| { | |
| "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: <one-line JSON>\n\nThe JSON object must follow the placements schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reconstruct the target pattern with full confidence, still emit a best-effort FINAL_JSON line with at least one placement; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", | |
| "user": "## 1. TASK\nChoose how to rotate and translate base shapes onto the grid so that their XOR-overlapped union exactly reproduces the target pattern.\nThe puzzle is solved when the rasterized pixel mask of the chosen placements equals the target pattern's pixel mask.\n\n## 2. WORLD MODEL\n- Grid: an integer grid of size `gridSize x gridSize`. The grid coordinate origin is the bottom-left corner; x increases to the right, y increases upward.\n- Base shape: a polygon defined by a sequence of named vertices V1, V2, ... in the shape's local coordinate frame. The local origin is `[0, 0]`.\n- Vertex id: the literal vertex name (e.g. \"V1\", \"V2\", ...) used to anchor a placement.\n- Placement: pick one base shape, rotate it clockwise around its local origin by 0/90/180/270 degrees, then translate so a chosen post-rotation vertex lands on a chosen grid coordinate.\n- XOR overlap: when shapes overlap, the overlapping region is removed (symmetric difference of pixel masks). XOR overlap is allowed. Overlapping black areas cancel each other out.\n- Target pattern: the goal black region painted on the grid.\n\n## 3. VISUAL LEGEND\n- Image 1: the target pattern, drawn on the grid with coordinate labels visible.\n- Image 2..N: one image per base shape, with vertex labels \"V1, V2, ...\" printed at each vertex and the local origin marked.\n- 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\": <shape id>, \"angle\": 0|90|180|270, \"vertex\": <vertex id>, \"grid\": [<int>, <int>]}\n- `shape` is one of the inventory shape ids above.\n- `angle` is the clockwise rotation in degrees, applied around the shape's local origin before translation.\n- `vertex` is the post-rotation vertex of the chosen shape used as the placement anchor.\n- `grid` is the global grid coordinate where the chosen anchor vertex lands.\n\n## 6. CONSTRAINTS\n- Each shape may be used at most once (no shape appears twice in the placements list).\n- `angle` must be exactly one of {0, 90, 180, 270}.\n- `vertex` must be a valid vertex id of the chosen shape (e.g. \"V1\" .. \"Vk\").\n- `grid` coordinates may extend outside `[0, gridSize)` only if the resulting placement still fits the puzzle's framing — overshooting cells outside the target are scored as misses.\n- The final XOR-union of all placement pixel masks must equal the target pattern's pixel mask for a perfect score.\n\n## 7. SOLVING ADVICE\n- Identify large unique shapes in the target first; small shapes are usually used to fill remaining gaps.\n- When XOR overlap is allowed, two shapes overlapping each other can carve a hole — useful when the target has concavities the base shapes cannot reproduce alone.\n- Anchor each placement to a corner vertex (V1 typically) when possible; it makes the translation reasoning easier to verify.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"placements\":[{\"shape\":\"<id>\",\"angle\":<0|90|180|270>,\"vertex\":\"<id>\",\"grid\":[<int>,<int>]}, ...]}\n- placements: list of placement objects.\n- shape: string, must be a key from the inventory.\n- angle: integer in {0, 90, 180, 270}.\n- vertex: string, a valid vertex id of the chosen shape.\n- grid: array of two integers `[gridX, gridY]`.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it." | |
| } | |
| } | |