id stringlengths 32 32 | question_interleave listlengths 2 2 | question_images images listlengths 1 1 | solution_interleave listlengths 2 10 | solution_images images listlengths 1 5 | answer stringclasses 82
values | options stringclasses 0
values | knowledge stringclasses 1
value | subknowledge stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|
hingefolding_level_1_puzzle_0001 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target configuration, the pink square must be positioned below the blue triangle. Rotating hinge A by 270 degrees swings the square downwards, shifting its diagonal to point vertically. This specific alignment matches the components perfectly with the target silhouette, complet... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0002 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape consists of a square on the upper left and a diamond extending downwards from the square's right edge. Rotating the blue diamond 270 degrees around hinge A swings it downward to sit below the right half of the red square. This positions the diamond perfectly to match the lo... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0003 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the blue segment so it points downward, perpendicular to the pink segment. This final move establishes the correct overlapping L-shape, completing the target configuration.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"content": "im... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0004 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees aligns the flat vertical edge of the pink triangle with the horizontal diagonal of the blue square. Because the hinge is centrally located on this edge, the rotation perfectly places one corner of the triangle at the exact center of the square, creating a high... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0005 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the blue square inward over the pink diamond. This precise rotation aligns the adjacent edge of the blue square directly along the horizontal diagonal of the pink piece, producing a compact, overlapping final shape.</think>\nA 90",
"index": 0,
"t... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0006 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the blue triangle inward, overlapping it with the pink square to form a compact structure. This rotation aligns the flat base of the triangle with the horizontal diagonal of the square. As this is the final active hinge, completing this fold achieves the... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0007 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the blue square to fold back over the pink square. This precise rotation aligns the vertices of the blue shape with the midpoints of the top and right edges of the pink shape, creating a compact overlapping geometry. Since no other hinges remain, this m... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0008 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees swings the blue triangle over the pink square, changing its orientation from pointing outward to pointing upward. This allows the triangle to partially overlap the square in a compact arrangement. Since there are no other hinges to fold, this move finalizes th... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0009 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the pink square so that its upper-left edge aligns closely with the bottom side of the blue triangle. This compactly folds the two shapes together into a cohesive block. Because there are no remaining hinges to fold, this effectively achieves the final... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0010 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration consists of a square with a diamond shape extending diagonally upward from its right side. Currently, the pink diamond is positioned directly to the right of the square. Rotating hinge A by 90 degrees pivots the diamond upward so it partially overlaps the square's t... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0011 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target silhouette, the triangular piece must point downwards and partially overlap the square. Rotating hinge A by 270 degrees swings the triangle into this downward-facing orientation. This aligns half of its flat base horizontally to the right of the square, precisely forming... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0012 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette features the diamond extending from the bottom-right of the square. Rotating the diamond 270 degrees around hinge A shifts it into this downward position. This aligns the diamond to partially overlap the square, matching the final shape perfectly.</think>\nA 270",
... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0013 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features two squares arranged diagonally with a shared overlapping corner. Rotating the right square 270 degrees around hinge A swings it downward, shifting it below the right half of the left square. This aligns the squares to partially overlap, perfectly matching ... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0014 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Hinge A connects the cyan and pink squares at a single vertex. Rotating hinge A by 90 degrees brings their adjacent edges into direct alignment. This merges the two squares into a solid, contiguous rectangle, completing the final target shape.</think>\nA 90",
"index": 0,
"type": "te... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0015 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette features a square on the lower left and a vertical rectangle positioned on the upper right. Currently, the blue segment extends horizontally from the right side of the pink square. Rotating hinge A by 90 degrees swings this blue segment into a vertical orientation, for... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0016 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees folds the right segment downwards and to the left, causing it to partially overlap with the bottom portion of the left segment. This movement achieves the target compact shape and serves as the final step to complete the puzzle.</think>\nA 270",
"index": ... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0017 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the pink diamond downward, folding it closely against the lower edge of the blue rectangle. This maximizes the overlap between the two shapes, creating a highly compact structural footprint. Since no further hinges remain, this maneuver successfully co... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0018 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the pink rectangle downward into a vertical orientation, tucking it partially beneath the blue square. This significantly compacts the structure into its target configuration. As there are no remaining hinges, this single fold completes the puzzle.</th... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0019 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The blue diamond is already positioned correctly according to the target shape. The pink rectangle is horizontal, but in the target configuration, it points straight up. Rotating hinge A by 90 degrees swings the pink rectangle into this vertical orientation, perfectly matching the target.</... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0020 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To form the target silhouette, the blue triangle must point downwards instead of to the right. Rotating the triangle around hinge A by 270 degrees achieves this exactly. This pivots the triangle so its vertical base becomes horizontal, overlapping the rectangle and completing the final shap... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0021 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the blue square so that it partially overlaps the pink square, maximizing their shared area. As there are no other hinges to manipulate, this final fold compacts the pieces into the completed target configuration.</think>\nA 90",
"index": 0,
"ty... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0022 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the square polygon counterclockwise so that it rests against the angled side of the triangle. This completes the folding sequence, resulting in a compact, overlapping shape.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "ima... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0023 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette shows the square section positioned higher than the triangle's rightmost point. Currently, the pink square is located directly to the right of hinge A. Rotating the square by 90 degrees around hinge A pivots it upward, placing the hinge at its bottom edge. This perfect... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0024 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the right tile around the midpoint of the shared edge. This aligns the tile to overlap precisely with the top-right quadrant of the left tile, completing the final target configuration.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"co... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0025 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape is an L-shape, requiring the right segment to point upwards relative to the left. Rotating hinge A by 90 degrees folds the right piece upward, perfectly matching the vertical section of the target.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0026 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features an L-shape where a vertical section extends upwards from the right side of a square base. In the current layout, the pink block extends horizontally to the right of the blue base block. Rotating hinge A by 90 degrees swings the pink block upward, positionin... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0027 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the red triangle upwards. This maneuver aligns its base horizontally across the blue square, seamlessly achieving the final target configuration.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "images/hingefolding_level_1_puz... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0028 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 180 degrees pivots the blue triangle around the rightmost tip of the pink triangle. This folds the blue shape to the left, causing it to overlap symmetrically with the pink shape to form a compact geometric configuration. Since this is the only remaining hinge, this fina... | A 180 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0029 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features a downward-pointing rectangular section attached to the right point of the triangle. In the current state, the pink rectangle extends horizontally to the right from hinge A. Rotating the rectangle by 270 degrees swings it into a vertical position pointing s... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0030 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features two squares arranged in a staggered, overlapping diagonal pattern. Currently, the squares lie horizontally side-by-side. Rotating hinge A by 90 degrees pivots one square upward so it partially overlaps the other, matching the target's shape perfectly.</thin... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0031 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees swings the rightmost rectangular piece from a horizontal to a vertical orientation, partially overlapping it with the triangular piece to form a compact shape. As this is the only hinge present in the structure, this single rotation completes the folding seque... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0032 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the pink square so its connecting edge becomes horizontal. This folds the square downwards, compactly overlapping it with the lower half of the blue triangle. As there are no remaining hinges, this move achieves the final folded configuration.</think>\... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0033 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the right block so that it partially overlaps the left block. This folds the currently extended horizontal structure into a more compact, stacked configuration. As there are no remaining hinges, this move successfully completes the puzzle.</think>\nA 90... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0034 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the blue triangle until its base becomes horizontal and its tip points straight down. This creates the rightward horizontal step and the lowest downward-pointing vertex exactly as they appear in the target shape. The resulting overlap between the two t... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0035 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>In the initial state, the pink triangle points to the right with its vertical edge centered on hinge A. The target shape reveals that the blue diamond stays in place, while the pink piece must form a horizontal top edge and point downwards. Rotating the pink triangle by 270 degrees pivots i... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0036 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the attached square, bringing its edges into closer alignment with the adjacent shape. As this is the final step, no further configuration analysis is needed.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "images/hingefoldin... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0037 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the rightmost segment downward into a vertical position. This establishes a perpendicular orientation between the two segments, successfully completing the final target configuration.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"co... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0038 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features two overlapping squares arranged in a diagonal step. Currently, the squares are positioned side-by-side and connected at the midpoint of their shared edge by hinge A. Pivoting one square 90 degrees around this hinge swings it upward and partially over the o... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0039 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration is an L-shape that requires a vertical segment on its right side. Currently, the chain is entirely horizontal. Rotating hinge A by 90 degrees pivots the right segment upward, creating the necessary vertical extension and perfectly matching the target silhouette.</th... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0040 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The pink triangle and the blue square meet at hinge A, where the pink triangle features a 90-degree vertex. Rotating hinge A by 90 degrees pivots the square so that its lower edge aligns perfectly flush with the upper edge of the triangle. This eliminates the gap between the shapes, resulti... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0041 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To reach a compact state, the blue piece must be folded over the pink one. A 270-degree rotation around hinge A swings the blue square downwards, aligning it into a specific overlapping position with the bottom portion of the pink rectangle. This maneuver successfully forms the final requir... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0042 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features a vertical segment extending downwards from the right side of the horizontal block. Rotating hinge A by 270 degrees pivots the rightmost section downward into this exact position. This movement perfectly forms the required L-shape to match the target.</thin... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0043 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>In the target shape, the rectangular section extends vertically upwards from the right corner of the diamond base. Currently, the blue rectangle points horizontally to the right from hinge A. Rotating it by 90 degrees around hinge A aligns it perfectly with this upward vertical orientation,... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0044 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating the pink diamond by 270 degrees around hinge A swings it downward so that it is positioned directly below the joint. This overlaps the diamond with the bottom-right corner of the blue square, perfectly forming the overall silhouette of the target shape.</think>\nA 270",
"index"... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0045 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The two square tiles currently meet only at the corner point of hinge A. By rotating hinge A by 90 degrees, the adjacent edges of the pink and blue tiles will perfectly align and lie flush against each other. This folds the separated pieces into a single, compact rectangular shape, finalizi... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0046 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the right tile so its edge sits flush against the upper-right edge of the left tile. This closes the gap between the pieces, consolidating the shape into a single compact rectangle and completing the puzzle.</think>\nA 90",
"index": 0,
"type": "... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0047 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Currently, the pink square sits to the right of the blue rectangle, joined at hinge A. The target shape requires the pink square to be positioned below the blue piece, exactly overlapping its bottom-right quadrant. Rotating hinge A by 270 degrees swings the pink square into this precise ali... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0048 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees swings the blue square into a compact overlapping position with the pink triangle. This movement minimizes the overall footprint of the shapes by bringing their edges into alignment. Since this is the final rotation, this maneuver successfully completes the pu... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0049 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features a horizontal left segment and a vertical right segment extending downwards. To achieve this structure, the right section of the chain must be folded downward to form the vertical portion. Rotating hinge A by 270 degrees correctly positions the blue piece ve... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0050 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration shows the square positioned above the triangle's rightmost vertex. Rotating hinge A by 90 degrees pivots the square so that its original connecting edge becomes a horizontal bottom edge centered on the hinge. This shifts the square into the upper-right position, per... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0051 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the blue square directly onto the pink diamond. This aligns the square's left edge with the horizontal diagonal of the diamond, maximizing surface overlap. As this is the final step, it perfectly resolves the puzzle into its compact target configuration.... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0052 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape consists of a horizontal section on the left and a vertical section on the right, forming an L-like structure. By folding hinge A by 90 degrees, the right block is shifted from a horizontal to a vertical orientation. This perfectly aligns the blocks to match the required si... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0053 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape features an upward-pointing peak on the right side. By rotating hinge A by 90 degrees, the blue triangle's orientation shifts from pointing right to pointing up. This correctly aligns the components to form the final silhouette.</think>\nA 90",
"index": 0,
"type": "... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0054 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the pink triangle around the central connection point. This shifts its base from a vertical to a horizontal orientation, folding the triangle upwards to partially overlap the blue square. As there are no remaining hinges to adjust, this move directly co... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0055 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette consists of a square top section and a rectangular section extending vertically downwards from its right side. In the current state, the pink rectangle extends horizontally to the right. Rotating it 270 degrees around hinge A swings it into a vertical position pointing... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0056 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the horizontal red rectangle into a vertical orientation. This maneuver brings it into the correct overlapping alignment with the blue diamond. As there are no further hinges to manipulate, this move completes the final target configuration.</think>\nA ... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0057 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the blue square inward toward the pink triangle, significantly reducing the overall footprint of the shape. This fold resolves the extended outward layout, bringing the pieces into a tightly packed configuration. Since there are no other hinges left to ... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0058 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration features an upward-pointing triangle extending from the right side of the square. In the current configuration, the triangle points to the right and is connected to the square's right edge at hinge A. Rotating the triangle by 90 degrees around hinge A shifts its tip... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0059 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target silhouette, the rectangular piece must point directly downward from the right point of the diamond. Rotating hinge A by 270 degrees shifts the blue rectangle from its horizontal position to a vertical, downward-facing orientation. This perfectly aligns the parts to match... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0060 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 180 degrees folds the blue triangular piece directly over the pink diamond. This maximizes the overlap between the two pieces, resulting in a compact final configuration.</think>\nA 180",
"index": 0,
"type": "text"
},
{
"content": "images/hingefolding_lev... | A 180 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0061 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To form the target shape, the pink square must be shifted downward to overlap with the bottom-right half of the blue diamond. Rotating the pink square 270 degrees around hinge A swings it into this lower position, transforming its vertical left edge into a horizontal top edge. Because hinge... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0062 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the right segment into a perpendicular alignment with the left segment. This fold introduces the necessary overlap between the pieces to achieve the desired compact shape. Since there are no remaining hinges to rotate, this maneuver directly completes t... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0063 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape features two squares positioned diagonally from one another. Currently, the blue and pink squares are horizontally adjacent, sharing a vertical edge where hinge A is located. Rotating hinge A by 90 degrees pivots the right square upward. This shifts it into the exact diagon... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0064 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the rightmost triangle downwards, bringing its flat vertical edge into a horizontal alignment. This maneuver neatly folds the unconstrained piece over the base structure to minimize the overall footprint. Since no other hinges remain, this fully resolv... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0065 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The puzzle currently consists of a blue square and a pink triangle laid out flat, connected at hinge A. Rotating hinge A by 180 degrees folds the pink triangle directly backward so that it overlaps the blue square. Because this is a two-piece puzzle, this single maneuver successfully conden... | A 180 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0066 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating the blue diamond 270 degrees around hinge A swings it downwards so it is centered directly below the hinge. This folds a portion of the diamond over the bottom-right corner of the pink square, while its lower half creates the distinct angled downward protrusion required to match th... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0067 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape features a horizontal section with a vertical section extending downwards from its right edge. Currently, both parts are aligned horizontally. Rotating the right part around hinge A by 270 degrees swings it to point straight down, perfectly forming the required configuratio... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0068 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the red diamond so that one of its lower edges aligns flush against the top slanted edge of the blue triangle. This neatly closes the gap between the two pieces, forming a single compact geometric shape. Since there are no remaining hinges to rotate, th... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0069 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the pink square so it overlaps the lower-right section of the blue diamond. This movement perfectly aligns the square's resulting top edge with the diamond's horizontal axis and places its corner exactly at the diamond's center, achieving a tightly int... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0070 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the pink shape downward to partially overlap the blue square. This folds the components into a compact arrangement, completing the final target configuration.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"content": "images/hingefold... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0071 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees shifts the blue rectangle into a perpendicular alignment, folding it compactly over the pink triangle. This achieves the necessary overlapping arrangement and completes the final puzzle configuration.</think>\nA 90",
"index": 0,
"type": "text"
},
{... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0072 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape requires the triangle to point upwards and overlap the top right of the square. Currently, the triangle points to the right and connects to the square at hinge A. Rotating the triangle 90 degrees around hinge A pivots its point towards the top. This correctly positions it t... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0073 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the pink diamond shape over the blue rectangle, significantly reducing the structure's footprint. This aligns the pieces into their final, compact overlapping configuration. Since there are no more hinges to adjust, this completes the puzzle.</think>\nA ... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0074 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees shifts the pink panel so that it overlaps with the blue panel, effectively folding the two ends of the chain together into the required compact final shape.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"content": "images/hingefolding_level... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0075 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the pink triangular piece downwards, causing it to partially overlap the blue square. Since there are no other hinges left to fold, this final rotation creates a compact, unified shape and completes the puzzle.</think>\nA 270",
"index": 0,
"typ... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0076 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the pink piece into a perpendicular alignment, partially overlapping the blue square. This efficiently packs the two pieces together, completing the puzzle by achieving the final target configuration.</think>\nA 90",
"index": 0,
"type": "text"
... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0077 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees folds the pink triangle counterclockwise over the blue square, aligning it into a more compact overlapping position. Since there are no further hinges to rotate, this completes the shape.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"conte... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0078 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Hinge A connects the horizontal pink rectangle to the blue square. Rotating hinge A by 90 degrees pivots the rectangle into a vertical orientation, causing it to partially overlap the blue square. Since there are no other hinges, this rotation achieves the most compact target configuration,... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0079 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the blue triangle inward to correctly overlap with the pink piece. Because no other hinges remain to be rotated, this step directly achieves the final target configuration.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "image... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0080 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target silhouette, the blue triangle needs to point downwards. Rotating hinge A by 270 degrees pivots the blue triangle so its tip faces straight down and its previously vertical edge becomes horizontal. This seamlessly aligns the blue shape with the pink triangle to form the e... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0081 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the red triangle so that its point faces downward. This motion aligns the flat base of the triangle horizontally, overlapping the lower right portion of the blue square. As this is the final step, it directly completes the target compact shape.</think>... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0082 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette features a square top-left section with a downward-pointing triangular extension. Currently, the triangle points horizontally to the right from the square's right edge. Rotating hinge A by 270 degrees pivots the triangle so its tip points straight down and its base bec... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0083 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the blue square downward, aligning its edge perfectly with the lower-right edge of the pink square. This final fold consolidates the puzzle into a single, compact rectangular shape.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"cont... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0084 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To form the target shape, the square must be repositioned to overlap the lower portion of the triangle. Rotating hinge A by 270 degrees swings the square downwards, aligning its edges to create the exact silhouette of the target.</think>\nA 270",
"index": 0,
"type": "text"
},
{
... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0085 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>In the target configuration, the square section sits above the right vertex of the triangle. Currently, the blue square is connected to this vertex at hinge A along its vertical left edge. Rotating hinge A by 90 degrees pivots the square so that this edge becomes horizontal, positioning the... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0086 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape features a triangular top pointing upwards from the rectangular base. Currently, the triangular piece connected at hinge A points horizontally to the right. Rotating hinge A by 90 degrees pivots this triangle into the correct upright position, overlapping the rectangle to c... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0087 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target silhouette, the square must be repositioned to form the lower right rectangular section. Rotating hinge A by 270 degrees pivots the square downward, turning its originally vertical connecting edge into a horizontal top edge. This partially overlaps the square with the tr... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0088 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees swings the red triangle upward. This positions its flat edge horizontally and places one vertex precisely at the center of the blue square. As this is the final step, it neatly overlaps the pieces to complete the target shape.</think>\nA 90",
"index": 0,
... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0089 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees pivots the blue triangle to fold over the pink square. This aligns the triangle's edge horizontally, forming a compact overlapping structure and completing the puzzle.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"content": "images/hingefold... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0090 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees pivots the blue square around the midpoint of the shared edge. This swings the blue square downwards and to the left, positioning it so that its top-left quadrant exactly overlaps the bottom-right quadrant of the pink square. As there are no remaining steps, ... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0091 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape requires the rectangular piece to extend directly downwards from the right vertex of the diamond. Rotating the pink rectangle around hinge A by 270 degrees swings it from a horizontal to a vertical orientation. This single adjustment correctly positions the rectangle to per... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0092 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>In the target configuration, the diamond shape is angled upward rather than extending horizontally to the right. Rotating the diamond by 90 degrees around hinge A swings it into this precise position. This single fold aligns the shapes to perfectly match the target silhouette.</think>\nA 90... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0093 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>To match the target L-shape, the right segment must be oriented vertically and extend downwards. Rotating hinge A by 270 degrees pivots this segment into the required perpendicular alignment. This single fold perfectly forms the final target configuration.</think>\nA 270",
"index": 0,
... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0094 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration requires the square piece to partially overlap the upper-right section of the diamond piece. Currently, the square is positioned entirely to the right. Rotating it 90 degrees around hinge A swings it upward, merging the two shapes to perfectly match the target silho... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0095 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target configuration consists of a diamond connected to a vertical rectangular segment. In the current state, the pink rectangle extends horizontally to the right. By rotating hinge A 90 degrees, the rectangle pivots into a vertical orientation, perfectly matching the target silhouette.... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0096 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target shape features a vertical rectangular section hanging directly below the right corner of the diamond. Currently, the pink rectangle extends horizontally to the right from this corner. Rotating hinge A by 270 degrees pivots the rectangle into a downward-pointing vertical position,... | A 270 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0097 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 90 degrees folds the red rectangle upward, causing it to partially overlap the blue shape to achieve the desired compact state. Since this is the only hinge, this move successfully completes the puzzle.</think>\nA 90",
"index": 0,
"type": "text"
},
{
"con... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0098 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette features a distinct upward-pointing triangular peak. Currently, the pink triangle is oriented horizontally, pointing to the right. Rotating it by 90 degrees around hinge A pivots the shape so its tip points vertically upwards. This alignment directly matches the top pr... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0099 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>The target silhouette features a prominent upward-pointing peak on the right. Rotating hinge A by 90 degrees pivots the blue triangle so that it points straight up, aligning its base horizontally to perfectly match this final shape.</think>\nA 90",
"index": 0,
"type": "text"
},
... | A 90 | null | HingeFolding | HingeFolding | ||
hingefolding_level_1_puzzle_0100 | [
{
"content": "The image shows, on the left, several rigid shapes connected in a kinematic chain by labeled hinges (A, B, C, ...); on the right is a target folded configuration. Rotating hinge N rotates the shape on the right side of that hinge (and everything further right) anti-clockwise; shapes left of the hi... | [
{
"content": "<think>Rotating hinge A by 270 degrees swings the blue rectangle downward, aligning its edge with the lower right side of the pink square. This compacts the two pieces into their final interlocking position.</think>\nA 270",
"index": 0,
"type": "text"
},
{
"content": "images/hingef... | A 270 | null | HingeFolding | HingeFolding |
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