png", "S6": "images/voi-442/shape_S6.png"}}, "__sample_id__": "voi-442"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[4, 2], [4, 1], [6, 1], [6, 2]]}, {"polygon": [[6, 3], [6, 4], [4, 4], [4, 3]]}, {"polygon": [[5, 6], [3, 6], [3, 5], [4, 5], [4, 3], [5, 3]]}], "meta": {"seed": 4206069, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 444, "strictValidation": true}, "imageAssets": {"target": "../images/voi-443/target.png", "shapes": {"S1": "../images/voi-443/shape_S1.png", "S2": "../images/voi-443/shape_S2.png", "S3": "../images/voi-443/shape_S3.png", "S4": "../images/voi-443/shape_S4.png", "S5": "../images/voi-443/shape_S5.png", "S6": "../images/voi-443/shape_S6.png"}}, "ID": "voi-443", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [5, 3]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 1]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [4, 3]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [5, 6]}]}, "legacy_answer": "S1 0 V1 [5,3]\nS3 90 V3 [6,1]\nS4 270 V4 [4,3]\nS5 180 V1 [5,6]", "solutionText": "S1 0 V1 [5,3]\nS3 90 V3 [6,1]\nS4 270 V4 [4,3]\nS5 180 V1 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-443\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-443/target.png", "shapes": {"S1": "images/voi-443/shape_S1.png", "S2": "images/voi-443/shape_S2.png", "S3": "images/voi-443/shape_S3.png", "S4": "images/voi-443/shape_S4.png", "S5": "images/voi-443/shape_S5.png", "S6": "images/voi-443/shape_S6.png"}}, "__sample_id__": "voi-443"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 7], [4, 7], [4, 5], [6, 5]]}, {"polygon": [[3, 6], [3, 5], [4, 6]]}, {"polygon": [[3, 5], [3, 2], [5, 2], [5, 5]]}, {"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}], "meta": {"seed": 4206070, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 45, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 445, "strictValidation": true}, "imageAssets": {"target": "../images/voi-444/target.png", "shapes": {"S1": "../images/voi-444/shape_S1.png", "S2": "../images/voi-444/shape_S2.png", "S3": "../images/voi-444/shape_S3.png", "S4": "../images/voi-444/shape_S4.png", "S5": "../images/voi-444/shape_S5.png", "S6": "../images/voi-444/shape_S6.png"}}, "ID": "voi-444", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [6, 5]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [3, 6]}, {"shape": "S5", "angle": 90, "vertex": "V4", "grid": [5, 5]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [3, 1]}]}, "legacy_answer": "S1 180 V4 [6,5]\nS3 90 V1 [3,6]\nS5 90 V4 [5,5]\nS6 90 V2 [3,1]", "solutionText": "S1 180 V4 [6,5]\nS3 90 V1 [3,6]\nS5 90 V4 [5,5]\nS6 90 V2 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-444\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-444/target.png", "shapes": {"S1": "images/voi-444/shape_S1.png", "S2": "images/voi-444/shape_S2.png", "S3": "images/voi-444/shape_S3.png", "S4": "images/voi-444/shape_S4.png", "S5": "images/voi-444/shape_S5.png", "S6": "images/voi-444/shape_S6.png"}}, "__sample_id__": "voi-444"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 1], [1, 3], [0, 3], [0, 1]]}, {"polygon": [[8, 10], [7, 10], [7, 7], [8, 7]]}, {"polygon": [[0, 0], [2, 0], [2, 2], [0, 2]]}, {"polygon": [[3, 4], [0, 4], [0, 2], [3, 2]]}], "meta": {"seed": 4206071, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.763333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 446, "strictValidation": true}, "imageAssets": {"target": "../images/voi-445/target.png", "shapes": {"S1": "../images/voi-445/shape_S1.png", "S2": "../images/voi-445/shape_S2.png", "S3": "../images/voi-445/shape_S3.png", "S4": "../images/voi-445/shape_S4.png", "S5": "../images/voi-445/shape_S5.png", "S6": "../images/voi-445/shape_S6.png"}}, "ID": "voi-445", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [1, 1]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [7, 7]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [2, 0]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [0, 4]}]}, "legacy_answer": "S2 270 V1 [1,1]\nS4 180 V3 [7,7]\nS5 0 V2 [2,0]\nS6 180 V2 [0,4]", "solutionText": "S2 270 V1 [1,1]\nS4 180 V3 [7,7]\nS5 0 V2 [2,0]\nS6 180 V2 [0,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-445\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-445/target.png", "shapes": {"S1": "images/voi-445/shape_S1.png", "S2": "images/voi-445/shape_S2.png", "S3": "images/voi-445/shape_S3.png", "S4": "images/voi-445/shape_S4.png", "S5": "images/voi-445/shape_S5.png", "S6": "images/voi-445/shape_S6.png"}}, "__sample_id__": "voi-445"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[5, 5], [5, 3], [7, 3], [7, 5]]}, {"polygon": [[3, 1], [3, 0], [4, 0], [4, 1]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}], "meta": {"seed": 4206072, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.11, "difficultyScore": 0.513333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 447, "strictValidation": true}, "imageAssets": {"target": "../images/voi-446/target.png", "shapes": {"S1": "../images/voi-446/shape_S1.png", "S2": "../images/voi-446/shape_S2.png", "S3": "../images/voi-446/shape_S3.png", "S4": "../images/voi-446/shape_S4.png", "S5": "../images/voi-446/shape_S5.png", "S6": "../images/voi-446/shape_S6.png"}}, "ID": "voi-446", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [4, 1]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [7, 5]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [4, 0]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [5, 1]}]}, "legacy_answer": "S2 270 V4 [4,1]\nS3 90 V4 [7,5]\nS5 90 V3 [4,0]\nS6 90 V3 [5,1]", "solutionText": "S2 270 V4 [4,1]\nS3 90 V4 [7,5]\nS5 90 V3 [4,0]\nS6 90 V3 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-446\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-446/target.png", "shapes": {"S1": "images/voi-446/shape_S1.png", "S2": "images/voi-446/shape_S2.png", "S3": "images/voi-446/shape_S3.png", "S4": "images/voi-446/shape_S4.png", "S5": "images/voi-446/shape_S5.png", "S6": "images/voi-446/shape_S6.png"}}, "__sample_id__": "voi-446"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[9, 6], [9, 8], [8, 8], [8, 7], [6, 7], [6, 6]]}, {"polygon": [[3, 10], [0, 10], [0, 8], [3, 8]]}, {"polygon": [[0, 10], [0, 7], [1, 8], [1, 10]]}, {"polygon": [[2, 8], [1, 8], [1, 6], [2, 6]]}], "meta": {"seed": 4206073, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 46, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.7383, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 448, "strictValidation": true}, "imageAssets": {"target": "../images/voi-447/target.png", "shapes": {"S1": "../images/voi-447/shape_S1.png", "S2": "../images/voi-447/shape_S2.png", "S3": "../images/voi-447/shape_S3.png", "S4": "../images/voi-447/shape_S4.png", "S5": "../images/voi-447/shape_S5.png", "S6": "../images/voi-447/shape_S6.png"}}, "ID": "voi-447", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V5", "grid": [6, 7]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [3, 8]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [1, 10]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [1, 6]}]}, "legacy_answer": "S2 270 V5 [6,7]\nS3 180 V4 [3,8]\nS4 90 V4 [1,10]\nS5 180 V3 [1,6]", "solutionText": "S2 270 V5 [6,7]\nS3 180 V4 [3,8]\nS4 90 V4 [1,10]\nS5 180 V3 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-447\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-447/target.png", "shapes": {"S1": "images/voi-447/shape_S1.png", "S2": "images/voi-447/shape_S2.png", "S3": "images/voi-447/shape_S3.png", "S4": "images/voi-447/shape_S4.png", "S5": "images/voi-447/shape_S5.png", "S6": "images/voi-447/shape_S6.png"}}, "__sample_id__": "voi-447"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[0, 7], [0, 4], [2, 4], [2, 7]]}, {"polygon": [[4, 9], [2, 9], [2, 7], [4, 7]]}, {"polygon": [[0, 7], [0, 5], [1, 5], [1, 7]]}, {"polygon": [[4, 8], [4, 6], [5, 6], [5, 8]]}], "meta": {"seed": 4206074, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.707143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 449, "strictValidation": true}, "imageAssets": {"target": "../images/voi-448/target.png", "shapes": {"S1": "../images/voi-448/shape_S1.png", "S2": "../images/voi-448/shape_S2.png", "S3": "../images/voi-448/shape_S3.png", "S4": "../images/voi-448/shape_S4.png", "S5": "../images/voi-448/shape_S5.png", "S6": "../images/voi-448/shape_S6.png"}}, "ID": "voi-448", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [2, 7]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 9]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [1, 5]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [4, 8]}]}, "legacy_answer": "S1 90 V4 [2,7]\nS2 180 V1 [4,9]\nS3 90 V3 [1,5]\nS4 90 V1 [4,8]", "solutionText": "S1 90 V4 [2,7]\nS2 180 V1 [4,9]\nS3 90 V3 [1,5]\nS4 90 V1 [4,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-448\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-448/target.png", "shapes": {"S1": "images/voi-448/shape_S1.png", "S2": "images/voi-448/shape_S2.png", "S3": "images/voi-448/shape_S3.png", "S4": "images/voi-448/shape_S4.png", "S5": "images/voi-448/shape_S5.png", "S6": "images/voi-448/shape_S6.png"}}, "__sample_id__": "voi-448"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 5], [2, 5], [1, 6]]}, {"polygon": [[4, 9], [7, 9], [6, 10], [4, 10]]}, {"polygon": [[6, 9], [6, 6], [8, 6], [8, 9]]}, {"polygon": [[7, 10], [7, 7], [9, 7], [9, 10]]}], "meta": {"seed": 4206075, "requiredShapeCount": 4, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 78, "connectedComponents": 2, "fillRatio": 0.110625, "difficultyScore": 0.766509, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 450, "strictValidation": true}, "imageAssets": {"target": "../images/voi-449/target.png", "shapes": {"S1": "../images/voi-449/shape_S1.png", "S2": "../images/voi-449/shape_S2.png", "S3": "../images/voi-449/shape_S3.png", "S4": "../images/voi-449/shape_S4.png", "S5": "../images/voi-449/shape_S5.png", "S6": "../images/voi-449/shape_S6.png"}}, "ID": "voi-449", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [1, 6]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [4, 10]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [8, 9]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [7, 7]}]}, "legacy_answer": "S1 0 V3 [1,6]\nS3 0 V4 [4,10]\nS4 90 V4 [8,9]\nS6 90 V2 [7,7]", "solutionText": "S1 0 V3 [1,6]\nS3 0 V4 [4,10]\nS4 90 V4 [8,9]\nS6 90 V2 [7,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-449\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-449/target.png", "shapes": {"S1": "images/voi-449/shape_S1.png", "S2": "images/voi-449/shape_S2.png", "S3": "images/voi-449/shape_S3.png", "S4": "images/voi-449/shape_S4.png", "S5": "images/voi-449/shape_S5.png", "S6": "images/voi-449/shape_S6.png"}}, "__sample_id__": "voi-449"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 3], [6, 2], [9, 2], [9, 3]]}, {"polygon": [[6, 0], [6, 3], [4, 3], [4, 0]]}, {"polygon": [[5, 0], [6, 0], [6, 2], [5, 2]]}, {"polygon": [[1, 3], [3, 3], [3, 4], [2, 4], [2, 6], [1, 6]]}], "meta": {"seed": 4207001, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.903333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 451, "strictValidation": true}, "imageAssets": {"target": "../images/voi-450/target.png", "shapes": {"S1": "../images/voi-450/shape_S1.png", "S2": "../images/voi-450/shape_S2.png", "S3": "../images/voi-450/shape_S3.png", "S4": "../images/voi-450/shape_S4.png", "S5": "../images/voi-450/shape_S5.png", "S6": "../images/voi-450/shape_S6.png", "S7": "../images/voi-450/shape_S7.png"}}, "ID": "voi-450", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V4", "grid": [9, 3]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [6, 3]}, {"shape": "S6", "angle": 0, "vertex": "V4", "grid": [5, 2]}, {"shape": "S7", "angle": 0, "vertex": "V3", "grid": [3, 4]}]}, "legacy_answer": "S3 90 V4 [9,3]\nS4 270 V2 [6,3]\nS6 0 V4 [5,2]\nS7 0 V3 [3,4]", "solutionText": "S3 90 V4 [9,3]\nS4 270 V2 [6,3]\nS6 0 V4 [5,2]\nS7 0 V3 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-450\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-450/target.png", "shapes": {"S1": "images/voi-450/shape_S1.png", "S2": "images/voi-450/shape_S2.png", "S3": "images/voi-450/shape_S3.png", "S4": "images/voi-450/shape_S4.png", "S5": "images/voi-450/shape_S5.png", "S6": "images/voi-450/shape_S6.png", "S7": "images/voi-450/shape_S7.png"}}, "__sample_id__": "voi-450"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 9], [4, 7], [5, 7], [5, 8], [7, 8], [7, 9]]}, {"polygon": [[6, 6], [8, 6], [8, 7], [7, 7], [7, 9], [6, 9]]}, {"polygon": [[6, 10], [5, 10], [5, 7], [6, 7]]}, {"polygon": [[3, 7], [4, 7], [4, 10], [3, 10]]}], "meta": {"seed": 4207002, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 452, "strictValidation": true}, "imageAssets": {"target": "../images/voi-451/target.png", "shapes": {"S1": "../images/voi-451/shape_S1.png", "S2": "../images/voi-451/shape_S2.png", "S3": "../images/voi-451/shape_S3.png", "S4": "../images/voi-451/shape_S4.png", "S5": "../images/voi-451/shape_S5.png", "S6": "../images/voi-451/shape_S6.png", "S7": "../images/voi-451/shape_S7.png"}}, "ID": "voi-451", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V5", "grid": [7, 8]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [8, 6]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [6, 10]}, {"shape": "S7", "angle": 0, "vertex": "V1", "grid": [3, 7]}]}, "legacy_answer": "S1 90 V5 [7,8]\nS2 0 V2 [8,6]\nS5 180 V1 [6,10]\nS7 0 V1 [3,7]", "solutionText": "S1 90 V5 [7,8]\nS2 0 V2 [8,6]\nS5 180 V1 [6,10]\nS7 0 V1 [3,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-451\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-451/target.png", "shapes": {"S1": "images/voi-451/shape_S1.png", "S2": "images/voi-451/shape_S2.png", "S3": "images/voi-451/shape_S3.png", "S4": "images/voi-451/shape_S4.png", "S5": "images/voi-451/shape_S5.png", "S6": "images/voi-451/shape_S6.png", "S7": "images/voi-451/shape_S7.png"}}, "__sample_id__": "voi-451"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [2, 4], [2, 2], [3, 2]]}, {"polygon": [[5, 8], [3, 8], [3, 6], [5, 6]]}, {"polygon": [[2, 4], [4, 4], [4, 6], [2, 6]]}, {"polygon": [[5, 4], [2, 4], [2, 2], [5, 2]]}], "meta": {"seed": 4207003, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.12, "difficultyScore": 0.7, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 453, "strictValidation": true}, "imageAssets": {"target": "../images/voi-452/target.png", "shapes": {"S1": "../images/voi-452/shape_S1.png", "S2": "../images/voi-452/shape_S2.png", "S3": "../images/voi-452/shape_S3.png", "S4": "../images/voi-452/shape_S4.png", "S5": "../images/voi-452/shape_S5.png", "S6": "../images/voi-452/shape_S6.png", "S7": "../images/voi-452/shape_S7.png"}}, "ID": "voi-452", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [3, 8]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [4, 6]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [2, 4]}]}, "legacy_answer": "S2 180 V1 [3,4]\nS3 180 V2 [3,8]\nS5 0 V3 [4,6]\nS6 180 V2 [2,4]", "solutionText": "S2 180 V1 [3,4]\nS3 180 V2 [3,8]\nS5 0 V3 [4,6]\nS6 180 V2 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-452\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-452/target.png", "shapes": {"S1": "images/voi-452/shape_S1.png", "S2": "images/voi-452/shape_S2.png", "S3": "images/voi-452/shape_S3.png", "S4": "images/voi-452/shape_S4.png", "S5": "images/voi-452/shape_S5.png", "S6": "images/voi-452/shape_S6.png", "S7": "images/voi-452/shape_S7.png"}}, "__sample_id__": "voi-452"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [2, 7], [2, 6], [3, 6], [3, 4], [4, 4]]}, {"polygon": [[4, 4], [6, 4], [6, 5], [5, 5], [5, 7], [4, 7]]}, {"polygon": [[7, 5], [4, 5], [4, 4], [7, 4]]}, {"polygon": [[5, 2], [5, 4], [3, 4], [3, 2]]}], "meta": {"seed": 4207004, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.903333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 454, "strictValidation": true}, "imageAssets": {"target": "../images/voi-453/target.png", "shapes": {"S1": "../images/voi-453/shape_S1.png", "S2": "../images/voi-453/shape_S2.png", "S3": "../images/voi-453/shape_S3.png", "S4": "../images/voi-453/shape_S4.png", "S5": "../images/voi-453/shape_S5.png", "S6": "../images/voi-453/shape_S6.png", "S7": "../images/voi-453/shape_S7.png"}}, "ID": "voi-453", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V6", "grid": [4, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [4, 4]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [4, 4]}, {"shape": "S7", "angle": 270, "vertex": "V1", "grid": [5, 2]}]}, "legacy_answer": "S2 180 V6 [4,4]\nS4 0 V1 [4,4]\nS6 180 V3 [4,4]\nS7 270 V1 [5,2]", "solutionText": "S2 180 V6 [4,4]\nS4 0 V1 [4,4]\nS6 180 V3 [4,4]\nS7 270 V1 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-453\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-453/target.png", "shapes": {"S1": "images/voi-453/shape_S1.png", "S2": "images/voi-453/shape_S2.png", "S3": "images/voi-453/shape_S3.png", "S4": "images/voi-453/shape_S4.png", "S5": "images/voi-453/shape_S5.png", "S6": "images/voi-453/shape_S6.png", "S7": "images/voi-453/shape_S7.png"}}, "__sample_id__": "voi-453"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 5], [6, 7], [4, 7], [4, 5]]}, {"polygon": [[3, 5], [4, 5], [4, 8], [3, 8]]}, {"polygon": [[9, 0], [10, 0], [10, 3], [9, 3]]}, {"polygon": [[7, 5], [7, 7], [6, 7], [6, 6], [4, 6], [4, 5]]}], "meta": {"seed": 4207005, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 455, "strictValidation": true}, "imageAssets": {"target": "../images/voi-454/target.png", "shapes": {"S1": "../images/voi-454/shape_S1.png", "S2": "../images/voi-454/shape_S2.png", "S3": "../images/voi-454/shape_S3.png", "S4": "../images/voi-454/shape_S4.png", "S5": "../images/voi-454/shape_S5.png", "S6": "../images/voi-454/shape_S6.png", "S7": "../images/voi-454/shape_S7.png"}}, "ID": "voi-454", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [4, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [3, 5]}, {"shape": "S5", "angle": 0, "vertex": "V2", "grid": [10, 0]}, {"shape": "S7", "angle": 270, "vertex": "V1", "grid": [7, 5]}]}, "legacy_answer": "S2 270 V4 [4,5]\nS4 0 V1 [3,5]\nS5 0 V2 [10,0]\nS7 270 V1 [7,5]", "solutionText": "S2 270 V4 [4,5]\nS4 0 V1 [3,5]\nS5 0 V2 [10,0]\nS7 270 V1 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-454\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-454/target.png", "shapes": {"S1": "images/voi-454/shape_S1.png", "S2": "images/voi-454/shape_S2.png", "S3": "images/voi-454/shape_S3.png", "S4": "images/voi-454/shape_S4.png", "S5": "images/voi-454/shape_S5.png", "S6": "images/voi-454/shape_S6.png", "S7": "images/voi-454/shape_S7.png"}}, "__sample_id__": "voi-454"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[9, 7], [6, 7], [6, 5], [9, 5]]}, {"polygon": [[6, 3], [9, 3], [9, 5], [6, 5]]}, {"polygon": [[5, 2], [7, 2], [7, 3], [6, 3], [6, 5], [5, 5]]}, {"polygon": [[7, 7], [7, 4], [8, 4], [8, 7]]}], "meta": {"seed": 4207006, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.13, "difficultyScore": 0.416842, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 456, "strictValidation": true}, "imageAssets": {"target": "../images/voi-455/target.png", "shapes": {"S1": "../images/voi-455/shape_S1.png", "S2": "../images/voi-455/shape_S2.png", "S3": "../images/voi-455/shape_S3.png", "S4": "../images/voi-455/shape_S4.png", "S5": "../images/voi-455/shape_S5.png", "S6": "../images/voi-455/shape_S6.png", "S7": "../images/voi-455/shape_S7.png"}}, "ID": "voi-455", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V4", "grid": [9, 5]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [6, 3]}, {"shape": "S5", "angle": 0, "vertex": "V4", "grid": [6, 3]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [7, 7]}]}, "legacy_answer": "S2 180 V4 [9,5]\nS3 0 V1 [6,3]\nS5 0 V4 [6,3]\nS6 90 V1 [7,7]", "solutionText": "S2 180 V4 [9,5]\nS3 0 V1 [6,3]\nS5 0 V4 [6,3]\nS6 90 V1 [7,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-455\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-455/target.png", "shapes": {"S1": "images/voi-455/shape_S1.png", "S2": "images/voi-455/shape_S2.png", "S3": "images/voi-455/shape_S3.png", "S4": "images/voi-455/shape_S4.png", "S5": "images/voi-455/shape_S5.png", "S6": "images/voi-455/shape_S6.png", "S7": "images/voi-455/shape_S7.png"}}, "__sample_id__": "voi-455"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 7], [0, 7], [0, 6], [3, 6]]}, {"polygon": [[5, 9], [5, 8], [8, 8], [8, 9]]}, {"polygon": [[3, 6], [2, 6], [2, 4], [3, 4]]}, {"polygon": [[0, 7], [0, 4], [2, 4], [2, 7]]}], "meta": {"seed": 4207007, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 457, "strictValidation": true}, "imageAssets": {"target": "../images/voi-456/target.png", "shapes": {"S1": "../images/voi-456/shape_S1.png", "S2": "../images/voi-456/shape_S2.png", "S3": "../images/voi-456/shape_S3.png", "S4": "../images/voi-456/shape_S4.png", "S5": "../images/voi-456/shape_S5.png", "S6": "../images/voi-456/shape_S6.png", "S7": "../images/voi-456/shape_S7.png"}}, "ID": "voi-456", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [0, 7]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [8, 9]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [3, 6]}, {"shape": "S7", "angle": 90, "vertex": "V4", "grid": [2, 7]}]}, "legacy_answer": "S1 180 V2 [0,7]\nS2 90 V4 [8,9]\nS4 180 V1 [3,6]\nS7 90 V4 [2,7]", "solutionText": "S1 180 V2 [0,7]\nS2 90 V4 [8,9]\nS4 180 V1 [3,6]\nS7 90 V4 [2,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-456\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-456/target.png", "shapes": {"S1": "images/voi-456/shape_S1.png", "S2": "images/voi-456/shape_S2.png", "S3": "images/voi-456/shape_S3.png", "S4": "images/voi-456/shape_S4.png", "S5": "images/voi-456/shape_S5.png", "S6": "images/voi-456/shape_S6.png", "S7": "images/voi-456/shape_S7.png"}}, "__sample_id__": "voi-456"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}, {"polygon": [[4, 4], [4, 1], [6, 1], [6, 4]]}, {"polygon": [[2, 2], [2, 0], [3, 0], [3, 1], [5, 1], [5, 2]]}, {"polygon": [[5, 2], [3, 2], [3, 0], [5, 0]]}], "meta": {"seed": 4207008, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.14, "difficultyScore": 0.771111, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 458, "strictValidation": true}, "imageAssets": {"target": "../images/voi-457/target.png", "shapes": {"S1": "../images/voi-457/shape_S1.png", "S2": "../images/voi-457/shape_S2.png", "S3": "../images/voi-457/shape_S3.png", "S4": "../images/voi-457/shape_S4.png", "S5": "../images/voi-457/shape_S5.png", "S6": "../images/voi-457/shape_S6.png", "S7": "../images/voi-457/shape_S7.png"}}, "ID": "voi-457", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [6, 1]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [2, 2]}, {"shape": "S6", "angle": 180, "vertex": "V1", "grid": [5, 2]}]}, "legacy_answer": "S2 270 V2 [5,6]\nS4 90 V3 [6,1]\nS5 90 V1 [2,2]\nS6 180 V1 [5,2]", "solutionText": "S2 270 V2 [5,6]\nS4 90 V3 [6,1]\nS5 90 V1 [2,2]\nS6 180 V1 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-457\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-457/target.png", "shapes": {"S1": "images/voi-457/shape_S1.png", "S2": "images/voi-457/shape_S2.png", "S3": "images/voi-457/shape_S3.png", "S4": "images/voi-457/shape_S4.png", "S5": "images/voi-457/shape_S5.png", "S6": "images/voi-457/shape_S6.png", "S7": "images/voi-457/shape_S7.png"}}, "__sample_id__": "voi-457"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 2], [4, 1], [7, 1], [7, 2]]}, {"polygon": [[4, 2], [1, 2], [1, 0], [4, 0]]}, {"polygon": [[0, 0], [2, 0], [2, 2], [0, 2]]}, {"polygon": [[3, 3], [3, 2], [6, 2], [6, 3]]}], "meta": {"seed": 4207009, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.95, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 459, "strictValidation": true}, "imageAssets": {"target": "../images/voi-458/target.png", "shapes": {"S1": "../images/voi-458/shape_S1.png", "S2": "../images/voi-458/shape_S2.png", "S3": "../images/voi-458/shape_S3.png", "S4": "../images/voi-458/shape_S4.png", "S5": "../images/voi-458/shape_S5.png", "S6": "../images/voi-458/shape_S6.png", "S7": "../images/voi-458/shape_S7.png"}}, "ID": "voi-458", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [7, 2]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 2]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [0, 0]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S1 90 V4 [7,2]\nS2 180 V1 [4,2]\nS5 0 V1 [0,0]\nS6 90 V1 [3,3]", "solutionText": "S1 90 V4 [7,2]\nS2 180 V1 [4,2]\nS5 0 V1 [0,0]\nS6 90 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-458\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S7: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-458/target.png", "shapes": {"S1": "images/voi-458/shape_S1.png", "S2": "images/voi-458/shape_S2.png", "S3": "images/voi-458/shape_S3.png", "S4": "images/voi-458/shape_S4.png", "S5": "images/voi-458/shape_S5.png", "S6": "images/voi-458/shape_S6.png", "S7": "images/voi-458/shape_S7.png"}}, "__sample_id__": "voi-458"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 8], [1, 6], [2, 6], [2, 7], [4, 7], [4, 8]]}, {"polygon": [[2, 5], [2, 7], [0, 7], [0, 5]]}, {"polygon": [[3, 8], [5, 8], [5, 10], [3, 10]]}, {"polygon": [[4, 10], [4, 7], [6, 7], [6, 10]]}], "meta": {"seed": 4207010, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.616667, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 460, "strictValidation": true}, "imageAssets": {"target": "../images/voi-459/target.png", "shapes": {"S1": "../images/voi-459/shape_S1.png", "S2": "../images/voi-459/shape_S2.png", "S3": "../images/voi-459/shape_S3.png", "S4": "../images/voi-459/shape_S4.png", "S5": "../images/voi-459/shape_S5.png", "S6": "../images/voi-459/shape_S6.png", "S7": "../images/voi-459/shape_S7.png"}}, "ID": "voi-459", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [1, 8]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 7]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [5, 8]}, {"shape": "S7", "angle": 90, "vertex": "V4", "grid": [6, 10]}]}, "legacy_answer": "S1 90 V1 [1,8]\nS2 270 V3 [0,7]\nS4 0 V2 [5,8]\nS7 90 V4 [6,10]", "solutionText": "S1 90 V1 [1,8]\nS2 270 V3 [0,7]\nS4 0 V2 [5,8]\nS7 90 V4 [6,10]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-459\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-459/target.png", "shapes": {"S1": "images/voi-459/shape_S1.png", "S2": "images/voi-459/shape_S2.png", "S3": "images/voi-459/shape_S3.png", "S4": "images/voi-459/shape_S4.png", "S5": "images/voi-459/shape_S5.png", "S6": "images/voi-459/shape_S6.png", "S7": "images/voi-459/shape_S7.png"}}, "__sample_id__": "voi-459"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 5], [5, 5], [5, 6], [2, 6]]}, {"polygon": [[4, 7], [1, 7], [1, 5], [4, 5]]}, {"polygon": [[0, 5], [0, 3], [2, 3], [2, 5]]}, {"polygon": [[4, 8], [4, 6], [6, 8]]}], "meta": {"seed": 4207011, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.110625, "difficultyScore": 0.656509, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 461, "strictValidation": true}, "imageAssets": {"target": "../images/voi-460/target.png", "shapes": {"S1": "../images/voi-460/shape_S1.png", "S2": "../images/voi-460/shape_S2.png", "S3": "../images/voi-460/shape_S3.png", "S4": "../images/voi-460/shape_S4.png", "S5": "../images/voi-460/shape_S5.png", "S6": "../images/voi-460/shape_S6.png", "S7": "../images/voi-460/shape_S7.png"}}, "ID": "voi-460", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [2, 6]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [1, 7]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [0, 3]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [4, 6]}]}, "legacy_answer": "S1 0 V4 [2,6]\nS2 180 V2 [1,7]\nS4 90 V2 [0,3]\nS6 90 V2 [4,6]", "solutionText": "S1 0 V4 [2,6]\nS2 180 V2 [1,7]\nS4 90 V2 [0,3]\nS6 90 V2 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-460\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-460/target.png", "shapes": {"S1": "images/voi-460/shape_S1.png", "S2": "images/voi-460/shape_S2.png", "S3": "images/voi-460/shape_S3.png", "S4": "images/voi-460/shape_S4.png", "S5": "images/voi-460/shape_S5.png", "S6": "images/voi-460/shape_S6.png", "S7": "images/voi-460/shape_S7.png"}}, "__sample_id__": "voi-460"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 6], [6, 6], [6, 8], [5, 8]]}, {"polygon": [[5, 4], [5, 7], [3, 7], [3, 4]]}, {"polygon": [[7, 3], [7, 5], [5, 5], [5, 3]]}, {"polygon": [[4, 9], [4, 6], [6, 6], [6, 9]]}], "meta": {"seed": 4207012, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.616667, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 462, "strictValidation": true}, "imageAssets": {"target": "../images/voi-461/target.png", "shapes": {"S1": "../images/voi-461/shape_S1.png", "S2": "../images/voi-461/shape_S2.png", "S3": "../images/voi-461/shape_S3.png", "S4": "../images/voi-461/shape_S4.png", "S5": "../images/voi-461/shape_S5.png", "S6": "../images/voi-461/shape_S6.png", "S7": "../images/voi-461/shape_S7.png"}}, "ID": "voi-461", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [5, 8]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [3, 4]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [7, 5]}, {"shape": "S7", "angle": 90, "vertex": "V3", "grid": [6, 6]}]}, "legacy_answer": "S1 0 V4 [5,8]\nS5 270 V4 [3,4]\nS6 270 V2 [7,5]\nS7 90 V3 [6,6]", "solutionText": "S1 0 V4 [5,8]\nS5 270 V4 [3,4]\nS6 270 V2 [7,5]\nS7 90 V3 [6,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-461\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-461/target.png", "shapes": {"S1": "images/voi-461/shape_S1.png", "S2": "images/voi-461/shape_S2.png", "S3": "images/voi-461/shape_S3.png", "S4": "images/voi-461/shape_S4.png", "S5": "images/voi-461/shape_S5.png", "S6": "images/voi-461/shape_S6.png", "S7": "images/voi-461/shape_S7.png"}}, "__sample_id__": "voi-461"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[9, 3], [9, 6], [7, 6], [7, 3]]}, {"polygon": [[9, 5], [9, 7], [7, 5]]}, {"polygon": [[10, 6], [10, 9], [9, 9], [9, 6]]}, {"polygon": [[7, 6], [9, 6], [9, 8], [7, 8]]}], "meta": {"seed": 4207013, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.273859, "contourComplexity": 74, "connectedComponents": 2, "fillRatio": 0.109375, "difficultyScore": 0.875814, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 463, "strictValidation": true}, "imageAssets": {"target": "../images/voi-462/target.png", "shapes": {"S1": "../images/voi-462/shape_S1.png", "S2": "../images/voi-462/shape_S2.png", "S3": "../images/voi-462/shape_S3.png", "S4": "../images/voi-462/shape_S4.png", "S5": "../images/voi-462/shape_S5.png", "S6": "../images/voi-462/shape_S6.png", "S7": "../images/voi-462/shape_S7.png"}}, "ID": "voi-462", "answer": {"placements": [{"shape": "S3", "angle": 270, "vertex": "V2", "grid": [9, 6]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [9, 5]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [10, 6]}, {"shape": "S7", "angle": 0, "vertex": "V1", "grid": [7, 6]}]}, "legacy_answer": "S3 270 V2 [9,6]\nS4 270 V1 [9,5]\nS6 270 V1 [10,6]\nS7 0 V1 [7,6]", "solutionText": "S3 270 V2 [9,6]\nS4 270 V1 [9,5]\nS6 270 V1 [10,6]\nS7 0 V1 [7,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-462\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-462/target.png", "shapes": {"S1": "images/voi-462/shape_S1.png", "S2": "images/voi-462/shape_S2.png", "S3": "images/voi-462/shape_S3.png", "S4": "images/voi-462/shape_S4.png", "S5": "images/voi-462/shape_S5.png", "S6": "images/voi-462/shape_S6.png", "S7": "images/voi-462/shape_S7.png"}}, "__sample_id__": "voi-462"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 3], [6, 4], [4, 4], [4, 3]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}, {"polygon": [[9, 4], [9, 5], [6, 5], [6, 4]]}, {"polygon": [[4, 6], [4, 3], [6, 3], [6, 6]]}], "meta": {"seed": 4207014, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.13, "difficultyScore": 0.738824, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 464, "strictValidation": true}, "imageAssets": {"target": "../images/voi-463/target.png", "shapes": {"S1": "../images/voi-463/shape_S1.png", "S2": "../images/voi-463/shape_S2.png", "S3": "../images/voi-463/shape_S3.png", "S4": "../images/voi-463/shape_S4.png", "S5": "../images/voi-463/shape_S5.png", "S6": "../images/voi-463/shape_S6.png", "S7": "../images/voi-463/shape_S7.png"}}, "ID": "voi-463", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [6, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 4]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [6, 5]}, {"shape": "S7", "angle": 90, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S1 270 V2 [6,4]\nS2 90 V1 [3,4]\nS4 270 V3 [6,5]\nS7 90 V1 [4,6]", "solutionText": "S1 270 V2 [6,4]\nS2 90 V1 [3,4]\nS4 270 V3 [6,5]\nS7 90 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-463\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-463/target.png", "shapes": {"S1": "images/voi-463/shape_S1.png", "S2": "images/voi-463/shape_S2.png", "S3": "images/voi-463/shape_S3.png", "S4": "images/voi-463/shape_S4.png", "S5": "images/voi-463/shape_S5.png", "S6": "images/voi-463/shape_S6.png", "S7": "images/voi-463/shape_S7.png"}}, "__sample_id__": "voi-463"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [7, 3], [7, 4], [6, 4], [6, 6], [5, 6]]}, {"polygon": [[8, 4], [8, 7], [6, 7], [6, 4]]}, {"polygon": [[7, 1], [10, 1], [10, 2], [7, 2]]}, {"polygon": [[7, 1], [9, 1], [9, 2], [7, 2]]}], "meta": {"seed": 4207015, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.903333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 465, "strictValidation": true}, "imageAssets": {"target": "../images/voi-464/target.png", "shapes": {"S1": "../images/voi-464/shape_S1.png", "S2": "../images/voi-464/shape_S2.png", "S3": "../images/voi-464/shape_S3.png", "S4": "../images/voi-464/shape_S4.png", "S5": "../images/voi-464/shape_S5.png", "S6": "../images/voi-464/shape_S6.png", "S7": "../images/voi-464/shape_S7.png"}}, "ID": "voi-464", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [7, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [6, 7]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [7, 1]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [9, 2]}]}, "legacy_answer": "S1 0 V2 [7,3]\nS2 270 V3 [6,7]\nS3 0 V1 [7,1]\nS5 0 V3 [9,2]", "solutionText": "S1 0 V2 [7,3]\nS2 270 V3 [6,7]\nS3 0 V1 [7,1]\nS5 0 V3 [9,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-464\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-464/target.png", "shapes": {"S1": "images/voi-464/shape_S1.png", "S2": "images/voi-464/shape_S2.png", "S3": "images/voi-464/shape_S3.png", "S4": "images/voi-464/shape_S4.png", "S5": "images/voi-464/shape_S5.png", "S6": "images/voi-464/shape_S6.png", "S7": "images/voi-464/shape_S7.png"}}, "__sample_id__": "voi-464"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 4], [4, 6], [2, 4]]}, {"polygon": [[10, 7], [10, 9], [8, 9], [8, 7]]}, {"polygon": [[3, 7], [1, 7], [1, 6], [2, 6], [2, 4], [3, 4]]}, {"polygon": [[1, 5], [1, 3], [2, 3], [2, 4], [4, 4], [4, 5]]}], "meta": {"seed": 4207016, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 80, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.850972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 466, "strictValidation": true}, "imageAssets": {"target": "../images/voi-465/target.png", "shapes": {"S1": "../images/voi-465/shape_S1.png", "S2": "../images/voi-465/shape_S2.png", "S3": "../images/voi-465/shape_S3.png", "S4": "../images/voi-465/shape_S4.png", "S5": "../images/voi-465/shape_S5.png", "S6": "../images/voi-465/shape_S6.png", "S7": "../images/voi-465/shape_S7.png"}}, "ID": "voi-465", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [2, 4]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [8, 7]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [1, 6]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [2, 3]}]}, "legacy_answer": "S1 270 V3 [2,4]\nS3 270 V4 [8,7]\nS4 180 V3 [1,6]\nS6 90 V3 [2,3]", "solutionText": "S1 270 V3 [2,4]\nS3 270 V4 [8,7]\nS4 180 V3 [1,6]\nS6 90 V3 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-465\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-465/target.png", "shapes": {"S1": "images/voi-465/shape_S1.png", "S2": "images/voi-465/shape_S2.png", "S3": "images/voi-465/shape_S3.png", "S4": "images/voi-465/shape_S4.png", "S5": "images/voi-465/shape_S5.png", "S6": "images/voi-465/shape_S6.png", "S7": "images/voi-465/shape_S7.png"}}, "__sample_id__": "voi-465"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}, {"polygon": [[2, 2], [4, 2], [2, 4]]}, {"polygon": [[5, 4], [2, 4], [2, 2], [5, 2]]}, {"polygon": [[7, 3], [7, 5], [5, 5], [5, 3]]}], "meta": {"seed": 4207017, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.228374, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.139375, "difficultyScore": 0.747755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 467, "strictValidation": true}, "imageAssets": {"target": "../images/voi-466/target.png", "shapes": {"S1": "../images/voi-466/shape_S1.png", "S2": "../images/voi-466/shape_S2.png", "S3": "../images/voi-466/shape_S3.png", "S4": "../images/voi-466/shape_S4.png", "S5": "../images/voi-466/shape_S5.png", "S6": "../images/voi-466/shape_S6.png", "S7": "../images/voi-466/shape_S7.png"}}, "ID": "voi-466", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [5, 7]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [2, 2]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S7", "angle": 270, "vertex": "V4", "grid": [5, 3]}]}, "legacy_answer": "S1 90 V4 [5,7]\nS3 0 V1 [2,2]\nS4 180 V4 [5,2]\nS7 270 V4 [5,3]", "solutionText": "S1 90 V4 [5,7]\nS3 0 V1 [2,2]\nS4 180 V4 [5,2]\nS7 270 V4 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-466\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-466/target.png", "shapes": {"S1": "images/voi-466/shape_S1.png", "S2": "images/voi-466/shape_S2.png", "S3": "images/voi-466/shape_S3.png", "S4": "images/voi-466/shape_S4.png", "S5": "images/voi-466/shape_S5.png", "S6": "images/voi-466/shape_S6.png", "S7": "images/voi-466/shape_S7.png"}}, "__sample_id__": "voi-466"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 3], [5, 3], [5, 4], [4, 4], [4, 6], [3, 6]]}, {"polygon": [[10, 5], [10, 8], [8, 8], [8, 5]]}, {"polygon": [[9, 8], [9, 6], [10, 6], [10, 8]]}, {"polygon": [[6, 9], [6, 6], [8, 6], [8, 9]]}], "meta": {"seed": 4207018, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.14, "difficultyScore": 1.021111, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 468, "strictValidation": true}, "imageAssets": {"target": "../images/voi-467/target.png", "shapes": {"S1": "../images/voi-467/shape_S1.png", "S2": "../images/voi-467/shape_S2.png", "S3": "../images/voi-467/shape_S3.png", "S4": "../images/voi-467/shape_S4.png", "S5": "../images/voi-467/shape_S5.png", "S6": "../images/voi-467/shape_S6.png", "S7": "../images/voi-467/shape_S7.png"}}, "ID": "voi-467", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 3]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [8, 5]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [10, 6]}, {"shape": "S6", "angle": 90, "vertex": "V1", "grid": [6, 9]}]}, "legacy_answer": "S2 0 V2 [5,3]\nS4 270 V4 [8,5]\nS5 90 V3 [10,6]\nS6 90 V1 [6,9]", "solutionText": "S2 0 V2 [5,3]\nS4 270 V4 [8,5]\nS5 90 V3 [10,6]\nS6 90 V1 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-467\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-467/target.png", "shapes": {"S1": "images/voi-467/shape_S1.png", "S2": "images/voi-467/shape_S2.png", "S3": "images/voi-467/shape_S3.png", "S4": "images/voi-467/shape_S4.png", "S5": "images/voi-467/shape_S5.png", "S6": "images/voi-467/shape_S6.png", "S7": "images/voi-467/shape_S7.png"}}, "__sample_id__": "voi-467"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 7], [7, 10], [5, 10], [5, 7]]}, {"polygon": [[3, 9], [3, 7], [4, 7], [4, 9]]}, {"polygon": [[6, 9], [6, 7], [8, 7], [8, 9]]}, {"polygon": [[6, 7], [3, 7], [4, 6], [6, 6]]}], "meta": {"seed": 4207019, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.8783, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 469, "strictValidation": true}, "imageAssets": {"target": "../images/voi-468/target.png", "shapes": {"S1": "../images/voi-468/shape_S1.png", "S2": "../images/voi-468/shape_S2.png", "S3": "../images/voi-468/shape_S3.png", "S4": "../images/voi-468/shape_S4.png", "S5": "../images/voi-468/shape_S5.png", "S6": "../images/voi-468/shape_S6.png", "S7": "../images/voi-468/shape_S7.png"}}, "ID": "voi-468", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 7]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 9]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [8, 9]}, {"shape": "S7", "angle": 180, "vertex": "V3", "grid": [4, 6]}]}, "legacy_answer": "S1 270 V4 [5,7]\nS2 90 V1 [3,9]\nS3 90 V4 [8,9]\nS7 180 V3 [4,6]", "solutionText": "S1 270 V4 [5,7]\nS2 90 V1 [3,9]\nS3 90 V4 [8,9]\nS7 180 V3 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-468\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-468/target.png", "shapes": {"S1": "images/voi-468/shape_S1.png", "S2": "images/voi-468/shape_S2.png", "S3": "images/voi-468/shape_S3.png", "S4": "images/voi-468/shape_S4.png", "S5": "images/voi-468/shape_S5.png", "S6": "images/voi-468/shape_S6.png", "S7": "images/voi-468/shape_S7.png"}}, "__sample_id__": "voi-468"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 7], [6, 7], [6, 8], [4, 8]]}, {"polygon": [[6, 5], [6, 8], [4, 8], [4, 5]]}, {"polygon": [[4, 6], [2, 6], [4, 4]]}, {"polygon": [[0, 5], [2, 5], [2, 6], [1, 6], [1, 8], [0, 8]]}], "meta": {"seed": 4207020, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.284444, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.100625, "difficultyScore": 0.600972, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 470, "strictValidation": true}, "imageAssets": {"target": "../images/voi-469/target.png", "shapes": {"S1": "../images/voi-469/shape_S1.png", "S2": "../images/voi-469/shape_S2.png", "S3": "../images/voi-469/shape_S3.png", "S4": "../images/voi-469/shape_S4.png", "S5": "../images/voi-469/shape_S5.png", "S6": "../images/voi-469/shape_S6.png", "S7": "../images/voi-469/shape_S7.png"}}, "ID": "voi-469", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V3", "grid": [6, 8]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [6, 8]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [4, 6]}, {"shape": "S6", "angle": 0, "vertex": "V1", "grid": [0, 5]}]}, "legacy_answer": "S2 0 V3 [6,8]\nS3 270 V2 [6,8]\nS5 180 V1 [4,6]\nS6 0 V1 [0,5]", "solutionText": "S2 0 V3 [6,8]\nS3 270 V2 [6,8]\nS5 180 V1 [4,6]\nS6 0 V1 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-469\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S7: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-469/target.png", "shapes": {"S1": "images/voi-469/shape_S1.png", "S2": "images/voi-469/shape_S2.png", "S3": "images/voi-469/shape_S3.png", "S4": "images/voi-469/shape_S4.png", "S5": "images/voi-469/shape_S5.png", "S6": "images/voi-469/shape_S6.png", "S7": "images/voi-469/shape_S7.png"}}, "__sample_id__": "voi-469"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 3], [2, 3], [2, 6], [1, 6]]}, {"polygon": [[5, 5], [2, 5], [2, 3], [5, 3]]}, {"polygon": [[0, 3], [0, 0], [2, 0], [2, 3]]}, {"polygon": [[3, 6], [1, 6], [1, 4], [3, 4]]}], "meta": {"seed": 4207021, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.666842, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 471, "strictValidation": true}, "imageAssets": {"target": "../images/voi-470/target.png", "shapes": {"S1": "../images/voi-470/shape_S1.png", "S2": "../images/voi-470/shape_S2.png", "S3": "../images/voi-470/shape_S3.png", "S4": "../images/voi-470/shape_S4.png", "S5": "../images/voi-470/shape_S5.png", "S6": "../images/voi-470/shape_S6.png", "S7": "../images/voi-470/shape_S7.png"}}, "ID": "voi-470", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [2, 6]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [2, 3]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [0, 3]}, {"shape": "S7", "angle": 180, "vertex": "V2", "grid": [1, 6]}]}, "legacy_answer": "S1 0 V3 [2,6]\nS2 180 V3 [2,3]\nS3 90 V1 [0,3]\nS7 180 V2 [1,6]", "solutionText": "S1 0 V3 [2,6]\nS2 180 V3 [2,3]\nS3 90 V1 [0,3]\nS7 180 V2 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-470\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-470/target.png", "shapes": {"S1": "images/voi-470/shape_S1.png", "S2": "images/voi-470/shape_S2.png", "S3": "images/voi-470/shape_S3.png", "S4": "images/voi-470/shape_S4.png", "S5": "images/voi-470/shape_S5.png", "S6": "images/voi-470/shape_S6.png", "S7": "images/voi-470/shape_S7.png"}}, "__sample_id__": "voi-470"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [5, 6], [5, 4], [6, 4]]}, {"polygon": [[5, 7], [5, 5], [6, 5], [6, 6], [8, 6], [8, 7]]}, {"polygon": [[4, 5], [4, 3], [6, 3], [6, 5]]}, {"polygon": [[8, 8], [8, 6], [10, 6], [10, 8]]}], "meta": {"seed": 4207022, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 472, "strictValidation": true}, "imageAssets": {"target": "../images/voi-471/target.png", "shapes": {"S1": "../images/voi-471/shape_S1.png", "S2": "../images/voi-471/shape_S2.png", "S3": "../images/voi-471/shape_S3.png", "S4": "../images/voi-471/shape_S4.png", "S5": "../images/voi-471/shape_S5.png", "S6": "../images/voi-471/shape_S6.png", "S7": "../images/voi-471/shape_S7.png"}}, "ID": "voi-471", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [5, 6]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [6, 6]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [4, 3]}, {"shape": "S7", "angle": 90, "vertex": "V2", "grid": [8, 6]}]}, "legacy_answer": "S1 180 V2 [5,6]\nS2 90 V4 [6,6]\nS6 90 V2 [4,3]\nS7 90 V2 [8,6]", "solutionText": "S1 180 V2 [5,6]\nS2 90 V4 [6,6]\nS6 90 V2 [4,3]\nS7 90 V2 [8,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-471\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-471/target.png", "shapes": {"S1": "images/voi-471/shape_S1.png", "S2": "images/voi-471/shape_S2.png", "S3": "images/voi-471/shape_S3.png", "S4": "images/voi-471/shape_S4.png", "S5": "images/voi-471/shape_S5.png", "S6": "images/voi-471/shape_S6.png", "S7": "images/voi-471/shape_S7.png"}}, "__sample_id__": "voi-471"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 2], [3, 2], [4, 1], [6, 1]]}, {"polygon": [[2, 3], [2, 2], [3, 3]]}, {"polygon": [[2, 1], [5, 1], [5, 3], [2, 3]]}, {"polygon": [[0, 3], [0, 0], [2, 0], [2, 3]]}], "meta": {"seed": 4207023, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.273859, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.109375, "difficultyScore": 0.875814, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 473, "strictValidation": true}, "imageAssets": {"target": "../images/voi-472/target.png", "shapes": {"S1": "../images/voi-472/shape_S1.png", "S2": "../images/voi-472/shape_S2.png", "S3": "../images/voi-472/shape_S3.png", "S4": "../images/voi-472/shape_S4.png", "S5": "../images/voi-472/shape_S5.png", "S6": "../images/voi-472/shape_S6.png", "S7": "../images/voi-472/shape_S7.png"}}, "ID": "voi-472", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [3, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [2, 3]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [5, 3]}, {"shape": "S7", "angle": 90, "vertex": "V2", "grid": [0, 0]}]}, "legacy_answer": "S1 180 V2 [3,2]\nS4 90 V1 [2,3]\nS6 0 V3 [5,3]\nS7 90 V2 [0,0]", "solutionText": "S1 180 V2 [3,2]\nS4 90 V1 [2,3]\nS6 0 V3 [5,3]\nS7 90 V2 [0,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-472\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-472/target.png", "shapes": {"S1": "images/voi-472/shape_S1.png", "S2": "images/voi-472/shape_S2.png", "S3": "images/voi-472/shape_S3.png", "S4": "images/voi-472/shape_S4.png", "S5": "images/voi-472/shape_S5.png", "S6": "images/voi-472/shape_S6.png", "S7": "images/voi-472/shape_S7.png"}}, "__sample_id__": "voi-472"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [5, 6], [3, 6], [3, 3]]}, {"polygon": [[7, 1], [7, 3], [6, 3], [6, 2], [4, 2], [4, 1]]}, {"polygon": [[3, 4], [3, 7], [1, 7], [1, 4]]}, {"polygon": [[5, 5], [3, 5], [3, 3], [5, 3]]}], "meta": {"seed": 4207024, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.4, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.87, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 474, "strictValidation": true}, "imageAssets": {"target": "../images/voi-473/target.png", "shapes": {"S1": "../images/voi-473/shape_S1.png", "S2": "../images/voi-473/shape_S2.png", "S3": "../images/voi-473/shape_S3.png", "S4": "../images/voi-473/shape_S4.png", "S5": "../images/voi-473/shape_S5.png", "S6": "../images/voi-473/shape_S6.png", "S7": "../images/voi-473/shape_S7.png"}}, "ID": "voi-473", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 6]}, {"shape": "S3", "angle": 270, "vertex": "V6", "grid": [4, 1]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [3, 4]}, {"shape": "S7", "angle": 180, "vertex": "V4", "grid": [5, 3]}]}, "legacy_answer": "S1 270 V3 [3,6]\nS3 270 V6 [4,1]\nS6 270 V1 [3,4]\nS7 180 V4 [5,3]", "solutionText": "S1 270 V3 [3,6]\nS3 270 V6 [4,1]\nS6 270 V1 [3,4]\nS7 180 V4 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-473\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-473/target.png", "shapes": {"S1": "images/voi-473/shape_S1.png", "S2": "images/voi-473/shape_S2.png", "S3": "images/voi-473/shape_S3.png", "S4": "images/voi-473/shape_S4.png", "S5": "images/voi-473/shape_S5.png", "S6": "images/voi-473/shape_S6.png", "S7": "images/voi-473/shape_S7.png"}}, "__sample_id__": "voi-473"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[2, 7], [5, 7], [5, 9], [2, 9]]}, {"polygon": [[2, 7], [4, 7], [4, 8], [2, 8]]}, {"polygon": [[6, 7], [6, 4], [8, 4], [8, 7]]}, {"polygon": [[8, 9], [6, 9], [8, 7]]}], "meta": {"seed": 4207025, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 74, "connectedComponents": 2, "fillRatio": 0.120625, "difficultyScore": 0.952641, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 475, "strictValidation": true}, "imageAssets": {"target": "../images/voi-474/target.png", "shapes": {"S1": "../images/voi-474/shape_S1.png", "S2": "../images/voi-474/shape_S2.png", "S3": "../images/voi-474/shape_S3.png", "S4": "../images/voi-474/shape_S4.png", "S5": "../images/voi-474/shape_S5.png", "S6": "../images/voi-474/shape_S6.png", "S7": "../images/voi-474/shape_S7.png"}}, "ID": "voi-474", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 7]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [4, 8]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [8, 7]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [6, 9]}]}, "legacy_answer": "S1 0 V2 [5,7]\nS2 0 V3 [4,8]\nS4 90 V4 [8,7]\nS5 180 V2 [6,9]", "solutionText": "S1 0 V2 [5,7]\nS2 0 V3 [4,8]\nS4 90 V4 [8,7]\nS5 180 V2 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-474\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-474/target.png", "shapes": {"S1": "images/voi-474/shape_S1.png", "S2": "images/voi-474/shape_S2.png", "S3": "images/voi-474/shape_S3.png", "S4": "images/voi-474/shape_S4.png", "S5": "images/voi-474/shape_S5.png", "S6": "images/voi-474/shape_S6.png", "S7": "images/voi-474/shape_S7.png"}}, "__sample_id__": "voi-474"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 6], [1, 4], [3, 6]]}, {"polygon": [[1, 2], [3, 2], [3, 4], [1, 4]]}, {"polygon": [[4, 5], [4, 2], [6, 2], [6, 5]]}, {"polygon": [[5, 4], [3, 4], [3, 2], [5, 2]]}], "meta": {"seed": 4207026, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.249027, "contourComplexity": 74, "connectedComponents": 2, "fillRatio": 0.120625, "difficultyScore": 0.952641, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 476, "strictValidation": true}, "imageAssets": {"target": "../images/voi-475/target.png", "shapes": {"S1": "../images/voi-475/shape_S1.png", "S2": "../images/voi-475/shape_S2.png", "S3": "../images/voi-475/shape_S3.png", "S4": "../images/voi-475/shape_S4.png", "S5": "../images/voi-475/shape_S5.png", "S6": "../images/voi-475/shape_S6.png", "S7": "../images/voi-475/shape_S7.png"}}, "ID": "voi-475", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 6]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [1, 2]}, {"shape": "S5", "angle": 90, "vertex": "V2", "grid": [4, 2]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S2 90 V3 [3,6]\nS3 0 V1 [1,2]\nS5 90 V2 [4,2]\nS6 180 V3 [3,2]", "solutionText": "S2 90 V3 [3,6]\nS3 0 V1 [1,2]\nS5 90 V2 [4,2]\nS6 180 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-475\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-475/target.png", "shapes": {"S1": "images/voi-475/shape_S1.png", "S2": "images/voi-475/shape_S2.png", "S3": "images/voi-475/shape_S3.png", "S4": "images/voi-475/shape_S4.png", "S5": "images/voi-475/shape_S5.png", "S6": "images/voi-475/shape_S6.png", "S7": "images/voi-475/shape_S7.png"}}, "__sample_id__": "voi-475"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 8], [1, 7], [4, 7], [4, 8]]}, {"polygon": [[5, 1], [8, 1], [8, 2], [5, 2]]}, {"polygon": [[8, 2], [8, 3], [6, 3], [6, 2]]}, {"polygon": [[5, 2], [8, 2], [8, 4], [5, 4]]}], "meta": {"seed": 4207027, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 477, "strictValidation": true}, "imageAssets": {"target": "../images/voi-476/target.png", "shapes": {"S1": "../images/voi-476/shape_S1.png", "S2": "../images/voi-476/shape_S2.png", "S3": "../images/voi-476/shape_S3.png", "S4": "../images/voi-476/shape_S4.png", "S5": "../images/voi-476/shape_S5.png", "S6": "../images/voi-476/shape_S6.png", "S7": "../images/voi-476/shape_S7.png"}}, "ID": "voi-476", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [4, 8]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [8, 2]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [8, 2]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [5, 2]}]}, "legacy_answer": "S1 90 V4 [4,8]\nS2 0 V3 [8,2]\nS4 270 V1 [8,2]\nS5 0 V1 [5,2]", "solutionText": "S1 90 V4 [4,8]\nS2 0 V3 [8,2]\nS4 270 V1 [8,2]\nS5 0 V1 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-476\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-476/target.png", "shapes": {"S1": "images/voi-476/shape_S1.png", "S2": "images/voi-476/shape_S2.png", "S3": "images/voi-476/shape_S3.png", "S4": "images/voi-476/shape_S4.png", "S5": "images/voi-476/shape_S5.png", "S6": "images/voi-476/shape_S6.png", "S7": "images/voi-476/shape_S7.png"}}, "__sample_id__": "voi-476"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[7, 6], [5, 6], [5, 4], [7, 4]]}, {"polygon": [[1, 9], [1, 7], [2, 7], [2, 8], [4, 8], [4, 9]]}, {"polygon": [[0, 7], [3, 7], [3, 9], [0, 9]]}, {"polygon": [[3, 8], [3, 10], [1, 8]]}], "meta": {"seed": 4207028, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.373541, "contourComplexity": 80, "connectedComponents": 2, "fillRatio": 0.100625, "difficultyScore": 0.802913, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 478, "strictValidation": true}, "imageAssets": {"target": "../images/voi-477/target.png", "shapes": {"S1": "../images/voi-477/shape_S1.png", "S2": "../images/voi-477/shape_S2.png", "S3": "../images/voi-477/shape_S3.png", "S4": "../images/voi-477/shape_S4.png", "S5": "../images/voi-477/shape_S5.png", "S6": "../images/voi-477/shape_S6.png", "S7": "../images/voi-477/shape_S7.png"}}, "ID": "voi-477", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V2", "grid": [5, 6]}, {"shape": "S4", "angle": 90, "vertex": "V6", "grid": [4, 9]}, {"shape": "S5", "angle": 0, "vertex": "V1", "grid": [0, 7]}, {"shape": "S7", "angle": 270, "vertex": "V1", "grid": [3, 8]}]}, "legacy_answer": "S3 180 V2 [5,6]\nS4 90 V6 [4,9]\nS5 0 V1 [0,7]\nS7 270 V1 [3,8]", "solutionText": "S3 180 V2 [5,6]\nS4 90 V6 [4,9]\nS5 0 V1 [0,7]\nS7 270 V1 [3,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-477\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-477/target.png", "shapes": {"S1": "images/voi-477/shape_S1.png", "S2": "images/voi-477/shape_S2.png", "S3": "images/voi-477/shape_S3.png", "S4": "images/voi-477/shape_S4.png", "S5": "images/voi-477/shape_S5.png", "S6": "images/voi-477/shape_S6.png", "S7": "images/voi-477/shape_S7.png"}}, "__sample_id__": "voi-477"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 1], [4, 1], [4, 2], [3, 2], [3, 4], [2, 4]]}, {"polygon": [[2, 5], [2, 2], [4, 2], [4, 5]]}, {"polygon": [[2, 7], [1, 7], [1, 4], [2, 4]]}, {"polygon": [[4, 10], [3, 10], [3, 9], [4, 9]]}], "meta": {"seed": 4207029, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 479, "strictValidation": true}, "imageAssets": {"target": "../images/voi-478/target.png", "shapes": {"S1": "../images/voi-478/shape_S1.png", "S2": "../images/voi-478/shape_S2.png", "S3": "../images/voi-478/shape_S3.png", "S4": "../images/voi-478/shape_S4.png", "S5": "../images/voi-478/shape_S5.png", "S6": "../images/voi-478/shape_S6.png", "S7": "../images/voi-478/shape_S7.png"}}, "ID": "voi-478", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [4, 1]}, {"shape": "S4", "angle": 90, "vertex": "V4", "grid": [4, 5]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [1, 7]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [3, 9]}]}, "legacy_answer": "S1 0 V2 [4,1]\nS4 90 V4 [4,5]\nS5 180 V2 [1,7]\nS6 180 V3 [3,9]", "solutionText": "S1 0 V2 [4,1]\nS4 90 V4 [4,5]\nS5 180 V2 [1,7]\nS6 180 V3 [3,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-478\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-478/target.png", "shapes": {"S1": "images/voi-478/shape_S1.png", "S2": "images/voi-478/shape_S2.png", "S3": "images/voi-478/shape_S3.png", "S4": "images/voi-478/shape_S4.png", "S5": "images/voi-478/shape_S5.png", "S6": "images/voi-478/shape_S6.png", "S7": "images/voi-478/shape_S7.png"}}, "__sample_id__": "voi-478"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 7], [0, 7], [0, 5], [3, 5]]}, {"polygon": [[7, 6], [6, 6], [6, 5], [7, 5]]}, {"polygon": [[4, 5], [4, 7], [3, 7], [3, 6], [1, 6], [1, 5]]}, {"polygon": [[6, 4], [6, 6], [5, 6], [5, 5], [3, 5], [3, 4]]}], "meta": {"seed": 4207030, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.11, "difficultyScore": 0.653333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 480, "strictValidation": true}, "imageAssets": {"target": "../images/voi-479/target.png", "shapes": {"S1": "../images/voi-479/shape_S1.png", "S2": "../images/voi-479/shape_S2.png", "S3": "../images/voi-479/shape_S3.png", "S4": "../images/voi-479/shape_S4.png", "S5": "../images/voi-479/shape_S5.png", "S6": "../images/voi-479/shape_S6.png", "S7": "../images/voi-479/shape_S7.png"}}, "ID": "voi-479", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [0, 5]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [7, 6]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [3, 6]}, {"shape": "S7", "angle": 270, "vertex": "V5", "grid": [3, 5]}]}, "legacy_answer": "S2 180 V3 [0,5]\nS4 180 V1 [7,6]\nS5 270 V4 [3,6]\nS7 270 V5 [3,5]", "solutionText": "S2 180 V3 [0,5]\nS4 180 V1 [7,6]\nS5 270 V4 [3,6]\nS7 270 V5 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-479\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-479/target.png", "shapes": {"S1": "images/voi-479/shape_S1.png", "S2": "images/voi-479/shape_S2.png", "S3": "images/voi-479/shape_S3.png", "S4": "images/voi-479/shape_S4.png", "S5": "images/voi-479/shape_S5.png", "S6": "images/voi-479/shape_S6.png", "S7": "images/voi-479/shape_S7.png"}}, "__sample_id__": "voi-479"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[9, 4], [9, 7], [7, 7], [7, 4]]}, {"polygon": [[5, 4], [7, 4], [7, 5], [6, 5], [6, 7], [5, 7]]}, {"polygon": [[7, 7], [7, 9], [6, 9], [6, 8], [4, 8], [4, 7]]}, {"polygon": [[5, 5], [8, 5], [8, 6], [5, 6]]}], "meta": {"seed": 4207031, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.235294, "contourComplexity": 23, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.988824, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 481, "strictValidation": true}, "imageAssets": {"target": "../images/voi-480/target.png", "shapes": {"S1": "../images/voi-480/shape_S1.png", "S2": "../images/voi-480/shape_S2.png", "S3": "../images/voi-480/shape_S3.png", "S4": "../images/voi-480/shape_S4.png", "S5": "../images/voi-480/shape_S5.png", "S6": "../images/voi-480/shape_S6.png", "S7": "../images/voi-480/shape_S7.png"}}, "ID": "voi-480", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [7, 7]}, {"shape": "S2", "angle": 0, "vertex": "V6", "grid": [5, 7]}, {"shape": "S3", "angle": 270, "vertex": "V6", "grid": [4, 7]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [8, 6]}]}, "legacy_answer": "S1 270 V3 [7,7]\nS2 0 V6 [5,7]\nS3 270 V6 [4,7]\nS5 0 V3 [8,6]", "solutionText": "S1 270 V3 [7,7]\nS2 0 V6 [5,7]\nS3 270 V6 [4,7]\nS5 0 V3 [8,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-480\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-480/target.png", "shapes": {"S1": "images/voi-480/shape_S1.png", "S2": "images/voi-480/shape_S2.png", "S3": "images/voi-480/shape_S3.png", "S4": "images/voi-480/shape_S4.png", "S5": "images/voi-480/shape_S5.png", "S6": "images/voi-480/shape_S6.png", "S7": "images/voi-480/shape_S7.png"}}, "__sample_id__": "voi-480"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[4, 5], [4, 3], [5, 3], [5, 4], [7, 4], [7, 5]]}, {"polygon": [[4, 6], [1, 6], [1, 4], [4, 4]]}, {"polygon": [[4, 1], [4, 2], [3, 1]]}, {"polygon": [[7, 5], [5, 5], [5, 3], [7, 3]]}], "meta": {"seed": 4207032, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.8783, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 482, "strictValidation": true}, "imageAssets": {"target": "../images/voi-481/target.png", "shapes": {"S1": "../images/voi-481/shape_S1.png", "S2": "../images/voi-481/shape_S2.png", "S3": "../images/voi-481/shape_S3.png", "S4": "../images/voi-481/shape_S4.png", "S5": "../images/voi-481/shape_S5.png", "S6": "../images/voi-481/shape_S6.png", "S7": "../images/voi-481/shape_S7.png"}}, "ID": "voi-481", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [4, 3]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 6]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [4, 1]}, {"shape": "S5", "angle": 180, "vertex": "V1", "grid": [7, 5]}]}, "legacy_answer": "S1 90 V2 [4,3]\nS2 180 V1 [4,6]\nS3 270 V1 [4,1]\nS5 180 V1 [7,5]", "solutionText": "S1 90 V2 [4,3]\nS2 180 V1 [4,6]\nS3 270 V1 [4,1]\nS5 180 V1 [7,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-481\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-481/target.png", "shapes": {"S1": "images/voi-481/shape_S1.png", "S2": "images/voi-481/shape_S2.png", "S3": "images/voi-481/shape_S3.png", "S4": "images/voi-481/shape_S4.png", "S5": "images/voi-481/shape_S5.png", "S6": "images/voi-481/shape_S6.png", "S7": "images/voi-481/shape_S7.png"}}, "__sample_id__": "voi-481"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 10], [7, 7], [9, 7], [9, 10]]}, {"polygon": [[9, 8], [6, 8], [6, 6], [9, 6]]}, {"polygon": [[1, 3], [1, 4], [0, 4], [0, 3]]}, {"polygon": [[5, 8], [7, 8], [7, 9], [5, 9]]}], "meta": {"seed": 4207033, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 16, "connectedComponents": 2, "fillRatio": 0.11, "difficultyScore": 0.903333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 483, "strictValidation": true}, "imageAssets": {"target": "../images/voi-482/target.png", "shapes": {"S1": "../images/voi-482/shape_S1.png", "S2": "../images/voi-482/shape_S2.png", "S3": "../images/voi-482/shape_S3.png", "S4": "../images/voi-482/shape_S4.png", "S5": "../images/voi-482/shape_S5.png", "S6": "../images/voi-482/shape_S6.png", "S7": "../images/voi-482/shape_S7.png"}}, "ID": "voi-482", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [7, 10]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [6, 6]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [1, 3]}, {"shape": "S6", "angle": 0, "vertex": "V3", "grid": [7, 9]}]}, "legacy_answer": "S2 90 V1 [7,10]\nS3 180 V3 [6,6]\nS4 270 V1 [1,3]\nS6 0 V3 [7,9]", "solutionText": "S2 90 V1 [7,10]\nS3 180 V3 [6,6]\nS4 270 V1 [1,3]\nS6 0 V3 [7,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-482\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-482/target.png", "shapes": {"S1": "images/voi-482/shape_S1.png", "S2": "images/voi-482/shape_S2.png", "S3": "images/voi-482/shape_S3.png", "S4": "images/voi-482/shape_S4.png", "S5": "images/voi-482/shape_S5.png", "S6": "images/voi-482/shape_S6.png", "S7": "images/voi-482/shape_S7.png"}}, "__sample_id__": "voi-482"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[8, 6], [8, 7], [5, 7], [5, 6]]}, {"polygon": [[9, 2], [9, 5], [7, 5], [7, 2]]}, {"polygon": [[6, 7], [6, 5], [8, 7]]}, {"polygon": [[6, 6], [8, 6], [8, 7], [7, 7], [7, 9], [6, 9]]}], "meta": {"seed": 4207034, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.110625, "difficultyScore": 0.906509, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 484, "strictValidation": true}, "imageAssets": {"target": "../images/voi-483/target.png", "shapes": {"S1": "../images/voi-483/shape_S1.png", "S2": "../images/voi-483/shape_S2.png", "S3": "../images/voi-483/shape_S3.png", "S4": "../images/voi-483/shape_S4.png", "S5": "../images/voi-483/shape_S5.png", "S6": "../images/voi-483/shape_S6.png", "S7": "../images/voi-483/shape_S7.png"}}, "ID": "voi-483", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [8, 7]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [7, 2]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [6, 7]}, {"shape": "S4", "angle": 0, "vertex": "V6", "grid": [6, 9]}]}, "legacy_answer": "S1 270 V2 [8,7]\nS2 270 V4 [7,2]\nS3 90 V1 [6,7]\nS4 0 V6 [6,9]", "solutionText": "S1 270 V2 [8,7]\nS2 270 V4 [7,2]\nS3 90 V1 [6,7]\nS4 0 V6 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-483\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S7: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-483/target.png", "shapes": {"S1": "images/voi-483/shape_S1.png", "S2": "images/voi-483/shape_S2.png", "S3": "images/voi-483/shape_S3.png", "S4": "images/voi-483/shape_S4.png", "S5": "images/voi-483/shape_S5.png", "S6": "images/voi-483/shape_S6.png", "S7": "images/voi-483/shape_S7.png"}}, "__sample_id__": "voi-483"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 5], [3, 8], [1, 8], [1, 5]]}, {"polygon": [[6, 2], [3, 2], [3, 1], [6, 1]]}, {"polygon": [[2, 8], [2, 6], [3, 6], [3, 8]]}, {"polygon": [[5, 2], [5, 5], [4, 5], [4, 2]]}], "meta": {"seed": 4207035, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 485, "strictValidation": true}, "imageAssets": {"target": "../images/voi-484/target.png", "shapes": {"S1": "../images/voi-484/shape_S1.png", "S2": "../images/voi-484/shape_S2.png", "S3": "../images/voi-484/shape_S3.png", "S4": "../images/voi-484/shape_S4.png", "S5": "../images/voi-484/shape_S5.png", "S6": "../images/voi-484/shape_S6.png", "S7": "../images/voi-484/shape_S7.png"}}, "ID": "voi-484", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [3, 1]}, {"shape": "S6", "angle": 90, "vertex": "V2", "grid": [2, 6]}, {"shape": "S7", "angle": 270, "vertex": "V1", "grid": [5, 2]}]}, "legacy_answer": "S1 270 V1 [3,5]\nS3 180 V3 [3,1]\nS6 90 V2 [2,6]\nS7 270 V1 [5,2]", "solutionText": "S1 270 V1 [3,5]\nS3 180 V3 [3,1]\nS6 90 V2 [2,6]\nS7 270 V1 [5,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-484\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-484/target.png", "shapes": {"S1": "images/voi-484/shape_S1.png", "S2": "images/voi-484/shape_S2.png", "S3": "images/voi-484/shape_S3.png", "S4": "images/voi-484/shape_S4.png", "S5": "images/voi-484/shape_S5.png", "S6": "images/voi-484/shape_S6.png", "S7": "images/voi-484/shape_S7.png"}}, "__sample_id__": "voi-484"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 1], [8, 2], [6, 2], [6, 1]]}, {"polygon": [[6, 0], [9, 0], [9, 2], [6, 2]]}, {"polygon": [[2, 9], [0, 9], [0, 7], [2, 7]]}, {"polygon": [[8, 3], [8, 2], [10, 2], [10, 3]]}], "meta": {"seed": 4207036, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 486, "strictValidation": true}, "imageAssets": {"target": "../images/voi-485/target.png", "shapes": {"S1": "../images/voi-485/shape_S1.png", "S2": "../images/voi-485/shape_S2.png", "S3": "../images/voi-485/shape_S3.png", "S4": "../images/voi-485/shape_S4.png", "S5": "../images/voi-485/shape_S5.png", "S6": "../images/voi-485/shape_S6.png", "S7": "../images/voi-485/shape_S7.png"}}, "ID": "voi-485", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [6, 1]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [9, 2]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [0, 9]}, {"shape": "S7", "angle": 90, "vertex": "V4", "grid": [10, 3]}]}, "legacy_answer": "S2 270 V4 [6,1]\nS4 0 V3 [9,2]\nS6 180 V2 [0,9]\nS7 90 V4 [10,3]", "solutionText": "S2 270 V4 [6,1]\nS4 0 V3 [9,2]\nS6 180 V2 [0,9]\nS7 90 V4 [10,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-485\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-485/target.png", "shapes": {"S1": "images/voi-485/shape_S1.png", "S2": "images/voi-485/shape_S2.png", "S3": "images/voi-485/shape_S3.png", "S4": "images/voi-485/shape_S4.png", "S5": "images/voi-485/shape_S5.png", "S6": "images/voi-485/shape_S6.png", "S7": "images/voi-485/shape_S7.png"}}, "__sample_id__": "voi-485"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 5], [2, 3], [3, 3], [3, 4], [5, 4], [5, 5]]}, {"polygon": [[6, 5], [6, 2], [8, 2], [8, 5]]}, {"polygon": [[7, 3], [7, 5], [6, 5], [6, 3]]}, {"polygon": [[5, 2], [5, 4], [3, 4], [3, 2]]}], "meta": {"seed": 4207037, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.95, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 487, "strictValidation": true}, "imageAssets": {"target": "../images/voi-486/target.png", "shapes": {"S1": "../images/voi-486/shape_S1.png", "S2": "../images/voi-486/shape_S2.png", "S3": "../images/voi-486/shape_S3.png", "S4": "../images/voi-486/shape_S4.png", "S5": "../images/voi-486/shape_S5.png", "S6": "../images/voi-486/shape_S6.png", "S7": "../images/voi-486/shape_S7.png"}}, "ID": "voi-486", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [8, 5]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [7, 5]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [5, 4]}]}, "legacy_answer": "S2 90 V3 [3,3]\nS3 90 V4 [8,5]\nS4 270 V2 [7,5]\nS6 270 V2 [5,4]", "solutionText": "S2 90 V3 [3,3]\nS3 90 V4 [8,5]\nS4 270 V2 [7,5]\nS6 270 V2 [5,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-486\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-486/target.png", "shapes": {"S1": "images/voi-486/shape_S1.png", "S2": "images/voi-486/shape_S2.png", "S3": "images/voi-486/shape_S3.png", "S4": "images/voi-486/shape_S4.png", "S5": "images/voi-486/shape_S5.png", "S6": "images/voi-486/shape_S6.png", "S7": "images/voi-486/shape_S7.png"}}, "__sample_id__": "voi-486"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[5, 10], [3, 10], [3, 9], [4, 9], [4, 7], [5, 7]]}, {"polygon": [[3, 8], [3, 10], [2, 10], [2, 9], [0, 9], [0, 8]]}, {"polygon": [[3, 10], [3, 7], [4, 8], [4, 10]]}, {"polygon": [[7, 10], [4, 10], [4, 8], [7, 8]]}], "meta": {"seed": 4207038, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.362949, "contourComplexity": 48, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.751171, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 488, "strictValidation": true}, "imageAssets": {"target": "../images/voi-487/target.png", "shapes": {"S1": "../images/voi-487/shape_S1.png", "S2": "../images/voi-487/shape_S2.png", "S3": "../images/voi-487/shape_S3.png", "S4": "../images/voi-487/shape_S4.png", "S5": "../images/voi-487/shape_S5.png", "S6": "../images/voi-487/shape_S6.png", "S7": "../images/voi-487/shape_S7.png"}}, "ID": "voi-487", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 10]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [3, 10]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [4, 8]}, {"shape": "S6", "angle": 180, "vertex": "V4", "grid": [7, 8]}]}, "legacy_answer": "S1 180 V1 [5,10]\nS4 270 V2 [3,10]\nS5 90 V3 [4,8]\nS6 180 V4 [7,8]", "solutionText": "S1 180 V1 [5,10]\nS4 270 V2 [3,10]\nS5 90 V3 [4,8]\nS6 180 V4 [7,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-487\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-487/target.png", "shapes": {"S1": "images/voi-487/shape_S1.png", "S2": "images/voi-487/shape_S2.png", "S3": "images/voi-487/shape_S3.png", "S4": "images/voi-487/shape_S4.png", "S5": "images/voi-487/shape_S5.png", "S6": "images/voi-487/shape_S6.png", "S7": "images/voi-487/shape_S7.png"}}, "__sample_id__": "voi-487"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 8], [5, 8], [5, 6], [8, 6]]}, {"polygon": [[8, 7], [5, 7], [6, 6], [8, 6]]}, {"polygon": [[5, 5], [3, 5], [3, 4], [5, 4]]}, {"polygon": [[6, 7], [3, 7], [3, 5], [6, 5]]}], "meta": {"seed": 4207039, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.362949, "contourComplexity": 43, "connectedComponents": 1, "fillRatio": 0.105313, "difficultyScore": 0.501171, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 489, "strictValidation": true}, "imageAssets": {"target": "../images/voi-488/target.png", "shapes": {"S1": "../images/voi-488/shape_S1.png", "S2": "../images/voi-488/shape_S2.png", "S3": "../images/voi-488/shape_S3.png", "S4": "../images/voi-488/shape_S4.png", "S5": "../images/voi-488/shape_S5.png", "S6": "../images/voi-488/shape_S6.png", "S7": "../images/voi-488/shape_S7.png"}}, "ID": "voi-488", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V1", "grid": [8, 8]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 7]}, {"shape": "S6", "angle": 180, "vertex": "V3", "grid": [3, 4]}, {"shape": "S7", "angle": 180, "vertex": "V1", "grid": [6, 7]}]}, "legacy_answer": "S3 180 V1 [8,8]\nS4 180 V2 [5,7]\nS6 180 V3 [3,4]\nS7 180 V1 [6,7]", "solutionText": "S3 180 V1 [8,8]\nS4 180 V2 [5,7]\nS6 180 V3 [3,4]\nS7 180 V1 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-488\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-488/target.png", "shapes": {"S1": "images/voi-488/shape_S1.png", "S2": "images/voi-488/shape_S2.png", "S3": "images/voi-488/shape_S3.png", "S4": "images/voi-488/shape_S4.png", "S5": "images/voi-488/shape_S5.png", "S6": "images/voi-488/shape_S6.png", "S7": "images/voi-488/shape_S7.png"}}, "__sample_id__": "voi-488"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [6, 3], [8, 3], [8, 6]]}, {"polygon": [[6, 3], [6, 6], [5, 5], [5, 3]]}, {"polygon": [[5, 5], [5, 6], [4, 6], [4, 5]]}, {"polygon": [[8, 5], [8, 8], [6, 8], [6, 5]]}], "meta": {"seed": 4207040, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.257545, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.115312, "difficultyScore": 0.929194, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 490, "strictValidation": true}, "imageAssets": {"target": "../images/voi-489/target.png", "shapes": {"S1": "../images/voi-489/shape_S1.png", "S2": "../images/voi-489/shape_S2.png", "S3": "../images/voi-489/shape_S3.png", "S4": "../images/voi-489/shape_S4.png", "S5": "../images/voi-489/shape_S5.png", "S6": "../images/voi-489/shape_S6.png", "S7": "../images/voi-489/shape_S7.png"}}, "ID": "voi-489", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [6, 6]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [5, 3]}, {"shape": "S6", "angle": 270, "vertex": "V2", "grid": [5, 6]}, {"shape": "S7", "angle": 270, "vertex": "V4", "grid": [6, 5]}]}, "legacy_answer": "S1 90 V1 [6,6]\nS5 270 V4 [5,3]\nS6 270 V2 [5,6]\nS7 270 V4 [6,5]", "solutionText": "S1 90 V1 [6,6]\nS5 270 V4 [5,3]\nS6 270 V2 [5,6]\nS7 270 V4 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-489\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-489/target.png", "shapes": {"S1": "images/voi-489/shape_S1.png", "S2": "images/voi-489/shape_S2.png", "S3": "images/voi-489/shape_S3.png", "S4": "images/voi-489/shape_S4.png", "S5": "images/voi-489/shape_S5.png", "S6": "images/voi-489/shape_S6.png", "S7": "images/voi-489/shape_S7.png"}}, "__sample_id__": "voi-489"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 3], [1, 6], [0, 6], [0, 3]]}, {"polygon": [[1, 6], [4, 6], [4, 8], [1, 8]]}, {"polygon": [[1, 5], [3, 5], [3, 6], [2, 6], [2, 8], [1, 8]]}, {"polygon": [[4, 2], [4, 4], [2, 2]]}], "meta": {"seed": 4207041, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.26556, "contourComplexity": 76, "connectedComponents": 2, "fillRatio": 0.110625, "difficultyScore": 0.906509, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 491, "strictValidation": true}, "imageAssets": {"target": "../images/voi-490/target.png", "shapes": {"S1": "../images/voi-490/shape_S1.png", "S2": "../images/voi-490/shape_S2.png", "S3": "../images/voi-490/shape_S3.png", "S4": "../images/voi-490/shape_S4.png", "S5": "../images/voi-490/shape_S5.png", "S6": "../images/voi-490/shape_S6.png", "S7": "../images/voi-490/shape_S7.png"}}, "ID": "voi-490", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [4, 8]}, {"shape": "S5", "angle": 0, "vertex": "V3", "grid": [3, 6]}, {"shape": "S7", "angle": 270, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 270 V2 [1,6]\nS2 0 V3 [4,8]\nS5 0 V3 [3,6]\nS7 270 V2 [4,4]", "solutionText": "S1 270 V2 [1,6]\nS2 0 V3 [4,8]\nS5 0 V3 [3,6]\nS7 270 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-490\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-490/target.png", "shapes": {"S1": "images/voi-490/shape_S1.png", "S2": "images/voi-490/shape_S2.png", "S3": "images/voi-490/shape_S3.png", "S4": "images/voi-490/shape_S4.png", "S5": "images/voi-490/shape_S5.png", "S6": "images/voi-490/shape_S6.png", "S7": "images/voi-490/shape_S7.png"}}, "__sample_id__": "voi-490"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [6, 7], [6, 8], [4, 8]]}, {"polygon": [[5, 4], [7, 4], [7, 6], [5, 6]]}, {"polygon": [[6, 6], [6, 8], [5, 8], [5, 6]]}, {"polygon": [[6, 7], [6, 10], [4, 10], [4, 7]]}], "meta": {"seed": 4207042, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.1, "difficultyScore": 0.597143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 492, "strictValidation": true}, "imageAssets": {"target": "../images/voi-491/target.png", "shapes": {"S1": "../images/voi-491/shape_S1.png", "S2": "../images/voi-491/shape_S2.png", "S3": "../images/voi-491/shape_S3.png", "S4": "../images/voi-491/shape_S4.png", "S5": "../images/voi-491/shape_S5.png", "S6": "../images/voi-491/shape_S6.png", "S7": "../images/voi-491/shape_S7.png"}}, "ID": "voi-491", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [4, 7]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [7, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [6, 6]}, {"shape": "S7", "angle": 270, "vertex": "V1", "grid": [6, 7]}]}, "legacy_answer": "S1 0 V1 [4,7]\nS3 0 V2 [7,4]\nS4 270 V1 [6,6]\nS7 270 V1 [6,7]", "solutionText": "S1 0 V1 [4,7]\nS3 0 V2 [7,4]\nS4 270 V1 [6,6]\nS7 270 V1 [6,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-491\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-491/target.png", "shapes": {"S1": "images/voi-491/shape_S1.png", "S2": "images/voi-491/shape_S2.png", "S3": "images/voi-491/shape_S3.png", "S4": "images/voi-491/shape_S4.png", "S5": "images/voi-491/shape_S5.png", "S6": "images/voi-491/shape_S6.png", "S7": "images/voi-491/shape_S7.png"}}, "__sample_id__": "voi-491"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 8], [4, 8], [4, 6], [7, 6]]}, {"polygon": [[6, 8], [5, 8], [6, 7]]}, {"polygon": [[2, 7], [2, 8], [0, 8], [0, 7]]}, {"polygon": [[3, 7], [6, 7], [6, 9], [3, 9]]}], "meta": {"seed": 4207043, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 47, "connectedComponents": 2, "fillRatio": 0.105313, "difficultyScore": 0.8783, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 493, "strictValidation": true}, "imageAssets": {"target": "../images/voi-492/target.png", "shapes": {"S1": "../images/voi-492/shape_S1.png", "S2": "../images/voi-492/shape_S2.png", "S3": "../images/voi-492/shape_S3.png", "S4": "../images/voi-492/shape_S4.png", "S5": "../images/voi-492/shape_S5.png", "S6": "../images/voi-492/shape_S6.png", "S7": "../images/voi-492/shape_S7.png"}}, "ID": "voi-492", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [4, 8]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [6, 8]}, {"shape": "S6", "angle": 270, "vertex": "V3", "grid": [0, 8]}, {"shape": "S7", "angle": 0, "vertex": "V3", "grid": [6, 9]}]}, "legacy_answer": "S1 180 V2 [4,8]\nS3 180 V1 [6,8]\nS6 270 V3 [0,8]\nS7 0 V3 [6,9]", "solutionText": "S1 180 V2 [4,8]\nS3 180 V1 [6,8]\nS6 270 V3 [0,8]\nS7 0 V3 [6,9]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-492\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-492/target.png", "shapes": {"S1": "images/voi-492/shape_S1.png", "S2": "images/voi-492/shape_S2.png", "S3": "images/voi-492/shape_S3.png", "S4": "images/voi-492/shape_S4.png", "S5": "images/voi-492/shape_S5.png", "S6": "images/voi-492/shape_S6.png", "S7": "images/voi-492/shape_S7.png"}}, "__sample_id__": "voi-492"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [5, 2], [5, 4], [3, 4]]}, {"polygon": [[4, 7], [4, 5], [5, 5], [5, 7]]}, {"polygon": [[6, 3], [6, 4], [4, 4], [4, 3]]}, {"polygon": [[6, 6], [3, 6], [3, 4], [6, 4]]}], "meta": {"seed": 4207044, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 18, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.847143, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 494, "strictValidation": true}, "imageAssets": {"target": "../images/voi-493/target.png", "shapes": {"S1": "../images/voi-493/shape_S1.png", "S2": "../images/voi-493/shape_S2.png", "S3": "../images/voi-493/shape_S3.png", "S4": "../images/voi-493/shape_S4.png", "S5": "../images/voi-493/shape_S5.png", "S6": "../images/voi-493/shape_S6.png", "S7": "../images/voi-493/shape_S7.png"}}, "ID": "voi-493", "answer": {"placements": [{"shape": "S3", "angle": 0, "vertex": "V2", "grid": [5, 2]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [4, 7]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [4, 3]}, {"shape": "S6", "angle": 180, "vertex": "V4", "grid": [6, 4]}]}, "legacy_answer": "S3 0 V2 [5,2]\nS4 90 V1 [4,7]\nS5 270 V4 [4,3]\nS6 180 V4 [6,4]", "solutionText": "S3 0 V2 [5,2]\nS4 90 V1 [4,7]\nS5 270 V4 [4,3]\nS6 180 V4 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-493\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-493/target.png", "shapes": {"S1": "images/voi-493/shape_S1.png", "S2": "images/voi-493/shape_S2.png", "S3": "images/voi-493/shape_S3.png", "S4": "images/voi-493/shape_S4.png", "S5": "images/voi-493/shape_S5.png", "S6": "images/voi-493/shape_S6.png", "S7": "images/voi-493/shape_S7.png"}}, "__sample_id__": "voi-493"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 8], [5, 8], [5, 10], [2, 10]]}, {"polygon": [[6, 3], [6, 1], [8, 1], [8, 3]]}, {"polygon": [[8, 4], [8, 1], [10, 1], [10, 4]]}, {"polygon": [[7, 1], [10, 1], [10, 2], [7, 2]]}], "meta": {"seed": 4207045, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.315789, "contourComplexity": 12, "connectedComponents": 2, "fillRatio": 0.13, "difficultyScore": 0.666842, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 495, "strictValidation": true}, "imageAssets": {"target": "../images/voi-494/target.png", "shapes": {"S1": "../images/voi-494/shape_S1.png", "S2": "../images/voi-494/shape_S2.png", "S3": "../images/voi-494/shape_S3.png", "S4": "../images/voi-494/shape_S4.png", "S5": "../images/voi-494/shape_S5.png", "S6": "../images/voi-494/shape_S6.png", "S7": "../images/voi-494/shape_S7.png"}}, "ID": "voi-494", "answer": {"placements": [{"shape": "S3", "angle": 0, "vertex": "V2", "grid": [5, 8]}, {"shape": "S5", "angle": 90, "vertex": "V1", "grid": [6, 3]}, {"shape": "S6", "angle": 90, "vertex": "V3", "grid": [10, 1]}, {"shape": "S7", "angle": 0, "vertex": "V3", "grid": [10, 2]}]}, "legacy_answer": "S3 0 V2 [5,8]\nS5 90 V1 [6,3]\nS6 90 V3 [10,1]\nS7 0 V3 [10,2]", "solutionText": "S3 0 V2 [5,8]\nS5 90 V1 [6,3]\nS6 90 V3 [10,1]\nS7 0 V3 [10,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-494\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S7: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-494/target.png", "shapes": {"S1": "images/voi-494/shape_S1.png", "S2": "images/voi-494/shape_S2.png", "S3": "images/voi-494/shape_S3.png", "S4": "images/voi-494/shape_S4.png", "S5": "images/voi-494/shape_S5.png", "S6": "images/voi-494/shape_S6.png", "S7": "images/voi-494/shape_S7.png"}}, "__sample_id__": "voi-494"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 7], [3, 4], [5, 4], [5, 7]]}, {"polygon": [[7, 9], [4, 9], [4, 7], [7, 7]]}, {"polygon": [[4, 5], [4, 3], [6, 3], [6, 5]]}, {"polygon": [[6, 4], [3, 4], [4, 3], [6, 3]]}], "meta": {"seed": 4207046, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.323777, "contourComplexity": 44, "connectedComponents": 2, "fillRatio": 0.125312, "difficultyScore": 0.644265, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 496, "strictValidation": true}, "imageAssets": {"target": "../images/voi-495/target.png", "shapes": {"S1": "../images/voi-495/shape_S1.png", "S2": "../images/voi-495/shape_S2.png", "S3": "../images/voi-495/shape_S3.png", "S4": "../images/voi-495/shape_S4.png", "S5": "../images/voi-495/shape_S5.png", "S6": "../images/voi-495/shape_S6.png", "S7": "../images/voi-495/shape_S7.png"}}, "ID": "voi-495", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [4, 7]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [4, 5]}, {"shape": "S6", "angle": 180, "vertex": "V2", "grid": [3, 4]}]}, "legacy_answer": "S1 90 V2 [3,4]\nS2 180 V3 [4,7]\nS4 90 V1 [4,5]\nS6 180 V2 [3,4]", "solutionText": "S1 90 V2 [3,4]\nS2 180 V3 [4,7]\nS4 90 V1 [4,5]\nS6 180 V2 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-495\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S6: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-495/target.png", "shapes": {"S1": "images/voi-495/shape_S1.png", "S2": "images/voi-495/shape_S2.png", "S3": "images/voi-495/shape_S3.png", "S4": "images/voi-495/shape_S4.png", "S5": "images/voi-495/shape_S5.png", "S6": "images/voi-495/shape_S6.png", "S7": "images/voi-495/shape_S7.png"}}, "__sample_id__": "voi-495"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 7], [8, 7], [8, 9], [5, 9]]}, {"polygon": [[2, 5], [2, 8], [1, 7], [1, 5]]}, {"polygon": [[9, 8], [7, 8], [9, 6]]}, {"polygon": [[6, 8], [6, 5], [8, 5], [8, 8]]}], "meta": {"seed": 4207047, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.241055, "contourComplexity": 109, "connectedComponents": 2, "fillRatio": 0.125938, "difficultyScore": 0.973907, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 497, "strictValidation": true}, "imageAssets": {"target": "../images/voi-496/target.png", "shapes": {"S1": "../images/voi-496/shape_S1.png", "S2": "../images/voi-496/shape_S2.png", "S3": "../images/voi-496/shape_S3.png", "S4": "../images/voi-496/shape_S4.png", "S5": "../images/voi-496/shape_S5.png", "S6": "../images/voi-496/shape_S6.png", "S7": "../images/voi-496/shape_S7.png"}}, "ID": "voi-496", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [8, 9]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [9, 6]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [8, 5]}]}, "legacy_answer": "S1 0 V3 [8,9]\nS2 270 V4 [1,5]\nS3 180 V3 [9,6]\nS5 90 V3 [8,5]", "solutionText": "S1 0 V3 [8,9]\nS2 270 V4 [1,5]\nS3 180 V3 [9,6]\nS5 90 V3 [8,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-496\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S7: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-496/target.png", "shapes": {"S1": "images/voi-496/shape_S1.png", "S2": "images/voi-496/shape_S2.png", "S3": "images/voi-496/shape_S3.png", "S4": "images/voi-496/shape_S4.png", "S5": "images/voi-496/shape_S5.png", "S6": "images/voi-496/shape_S6.png", "S7": "images/voi-496/shape_S7.png"}}, "__sample_id__": "voi-496"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 6], [5, 6], [5, 4], [8, 4]]}, {"polygon": [[5, 1], [5, 4], [3, 4], [3, 1]]}, {"polygon": [[4, 4], [3, 4], [3, 2], [4, 2]]}, {"polygon": [[5, 0], [6, 0], [6, 2], [5, 2]]}], "meta": {"seed": 4207048, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.12, "difficultyScore": 0.95, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 498, "strictValidation": true}, "imageAssets": {"target": "../images/voi-497/target.png", "shapes": {"S1": "../images/voi-497/shape_S1.png", "S2": "../images/voi-497/shape_S2.png", "S3": "../images/voi-497/shape_S3.png", "S4": "../images/voi-497/shape_S4.png", "S5": "../images/voi-497/shape_S5.png", "S6": "../images/voi-497/shape_S6.png", "S7": "../images/voi-497/shape_S7.png"}}, "ID": "voi-497", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [3, 1]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S7", "angle": 0, "vertex": "V1", "grid": [5, 0]}]}, "legacy_answer": "S3 180 V3 [5,4]\nS4 270 V4 [3,1]\nS5 180 V2 [3,4]\nS7 0 V1 [5,0]", "solutionText": "S3 180 V3 [5,4]\nS4 270 V4 [3,1]\nS5 180 V2 [3,4]\nS7 0 V1 [5,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-497\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-497/target.png", "shapes": {"S1": "images/voi-497/shape_S1.png", "S2": "images/voi-497/shape_S2.png", "S3": "images/voi-497/shape_S3.png", "S4": "images/voi-497/shape_S4.png", "S5": "images/voi-497/shape_S5.png", "S6": "images/voi-497/shape_S6.png", "S7": "images/voi-497/shape_S7.png"}}, "__sample_id__": "voi-497"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S6": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S7": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[8, 4], [5, 4], [5, 3], [8, 3]]}, {"polygon": [[4, 5], [4, 4], [7, 4], [7, 5]]}, {"polygon": [[9, 5], [6, 5], [6, 3], [9, 3]]}, {"polygon": [[9, 3], [7, 3], [7, 1], [9, 1]]}], "meta": {"seed": 4207049, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.375, "contourComplexity": 14, "connectedComponents": 2, "fillRatio": 0.1, "difficultyScore": 0.81, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 499, "strictValidation": true}, "imageAssets": {"target": "../images/voi-498/target.png", "shapes": {"S1": "../images/voi-498/shape_S1.png", "S2": "../images/voi-498/shape_S2.png", "S3": "../images/voi-498/shape_S3.png", "S4": "../images/voi-498/shape_S4.png", "S5": "../images/voi-498/shape_S5.png", "S6": "../images/voi-498/shape_S6.png", "S7": "../images/voi-498/shape_S7.png"}}, "ID": "voi-498", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V3", "grid": [5, 3]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [4, 4]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [6, 5]}, {"shape": "S5", "angle": 180, "vertex": "V2", "grid": [7, 3]}]}, "legacy_answer": "S2 180 V3 [5,3]\nS3 90 V2 [4,4]\nS4 180 V2 [6,5]\nS5 180 V2 [7,3]", "solutionText": "S2 180 V3 [5,3]\nS3 90 V2 [4,4]\nS4 180 V2 [6,5]\nS5 180 V2 [7,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-498\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S6: V1=[0,0], V2=[1,0], V3=[0,1]\n- S7: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-498/target.png", "shapes": {"S1": "images/voi-498/shape_S1.png", "S2": "images/voi-498/shape_S2.png", "S3": "images/voi-498/shape_S3.png", "S4": "images/voi-498/shape_S4.png", "S5": "images/voi-498/shape_S5.png", "S6": "images/voi-498/shape_S6.png", "S7": "images/voi-498/shape_S7.png"}}, "__sample_id__": "voi-498"} {"gridSize": 10, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S6": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S7": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[10, 4], [8, 4], [10, 2]]}, {"polygon": [[10, 4], [7, 4], [7, 2], [10, 2]]}, {"polygon": [[7, 1], [7, 3], [6, 3], [6, 2], [4, 2], [4, 1]]}, {"polygon": [[6, 4], [9, 4], [9, 5], [6, 5]]}], "meta": {"seed": 4207050, "requiredShapeCount": 4, "distractorShapeCount": 3, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.273859, "contourComplexity": 76, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.625814, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 500, "strictValidation": true}, "imageAssets": {"target": "../images/voi-499/target.png", "shapes": {"S1": "../images/voi-499/shape_S1.png", "S2": "../images/voi-499/shape_S2.png", "S3": "../images/voi-499/shape_S3.png", "S4": "../images/voi-499/shape_S4.png", "S5": "../images/voi-499/shape_S5.png", "S6": "../images/voi-499/shape_S6.png", "S7": "../images/voi-499/shape_S7.png"}}, "ID": "voi-499", "answer": {"placements": [{"shape": "S3", "angle": 180, "vertex": "V1", "grid": [10, 4]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [7, 2]}, {"shape": "S6", "angle": 270, "vertex": "V1", "grid": [7, 1]}, {"shape": "S7", "angle": 0, "vertex": "V4", "grid": [6, 5]}]}, "legacy_answer": "S3 180 V1 [10,4]\nS4 180 V3 [7,2]\nS6 270 V1 [7,1]\nS7 0 V4 [6,5]", "solutionText": "S3 180 V1 [10,4]\nS4 180 V3 [7,2]\nS6 270 V1 [7,1]\nS7 0 V4 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-499\n- grid_size: 10x10\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 4\n- distractor_shapes: 3\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S6: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S7: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-499/target.png", "shapes": {"S1": "images/voi-499/shape_S1.png", "S2": "images/voi-499/shape_S2.png", "S3": "images/voi-499/shape_S3.png", "S4": "images/voi-499/shape_S4.png", "S5": "images/voi-499/shape_S5.png", "S6": "images/voi-499/shape_S6.png", "S7": "images/voi-499/shape_S7.png"}}, "__sample_id__": "voi-499"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 0], [4, 2], [2, 2], [2, 0]]}, {"polygon": [[1, 2], [1, 0], [3, 2]]}], "meta": {"seed": 4701001, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 501, "strictValidation": true}, "imageAssets": {"target": "../images/voi-500/target.png", "shapes": {"S1": "../images/voi-500/shape_S1.png", "S2": "../images/voi-500/shape_S2.png"}}, "ID": "voi-500", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [2, 0]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [1, 0]}]}, "legacy_answer": "S1 270 V4 [2,0]\nS2 90 V2 [1,0]", "solutionText": "S1 270 V4 [2,0]\nS2 90 V2 [1,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-500\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-500/target.png", "shapes": {"S1": "images/voi-500/shape_S1.png", "S2": "images/voi-500/shape_S2.png"}}, "__sample_id__": "voi-500"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[0, 0], [2, 0], [2, 2], [0, 2]]}, {"polygon": [[1, 2], [0, 2], [1, 1]]}], "meta": {"seed": 4701002, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 502, "strictValidation": true}, "imageAssets": {"target": "../images/voi-501/target.png", "shapes": {"S1": "../images/voi-501/shape_S1.png", "S2": "../images/voi-501/shape_S2.png"}}, "ID": "voi-501", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [0, 0]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [0, 2]}]}, "legacy_answer": "S1 0 V1 [0,0]\nS2 180 V2 [0,2]", "solutionText": "S1 0 V1 [0,0]\nS2 180 V2 [0,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-501\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-501/target.png", "shapes": {"S1": "images/voi-501/shape_S1.png", "S2": "images/voi-501/shape_S2.png"}}, "__sample_id__": "voi-501"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 6], [4, 6], [4, 4], [6, 4]]}, {"polygon": [[6, 6], [5, 6], [6, 5]]}], "meta": {"seed": 4701004, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 503, "strictValidation": true}, "imageAssets": {"target": "../images/voi-502/target.png", "shapes": {"S1": "../images/voi-502/shape_S1.png", "S2": "../images/voi-502/shape_S2.png"}}, "ID": "voi-502", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [4, 6]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S1 180 V2 [4,6]\nS2 180 V3 [6,5]", "solutionText": "S1 180 V2 [4,6]\nS2 180 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-502\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-502/target.png", "shapes": {"S1": "images/voi-502/shape_S1.png", "S2": "images/voi-502/shape_S2.png"}}, "__sample_id__": "voi-502"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [5, 4], [3, 2]]}, {"polygon": [[3, 3], [5, 3], [5, 5], [3, 5]]}], "meta": {"seed": 4701005, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 504, "strictValidation": true}, "imageAssets": {"target": "../images/voi-503/target.png", "shapes": {"S1": "../images/voi-503/shape_S1.png", "S2": "../images/voi-503/shape_S2.png"}}, "ID": "voi-503", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [5, 4]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [5, 5]}]}, "legacy_answer": "S1 270 V2 [5,4]\nS2 0 V3 [5,5]", "solutionText": "S1 270 V2 [5,4]\nS2 0 V3 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-503\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-503/target.png", "shapes": {"S1": "images/voi-503/shape_S1.png", "S2": "images/voi-503/shape_S2.png"}}, "__sample_id__": "voi-503"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}, {"polygon": [[4, 1], [5, 1], [4, 2]]}], "meta": {"seed": 4701006, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 505, "strictValidation": true}, "imageAssets": {"target": "../images/voi-504/target.png", "shapes": {"S1": "../images/voi-504/shape_S1.png", "S2": "../images/voi-504/shape_S2.png"}}, "ID": "voi-504", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 1]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 1]}]}, "legacy_answer": "S1 90 V2 [3,1]\nS2 0 V2 [5,1]", "solutionText": "S1 90 V2 [3,1]\nS2 0 V2 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-504\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-504/target.png", "shapes": {"S1": "images/voi-504/shape_S1.png", "S2": "images/voi-504/shape_S2.png"}}, "__sample_id__": "voi-504"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[1, 5], [1, 3], [3, 5]]}], "meta": {"seed": 4701007, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 506, "strictValidation": true}, "imageAssets": {"target": "../images/voi-505/target.png", "shapes": {"S1": "../images/voi-505/shape_S1.png", "S2": "../images/voi-505/shape_S2.png"}}, "ID": "voi-505", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [3, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 5]}]}, "legacy_answer": "S1 270 V2 [3,4]\nS2 90 V1 [1,5]", "solutionText": "S1 270 V2 [3,4]\nS2 90 V1 [1,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-505\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-505/target.png", "shapes": {"S1": "images/voi-505/shape_S1.png", "S2": "images/voi-505/shape_S2.png"}}, "__sample_id__": "voi-505"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 6], [0, 4], [2, 6]]}, {"polygon": [[2, 5], [0, 5], [0, 3], [2, 3]]}], "meta": {"seed": 4701008, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 507, "strictValidation": true}, "imageAssets": {"target": "../images/voi-506/target.png", "shapes": {"S1": "../images/voi-506/shape_S1.png", "S2": "../images/voi-506/shape_S2.png"}}, "ID": "voi-506", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [0, 6]}, {"shape": "S2", "angle": 180, "vertex": "V3", "grid": [0, 3]}]}, "legacy_answer": "S1 90 V1 [0,6]\nS2 180 V3 [0,3]", "solutionText": "S1 90 V1 [0,6]\nS2 180 V3 [0,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-506\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-506/target.png", "shapes": {"S1": "images/voi-506/shape_S1.png", "S2": "images/voi-506/shape_S2.png"}}, "__sample_id__": "voi-506"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [1, 2], [3, 0]]}, {"polygon": [[1, 3], [1, 1], [3, 3]]}], "meta": {"seed": 4701009, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.136364, "contourComplexity": 128, "connectedComponents": 1, "fillRatio": 0.098958, "difficultyScore": 0.456629, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 508, "strictValidation": true}, "imageAssets": {"target": "../images/voi-507/target.png", "shapes": {"S1": "../images/voi-507/shape_S1.png", "S2": "../images/voi-507/shape_S2.png"}}, "ID": "voi-507", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 0]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 3]}]}, "legacy_answer": "S1 180 V3 [3,0]\nS2 90 V1 [1,3]", "solutionText": "S1 180 V3 [3,0]\nS2 90 V1 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-507\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-507/target.png", "shapes": {"S1": "images/voi-507/shape_S1.png", "S2": "images/voi-507/shape_S2.png"}}, "__sample_id__": "voi-507"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[6, 1], [6, 3], [4, 3], [4, 1]]}, {"polygon": [[3, 1], [5, 1], [3, 3]]}], "meta": {"seed": 4701010, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 509, "strictValidation": true}, "imageAssets": {"target": "../images/voi-508/target.png", "shapes": {"S1": "../images/voi-508/shape_S1.png", "S2": "../images/voi-508/shape_S2.png"}}, "ID": "voi-508", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [6, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [3, 1]}]}, "legacy_answer": "S1 270 V2 [6,3]\nS2 0 V1 [3,1]", "solutionText": "S1 270 V2 [6,3]\nS2 0 V1 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-508\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-508/target.png", "shapes": {"S1": "images/voi-508/shape_S1.png", "S2": "images/voi-508/shape_S2.png"}}, "__sample_id__": "voi-508"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 0], [4, 2], [2, 2], [2, 0]]}, {"polygon": [[1, 0], [3, 0], [1, 2]]}], "meta": {"seed": 4701011, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 510, "strictValidation": true}, "imageAssets": {"target": "../images/voi-509/target.png", "shapes": {"S1": "../images/voi-509/shape_S1.png", "S2": "../images/voi-509/shape_S2.png"}}, "ID": "voi-509", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [2, 0]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [1, 2]}]}, "legacy_answer": "S1 270 V4 [2,0]\nS2 0 V3 [1,2]", "solutionText": "S1 270 V4 [2,0]\nS2 0 V3 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-509\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-509/target.png", "shapes": {"S1": "images/voi-509/shape_S1.png", "S2": "images/voi-509/shape_S2.png"}}, "__sample_id__": "voi-509"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 0], [1, 0], [0, 1]]}, {"polygon": [[0, 0], [2, 0], [2, 2], [0, 2]]}], "meta": {"seed": 4701012, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.234483, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.096354, "difficultyScore": 0.745223, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 511, "strictValidation": true}, "imageAssets": {"target": "../images/voi-510/target.png", "shapes": {"S1": "../images/voi-510/shape_S1.png", "S2": "../images/voi-510/shape_S2.png"}}, "ID": "voi-510", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [0, 1]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [0, 2]}]}, "legacy_answer": "S1 0 V3 [0,1]\nS2 0 V4 [0,2]", "solutionText": "S1 0 V3 [0,1]\nS2 0 V4 [0,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-510\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-510/target.png", "shapes": {"S1": "images/voi-510/shape_S1.png", "S2": "images/voi-510/shape_S2.png"}}, "__sample_id__": "voi-510"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 2], [1, 0], [3, 0], [3, 2]]}, {"polygon": [[4, 0], [4, 2], [2, 0]]}], "meta": {"seed": 4701013, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 512, "strictValidation": true}, "imageAssets": {"target": "../images/voi-511/target.png", "shapes": {"S1": "../images/voi-511/shape_S1.png", "S2": "../images/voi-511/shape_S2.png"}}, "ID": "voi-511", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [3, 2]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [2, 0]}]}, "legacy_answer": "S1 90 V4 [3,2]\nS2 270 V3 [2,0]", "solutionText": "S1 90 V4 [3,2]\nS2 270 V3 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-511\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-511/target.png", "shapes": {"S1": "images/voi-511/shape_S1.png", "S2": "images/voi-511/shape_S2.png"}}, "__sample_id__": "voi-511"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 2], [3, 2], [5, 0]]}, {"polygon": [[2, 0], [4, 0], [4, 2], [2, 2]]}], "meta": {"seed": 4701014, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 513, "strictValidation": true}, "imageAssets": {"target": "../images/voi-512/target.png", "shapes": {"S1": "../images/voi-512/shape_S1.png", "S2": "../images/voi-512/shape_S2.png"}}, "ID": "voi-512", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 2]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [2, 2]}]}, "legacy_answer": "S1 180 V1 [5,2]\nS2 0 V4 [2,2]", "solutionText": "S1 180 V1 [5,2]\nS2 0 V4 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-512\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-512/target.png", "shapes": {"S1": "images/voi-512/shape_S1.png", "S2": "images/voi-512/shape_S2.png"}}, "__sample_id__": "voi-512"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}, {"polygon": [[3, 0], [5, 0], [3, 2]]}], "meta": {"seed": 4701015, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 514, "strictValidation": true}, "imageAssets": {"target": "../images/voi-513/target.png", "shapes": {"S1": "../images/voi-513/shape_S1.png", "S2": "../images/voi-513/shape_S2.png"}}, "ID": "voi-513", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [3, 3]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [3, 2]}]}, "legacy_answer": "S1 90 V1 [3,3]\nS2 0 V3 [3,2]", "solutionText": "S1 90 V1 [3,3]\nS2 0 V3 [3,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-513\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-513/target.png", "shapes": {"S1": "images/voi-513/shape_S1.png", "S2": "images/voi-513/shape_S2.png"}}, "__sample_id__": "voi-513"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[1, 5], [1, 3], [3, 3], [3, 5]]}, {"polygon": [[1, 6], [1, 4], [3, 6]]}], "meta": {"seed": 4701016, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 515, "strictValidation": true}, "imageAssets": {"target": "../images/voi-514/target.png", "shapes": {"S1": "../images/voi-514/shape_S1.png", "S2": "../images/voi-514/shape_S2.png"}}, "ID": "voi-514", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [1, 5]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [1, 6]}]}, "legacy_answer": "S1 90 V1 [1,5]\nS2 90 V1 [1,6]", "solutionText": "S1 90 V1 [1,5]\nS2 90 V1 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-514\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-514/target.png", "shapes": {"S1": "images/voi-514/shape_S1.png", "S2": "images/voi-514/shape_S2.png"}}, "__sample_id__": "voi-514"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 6], [1, 6], [3, 4]]}, {"polygon": [[3, 3], [3, 5], [1, 5], [1, 3]]}], "meta": {"seed": 4701017, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 516, "strictValidation": true}, "imageAssets": {"target": "../images/voi-515/target.png", "shapes": {"S1": "../images/voi-515/shape_S1.png", "S2": "../images/voi-515/shape_S2.png"}}, "ID": "voi-515", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V2 [1,6]\nS2 270 V1 [3,3]", "solutionText": "S1 180 V2 [1,6]\nS2 270 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-515\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-515/target.png", "shapes": {"S1": "images/voi-515/shape_S1.png", "S2": "images/voi-515/shape_S2.png"}}, "__sample_id__": "voi-515"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 2], [5, 4], [3, 4], [3, 2]]}, {"polygon": [[6, 4], [4, 4], [6, 2]]}], "meta": {"seed": 4701018, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 517, "strictValidation": true}, "imageAssets": {"target": "../images/voi-516/target.png", "shapes": {"S1": "../images/voi-516/shape_S1.png", "S2": "../images/voi-516/shape_S2.png"}}, "ID": "voi-516", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 4]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [4, 4]}]}, "legacy_answer": "S1 270 V3 [3,4]\nS2 180 V2 [4,4]", "solutionText": "S1 270 V3 [3,4]\nS2 180 V2 [4,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-516\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-516/target.png", "shapes": {"S1": "images/voi-516/shape_S1.png", "S2": "images/voi-516/shape_S2.png"}}, "__sample_id__": "voi-516"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 3], [0, 3], [2, 1]]}, {"polygon": [[2, 0], [2, 2], [0, 2], [0, 0]]}], "meta": {"seed": 4701019, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 518, "strictValidation": true}, "imageAssets": {"target": "../images/voi-517/target.png", "shapes": {"S1": "../images/voi-517/shape_S1.png", "S2": "../images/voi-517/shape_S2.png"}}, "ID": "voi-517", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [2, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 2]}]}, "legacy_answer": "S1 180 V1 [2,3]\nS2 270 V3 [0,2]", "solutionText": "S1 180 V1 [2,3]\nS2 270 V3 [0,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-517\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-517/target.png", "shapes": {"S1": "images/voi-517/shape_S1.png", "S2": "images/voi-517/shape_S2.png"}}, "__sample_id__": "voi-517"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 4], [3, 4], [5, 2]]}, {"polygon": [[3, 3], [3, 1], [5, 1], [5, 3]]}], "meta": {"seed": 4701020, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 519, "strictValidation": true}, "imageAssets": {"target": "../images/voi-518/target.png", "shapes": {"S1": "../images/voi-518/shape_S1.png", "S2": "../images/voi-518/shape_S2.png"}}, "ID": "voi-518", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [5, 2]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V3 [5,2]\nS2 90 V1 [3,3]", "solutionText": "S1 180 V3 [5,2]\nS2 90 V1 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-518\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-518/target.png", "shapes": {"S1": "images/voi-518/shape_S1.png", "S2": "images/voi-518/shape_S2.png"}}, "__sample_id__": "voi-518"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 5], [0, 3], [2, 5]]}, {"polygon": [[1, 3], [3, 3], [3, 5], [1, 5]]}], "meta": {"seed": 4701021, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 520, "strictValidation": true}, "imageAssets": {"target": "../images/voi-519/target.png", "shapes": {"S1": "../images/voi-519/shape_S1.png", "S2": "../images/voi-519/shape_S2.png"}}, "ID": "voi-519", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [0, 5]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [1, 5]}]}, "legacy_answer": "S1 90 V1 [0,5]\nS2 0 V4 [1,5]", "solutionText": "S1 90 V1 [0,5]\nS2 0 V4 [1,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-519\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-519/target.png", "shapes": {"S1": "images/voi-519/shape_S1.png", "S2": "images/voi-519/shape_S2.png"}}, "__sample_id__": "voi-519"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 4], [5, 6], [3, 4]]}, {"polygon": [[2, 4], [4, 4], [4, 6], [2, 6]]}], "meta": {"seed": 4701022, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 521, "strictValidation": true}, "imageAssets": {"target": "../images/voi-520/target.png", "shapes": {"S1": "../images/voi-520/shape_S1.png", "S2": "../images/voi-520/shape_S2.png"}}, "ID": "voi-520", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [3, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S1 270 V3 [3,4]\nS2 0 V1 [2,4]", "solutionText": "S1 270 V3 [3,4]\nS2 0 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-520\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-520/target.png", "shapes": {"S1": "images/voi-520/shape_S1.png", "S2": "images/voi-520/shape_S2.png"}}, "__sample_id__": "voi-520"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 3], [3, 5], [1, 3]]}, {"polygon": [[3, 4], [3, 6], [1, 6], [1, 4]]}], "meta": {"seed": 4701023, "requiredShapeCount": 2, "distractorShapeCount": 0, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.423253, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 522, "strictValidation": true}, "imageAssets": {"target": "../images/voi-521/target.png", "shapes": {"S1": "../images/voi-521/shape_S1.png", "S2": "../images/voi-521/shape_S2.png"}}, "ID": "voi-521", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [1, 6]}]}, "legacy_answer": "S1 270 V1 [3,3]\nS2 270 V3 [1,6]", "solutionText": "S1 270 V1 [3,3]\nS2 270 V3 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-521\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 2\n- distractor_shapes: 0\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-521/target.png", "shapes": {"S1": "images/voi-521/shape_S1.png", "S2": "images/voi-521/shape_S2.png"}}, "__sample_id__": "voi-521"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 5], [5, 6], [4, 5]]}, {"polygon": [[6, 6], [4, 6], [4, 4], [6, 4]]}, {"polygon": [[4, 6], [2, 6], [4, 4]]}], "meta": {"seed": 4702001, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 100, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 523, "strictValidation": true}, "imageAssets": {"target": "../images/voi-522/target.png", "shapes": {"S1": "../images/voi-522/shape_S1.png", "S2": "../images/voi-522/shape_S2.png", "S3": "../images/voi-522/shape_S3.png", "S4": "../images/voi-522/shape_S4.png"}}, "ID": "voi-522", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [5, 5]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [4, 4]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S2 270 V1 [5,5]\nS3 180 V3 [4,4]\nS4 180 V1 [4,6]", "solutionText": "S2 270 V1 [5,5]\nS3 180 V3 [4,4]\nS4 180 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-522\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-522/target.png", "shapes": {"S1": "images/voi-522/shape_S1.png", "S2": "images/voi-522/shape_S2.png", "S3": "images/voi-522/shape_S3.png", "S4": "images/voi-522/shape_S4.png"}}, "__sample_id__": "voi-522"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 3], [3, 3], [2, 4]]}, {"polygon": [[2, 6], [2, 4], [4, 4], [4, 6]]}, {"polygon": [[1, 6], [1, 4], [3, 6]]}], "meta": {"seed": 4702002, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 524, "strictValidation": true}, "imageAssets": {"target": "../images/voi-523/target.png", "shapes": {"S1": "../images/voi-523/shape_S1.png", "S2": "../images/voi-523/shape_S2.png", "S3": "../images/voi-523/shape_S3.png", "S4": "../images/voi-523/shape_S4.png"}}, "ID": "voi-523", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [2, 4]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [2, 6]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [1, 6]}]}, "legacy_answer": "S1 0 V3 [2,4]\nS2 90 V1 [2,6]\nS4 90 V1 [1,6]", "solutionText": "S1 0 V3 [2,4]\nS2 90 V1 [2,6]\nS4 90 V1 [1,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-523\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-523/target.png", "shapes": {"S1": "images/voi-523/shape_S1.png", "S2": "images/voi-523/shape_S2.png", "S3": "images/voi-523/shape_S3.png", "S4": "images/voi-523/shape_S4.png"}}, "__sample_id__": "voi-523"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 2], [3, 4], [1, 4], [1, 2]]}, {"polygon": [[2, 4], [2, 3], [3, 4]]}, {"polygon": [[4, 1], [4, 3], [3, 3], [3, 1]]}], "meta": {"seed": 4702003, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 525, "strictValidation": true}, "imageAssets": {"target": "../images/voi-524/target.png", "shapes": {"S1": "../images/voi-524/shape_S1.png", "S2": "../images/voi-524/shape_S2.png", "S3": "../images/voi-524/shape_S3.png", "S4": "../images/voi-524/shape_S4.png"}}, "ID": "voi-524", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [3, 2]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [3, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 3]}]}, "legacy_answer": "S1 270 V1 [3,2]\nS2 90 V3 [3,4]\nS3 270 V2 [4,3]", "solutionText": "S1 270 V1 [3,2]\nS2 90 V3 [3,4]\nS3 270 V2 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-524\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-524/target.png", "shapes": {"S1": "images/voi-524/shape_S1.png", "S2": "images/voi-524/shape_S2.png", "S3": "images/voi-524/shape_S3.png", "S4": "images/voi-524/shape_S4.png"}}, "__sample_id__": "voi-524"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 3], [3, 3], [3, 4], [1, 4]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}, {"polygon": [[2, 4], [0, 4], [0, 2], [2, 2]]}], "meta": {"seed": 4702004, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.222222, "difficultyScore": 0.195556, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 526, "strictValidation": true}, "imageAssets": {"target": "../images/voi-525/target.png", "shapes": {"S1": "../images/voi-525/shape_S1.png", "S2": "../images/voi-525/shape_S2.png", "S3": "../images/voi-525/shape_S3.png", "S4": "../images/voi-525/shape_S4.png"}}, "ID": "voi-525", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 3]}, {"shape": "S3", "angle": 0, "vertex": "V4", "grid": [2, 3]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [2, 2]}]}, "legacy_answer": "S2 0 V1 [1,3]\nS3 0 V4 [2,3]\nS4 180 V4 [2,2]", "solutionText": "S2 0 V1 [1,3]\nS3 0 V4 [2,3]\nS4 180 V4 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-525\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-525/target.png", "shapes": {"S1": "images/voi-525/shape_S1.png", "S2": "images/voi-525/shape_S2.png", "S3": "images/voi-525/shape_S3.png", "S4": "images/voi-525/shape_S4.png"}}, "__sample_id__": "voi-525"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 0], [4, 0], [4, 2], [2, 2]]}, {"polygon": [[1, 2], [1, 0], [3, 2]]}, {"polygon": [[5, 3], [4, 3], [4, 1], [5, 1]]}], "meta": {"seed": 4702005, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 527, "strictValidation": true}, "imageAssets": {"target": "../images/voi-526/target.png", "shapes": {"S1": "../images/voi-526/shape_S1.png", "S2": "../images/voi-526/shape_S2.png", "S3": "../images/voi-526/shape_S3.png", "S4": "../images/voi-526/shape_S4.png"}}, "ID": "voi-526", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [2, 0]}, {"shape": "S3", "angle": 90, "vertex": "V1", "grid": [1, 2]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [5, 1]}]}, "legacy_answer": "S1 0 V1 [2,0]\nS3 90 V1 [1,2]\nS4 180 V4 [5,1]", "solutionText": "S1 0 V1 [2,0]\nS3 90 V1 [1,2]\nS4 180 V4 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-526\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-526/target.png", "shapes": {"S1": "images/voi-526/shape_S1.png", "S2": "images/voi-526/shape_S2.png", "S3": "images/voi-526/shape_S3.png", "S4": "images/voi-526/shape_S4.png"}}, "__sample_id__": "voi-526"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 5], [2, 5], [4, 3]]}, {"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}, {"polygon": [[6, 4], [6, 6], [4, 6], [4, 4]]}], "meta": {"seed": 4702006, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.25, "difficultyScore": 0.43764, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 528, "strictValidation": true}, "imageAssets": {"target": "../images/voi-527/target.png", "shapes": {"S1": "../images/voi-527/shape_S1.png", "S2": "../images/voi-527/shape_S2.png", "S3": "../images/voi-527/shape_S3.png", "S4": "../images/voi-527/shape_S4.png"}}, "ID": "voi-527", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [2, 5]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [2, 2]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [6, 4]}]}, "legacy_answer": "S1 180 V2 [2,5]\nS2 90 V2 [2,2]\nS4 270 V1 [6,4]", "solutionText": "S1 180 V2 [2,5]\nS2 90 V2 [2,2]\nS4 270 V1 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-527\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-527/target.png", "shapes": {"S1": "images/voi-527/shape_S1.png", "S2": "images/voi-527/shape_S2.png", "S3": "images/voi-527/shape_S3.png", "S4": "images/voi-527/shape_S4.png"}}, "__sample_id__": "voi-527"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 3], [6, 4], [5, 3]]}, {"polygon": [[4, 4], [3, 4], [3, 2], [4, 2]]}, {"polygon": [[4, 4], [4, 2], [6, 2], [6, 4]]}], "meta": {"seed": 4702007, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 529, "strictValidation": true}, "imageAssets": {"target": "../images/voi-528/target.png", "shapes": {"S1": "../images/voi-528/shape_S1.png", "S2": "../images/voi-528/shape_S2.png", "S3": "../images/voi-528/shape_S3.png", "S4": "../images/voi-528/shape_S4.png"}}, "ID": "voi-528", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [6, 4]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 4]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [6, 2]}]}, "legacy_answer": "S1 270 V2 [6,4]\nS2 180 V1 [4,4]\nS4 90 V3 [6,2]", "solutionText": "S1 270 V2 [6,4]\nS2 180 V1 [4,4]\nS4 90 V3 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-528\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-528/target.png", "shapes": {"S1": "images/voi-528/shape_S1.png", "S2": "images/voi-528/shape_S2.png", "S3": "images/voi-528/shape_S3.png", "S4": "images/voi-528/shape_S4.png"}}, "__sample_id__": "voi-528"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 5], [3, 6], [1, 6], [1, 5]]}, {"polygon": [[4, 6], [2, 6], [4, 4]]}, {"polygon": [[2, 5], [2, 4], [3, 4], [3, 5]]}], "meta": {"seed": 4702008, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.111111, "difficultyScore": 0.457284, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 530, "strictValidation": true}, "imageAssets": {"target": "../images/voi-529/target.png", "shapes": {"S1": "../images/voi-529/shape_S1.png", "S2": "../images/voi-529/shape_S2.png", "S3": "../images/voi-529/shape_S3.png", "S4": "../images/voi-529/shape_S4.png"}}, "ID": "voi-529", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [3, 5]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [4, 6]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [3, 4]}]}, "legacy_answer": "S2 270 V1 [3,5]\nS3 180 V1 [4,6]\nS4 90 V3 [3,4]", "solutionText": "S2 270 V1 [3,5]\nS3 180 V1 [4,6]\nS4 90 V3 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-529\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-529/target.png", "shapes": {"S1": "images/voi-529/shape_S1.png", "S2": "images/voi-529/shape_S2.png", "S3": "images/voi-529/shape_S3.png", "S4": "images/voi-529/shape_S4.png"}}, "__sample_id__": "voi-529"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 6], [1, 6], [1, 5], [3, 5]]}, {"polygon": [[1, 4], [3, 4], [1, 6]]}, {"polygon": [[3, 5], [3, 3], [5, 5]]}], "meta": {"seed": 4702009, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.173469, "contourComplexity": 134, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.384872, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 531, "strictValidation": true}, "imageAssets": {"target": "../images/voi-530/target.png", "shapes": {"S1": "../images/voi-530/shape_S1.png", "S2": "../images/voi-530/shape_S2.png", "S3": "../images/voi-530/shape_S3.png", "S4": "../images/voi-530/shape_S4.png"}}, "ID": "voi-530", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [1, 6]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [1, 4]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V2 [1,6]\nS2 0 V1 [1,4]\nS4 90 V2 [3,3]", "solutionText": "S1 180 V2 [1,6]\nS2 0 V1 [1,4]\nS4 90 V2 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-530\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-530/target.png", "shapes": {"S1": "images/voi-530/shape_S1.png", "S2": "images/voi-530/shape_S2.png", "S3": "images/voi-530/shape_S3.png", "S4": "images/voi-530/shape_S4.png"}}, "__sample_id__": "voi-530"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 4], [4, 4], [4, 6], [3, 6]]}, {"polygon": [[6, 4], [4, 4], [4, 2], [6, 2]]}, {"polygon": [[5, 6], [3, 6], [5, 4]]}], "meta": {"seed": 4702010, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 73, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 532, "strictValidation": true}, "imageAssets": {"target": "../images/voi-531/target.png", "shapes": {"S1": "../images/voi-531/shape_S1.png", "S2": "../images/voi-531/shape_S2.png", "S3": "../images/voi-531/shape_S3.png", "S4": "../images/voi-531/shape_S4.png"}}, "ID": "voi-531", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 6]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [4, 4]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [5, 6]}]}, "legacy_answer": "S1 0 V4 [3,6]\nS2 180 V2 [4,4]\nS4 180 V1 [5,6]", "solutionText": "S1 0 V4 [3,6]\nS2 180 V2 [4,4]\nS4 180 V1 [5,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-531\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-531/target.png", "shapes": {"S1": "images/voi-531/shape_S1.png", "S2": "images/voi-531/shape_S2.png", "S3": "images/voi-531/shape_S3.png", "S4": "images/voi-531/shape_S4.png"}}, "__sample_id__": "voi-531"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [4, 3], [5, 2]]}, {"polygon": [[5, 0], [5, 1], [4, 0]]}, {"polygon": [[4, 1], [6, 1], [6, 3], [4, 3]]}], "meta": {"seed": 4702011, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.209877, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.111111, "difficultyScore": 0.457284, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 533, "strictValidation": true}, "imageAssets": {"target": "../images/voi-532/target.png", "shapes": {"S1": "../images/voi-532/shape_S1.png", "S2": "../images/voi-532/shape_S2.png", "S3": "../images/voi-532/shape_S3.png", "S4": "../images/voi-532/shape_S4.png"}}, "ID": "voi-532", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V1", "grid": [5, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [4, 0]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V1 [5,3]\nS2 270 V3 [4,0]\nS4 0 V4 [4,3]", "solutionText": "S1 180 V1 [5,3]\nS2 270 V3 [4,0]\nS4 0 V4 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-532\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-532/target.png", "shapes": {"S1": "images/voi-532/shape_S1.png", "S2": "images/voi-532/shape_S2.png", "S3": "images/voi-532/shape_S3.png", "S4": "images/voi-532/shape_S4.png"}}, "__sample_id__": "voi-532"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[1, 3], [1, 1], [2, 1], [2, 3]]}, {"polygon": [[2, 3], [2, 5], [0, 5], [0, 3]]}, {"polygon": [[2, 4], [2, 5], [1, 4]]}], "meta": {"seed": 4702012, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 534, "strictValidation": true}, "imageAssets": {"target": "../images/voi-533/target.png", "shapes": {"S1": "../images/voi-533/shape_S1.png", "S2": "../images/voi-533/shape_S2.png", "S3": "../images/voi-533/shape_S3.png", "S4": "../images/voi-533/shape_S4.png"}}, "ID": "voi-533", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V4", "grid": [2, 3]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [2, 5]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [2, 4]}]}, "legacy_answer": "S2 90 V4 [2,3]\nS3 270 V2 [2,5]\nS4 270 V1 [2,4]", "solutionText": "S2 90 V4 [2,3]\nS3 270 V2 [2,5]\nS4 270 V1 [2,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-533\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-533/target.png", "shapes": {"S1": "images/voi-533/shape_S1.png", "S2": "images/voi-533/shape_S2.png", "S3": "images/voi-533/shape_S3.png", "S4": "images/voi-533/shape_S4.png"}}, "__sample_id__": "voi-533"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 2], [3, 2], [3, 4], [1, 4]]}, {"polygon": [[1, 0], [3, 0], [3, 2], [1, 2]]}, {"polygon": [[2, 2], [2, 1], [3, 1], [3, 2]]}], "meta": {"seed": 4702013, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 535, "strictValidation": true}, "imageAssets": {"target": "../images/voi-534/target.png", "shapes": {"S1": "../images/voi-534/shape_S1.png", "S2": "../images/voi-534/shape_S2.png", "S3": "../images/voi-534/shape_S3.png", "S4": "../images/voi-534/shape_S4.png"}}, "ID": "voi-534", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [1, 2]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [3, 2]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [2, 1]}]}, "legacy_answer": "S1 0 V1 [1,2]\nS3 0 V3 [3,2]\nS4 90 V2 [2,1]", "solutionText": "S1 0 V1 [1,2]\nS3 0 V3 [3,2]\nS4 90 V2 [2,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-534\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-534/target.png", "shapes": {"S1": "images/voi-534/shape_S1.png", "S2": "images/voi-534/shape_S2.png", "S3": "images/voi-534/shape_S3.png", "S4": "images/voi-534/shape_S4.png"}}, "__sample_id__": "voi-534"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[2, 4], [2, 2], [4, 2], [4, 4]]}, {"polygon": [[2, 1], [2, 3], [0, 3], [0, 1]]}, {"polygon": [[0, 2], [0, 1], [1, 1], [1, 2]]}], "meta": {"seed": 4702014, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 536, "strictValidation": true}, "imageAssets": {"target": "../images/voi-535/target.png", "shapes": {"S1": "../images/voi-535/shape_S1.png", "S2": "../images/voi-535/shape_S2.png", "S3": "../images/voi-535/shape_S3.png", "S4": "../images/voi-535/shape_S4.png"}}, "ID": "voi-535", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [2, 4]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [2, 3]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [0, 1]}]}, "legacy_answer": "S2 90 V1 [2,4]\nS3 270 V2 [2,3]\nS4 90 V2 [0,1]", "solutionText": "S2 90 V1 [2,4]\nS3 270 V2 [2,3]\nS4 90 V2 [0,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-535\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-535/target.png", "shapes": {"S1": "images/voi-535/shape_S1.png", "S2": "images/voi-535/shape_S2.png", "S3": "images/voi-535/shape_S3.png", "S4": "images/voi-535/shape_S4.png"}}, "__sample_id__": "voi-535"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[4, 2], [4, 4], [3, 4], [3, 2]]}, {"polygon": [[0, 3], [2, 3], [2, 4], [0, 4]]}, {"polygon": [[2, 2], [4, 2], [2, 4]]}], "meta": {"seed": 4702015, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.381191, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 537, "strictValidation": true}, "imageAssets": {"target": "../images/voi-536/target.png", "shapes": {"S1": "../images/voi-536/shape_S1.png", "S2": "../images/voi-536/shape_S2.png", "S3": "../images/voi-536/shape_S3.png", "S4": "../images/voi-536/shape_S4.png"}}, "ID": "voi-536", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [4, 4]}, {"shape": "S2", "angle": 0, "vertex": "V4", "grid": [0, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [2, 2]}]}, "legacy_answer": "S1 270 V2 [4,4]\nS2 0 V4 [0,4]\nS4 0 V1 [2,2]", "solutionText": "S1 270 V2 [4,4]\nS2 0 V4 [0,4]\nS4 0 V1 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-536\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-536/target.png", "shapes": {"S1": "images/voi-536/shape_S1.png", "S2": "images/voi-536/shape_S2.png", "S3": "images/voi-536/shape_S3.png", "S4": "images/voi-536/shape_S4.png"}}, "__sample_id__": "voi-536"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 4], [3, 2], [5, 2], [5, 4]]}, {"polygon": [[5, 6], [3, 6], [3, 4], [5, 4]]}, {"polygon": [[4, 3], [3, 3], [3, 2], [4, 2]]}], "meta": {"seed": 4702016, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 538, "strictValidation": true}, "imageAssets": {"target": "../images/voi-537/target.png", "shapes": {"S1": "../images/voi-537/shape_S1.png", "S2": "../images/voi-537/shape_S2.png", "S3": "../images/voi-537/shape_S3.png", "S4": "../images/voi-537/shape_S4.png"}}, "ID": "voi-537", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [3, 6]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 3]}]}, "legacy_answer": "S1 90 V2 [3,2]\nS3 180 V2 [3,6]\nS4 180 V1 [4,3]", "solutionText": "S1 90 V2 [3,2]\nS3 180 V2 [3,6]\nS4 180 V1 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-537\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-537/target.png", "shapes": {"S1": "images/voi-537/shape_S1.png", "S2": "images/voi-537/shape_S2.png", "S3": "images/voi-537/shape_S3.png", "S4": "images/voi-537/shape_S4.png"}}, "__sample_id__": "voi-537"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[0, 2], [0, 0], [1, 0], [1, 2]]}, {"polygon": [[3, 2], [1, 2], [1, 0], [3, 0]]}, {"polygon": [[0, 0], [1, 0], [0, 1]]}], "meta": {"seed": 4702017, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.162679, "contourComplexity": 36, "connectedComponents": 1, "fillRatio": 0.15191, "difficultyScore": 0.405463, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 539, "strictValidation": true}, "imageAssets": {"target": "../images/voi-538/target.png", "shapes": {"S1": "../images/voi-538/shape_S1.png", "S2": "../images/voi-538/shape_S2.png", "S3": "../images/voi-538/shape_S3.png", "S4": "../images/voi-538/shape_S4.png"}}, "ID": "voi-538", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [0, 2]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [3, 0]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [0, 1]}]}, "legacy_answer": "S1 90 V1 [0,2]\nS2 180 V4 [3,0]\nS4 0 V3 [0,1]", "solutionText": "S1 90 V1 [0,2]\nS2 180 V4 [3,0]\nS4 0 V3 [0,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-538\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-538/target.png", "shapes": {"S1": "images/voi-538/shape_S1.png", "S2": "images/voi-538/shape_S2.png", "S3": "images/voi-538/shape_S3.png", "S4": "images/voi-538/shape_S4.png"}}, "__sample_id__": "voi-538"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 5], [3, 5], [5, 3]]}, {"polygon": [[3, 4], [3, 6], [1, 4]]}, {"polygon": [[5, 6], [3, 6], [5, 4]]}], "meta": {"seed": 4702018, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.171717, "contourComplexity": 197, "connectedComponents": 1, "fillRatio": 0.142361, "difficultyScore": 0.388409, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 540, "strictValidation": true}, "imageAssets": {"target": "../images/voi-539/target.png", "shapes": {"S1": "../images/voi-539/shape_S1.png", "S2": "../images/voi-539/shape_S2.png", "S3": "../images/voi-539/shape_S3.png", "S4": "../images/voi-539/shape_S4.png"}}, "ID": "voi-539", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [5, 3]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [3, 6]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [3, 6]}]}, "legacy_answer": "S1 180 V3 [5,3]\nS2 270 V2 [3,6]\nS4 180 V2 [3,6]", "solutionText": "S1 180 V3 [5,3]\nS2 270 V2 [3,6]\nS4 180 V2 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-539\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-539/target.png", "shapes": {"S1": "images/voi-539/shape_S1.png", "S2": "images/voi-539/shape_S2.png", "S3": "images/voi-539/shape_S3.png", "S4": "images/voi-539/shape_S4.png"}}, "__sample_id__": "voi-539"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[0, 1], [2, 1], [0, 3]]}, {"polygon": [[3, 4], [3, 2], [4, 2], [4, 4]]}, {"polygon": [[3, 3], [1, 3], [1, 1], [3, 1]]}], "meta": {"seed": 4702019, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.443979, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 541, "strictValidation": true}, "imageAssets": {"target": "../images/voi-540/target.png", "shapes": {"S1": "../images/voi-540/shape_S1.png", "S2": "../images/voi-540/shape_S2.png", "S3": "../images/voi-540/shape_S3.png", "S4": "../images/voi-540/shape_S4.png"}}, "ID": "voi-540", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [2, 1]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [4, 2]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [3, 1]}]}, "legacy_answer": "S1 0 V2 [2,1]\nS3 90 V3 [4,2]\nS4 180 V4 [3,1]", "solutionText": "S1 0 V2 [2,1]\nS3 90 V3 [4,2]\nS4 180 V4 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-540\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-540/target.png", "shapes": {"S1": "images/voi-540/shape_S1.png", "S2": "images/voi-540/shape_S2.png", "S3": "images/voi-540/shape_S3.png", "S4": "images/voi-540/shape_S4.png"}}, "__sample_id__": "voi-540"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [1, 2], [3, 0]]}, {"polygon": [[1, 0], [1, 2], [0, 2], [0, 0]]}, {"polygon": [[1, 1], [1, 0], [3, 0], [3, 1]]}], "meta": {"seed": 4702020, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.175258, "contourComplexity": 69, "connectedComponents": 1, "fillRatio": 0.138889, "difficultyScore": 0.381191, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 542, "strictValidation": true}, "imageAssets": {"target": "../images/voi-541/target.png", "shapes": {"S1": "../images/voi-541/shape_S1.png", "S2": "../images/voi-541/shape_S2.png", "S3": "../images/voi-541/shape_S3.png", "S4": "../images/voi-541/shape_S4.png"}}, "ID": "voi-541", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V3", "grid": [3, 0]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 2]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [3, 0]}]}, "legacy_answer": "S1 180 V3 [3,0]\nS2 270 V3 [0,2]\nS4 90 V3 [3,0]", "solutionText": "S1 180 V3 [3,0]\nS2 270 V3 [0,2]\nS4 90 V3 [3,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-541\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-541/target.png", "shapes": {"S1": "images/voi-541/shape_S1.png", "S2": "images/voi-541/shape_S2.png", "S3": "images/voi-541/shape_S3.png", "S4": "images/voi-541/shape_S4.png"}}, "__sample_id__": "voi-541"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[3, 3], [3, 5], [1, 3]]}, {"polygon": [[3, 3], [5, 3], [5, 5], [3, 5]]}, {"polygon": [[2, 3], [2, 4], [1, 3]]}], "meta": {"seed": 4702021, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.161137, "contourComplexity": 34, "connectedComponents": 1, "fillRatio": 0.153646, "difficultyScore": 0.408159, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 543, "strictValidation": true}, "imageAssets": {"target": "../images/voi-542/target.png", "shapes": {"S1": "../images/voi-542/shape_S1.png", "S2": "../images/voi-542/shape_S2.png", "S3": "../images/voi-542/shape_S3.png", "S4": "../images/voi-542/shape_S4.png"}}, "ID": "voi-542", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V3", "grid": [1, 3]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [5, 3]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [1, 3]}]}, "legacy_answer": "S1 270 V3 [1,3]\nS2 0 V2 [5,3]\nS4 270 V3 [1,3]", "solutionText": "S1 270 V3 [1,3]\nS2 0 V2 [5,3]\nS4 270 V3 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-542\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-542/target.png", "shapes": {"S1": "images/voi-542/shape_S1.png", "S2": "images/voi-542/shape_S2.png", "S3": "images/voi-542/shape_S3.png", "S4": "images/voi-542/shape_S4.png"}}, "__sample_id__": "voi-542"} {"gridSize": 6, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 1], [3, 1], [3, 2], [2, 2]]}, {"polygon": [[2, 3], [0, 3], [0, 1], [2, 1]]}, {"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}], "meta": {"seed": 4702022, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "low", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.194444, "difficultyScore": 0.34, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 544, "strictValidation": true}, "imageAssets": {"target": "../images/voi-543/target.png", "shapes": {"S1": "../images/voi-543/shape_S1.png", "S2": "../images/voi-543/shape_S2.png", "S3": "../images/voi-543/shape_S3.png", "S4": "../images/voi-543/shape_S4.png"}}, "ID": "voi-543", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [0, 3]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [1, 2]}]}, "legacy_answer": "S1 0 V3 [3,2]\nS3 180 V2 [0,3]\nS4 90 V2 [1,2]", "solutionText": "S1 0 V3 [3,2]\nS3 180 V2 [0,3]\nS4 90 V2 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-543\n- grid_size: 6x6\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-543/target.png", "shapes": {"S1": "images/voi-543/shape_S1.png", "S2": "images/voi-543/shape_S2.png", "S3": "images/voi-543/shape_S3.png", "S4": "images/voi-543/shape_S4.png"}}, "__sample_id__": "voi-543"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 5], [6, 3], [8, 3], [8, 5]]}, {"polygon": [[5, 2], [4, 2], [4, 1], [5, 1]]}, {"polygon": [[7, 1], [7, 3], [6, 3], [6, 2], [4, 2], [4, 1]]}], "meta": {"seed": 4703001, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 545, "strictValidation": true}, "imageAssets": {"target": "../images/voi-544/target.png", "shapes": {"S1": "../images/voi-544/shape_S1.png", "S2": "../images/voi-544/shape_S2.png", "S3": "../images/voi-544/shape_S3.png", "S4": "../images/voi-544/shape_S4.png"}}, "ID": "voi-544", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [6, 3]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [4, 2]}, {"shape": "S4", "angle": 270, "vertex": "V4", "grid": [6, 2]}]}, "legacy_answer": "S1 90 V2 [6,3]\nS2 180 V2 [4,2]\nS4 270 V4 [6,2]", "solutionText": "S1 90 V2 [6,3]\nS2 180 V2 [4,2]\nS4 270 V4 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-544\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-544/target.png", "shapes": {"S1": "images/voi-544/shape_S1.png", "S2": "images/voi-544/shape_S2.png", "S3": "images/voi-544/shape_S3.png", "S4": "images/voi-544/shape_S4.png"}}, "__sample_id__": "voi-544"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[8, 3], [8, 5], [7, 5], [7, 4], [5, 4], [5, 3]]}, {"polygon": [[4, 5], [4, 3], [6, 3], [6, 5]]}, {"polygon": [[7, 5], [6, 5], [6, 4], [7, 4]]}], "meta": {"seed": 4703002, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 546, "strictValidation": true}, "imageAssets": {"target": "../images/voi-545/target.png", "shapes": {"S1": "../images/voi-545/shape_S1.png", "S2": "../images/voi-545/shape_S2.png", "S3": "../images/voi-545/shape_S3.png", "S4": "../images/voi-545/shape_S4.png"}}, "ID": "voi-545", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V6", "grid": [5, 3]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [4, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [6, 5]}]}, "legacy_answer": "S1 270 V6 [5,3]\nS3 90 V2 [4,3]\nS4 180 V2 [6,5]", "solutionText": "S1 270 V6 [5,3]\nS3 90 V2 [4,3]\nS4 180 V2 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-545\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-545/target.png", "shapes": {"S1": "images/voi-545/shape_S1.png", "S2": "images/voi-545/shape_S2.png", "S3": "images/voi-545/shape_S3.png", "S4": "images/voi-545/shape_S4.png"}}, "__sample_id__": "voi-545"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 6], [5, 7], [4, 7], [4, 6]]}, {"polygon": [[4, 3], [4, 6], [3, 6], [3, 3]]}, {"polygon": [[6, 8], [3, 8], [3, 6], [6, 6]]}], "meta": {"seed": 4703003, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 547, "strictValidation": true}, "imageAssets": {"target": "../images/voi-546/target.png", "shapes": {"S1": "../images/voi-546/shape_S1.png", "S2": "../images/voi-546/shape_S2.png", "S3": "../images/voi-546/shape_S3.png", "S4": "../images/voi-546/shape_S4.png"}}, "ID": "voi-546", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 7]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [4, 3]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [6, 8]}]}, "legacy_answer": "S2 270 V2 [5,7]\nS3 270 V1 [4,3]\nS4 180 V1 [6,8]", "solutionText": "S2 270 V2 [5,7]\nS3 270 V1 [4,3]\nS4 180 V1 [6,8]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-546\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-546/target.png", "shapes": {"S1": "images/voi-546/shape_S1.png", "S2": "images/voi-546/shape_S2.png", "S3": "images/voi-546/shape_S3.png", "S4": "images/voi-546/shape_S4.png"}}, "__sample_id__": "voi-546"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[1, 7], [1, 4], [2, 4], [2, 7]]}, {"polygon": [[4, 6], [2, 6], [2, 5], [3, 5], [3, 3], [4, 3]]}, {"polygon": [[0, 4], [2, 4], [2, 5], [1, 5], [1, 7], [0, 7]]}], "meta": {"seed": 4703004, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 548, "strictValidation": true}, "imageAssets": {"target": "../images/voi-547/target.png", "shapes": {"S1": "../images/voi-547/shape_S1.png", "S2": "../images/voi-547/shape_S2.png", "S3": "../images/voi-547/shape_S3.png", "S4": "../images/voi-547/shape_S4.png"}}, "ID": "voi-547", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [2, 7]}, {"shape": "S2", "angle": 180, "vertex": "V5", "grid": [3, 3]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [1, 5]}]}, "legacy_answer": "S1 90 V4 [2,7]\nS2 180 V5 [3,3]\nS4 0 V4 [1,5]", "solutionText": "S1 90 V4 [2,7]\nS2 180 V5 [3,3]\nS4 0 V4 [1,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-547\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-547/target.png", "shapes": {"S1": "images/voi-547/shape_S1.png", "S2": "images/voi-547/shape_S2.png", "S3": "images/voi-547/shape_S3.png", "S4": "images/voi-547/shape_S4.png"}}, "__sample_id__": "voi-547"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[4, 5], [4, 4], [7, 4], [7, 5]]}, {"polygon": [[5, 4], [5, 1], [7, 1], [7, 4]]}, {"polygon": [[6, 4], [4, 4], [6, 2]]}], "meta": {"seed": 4703005, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.276836, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.557345, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 549, "strictValidation": true}, "imageAssets": {"target": "../images/voi-548/target.png", "shapes": {"S1": "../images/voi-548/shape_S1.png", "S2": "../images/voi-548/shape_S2.png", "S3": "../images/voi-548/shape_S3.png", "S4": "../images/voi-548/shape_S4.png"}}, "ID": "voi-548", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [4, 5]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [7, 4]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [6, 4]}]}, "legacy_answer": "S1 90 V1 [4,5]\nS2 90 V4 [7,4]\nS3 180 V1 [6,4]", "solutionText": "S1 90 V1 [4,5]\nS2 90 V4 [7,4]\nS3 180 V1 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-548\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-548/target.png", "shapes": {"S1": "images/voi-548/shape_S1.png", "S2": "images/voi-548/shape_S2.png", "S3": "images/voi-548/shape_S3.png", "S4": "images/voi-548/shape_S4.png"}}, "__sample_id__": "voi-548"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 5], [3, 5], [3, 3], [6, 3]]}, {"polygon": [[6, 4], [6, 6], [4, 4]]}, {"polygon": [[5, 8], [3, 8], [3, 7], [4, 7], [4, 5], [5, 5]]}], "meta": {"seed": 4703006, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.253886, "contourComplexity": 74, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.434294, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 550, "strictValidation": true}, "imageAssets": {"target": "../images/voi-549/target.png", "shapes": {"S1": "../images/voi-549/shape_S1.png", "S2": "../images/voi-549/shape_S2.png", "S3": "../images/voi-549/shape_S3.png", "S4": "../images/voi-549/shape_S4.png"}}, "ID": "voi-549", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [6, 3]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [6, 6]}, {"shape": "S4", "angle": 180, "vertex": "V6", "grid": [5, 5]}]}, "legacy_answer": "S1 180 V4 [6,3]\nS3 270 V2 [6,6]\nS4 180 V6 [5,5]", "solutionText": "S1 180 V4 [6,3]\nS3 270 V2 [6,6]\nS4 180 V6 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-549\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-549/target.png", "shapes": {"S1": "images/voi-549/shape_S1.png", "S2": "images/voi-549/shape_S2.png", "S3": "images/voi-549/shape_S3.png", "S4": "images/voi-549/shape_S4.png"}}, "__sample_id__": "voi-549"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 3], [3, 3], [3, 2], [5, 2]]}, {"polygon": [[4, 4], [4, 2], [5, 2], [5, 3], [7, 3], [7, 4]]}, {"polygon": [[1, 3], [4, 3], [4, 5], [1, 5]]}], "meta": {"seed": 4703007, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.166667, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.520833, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 551, "strictValidation": true}, "imageAssets": {"target": "../images/voi-550/target.png", "shapes": {"S1": "../images/voi-550/shape_S1.png", "S2": "../images/voi-550/shape_S2.png", "S3": "../images/voi-550/shape_S3.png", "S4": "../images/voi-550/shape_S4.png"}}, "ID": "voi-550", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [5, 2]}, {"shape": "S3", "angle": 90, "vertex": "V6", "grid": [7, 4]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 3]}]}, "legacy_answer": "S1 180 V4 [5,2]\nS3 90 V6 [7,4]\nS4 0 V2 [4,3]", "solutionText": "S1 180 V4 [5,2]\nS3 90 V6 [7,4]\nS4 0 V2 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-550\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-550/target.png", "shapes": {"S1": "images/voi-550/shape_S1.png", "S2": "images/voi-550/shape_S2.png", "S3": "images/voi-550/shape_S3.png", "S4": "images/voi-550/shape_S4.png"}}, "__sample_id__": "voi-550"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[2, 4], [5, 4], [4, 5], [2, 5]]}, {"polygon": [[3, 5], [3, 2], [5, 2], [5, 5]]}, {"polygon": [[3, 4], [6, 4], [6, 6], [3, 6]]}], "meta": {"seed": 4703008, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.275269, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.164551, "difficultyScore": 0.471974, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 552, "strictValidation": true}, "imageAssets": {"target": "../images/voi-551/target.png", "shapes": {"S1": "../images/voi-551/shape_S1.png", "S2": "../images/voi-551/shape_S2.png", "S3": "../images/voi-551/shape_S3.png", "S4": "../images/voi-551/shape_S4.png"}}, "ID": "voi-551", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [2, 4]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [3, 2]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S1 0 V1 [2,4]\nS2 90 V2 [3,2]\nS3 0 V2 [6,4]", "solutionText": "S1 0 V1 [2,4]\nS2 90 V2 [3,2]\nS3 0 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-551\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-551/target.png", "shapes": {"S1": "images/voi-551/shape_S1.png", "S2": "images/voi-551/shape_S2.png", "S3": "images/voi-551/shape_S3.png", "S4": "images/voi-551/shape_S4.png"}}, "__sample_id__": "voi-551"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[6, 5], [6, 6], [4, 6], [4, 5]]}, {"polygon": [[4, 6], [2, 6], [2, 4], [4, 4]]}, {"polygon": [[3, 5], [3, 4], [6, 4], [6, 5]]}], "meta": {"seed": 4703009, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 553, "strictValidation": true}, "imageAssets": {"target": "../images/voi-552/target.png", "shapes": {"S1": "../images/voi-552/shape_S1.png", "S2": "../images/voi-552/shape_S2.png", "S3": "../images/voi-552/shape_S3.png", "S4": "../images/voi-552/shape_S4.png"}}, "ID": "voi-552", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V2", "grid": [6, 6]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [4, 4]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [6, 4]}]}, "legacy_answer": "S2 270 V2 [6,6]\nS3 180 V4 [4,4]\nS4 90 V3 [6,4]", "solutionText": "S2 270 V2 [6,6]\nS3 180 V4 [4,4]\nS4 90 V3 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-552\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-552/target.png", "shapes": {"S1": "images/voi-552/shape_S1.png", "S2": "images/voi-552/shape_S2.png", "S3": "images/voi-552/shape_S3.png", "S4": "images/voi-552/shape_S4.png"}}, "__sample_id__": "voi-552"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[7, 6], [5, 6], [5, 5], [6, 5], [6, 3], [7, 3]]}, {"polygon": [[6, 8], [6, 6], [7, 6], [7, 8]]}, {"polygon": [[4, 6], [4, 4], [6, 4], [6, 6]]}], "meta": {"seed": 4703010, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 554, "strictValidation": true}, "imageAssets": {"target": "../images/voi-553/target.png", "shapes": {"S1": "../images/voi-553/shape_S1.png", "S2": "../images/voi-553/shape_S2.png", "S3": "../images/voi-553/shape_S3.png", "S4": "../images/voi-553/shape_S4.png"}}, "ID": "voi-553", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V4", "grid": [6, 5]}, {"shape": "S2", "angle": 90, "vertex": "V2", "grid": [6, 6]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [4, 6]}]}, "legacy_answer": "S1 180 V4 [6,5]\nS2 90 V2 [6,6]\nS4 90 V1 [4,6]", "solutionText": "S1 180 V4 [6,5]\nS2 90 V2 [6,6]\nS4 90 V1 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-553\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-553/target.png", "shapes": {"S1": "images/voi-553/shape_S1.png", "S2": "images/voi-553/shape_S2.png", "S3": "images/voi-553/shape_S3.png", "S4": "images/voi-553/shape_S4.png"}}, "__sample_id__": "voi-553"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[3, 2], [6, 2], [5, 3], [3, 3]]}, {"polygon": [[8, 2], [8, 4], [6, 4], [6, 2]]}, {"polygon": [[5, 3], [7, 3], [5, 5]]}], "meta": {"seed": 4703011, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.123636, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.770103, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 555, "strictValidation": true}, "imageAssets": {"target": "../images/voi-554/target.png", "shapes": {"S1": "../images/voi-554/shape_S1.png", "S2": "../images/voi-554/shape_S2.png", "S3": "../images/voi-554/shape_S3.png", "S4": "../images/voi-554/shape_S4.png"}}, "ID": "voi-554", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 3]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [6, 4]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [5, 3]}]}, "legacy_answer": "S1 0 V3 [5,3]\nS2 270 V3 [6,4]\nS4 0 V1 [5,3]", "solutionText": "S1 0 V3 [5,3]\nS2 270 V3 [6,4]\nS4 0 V1 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-554\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-554/target.png", "shapes": {"S1": "images/voi-554/shape_S1.png", "S2": "images/voi-554/shape_S2.png", "S3": "images/voi-554/shape_S3.png", "S4": "images/voi-554/shape_S4.png"}}, "__sample_id__": "voi-554"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[3, 2], [3, 4], [2, 4], [2, 3], [0, 3], [0, 2]]}, {"polygon": [[3, 2], [6, 2], [6, 4], [3, 4]]}, {"polygon": [[7, 2], [7, 4], [6, 4], [6, 3], [4, 3], [4, 2]]}], "meta": {"seed": 4703012, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 556, "strictValidation": true}, "imageAssets": {"target": "../images/voi-555/target.png", "shapes": {"S1": "../images/voi-555/shape_S1.png", "S2": "../images/voi-555/shape_S2.png", "S3": "../images/voi-555/shape_S3.png", "S4": "../images/voi-555/shape_S4.png"}}, "ID": "voi-555", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V6", "grid": [0, 2]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [6, 4]}, {"shape": "S4", "angle": 270, "vertex": "V6", "grid": [4, 2]}]}, "legacy_answer": "S1 270 V6 [0,2]\nS3 0 V3 [6,4]\nS4 270 V6 [4,2]", "solutionText": "S1 270 V6 [0,2]\nS3 0 V3 [6,4]\nS4 270 V6 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-555\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-555/target.png", "shapes": {"S1": "images/voi-555/shape_S1.png", "S2": "images/voi-555/shape_S2.png", "S3": "images/voi-555/shape_S3.png", "S4": "images/voi-555/shape_S4.png"}}, "__sample_id__": "voi-555"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [4, 5], [4, 7], [2, 7]]}, {"polygon": [[4, 3], [4, 6], [3, 6], [3, 3]]}, {"polygon": [[3, 5], [0, 5], [0, 4], [3, 4]]}], "meta": {"seed": 4703013, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 557, "strictValidation": true}, "imageAssets": {"target": "../images/voi-556/target.png", "shapes": {"S1": "../images/voi-556/shape_S1.png", "S2": "../images/voi-556/shape_S2.png", "S3": "../images/voi-556/shape_S3.png", "S4": "../images/voi-556/shape_S4.png"}}, "ID": "voi-556", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [4, 7]}, {"shape": "S2", "angle": 270, "vertex": "V4", "grid": [3, 3]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [0, 5]}]}, "legacy_answer": "S1 0 V3 [4,7]\nS2 270 V4 [3,3]\nS3 180 V2 [0,5]", "solutionText": "S1 0 V3 [4,7]\nS2 270 V4 [3,3]\nS3 180 V2 [0,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-556\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-556/target.png", "shapes": {"S1": "images/voi-556/shape_S1.png", "S2": "images/voi-556/shape_S2.png", "S3": "images/voi-556/shape_S3.png", "S4": "images/voi-556/shape_S4.png"}}, "__sample_id__": "voi-556"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 2], [5, 2], [4, 3]]}, {"polygon": [[3, 2], [5, 2], [5, 3], [4, 3], [4, 5], [3, 5]]}, {"polygon": [[6, 4], [4, 4], [4, 2], [6, 2]]}], "meta": {"seed": 4703014, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.433627, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 558, "strictValidation": true}, "imageAssets": {"target": "../images/voi-557/target.png", "shapes": {"S1": "../images/voi-557/shape_S1.png", "S2": "../images/voi-557/shape_S2.png", "S3": "../images/voi-557/shape_S3.png", "S4": "../images/voi-557/shape_S4.png"}}, "ID": "voi-557", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [5, 2]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [3, 2]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [4, 2]}]}, "legacy_answer": "S1 0 V2 [5,2]\nS3 0 V1 [3,2]\nS4 180 V3 [4,2]", "solutionText": "S1 0 V2 [5,2]\nS3 0 V1 [3,2]\nS4 180 V3 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-557\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-557/target.png", "shapes": {"S1": "images/voi-557/shape_S1.png", "S2": "images/voi-557/shape_S2.png", "S3": "images/voi-557/shape_S3.png", "S4": "images/voi-557/shape_S4.png"}}, "__sample_id__": "voi-557"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[5, 0], [5, 2], [4, 2], [4, 1], [2, 1], [2, 0]]}, {"polygon": [[5, 2], [5, 4], [3, 2]]}, {"polygon": [[2, 1], [4, 1], [4, 3], [2, 3]]}], "meta": {"seed": 4703015, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 68, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.79639, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 559, "strictValidation": true}, "imageAssets": {"target": "../images/voi-558/target.png", "shapes": {"S1": "../images/voi-558/shape_S1.png", "S2": "../images/voi-558/shape_S2.png", "S3": "../images/voi-558/shape_S3.png", "S4": "../images/voi-558/shape_S4.png"}}, "ID": "voi-558", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [4, 1]}, {"shape": "S2", "angle": 270, "vertex": "V2", "grid": [5, 4]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S1 270 V4 [4,1]\nS2 270 V2 [5,4]\nS4 0 V3 [4,3]", "solutionText": "S1 270 V4 [4,1]\nS2 270 V2 [5,4]\nS4 0 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-558\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-558/target.png", "shapes": {"S1": "images/voi-558/shape_S1.png", "S2": "images/voi-558/shape_S2.png", "S3": "images/voi-558/shape_S3.png", "S4": "images/voi-558/shape_S4.png"}}, "__sample_id__": "voi-558"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[3, 7], [3, 5], [5, 5], [5, 7]]}, {"polygon": [[2, 7], [2, 5], [4, 7]]}, {"polygon": [[2, 5], [2, 7], [1, 7], [1, 5]]}], "meta": {"seed": 4703016, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.131783, "contourComplexity": 70, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.754118, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 560, "strictValidation": true}, "imageAssets": {"target": "../images/voi-559/target.png", "shapes": {"S1": "../images/voi-559/shape_S1.png", "S2": "../images/voi-559/shape_S2.png", "S3": "../images/voi-559/shape_S3.png", "S4": "../images/voi-559/shape_S4.png"}}, "ID": "voi-559", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [5, 7]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [4, 7]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [2, 5]}]}, "legacy_answer": "S1 90 V4 [5,7]\nS2 90 V3 [4,7]\nS3 270 V1 [2,5]", "solutionText": "S1 90 V4 [5,7]\nS2 90 V3 [4,7]\nS3 270 V1 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-559\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-559/target.png", "shapes": {"S1": "images/voi-559/shape_S1.png", "S2": "images/voi-559/shape_S2.png", "S3": "images/voi-559/shape_S3.png", "S4": "images/voi-559/shape_S4.png"}}, "__sample_id__": "voi-559"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[5, 4], [5, 6], [3, 6], [3, 4]]}, {"polygon": [[3, 5], [3, 7], [1, 7], [1, 5]]}, {"polygon": [[4, 4], [4, 5], [1, 5], [1, 4]]}], "meta": {"seed": 4703017, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 561, "strictValidation": true}, "imageAssets": {"target": "../images/voi-560/target.png", "shapes": {"S1": "../images/voi-560/shape_S1.png", "S2": "../images/voi-560/shape_S2.png", "S3": "../images/voi-560/shape_S3.png", "S4": "../images/voi-560/shape_S4.png"}}, "ID": "voi-560", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [3, 4]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [1, 5]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 270 V4 [3,4]\nS3 270 V4 [1,5]\nS4 270 V2 [4,5]", "solutionText": "S1 270 V4 [3,4]\nS3 270 V4 [1,5]\nS4 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-560\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-560/target.png", "shapes": {"S1": "images/voi-560/shape_S1.png", "S2": "images/voi-560/shape_S2.png", "S3": "images/voi-560/shape_S3.png", "S4": "images/voi-560/shape_S4.png"}}, "__sample_id__": "voi-560"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[0, 3], [0, 1], [1, 1], [1, 2], [3, 2], [3, 3]]}, {"polygon": [[3, 0], [3, 3], [1, 3], [1, 0]]}, {"polygon": [[3, 3], [3, 1], [4, 1], [4, 2], [6, 2], [6, 3]]}], "meta": {"seed": 4703018, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 562, "strictValidation": true}, "imageAssets": {"target": "../images/voi-561/target.png", "shapes": {"S1": "../images/voi-561/shape_S1.png", "S2": "../images/voi-561/shape_S2.png", "S3": "../images/voi-561/shape_S3.png", "S4": "../images/voi-561/shape_S4.png"}}, "ID": "voi-561", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [1, 2]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [1, 3]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [3, 1]}]}, "legacy_answer": "S1 90 V4 [1,2]\nS2 270 V3 [1,3]\nS3 90 V2 [3,1]", "solutionText": "S1 90 V4 [1,2]\nS2 270 V3 [1,3]\nS3 90 V2 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-561\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-561/target.png", "shapes": {"S1": "images/voi-561/shape_S1.png", "S2": "images/voi-561/shape_S2.png", "S3": "images/voi-561/shape_S3.png", "S4": "images/voi-561/shape_S4.png"}}, "__sample_id__": "voi-561"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[4, 3], [4, 0], [5, 0], [5, 3]]}, {"polygon": [[5, 2], [2, 2], [2, 0], [5, 0]]}, {"polygon": [[4, 2], [4, 5], [2, 5], [2, 2]]}], "meta": {"seed": 4703019, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.266667, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.422917, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 563, "strictValidation": true}, "imageAssets": {"target": "../images/voi-562/target.png", "shapes": {"S1": "../images/voi-562/shape_S1.png", "S2": "../images/voi-562/shape_S2.png", "S3": "../images/voi-562/shape_S3.png", "S4": "../images/voi-562/shape_S4.png"}}, "ID": "voi-562", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [5, 3]}, {"shape": "S2", "angle": 180, "vertex": "V4", "grid": [5, 0]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [4, 5]}]}, "legacy_answer": "S1 90 V4 [5,3]\nS2 180 V4 [5,0]\nS3 270 V2 [4,5]", "solutionText": "S1 90 V4 [5,3]\nS2 180 V4 [5,0]\nS3 270 V2 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-562\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-562/target.png", "shapes": {"S1": "images/voi-562/shape_S1.png", "S2": "images/voi-562/shape_S2.png", "S3": "images/voi-562/shape_S3.png", "S4": "images/voi-562/shape_S4.png"}}, "__sample_id__": "voi-562"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 8], [3, 7], [4, 7], [4, 8]]}, {"polygon": [[5, 7], [5, 4], [7, 4], [7, 7]]}, {"polygon": [[6, 7], [6, 8], [3, 8], [3, 7]]}], "meta": {"seed": 4703020, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 564, "strictValidation": true}, "imageAssets": {"target": "../images/voi-563/target.png", "shapes": {"S1": "../images/voi-563/shape_S1.png", "S2": "../images/voi-563/shape_S2.png", "S3": "../images/voi-563/shape_S3.png", "S4": "../images/voi-563/shape_S4.png"}}, "ID": "voi-563", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V3", "grid": [4, 7]}, {"shape": "S2", "angle": 90, "vertex": "V3", "grid": [7, 4]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [3, 7]}]}, "legacy_answer": "S1 90 V3 [4,7]\nS2 90 V3 [7,4]\nS3 270 V4 [3,7]", "solutionText": "S1 90 V3 [4,7]\nS2 90 V3 [7,4]\nS3 270 V4 [3,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-563\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-563/target.png", "shapes": {"S1": "images/voi-563/shape_S1.png", "S2": "images/voi-563/shape_S2.png", "S3": "images/voi-563/shape_S3.png", "S4": "images/voi-563/shape_S4.png"}}, "__sample_id__": "voi-563"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[3, 5], [3, 7], [1, 7], [1, 5]]}, {"polygon": [[4, 4], [4, 5], [1, 5], [1, 4]]}, {"polygon": [[2, 5], [5, 5], [4, 6], [2, 6]]}], "meta": {"seed": 4703021, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.425304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 565, "strictValidation": true}, "imageAssets": {"target": "../images/voi-564/target.png", "shapes": {"S1": "../images/voi-564/shape_S1.png", "S2": "../images/voi-564/shape_S2.png", "S3": "../images/voi-564/shape_S3.png", "S4": "../images/voi-564/shape_S4.png"}}, "ID": "voi-564", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V4", "grid": [1, 5]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 5]}, {"shape": "S4", "angle": 0, "vertex": "V1", "grid": [2, 5]}]}, "legacy_answer": "S2 270 V4 [1,5]\nS3 270 V3 [1,5]\nS4 0 V1 [2,5]", "solutionText": "S2 270 V4 [1,5]\nS3 270 V3 [1,5]\nS4 0 V1 [2,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-564\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-564/target.png", "shapes": {"S1": "images/voi-564/shape_S1.png", "S2": "images/voi-564/shape_S2.png", "S3": "images/voi-564/shape_S3.png", "S4": "images/voi-564/shape_S4.png"}}, "__sample_id__": "voi-564"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 5], [2, 5], [3, 4]]}, {"polygon": [[2, 5], [4, 5], [2, 7]]}, {"polygon": [[3, 4], [6, 4], [6, 6], [3, 6]]}], "meta": {"seed": 4703022, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.123636, "contourComplexity": 98, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.770103, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 566, "strictValidation": true}, "imageAssets": {"target": "../images/voi-565/target.png", "shapes": {"S1": "../images/voi-565/shape_S1.png", "S2": "../images/voi-565/shape_S2.png", "S3": "../images/voi-565/shape_S3.png", "S4": "../images/voi-565/shape_S4.png"}}, "ID": "voi-565", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [3, 5]}, {"shape": "S3", "angle": 0, "vertex": "V2", "grid": [4, 5]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [6, 4]}]}, "legacy_answer": "S2 180 V1 [3,5]\nS3 0 V2 [4,5]\nS4 0 V2 [6,4]", "solutionText": "S2 180 V1 [3,5]\nS3 0 V2 [4,5]\nS4 0 V2 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-565\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-565/target.png", "shapes": {"S1": "images/voi-565/shape_S1.png", "S2": "images/voi-565/shape_S2.png", "S3": "images/voi-565/shape_S3.png", "S4": "images/voi-565/shape_S4.png"}}, "__sample_id__": "voi-565"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[6, 3], [6, 5], [4, 3]]}, {"polygon": [[5, 5], [6, 5], [6, 8], [5, 8]]}, {"polygon": [[4, 2], [6, 2], [6, 3], [5, 3], [5, 5], [4, 5]]}], "meta": {"seed": 4703023, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.117241, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.781034, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 567, "strictValidation": true}, "imageAssets": {"target": "../images/voi-566/target.png", "shapes": {"S1": "../images/voi-566/shape_S1.png", "S2": "../images/voi-566/shape_S2.png", "S3": "../images/voi-566/shape_S3.png", "S4": "../images/voi-566/shape_S4.png"}}, "ID": "voi-566", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V2", "grid": [6, 5]}, {"shape": "S2", "angle": 0, "vertex": "V2", "grid": [6, 5]}, {"shape": "S4", "angle": 0, "vertex": "V4", "grid": [5, 3]}]}, "legacy_answer": "S1 270 V2 [6,5]\nS2 0 V2 [6,5]\nS4 0 V4 [5,3]", "solutionText": "S1 270 V2 [6,5]\nS2 0 V2 [6,5]\nS4 0 V4 [5,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-566\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-566/target.png", "shapes": {"S1": "images/voi-566/shape_S1.png", "S2": "images/voi-566/shape_S2.png", "S3": "images/voi-566/shape_S3.png", "S4": "images/voi-566/shape_S4.png"}}, "__sample_id__": "voi-566"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 4], [4, 4], [4, 7], [3, 7]]}, {"polygon": [[5, 7], [4, 7], [4, 5], [5, 5]]}, {"polygon": [[6, 5], [3, 5], [3, 3], [6, 3]]}], "meta": {"seed": 4703024, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 568, "strictValidation": true}, "imageAssets": {"target": "../images/voi-567/target.png", "shapes": {"S1": "../images/voi-567/shape_S1.png", "S2": "../images/voi-567/shape_S2.png", "S3": "../images/voi-567/shape_S3.png", "S4": "../images/voi-567/shape_S4.png"}}, "ID": "voi-567", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V1", "grid": [3, 4]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 7]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [3, 5]}]}, "legacy_answer": "S1 0 V1 [3,4]\nS3 180 V2 [4,7]\nS4 180 V2 [3,5]", "solutionText": "S1 0 V1 [3,4]\nS3 180 V2 [4,7]\nS4 180 V2 [3,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-567\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-567/target.png", "shapes": {"S1": "images/voi-567/shape_S1.png", "S2": "images/voi-567/shape_S2.png", "S3": "images/voi-567/shape_S3.png", "S4": "images/voi-567/shape_S4.png"}}, "__sample_id__": "voi-567"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[5, 0], [5, 3], [3, 3], [3, 0]]}, {"polygon": [[5, 3], [8, 3], [8, 5], [5, 5]]}, {"polygon": [[6, 3], [4, 3], [4, 2], [5, 2], [5, 0], [6, 0]]}], "meta": {"seed": 4703025, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.125, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.21875, "difficultyScore": 0.5625, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 569, "strictValidation": true}, "imageAssets": {"target": "../images/voi-568/target.png", "shapes": {"S1": "../images/voi-568/shape_S1.png", "S2": "../images/voi-568/shape_S2.png", "S3": "../images/voi-568/shape_S3.png", "S4": "../images/voi-568/shape_S4.png"}}, "ID": "voi-568", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [3, 0]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [5, 3]}, {"shape": "S4", "angle": 180, "vertex": "V5", "grid": [5, 0]}]}, "legacy_answer": "S1 270 V4 [3,0]\nS3 0 V1 [5,3]\nS4 180 V5 [5,0]", "solutionText": "S1 270 V4 [3,0]\nS3 0 V1 [5,3]\nS4 180 V5 [5,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-568\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-568/target.png", "shapes": {"S1": "images/voi-568/shape_S1.png", "S2": "images/voi-568/shape_S2.png", "S3": "images/voi-568/shape_S3.png", "S4": "images/voi-568/shape_S4.png"}}, "__sample_id__": "voi-568"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 4], [2, 4], [2, 6], [1, 6]]}, {"polygon": [[0, 4], [2, 4], [2, 5], [1, 5], [1, 7], [0, 7]]}, {"polygon": [[1, 1], [1, 4], [0, 4], [0, 1]]}], "meta": {"seed": 4703026, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 570, "strictValidation": true}, "imageAssets": {"target": "../images/voi-569/target.png", "shapes": {"S1": "../images/voi-569/shape_S1.png", "S2": "../images/voi-569/shape_S2.png", "S3": "../images/voi-569/shape_S3.png", "S4": "../images/voi-569/shape_S4.png"}}, "ID": "voi-569", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [1, 6]}, {"shape": "S2", "angle": 0, "vertex": "V3", "grid": [2, 5]}, {"shape": "S3", "angle": 270, "vertex": "V2", "grid": [1, 4]}]}, "legacy_answer": "S1 0 V4 [1,6]\nS2 0 V3 [2,5]\nS3 270 V2 [1,4]", "solutionText": "S1 0 V4 [1,6]\nS2 0 V3 [2,5]\nS3 270 V2 [1,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-569\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-569/target.png", "shapes": {"S1": "images/voi-569/shape_S1.png", "S2": "images/voi-569/shape_S2.png", "S3": "images/voi-569/shape_S3.png", "S4": "images/voi-569/shape_S4.png"}}, "__sample_id__": "voi-569"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [3, 5], [3, 7], [2, 7]]}, {"polygon": [[1, 4], [1, 1], [3, 1], [3, 4]]}, {"polygon": [[3, 4], [3, 7], [1, 7], [1, 4]]}], "meta": {"seed": 4703027, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 6, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 571, "strictValidation": true}, "imageAssets": {"target": "../images/voi-570/target.png", "shapes": {"S1": "../images/voi-570/shape_S1.png", "S2": "../images/voi-570/shape_S2.png", "S3": "../images/voi-570/shape_S3.png", "S4": "../images/voi-570/shape_S4.png"}}, "ID": "voi-570", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V4", "grid": [2, 7]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [3, 1]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 4]}]}, "legacy_answer": "S2 0 V4 [2,7]\nS3 90 V3 [3,1]\nS4 270 V1 [3,4]", "solutionText": "S2 0 V4 [2,7]\nS3 90 V3 [3,1]\nS4 270 V1 [3,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-570\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-570/target.png", "shapes": {"S1": "images/voi-570/shape_S1.png", "S2": "images/voi-570/shape_S2.png", "S3": "images/voi-570/shape_S3.png", "S4": "images/voi-570/shape_S4.png"}}, "__sample_id__": "voi-570"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 1], [6, 2], [5, 2], [5, 1]]}, {"polygon": [[7, 3], [4, 3], [5, 2], [7, 2]]}, {"polygon": [[5, 0], [5, 3], [3, 3], [3, 0]]}], "meta": {"seed": 4703028, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.111475, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.132324, "difficultyScore": 0.78945, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 572, "strictValidation": true}, "imageAssets": {"target": "../images/voi-571/target.png", "shapes": {"S1": "../images/voi-571/shape_S1.png", "S2": "../images/voi-571/shape_S2.png", "S3": "../images/voi-571/shape_S3.png", "S4": "../images/voi-571/shape_S4.png"}}, "ID": "voi-571", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V4", "grid": [5, 1]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [7, 3]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [5, 0]}]}, "legacy_answer": "S1 270 V4 [5,1]\nS2 180 V1 [7,3]\nS3 270 V1 [5,0]", "solutionText": "S1 270 V4 [5,1]\nS2 180 V1 [7,3]\nS3 270 V1 [5,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-571\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-571/target.png", "shapes": {"S1": "images/voi-571/shape_S1.png", "S2": "images/voi-571/shape_S2.png", "S3": "images/voi-571/shape_S3.png", "S4": "images/voi-571/shape_S4.png"}}, "__sample_id__": "voi-571"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 2], [7, 2], [7, 3], [6, 3]]}, {"polygon": [[5, 4], [2, 4], [2, 2], [5, 2]]}, {"polygon": [[5, 3], [5, 1], [7, 1], [7, 3]]}], "meta": {"seed": 4703029, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.491477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 573, "strictValidation": true}, "imageAssets": {"target": "../images/voi-572/target.png", "shapes": {"S1": "../images/voi-572/shape_S1.png", "S2": "../images/voi-572/shape_S2.png", "S3": "../images/voi-572/shape_S3.png", "S4": "../images/voi-572/shape_S4.png"}}, "ID": "voi-572", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [7, 3]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [2, 4]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [5, 1]}]}, "legacy_answer": "S1 0 V3 [7,3]\nS2 180 V2 [2,4]\nS3 90 V2 [5,1]", "solutionText": "S1 0 V3 [7,3]\nS2 180 V2 [2,4]\nS3 90 V2 [5,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-572\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-572/target.png", "shapes": {"S1": "images/voi-572/shape_S1.png", "S2": "images/voi-572/shape_S2.png", "S3": "images/voi-572/shape_S3.png", "S4": "images/voi-572/shape_S4.png"}}, "__sample_id__": "voi-572"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 1], [6, 1], [6, 3], [3, 3]]}, {"polygon": [[3, 0], [5, 0], [5, 1], [4, 1], [4, 3], [3, 3]]}, {"polygon": [[8, 2], [6, 2], [6, 0], [8, 0]]}], "meta": {"seed": 4703030, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.285714, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.15625, "difficultyScore": 0.530357, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 574, "strictValidation": true}, "imageAssets": {"target": "../images/voi-573/target.png", "shapes": {"S1": "../images/voi-573/shape_S1.png", "S2": "../images/voi-573/shape_S2.png", "S3": "../images/voi-573/shape_S3.png", "S4": "../images/voi-573/shape_S4.png"}}, "ID": "voi-573", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V4", "grid": [3, 3]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [3, 0]}, {"shape": "S4", "angle": 180, "vertex": "V4", "grid": [8, 0]}]}, "legacy_answer": "S1 0 V4 [3,3]\nS2 0 V1 [3,0]\nS4 180 V4 [8,0]", "solutionText": "S1 0 V4 [3,3]\nS2 0 V1 [3,0]\nS4 180 V4 [8,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-573\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-573/target.png", "shapes": {"S1": "images/voi-573/shape_S1.png", "S2": "images/voi-573/shape_S2.png", "S3": "images/voi-573/shape_S3.png", "S4": "images/voi-573/shape_S4.png"}}, "__sample_id__": "voi-573"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 1], [4, 1], [4, 2], [3, 2], [3, 4], [2, 4]]}, {"polygon": [[3, 5], [0, 5], [0, 3], [3, 3]]}, {"polygon": [[2, 6], [2, 3], [4, 3], [4, 6]]}], "meta": {"seed": 4703031, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 17, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 575, "strictValidation": true}, "imageAssets": {"target": "../images/voi-574/target.png", "shapes": {"S1": "../images/voi-574/shape_S1.png", "S2": "../images/voi-574/shape_S2.png", "S3": "../images/voi-574/shape_S3.png", "S4": "../images/voi-574/shape_S4.png"}}, "ID": "voi-574", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V6", "grid": [2, 4]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [0, 5]}, {"shape": "S4", "angle": 90, "vertex": "V3", "grid": [4, 3]}]}, "legacy_answer": "S2 0 V6 [2,4]\nS3 180 V2 [0,5]\nS4 90 V3 [4,3]", "solutionText": "S2 0 V6 [2,4]\nS3 180 V2 [0,5]\nS4 90 V3 [4,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-574\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-574/target.png", "shapes": {"S1": "images/voi-574/shape_S1.png", "S2": "images/voi-574/shape_S2.png", "S3": "images/voi-574/shape_S3.png", "S4": "images/voi-574/shape_S4.png"}}, "__sample_id__": "voi-574"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[0, 1], [1, 1], [1, 4], [0, 4]]}, {"polygon": [[1, 4], [1, 1], [3, 1], [3, 4]]}, {"polygon": [[4, 2], [4, 4], [3, 4], [3, 3], [1, 3], [1, 2]]}], "meta": {"seed": 4703032, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.649519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 576, "strictValidation": true}, "imageAssets": {"target": "../images/voi-575/target.png", "shapes": {"S1": "../images/voi-575/shape_S1.png", "S2": "../images/voi-575/shape_S2.png", "S3": "../images/voi-575/shape_S3.png", "S4": "../images/voi-575/shape_S4.png"}}, "ID": "voi-575", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [1, 4]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [3, 4]}, {"shape": "S4", "angle": 270, "vertex": "V6", "grid": [1, 2]}]}, "legacy_answer": "S1 0 V3 [1,4]\nS2 90 V4 [3,4]\nS4 270 V6 [1,2]", "solutionText": "S1 0 V3 [1,4]\nS2 90 V4 [3,4]\nS4 270 V6 [1,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-575\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-575/target.png", "shapes": {"S1": "images/voi-575/shape_S1.png", "S2": "images/voi-575/shape_S2.png", "S3": "images/voi-575/shape_S3.png", "S4": "images/voi-575/shape_S4.png"}}, "__sample_id__": "voi-575"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[4, 6], [4, 4], [5, 4], [5, 5], [7, 5], [7, 6]]}, {"polygon": [[7, 4], [4, 4], [5, 3], [7, 3]]}, {"polygon": [[7, 4], [7, 5], [4, 5], [4, 4]]}], "meta": {"seed": 4703033, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.425304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 577, "strictValidation": true}, "imageAssets": {"target": "../images/voi-576/target.png", "shapes": {"S1": "../images/voi-576/shape_S1.png", "S2": "../images/voi-576/shape_S2.png", "S3": "../images/voi-576/shape_S3.png", "S4": "../images/voi-576/shape_S4.png"}}, "ID": "voi-576", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V6", "grid": [7, 6]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 4]}, {"shape": "S4", "angle": 270, "vertex": "V3", "grid": [4, 5]}]}, "legacy_answer": "S2 90 V6 [7,6]\nS3 180 V2 [4,4]\nS4 270 V3 [4,5]", "solutionText": "S2 90 V6 [7,6]\nS3 180 V2 [4,4]\nS4 270 V3 [4,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-576\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-576/target.png", "shapes": {"S1": "images/voi-576/shape_S1.png", "S2": "images/voi-576/shape_S2.png", "S3": "images/voi-576/shape_S3.png", "S4": "images/voi-576/shape_S4.png"}}, "__sample_id__": "voi-576"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[1, 4], [1, 2], [3, 2], [3, 4]]}, {"polygon": [[3, 3], [6, 3], [5, 4], [3, 4]]}, {"polygon": [[4, 3], [2, 3], [2, 2], [3, 2], [3, 0], [4, 0]]}], "meta": {"seed": 4703034, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.189911, "contourComplexity": 40, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.473755, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 578, "strictValidation": true}, "imageAssets": {"target": "../images/voi-577/target.png", "shapes": {"S1": "../images/voi-577/shape_S1.png", "S2": "../images/voi-577/shape_S2.png", "S3": "../images/voi-577/shape_S3.png", "S4": "../images/voi-577/shape_S4.png"}}, "ID": "voi-577", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [1, 2]}, {"shape": "S3", "angle": 0, "vertex": "V1", "grid": [3, 3]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [2, 2]}]}, "legacy_answer": "S1 90 V2 [1,2]\nS3 0 V1 [3,3]\nS4 180 V3 [2,2]", "solutionText": "S1 90 V2 [1,2]\nS3 0 V1 [3,3]\nS4 180 V3 [2,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-577\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-577/target.png", "shapes": {"S1": "images/voi-577/shape_S1.png", "S2": "images/voi-577/shape_S2.png", "S3": "images/voi-577/shape_S3.png", "S4": "images/voi-577/shape_S4.png"}}, "__sample_id__": "voi-577"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[7, 2], [4, 2], [4, 0], [7, 0]]}, {"polygon": [[5, 3], [5, 1], [6, 1], [6, 3]]}, {"polygon": [[3, 3], [3, 1], [4, 1], [4, 2], [6, 2], [6, 3]]}], "meta": {"seed": 4703035, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.333333, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.783333, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 579, "strictValidation": true}, "imageAssets": {"target": "../images/voi-578/target.png", "shapes": {"S1": "../images/voi-578/shape_S1.png", "S2": "../images/voi-578/shape_S2.png", "S3": "../images/voi-578/shape_S3.png", "S4": "../images/voi-578/shape_S4.png"}}, "ID": "voi-578", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V2", "grid": [4, 2]}, {"shape": "S3", "angle": 90, "vertex": "V3", "grid": [6, 1]}, {"shape": "S4", "angle": 90, "vertex": "V5", "grid": [6, 2]}]}, "legacy_answer": "S1 180 V2 [4,2]\nS3 90 V3 [6,1]\nS4 90 V5 [6,2]", "solutionText": "S1 180 V2 [4,2]\nS3 90 V3 [6,1]\nS4 90 V5 [6,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-578\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-578/target.png", "shapes": {"S1": "images/voi-578/shape_S1.png", "S2": "images/voi-578/shape_S2.png", "S3": "images/voi-578/shape_S3.png", "S4": "images/voi-578/shape_S4.png"}}, "__sample_id__": "voi-578"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 3], [1, 1], [3, 3]]}, {"polygon": [[6, 4], [3, 4], [3, 2], [6, 2]]}, {"polygon": [[3, 1], [3, 2], [1, 2], [1, 1]]}], "meta": {"seed": 4703036, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.10559, "contourComplexity": 72, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.79639, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 580, "strictValidation": true}, "imageAssets": {"target": "../images/voi-579/target.png", "shapes": {"S1": "../images/voi-579/shape_S1.png", "S2": "../images/voi-579/shape_S2.png", "S3": "../images/voi-579/shape_S3.png", "S4": "../images/voi-579/shape_S4.png"}}, "ID": "voi-579", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [1, 1]}, {"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 4]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [3, 1]}]}, "legacy_answer": "S1 90 V2 [1,1]\nS2 180 V2 [3,4]\nS4 270 V1 [3,1]", "solutionText": "S1 90 V2 [1,1]\nS2 180 V2 [3,4]\nS4 270 V1 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-579\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-579/target.png", "shapes": {"S1": "images/voi-579/shape_S1.png", "S2": "images/voi-579/shape_S2.png", "S3": "images/voi-579/shape_S3.png", "S4": "images/voi-579/shape_S4.png"}}, "__sample_id__": "voi-579"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[6, 7], [4, 7], [4, 6], [5, 6], [5, 4], [6, 4]]}, {"polygon": [[3, 4], [3, 3], [6, 3], [6, 4]]}, {"polygon": [[5, 7], [4, 7], [4, 4], [5, 4]]}], "meta": {"seed": 4703037, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 581, "strictValidation": true}, "imageAssets": {"target": "../images/voi-580/target.png", "shapes": {"S1": "../images/voi-580/shape_S1.png", "S2": "../images/voi-580/shape_S2.png", "S3": "../images/voi-580/shape_S3.png", "S4": "../images/voi-580/shape_S4.png"}}, "ID": "voi-580", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 7]}, {"shape": "S3", "angle": 90, "vertex": "V2", "grid": [3, 3]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [4, 7]}]}, "legacy_answer": "S2 180 V1 [6,7]\nS3 90 V2 [3,3]\nS4 180 V2 [4,7]", "solutionText": "S2 180 V1 [6,7]\nS3 90 V2 [3,3]\nS4 180 V2 [4,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-580\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-580/target.png", "shapes": {"S1": "images/voi-580/shape_S1.png", "S2": "images/voi-580/shape_S2.png", "S3": "images/voi-580/shape_S3.png", "S4": "images/voi-580/shape_S4.png"}}, "__sample_id__": "voi-580"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 2], [4, 2], [3, 3]]}, {"polygon": [[6, 3], [4, 3], [6, 1]]}, {"polygon": [[3, 4], [3, 1], [5, 1], [5, 4]]}], "meta": {"seed": 4703038, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.247273, "contourComplexity": 106, "connectedComponents": 1, "fillRatio": 0.101074, "difficultyScore": 0.486942, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 582, "strictValidation": true}, "imageAssets": {"target": "../images/voi-581/target.png", "shapes": {"S1": "../images/voi-581/shape_S1.png", "S2": "../images/voi-581/shape_S2.png", "S3": "../images/voi-581/shape_S3.png", "S4": "../images/voi-581/shape_S4.png"}}, "ID": "voi-581", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [3, 3]}, {"shape": "S3", "angle": 180, "vertex": "V1", "grid": [6, 3]}, {"shape": "S4", "angle": 90, "vertex": "V2", "grid": [3, 1]}]}, "legacy_answer": "S1 0 V3 [3,3]\nS3 180 V1 [6,3]\nS4 90 V2 [3,1]", "solutionText": "S1 0 V3 [3,3]\nS3 180 V1 [6,3]\nS4 90 V2 [3,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-581\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-581/target.png", "shapes": {"S1": "images/voi-581/shape_S1.png", "S2": "images/voi-581/shape_S2.png", "S3": "images/voi-581/shape_S3.png", "S4": "images/voi-581/shape_S4.png"}}, "__sample_id__": "voi-581"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 1], [8, 1], [8, 3], [6, 3]]}, {"polygon": [[7, 2], [5, 2], [5, 1], [7, 1]]}, {"polygon": [[5, 0], [8, 0], [8, 1], [5, 1]]}], "meta": {"seed": 4703039, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 11, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 583, "strictValidation": true}, "imageAssets": {"target": "../images/voi-582/target.png", "shapes": {"S1": "../images/voi-582/shape_S1.png", "S2": "../images/voi-582/shape_S2.png", "S3": "../images/voi-582/shape_S3.png", "S4": "../images/voi-582/shape_S4.png"}}, "ID": "voi-582", "answer": {"placements": [{"shape": "S2", "angle": 0, "vertex": "V2", "grid": [8, 1]}, {"shape": "S3", "angle": 180, "vertex": "V3", "grid": [5, 1]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [8, 1]}]}, "legacy_answer": "S2 0 V2 [8,1]\nS3 180 V3 [5,1]\nS4 0 V3 [8,1]", "solutionText": "S2 0 V2 [8,1]\nS3 180 V3 [5,1]\nS4 0 V3 [8,1]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-582\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-582/target.png", "shapes": {"S1": "images/voi-582/shape_S1.png", "S2": "images/voi-582/shape_S2.png", "S3": "images/voi-582/shape_S3.png", "S4": "images/voi-582/shape_S4.png"}}, "__sample_id__": "voi-582"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[4, 7], [4, 4], [6, 4], [6, 7]]}, {"polygon": [[4, 7], [1, 7], [1, 5], [4, 5]]}, {"polygon": [[6, 5], [3, 5], [3, 3], [6, 3]]}], "meta": {"seed": 4703040, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.21875, "difficultyScore": 0.173611, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 584, "strictValidation": true}, "imageAssets": {"target": "../images/voi-583/target.png", "shapes": {"S1": "../images/voi-583/shape_S1.png", "S2": "../images/voi-583/shape_S2.png", "S3": "../images/voi-583/shape_S3.png", "S4": "../images/voi-583/shape_S4.png"}}, "ID": "voi-583", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V1", "grid": [4, 7]}, {"shape": "S2", "angle": 180, "vertex": "V1", "grid": [4, 7]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [6, 5]}]}, "legacy_answer": "S1 90 V1 [4,7]\nS2 180 V1 [4,7]\nS4 180 V1 [6,5]", "solutionText": "S1 90 V1 [4,7]\nS2 180 V1 [4,7]\nS4 180 V1 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-583\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-583/target.png", "shapes": {"S1": "images/voi-583/shape_S1.png", "S2": "images/voi-583/shape_S2.png", "S3": "images/voi-583/shape_S3.png", "S4": "images/voi-583/shape_S4.png"}}, "__sample_id__": "voi-583"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 3], [3, 3], [3, 1], [6, 1]]}, {"polygon": [[7, 1], [4, 1], [4, 0], [7, 0]]}, {"polygon": [[3, 2], [4, 2], [4, 3], [3, 3]]}], "meta": {"seed": 4703041, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 585, "strictValidation": true}, "imageAssets": {"target": "../images/voi-584/target.png", "shapes": {"S1": "../images/voi-584/shape_S1.png", "S2": "../images/voi-584/shape_S2.png", "S3": "../images/voi-584/shape_S3.png", "S4": "../images/voi-584/shape_S4.png"}}, "ID": "voi-584", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V2", "grid": [3, 3]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [4, 1]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S2 180 V2 [3,3]\nS3 180 V2 [4,1]\nS4 0 V2 [4,2]", "solutionText": "S2 180 V2 [3,3]\nS3 180 V2 [4,1]\nS4 0 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-584\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-584/target.png", "shapes": {"S1": "images/voi-584/shape_S1.png", "S2": "images/voi-584/shape_S2.png", "S3": "images/voi-584/shape_S3.png", "S4": "images/voi-584/shape_S4.png"}}, "__sample_id__": "voi-584"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [0, 2]}}, "target": [{"polygon": [[5, 2], [7, 2], [5, 4]]}, {"polygon": [[6, 2], [8, 2], [8, 4], [6, 4]]}, {"polygon": [[7, 4], [7, 7], [6, 6], [6, 4]]}], "meta": {"seed": 4703042, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.123636, "contourComplexity": 102, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.770103, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 586, "strictValidation": true}, "imageAssets": {"target": "../images/voi-585/target.png", "shapes": {"S1": "../images/voi-585/shape_S1.png", "S2": "../images/voi-585/shape_S2.png", "S3": "../images/voi-585/shape_S3.png", "S4": "../images/voi-585/shape_S4.png"}}, "ID": "voi-585", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [5, 4]}, {"shape": "S2", "angle": 0, "vertex": "V1", "grid": [6, 2]}, {"shape": "S3", "angle": 270, "vertex": "V1", "grid": [7, 4]}]}, "legacy_answer": "S1 0 V3 [5,4]\nS2 0 V1 [6,2]\nS3 270 V1 [7,4]", "solutionText": "S1 0 V3 [5,4]\nS2 0 V1 [6,2]\nS3 270 V1 [7,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-585\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-585/target.png", "shapes": {"S1": "images/voi-585/shape_S1.png", "S2": "images/voi-585/shape_S2.png", "S3": "images/voi-585/shape_S3.png", "S4": "images/voi-585/shape_S4.png"}}, "__sample_id__": "voi-585"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}}, "target": [{"polygon": [[2, 5], [3, 5], [3, 7], [2, 7]]}, {"polygon": [[0, 7], [0, 4], [2, 4], [2, 7]]}, {"polygon": [[2, 4], [3, 4], [3, 6], [2, 6]]}], "meta": {"seed": 4703043, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.45, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 587, "strictValidation": true}, "imageAssets": {"target": "../images/voi-586/target.png", "shapes": {"S1": "../images/voi-586/shape_S1.png", "S2": "../images/voi-586/shape_S2.png", "S3": "../images/voi-586/shape_S3.png", "S4": "../images/voi-586/shape_S4.png"}}, "ID": "voi-586", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V2", "grid": [3, 5]}, {"shape": "S2", "angle": 90, "vertex": "V4", "grid": [2, 7]}, {"shape": "S4", "angle": 0, "vertex": "V3", "grid": [3, 6]}]}, "legacy_answer": "S1 0 V2 [3,5]\nS2 90 V4 [2,7]\nS4 0 V3 [3,6]", "solutionText": "S1 0 V2 [3,5]\nS2 90 V4 [2,7]\nS4 0 V3 [3,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-586\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-586/target.png", "shapes": {"S1": "images/voi-586/shape_S1.png", "S2": "images/voi-586/shape_S2.png", "S3": "images/voi-586/shape_S3.png", "S4": "images/voi-586/shape_S4.png"}}, "__sample_id__": "voi-586"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[3, 1], [5, 1], [5, 2], [4, 2], [4, 4], [3, 4]]}, {"polygon": [[3, 2], [3, 5], [1, 5], [1, 2]]}, {"polygon": [[5, 2], [2, 2], [2, 0], [5, 0]]}], "meta": {"seed": 4703044, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.25, "contourComplexity": 12, "connectedComponents": 1, "fillRatio": 0.1875, "difficultyScore": 0.325, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 588, "strictValidation": true}, "imageAssets": {"target": "../images/voi-587/target.png", "shapes": {"S1": "../images/voi-587/shape_S1.png", "S2": "../images/voi-587/shape_S2.png", "S3": "../images/voi-587/shape_S3.png", "S4": "../images/voi-587/shape_S4.png"}}, "ID": "voi-587", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V5", "grid": [4, 4]}, {"shape": "S2", "angle": 270, "vertex": "V1", "grid": [3, 2]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [2, 0]}]}, "legacy_answer": "S1 0 V5 [4,4]\nS2 270 V1 [3,2]\nS4 180 V3 [2,0]", "solutionText": "S1 0 V5 [4,4]\nS2 270 V1 [3,2]\nS4 180 V3 [2,0]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-587\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-587/target.png", "shapes": {"S1": "images/voi-587/shape_S1.png", "S2": "images/voi-587/shape_S2.png", "S3": "images/voi-587/shape_S3.png", "S4": "images/voi-587/shape_S4.png"}}, "__sample_id__": "voi-587"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[1, 0], [2, 0], [2, 1], [1, 1]]}, {"polygon": [[1, 1], [3, 1], [3, 3], [1, 3]]}, {"polygon": [[4, 2], [2, 2], [2, 0], [4, 0]]}], "meta": {"seed": 4703045, "requiredShapeCount": 3, "distractorShapeCount": 1, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.392361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 589, "strictValidation": true}, "imageAssets": {"target": "../images/voi-588/target.png", "shapes": {"S1": "../images/voi-588/shape_S1.png", "S2": "../images/voi-588/shape_S2.png", "S3": "../images/voi-588/shape_S3.png", "S4": "../images/voi-588/shape_S4.png"}}, "ID": "voi-588", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [2, 1]}, {"shape": "S3", "angle": 0, "vertex": "V3", "grid": [3, 3]}, {"shape": "S4", "angle": 180, "vertex": "V1", "grid": [4, 2]}]}, "legacy_answer": "S1 0 V3 [2,1]\nS3 0 V3 [3,3]\nS4 180 V1 [4,2]", "solutionText": "S1 0 V3 [2,1]\nS3 0 V3 [3,3]\nS4 180 V1 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-588\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 1\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-588/target.png", "shapes": {"S1": "images/voi-588/shape_S1.png", "S2": "images/voi-588/shape_S2.png", "S3": "images/voi-588/shape_S3.png", "S4": "images/voi-588/shape_S4.png"}}, "__sample_id__": "voi-588"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 6], [4, 6], [4, 5], [5, 5], [5, 3], [6, 3]]}, {"polygon": [[2, 6], [2, 3], [3, 3], [3, 6]]}, {"polygon": [[6, 5], [3, 5], [3, 3], [6, 3]]}], "meta": {"seed": 4704001, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.307692, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.549519, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 590, "strictValidation": true}, "imageAssets": {"target": "../images/voi-589/target.png", "shapes": {"S1": "../images/voi-589/shape_S1.png", "S2": "../images/voi-589/shape_S2.png", "S3": "../images/voi-589/shape_S3.png", "S4": "../images/voi-589/shape_S4.png", "S5": "../images/voi-589/shape_S5.png"}}, "ID": "voi-589", "answer": {"placements": [{"shape": "S1", "angle": 180, "vertex": "V5", "grid": [5, 3]}, {"shape": "S2", "angle": 90, "vertex": "V1", "grid": [2, 6]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [3, 3]}]}, "legacy_answer": "S1 180 V5 [5,3]\nS2 90 V1 [2,6]\nS5 180 V3 [3,3]", "solutionText": "S1 180 V5 [5,3]\nS2 90 V1 [2,6]\nS5 180 V3 [3,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-589\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-589/target.png", "shapes": {"S1": "images/voi-589/shape_S1.png", "S2": "images/voi-589/shape_S2.png", "S3": "images/voi-589/shape_S3.png", "S4": "images/voi-589/shape_S4.png", "S5": "images/voi-589/shape_S5.png"}}, "__sample_id__": "voi-589"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S2": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 4], [5, 7], [3, 7], [3, 4]]}, {"polygon": [[5, 3], [5, 5], [4, 5], [4, 4], [2, 4], [2, 3]]}, {"polygon": [[1, 3], [2, 3], [2, 4], [1, 4]]}], "meta": {"seed": 4704002, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.181818, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.140625, "difficultyScore": 0.591477, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 591, "strictValidation": true}, "imageAssets": {"target": "../images/voi-590/target.png", "shapes": {"S1": "../images/voi-590/shape_S1.png", "S2": "../images/voi-590/shape_S2.png", "S3": "../images/voi-590/shape_S3.png", "S4": "../images/voi-590/shape_S4.png", "S5": "../images/voi-590/shape_S5.png"}}, "ID": "voi-590", "answer": {"placements": [{"shape": "S1", "angle": 270, "vertex": "V1", "grid": [5, 4]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [4, 5]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [2, 3]}]}, "legacy_answer": "S1 270 V1 [5,4]\nS2 270 V3 [4,5]\nS4 0 V2 [2,3]", "solutionText": "S1 270 V1 [5,4]\nS2 270 V3 [4,5]\nS4 0 V2 [2,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-590\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S2: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-590/target.png", "shapes": {"S1": "images/voi-590/shape_S1.png", "S2": "images/voi-590/shape_S2.png", "S3": "images/voi-590/shape_S3.png", "S4": "images/voi-590/shape_S4.png", "S5": "images/voi-590/shape_S5.png"}}, "__sample_id__": "voi-590"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[1, 4], [1, 2], [2, 2], [2, 4]]}, {"polygon": [[2, 2], [2, 3], [0, 3], [0, 2]]}, {"polygon": [[3, 0], [3, 3], [1, 3], [1, 0]]}], "meta": {"seed": 4704003, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 592, "strictValidation": true}, "imageAssets": {"target": "../images/voi-591/target.png", "shapes": {"S1": "../images/voi-591/shape_S1.png", "S2": "../images/voi-591/shape_S2.png", "S3": "../images/voi-591/shape_S3.png", "S4": "../images/voi-591/shape_S4.png", "S5": "../images/voi-591/shape_S5.png"}}, "ID": "voi-591", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V2", "grid": [1, 2]}, {"shape": "S2", "angle": 270, "vertex": "V3", "grid": [0, 3]}, {"shape": "S3", "angle": 270, "vertex": "V3", "grid": [1, 3]}]}, "legacy_answer": "S1 90 V2 [1,2]\nS2 270 V3 [0,3]\nS3 270 V3 [1,3]", "solutionText": "S1 90 V2 [1,2]\nS2 270 V3 [0,3]\nS3 270 V3 [1,3]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-591\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[0,1]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-591/target.png", "shapes": {"S1": "images/voi-591/shape_S1.png", "S2": "images/voi-591/shape_S2.png", "S3": "images/voi-591/shape_S3.png", "S4": "images/voi-591/shape_S4.png", "S5": "images/voi-591/shape_S5.png"}}, "__sample_id__": "voi-591"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[5, 5], [5, 2], [7, 2], [7, 5]]}, {"polygon": [[7, 5], [7, 8], [5, 8], [5, 5]]}, {"polygon": [[7, 6], [6, 6], [6, 5], [7, 5]]}], "meta": {"seed": 4704004, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.153846, "contourComplexity": 8, "connectedComponents": 1, "fillRatio": 0.171875, "difficultyScore": 0.640865, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 593, "strictValidation": true}, "imageAssets": {"target": "../images/voi-592/target.png", "shapes": {"S1": "../images/voi-592/shape_S1.png", "S2": "../images/voi-592/shape_S2.png", "S3": "../images/voi-592/shape_S3.png", "S4": "../images/voi-592/shape_S4.png", "S5": "../images/voi-592/shape_S5.png"}}, "ID": "voi-592", "answer": {"placements": [{"shape": "S2", "angle": 90, "vertex": "V1", "grid": [5, 5]}, {"shape": "S4", "angle": 270, "vertex": "V1", "grid": [7, 5]}, {"shape": "S5", "angle": 180, "vertex": "V3", "grid": [6, 5]}]}, "legacy_answer": "S2 90 V1 [5,5]\nS4 270 V1 [7,5]\nS5 180 V3 [6,5]", "solutionText": "S2 90 V1 [5,5]\nS4 270 V1 [7,5]\nS5 180 V3 [6,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-592\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-592/target.png", "shapes": {"S1": "images/voi-592/shape_S1.png", "S2": "images/voi-592/shape_S2.png", "S3": "images/voi-592/shape_S3.png", "S4": "images/voi-592/shape_S4.png", "S5": "images/voi-592/shape_S5.png"}}, "__sample_id__": "voi-592"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 7], [3, 7], [3, 5], [6, 5]]}, {"polygon": [[5, 7], [5, 6], [6, 6], [6, 7]]}, {"polygon": [[2, 7], [4, 7], [4, 8], [2, 8]]}], "meta": {"seed": 4704005, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.222222, "contourComplexity": 10, "connectedComponents": 1, "fillRatio": 0.109375, "difficultyScore": 0.492361, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 594, "strictValidation": true}, "imageAssets": {"target": "../images/voi-593/target.png", "shapes": {"S1": "../images/voi-593/shape_S1.png", "S2": "../images/voi-593/shape_S2.png", "S3": "../images/voi-593/shape_S3.png", "S4": "../images/voi-593/shape_S4.png", "S5": "../images/voi-593/shape_S5.png"}}, "ID": "voi-593", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 7]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [6, 7]}, {"shape": "S4", "angle": 0, "vertex": "V2", "grid": [4, 7]}]}, "legacy_answer": "S2 180 V1 [6,7]\nS3 90 V4 [6,7]\nS4 0 V2 [4,7]", "solutionText": "S2 180 V1 [6,7]\nS3 90 V4 [6,7]\nS4 0 V2 [4,7]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-593\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-593/target.png", "shapes": {"S1": "images/voi-593/shape_S1.png", "S2": "images/voi-593/shape_S2.png", "S3": "images/voi-593/shape_S3.png", "S4": "images/voi-593/shape_S4.png", "S5": "images/voi-593/shape_S5.png"}}, "__sample_id__": "voi-593"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}}, "target": [{"polygon": [[6, 3], [3, 3], [4, 2], [6, 2]]}, {"polygon": [[4, 3], [4, 0], [6, 0], [6, 3]]}, {"polygon": [[4, 0], [4, 2], [2, 2], [2, 0]]}], "meta": {"seed": 4704006, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319202, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.610206, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 595, "strictValidation": true}, "imageAssets": {"target": "../images/voi-594/target.png", "shapes": {"S1": "../images/voi-594/shape_S1.png", "S2": "../images/voi-594/shape_S2.png", "S3": "../images/voi-594/shape_S3.png", "S4": "../images/voi-594/shape_S4.png", "S5": "../images/voi-594/shape_S5.png"}}, "ID": "voi-594", "answer": {"placements": [{"shape": "S2", "angle": 180, "vertex": "V1", "grid": [6, 3]}, {"shape": "S3", "angle": 90, "vertex": "V4", "grid": [6, 3]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [4, 2]}]}, "legacy_answer": "S2 180 V1 [6,3]\nS3 90 V4 [6,3]\nS5 270 V2 [4,2]", "solutionText": "S2 180 V1 [6,3]\nS3 90 V4 [6,3]\nS5 270 V2 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-594\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S3: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-594/target.png", "shapes": {"S1": "images/voi-594/shape_S1.png", "S2": "images/voi-594/shape_S2.png", "S3": "images/voi-594/shape_S3.png", "S4": "images/voi-594/shape_S4.png", "S5": "images/voi-594/shape_S5.png"}}, "__sample_id__": "voi-594"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}}, "target": [{"polygon": [[2, 4], [2, 1], [3, 2], [3, 4]]}, {"polygon": [[3, 3], [3, 5], [2, 5], [2, 4], [0, 4], [0, 3]]}, {"polygon": [[4, 3], [4, 6], [2, 6], [2, 3]]}], "meta": {"seed": 4704007, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.319202, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.133301, "difficultyScore": 0.610206, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 596, "strictValidation": true}, "imageAssets": {"target": "../images/voi-595/target.png", "shapes": {"S1": "../images/voi-595/shape_S1.png", "S2": "../images/voi-595/shape_S2.png", "S3": "../images/voi-595/shape_S3.png", "S4": "../images/voi-595/shape_S4.png", "S5": "../images/voi-595/shape_S5.png"}}, "ID": "voi-595", "answer": {"placements": [{"shape": "S1", "angle": 90, "vertex": "V4", "grid": [3, 4]}, {"shape": "S3", "angle": 270, "vertex": "V4", "grid": [2, 4]}, {"shape": "S4", "angle": 270, "vertex": "V2", "grid": [4, 6]}]}, "legacy_answer": "S1 90 V4 [3,4]\nS3 270 V4 [2,4]\nS4 270 V2 [4,6]", "solutionText": "S1 90 V4 [3,4]\nS3 270 V4 [2,4]\nS4 270 V2 [4,6]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-595\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S4: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S5: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-595/target.png", "shapes": {"S1": "images/voi-595/shape_S1.png", "S2": "images/voi-595/shape_S2.png", "S3": "images/voi-595/shape_S3.png", "S4": "images/voi-595/shape_S4.png", "S5": "images/voi-595/shape_S5.png"}}, "__sample_id__": "voi-595"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}}, "target": [{"polygon": [[6, 2], [6, 5], [4, 5], [4, 2]]}, {"polygon": [[6, 6], [4, 6], [4, 5], [6, 5]]}, {"polygon": [[5, 4], [5, 5], [4, 4]]}], "meta": {"seed": 4704008, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.124542, "contourComplexity": 38, "connectedComponents": 1, "fillRatio": 0.116699, "difficultyScore": 0.868433, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 597, "strictValidation": true}, "imageAssets": {"target": "../images/voi-596/target.png", "shapes": {"S1": "../images/voi-596/shape_S1.png", "S2": "../images/voi-596/shape_S2.png", "S3": "../images/voi-596/shape_S3.png", "S4": "../images/voi-596/shape_S4.png", "S5": "../images/voi-596/shape_S5.png"}}, "ID": "voi-596", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V1", "grid": [6, 2]}, {"shape": "S3", "angle": 180, "vertex": "V4", "grid": [6, 5]}, {"shape": "S5", "angle": 270, "vertex": "V2", "grid": [5, 5]}]}, "legacy_answer": "S2 270 V1 [6,2]\nS3 180 V4 [6,5]\nS5 270 V2 [5,5]", "solutionText": "S2 270 V1 [6,2]\nS3 180 V4 [6,5]\nS5 270 V2 [5,5]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-596\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[3,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-596/target.png", "shapes": {"S1": "images/voi-596/shape_S1.png", "S2": "images/voi-596/shape_S2.png", "S3": "images/voi-596/shape_S3.png", "S4": "images/voi-596/shape_S4.png", "S5": "images/voi-596/shape_S5.png"}}, "__sample_id__": "voi-596"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S2": {"V1": [0, 0], "V2": [3, 0], "V3": [3, 2], "V4": [0, 2]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [0, 1]}, "S4": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}, "S5": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}}, "target": [{"polygon": [[7, 1], [7, 4], [5, 4], [5, 1]]}, {"polygon": [[6, 4], [3, 4], [4, 3], [6, 3]]}, {"polygon": [[5, 2], [5, 3], [4, 3], [4, 2]]}], "meta": {"seed": 4704009, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.209836, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.117676, "difficultyScore": 0.525304, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 598, "strictValidation": true}, "imageAssets": {"target": "../images/voi-597/target.png", "shapes": {"S1": "../images/voi-597/shape_S1.png", "S2": "../images/voi-597/shape_S2.png", "S3": "../images/voi-597/shape_S3.png", "S4": "../images/voi-597/shape_S4.png", "S5": "../images/voi-597/shape_S5.png"}}, "ID": "voi-597", "answer": {"placements": [{"shape": "S2", "angle": 270, "vertex": "V3", "grid": [5, 4]}, {"shape": "S4", "angle": 180, "vertex": "V3", "grid": [4, 3]}, {"shape": "S5", "angle": 270, "vertex": "V4", "grid": [4, 2]}]}, "legacy_answer": "S2 270 V3 [5,4]\nS4 180 V3 [4,3]\nS5 270 V4 [4,2]", "solutionText": "S2 270 V3 [5,4]\nS4 180 V3 [4,3]\nS5 270 V4 [4,2]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-597\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S2: V1=[0,0], V2=[3,0], V3=[3,2], V4=[0,2]\n- S3: V1=[0,0], V2=[2,0], V3=[2,1], V4=[0,1]\n- S4: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n- S5: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-597/target.png", "shapes": {"S1": "images/voi-597/shape_S1.png", "S2": "images/voi-597/shape_S2.png", "S3": "images/voi-597/shape_S3.png", "S4": "images/voi-597/shape_S4.png", "S5": "images/voi-597/shape_S5.png"}}, "__sample_id__": "voi-597"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [0, 1]}, "S3": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S5": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}}, "target": [{"polygon": [[4, 1], [6, 1], [6, 2], [5, 2], [5, 4], [4, 4]]}, {"polygon": [[7, 3], [5, 3], [5, 1], [7, 1]]}, {"polygon": [[6, 4], [6, 3], [8, 3], [8, 4]]}], "meta": {"seed": 4704010, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.2, "contourComplexity": 14, "connectedComponents": 1, "fillRatio": 0.125, "difficultyScore": 0.55, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 599, "strictValidation": true}, "imageAssets": {"target": "../images/voi-598/target.png", "shapes": {"S1": "../images/voi-598/shape_S1.png", "S2": "../images/voi-598/shape_S2.png", "S3": "../images/voi-598/shape_S3.png", "S4": "../images/voi-598/shape_S4.png", "S5": "../images/voi-598/shape_S5.png"}}, "ID": "voi-598", "answer": {"placements": [{"shape": "S1", "angle": 0, "vertex": "V3", "grid": [6, 2]}, {"shape": "S3", "angle": 180, "vertex": "V2", "grid": [5, 3]}, {"shape": "S4", "angle": 90, "vertex": "V1", "grid": [6, 4]}]}, "legacy_answer": "S1 0 V3 [6,2]\nS3 180 V2 [5,3]\nS4 90 V1 [6,4]", "solutionText": "S1 0 V3 [6,2]\nS3 180 V2 [5,3]\nS4 90 V1 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-598\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[0,1]\n- S3: V1=[0,0], V2=[2,0], V3=[2,2], V4=[0,2]\n- S4: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S5: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-598/target.png", "shapes": {"S1": "images/voi-598/shape_S1.png", "S2": "images/voi-598/shape_S2.png", "S3": "images/voi-598/shape_S3.png", "S4": "images/voi-598/shape_S4.png", "S5": "images/voi-598/shape_S5.png"}}, "__sample_id__": "voi-598"} {"gridSize": 8, "inventory": {"S1": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 3], "V4": [0, 3]}, "S2": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 1], "V4": [0, 1]}, "S3": {"V1": [0, 0], "V2": [1, 0], "V3": [1, 2], "V4": [0, 2]}, "S4": {"V1": [0, 0], "V2": [2, 0], "V3": [2, 1], "V4": [1, 1], "V5": [1, 3], "V6": [0, 3]}, "S5": {"V1": [0, 0], "V2": [3, 0], "V3": [2, 1], "V4": [0, 1]}}, "target": [{"polygon": [[6, 6], [6, 5], [8, 5], [8, 6]]}, {"polygon": [[7, 5], [5, 5], [5, 4], [6, 4], [6, 2], [7, 2]]}, {"polygon": [[5, 6], [5, 3], [6, 4], [6, 6]]}], "meta": {"seed": 4704011, "requiredShapeCount": 3, "distractorShapeCount": 2, "shapePoolComplexity": "medium", "overlapAllowed": true, "overlapRatio": 0.234432, "contourComplexity": 42, "connectedComponents": 1, "fillRatio": 0.102051, "difficultyScore": 0.458169, "rasterScale": 16, "targetPackaging": "solution_xor_components", "catalogIndex": 600, "strictValidation": true}, "imageAssets": {"target": "../images/voi-599/target.png", "shapes": {"S1": "../images/voi-599/shape_S1.png", "S2": "../images/voi-599/shape_S2.png", "S3": "../images/voi-599/shape_S3.png", "S4": "../images/voi-599/shape_S4.png", "S5": "../images/voi-599/shape_S5.png"}}, "ID": "voi-599", "answer": {"placements": [{"shape": "S3", "angle": 90, "vertex": "V4", "grid": [8, 6]}, {"shape": "S4", "angle": 180, "vertex": "V2", "grid": [5, 5]}, {"shape": "S5", "angle": 90, "vertex": "V3", "grid": [6, 4]}]}, "legacy_answer": "S3 90 V4 [8,6]\nS4 180 V2 [5,5]\nS5 90 V3 [6,4]", "solutionText": "S3 90 V4 [8,6]\nS4 180 V2 [5,5]\nS5 90 V3 [6,4]", "prompt": {"system": "You are a Text-VOI spatial logic puzzle solver. Given a target pattern image and a set of base shapes, choose how to rotate and translate the shapes onto a grid so that their XOR-overlapping union matches the target pattern exactly.\n\nYou will receive: (a) one target pattern image showing the goal silhouette on a labeled grid, (b) one image per available base shape with vertex labels, and (c) a structured text body listing each shape's vertex coordinates, the grid size, the difficulty tier, the required and distractor shape counts, and the XOR-overlap rule.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- All images share the same grid coordinate system (origin bottom-left, x right, y up).\n\n## 4. INPUT FIELDS\n- level_id: voi-599\n- grid_size: 8x8\n- difficulty_tier: Unlabeled\n- minimum_required_shapes: 3\n- distractor_shapes: 2\n- xor_overlap_allowed: True\n- inventory (each base shape's vertex coordinates):\n- S1: V1=[0,0], V2=[1,0], V3=[1,3], V4=[0,3]\n- S2: V1=[0,0], V2=[1,0], V3=[1,1], V4=[0,1]\n- S3: V1=[0,0], V2=[1,0], V3=[1,2], V4=[0,2]\n- S4: V1=[0,0], V2=[2,0], V3=[2,1], V4=[1,1], V5=[1,3], V6=[0,3]\n- S5: V1=[0,0], V2=[3,0], V3=[2,1], V4=[0,1]\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of `placement` objects:\n- placement: {\"shape\": , \"angle\": 0|90|180|270, \"vertex\": , \"grid\": [, ]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"\",\"angle\":<0|90|180|270>,\"vertex\":\"\",\"grid\":[,]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"target": "images/voi-599/target.png", "shapes": {"S1": "images/voi-599/shape_S1.png", "S2": "images/voi-599/shape_S2.png", "S3": "images/voi-599/shape_S3.png", "S4": "images/voi-599/shape_S4.png", "S5": "images/voi-599/shape_S5.png"}}, "__sample_id__": "voi-599"}