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3x3_inst10_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst10/assembly/3x3_inst10assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/assembly/3x3_inst10assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/assembly/3x3_inst10assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/assembly/3x3_inst10assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/assembly/3x3_inst10assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.08300347331815172, 0.9129260346492023, 0.030327958859172166], "cell_center": [4.5, 4.5]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3863759873563767, 0.3560346662754732, 0.9984770026551721], "cell_center": [1.5, 1.5]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.8361559109194318, 0.10012585524596118, 0.741018254845187], "cell_center": [1.5, 4.5]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 1, 3], "color": [0.6956976668525877, 0.5614724968196306, 0.20881351979388718], "cell_center": [4.5, 1.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst0_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x, y) = (1, 2).
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Step 3: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 2).
Step 5: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_5.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.7898276832817946, 0.4878925327916963, 0.09710359553248094], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777], "cell_center": [9.330127018922195, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n11\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst14_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 3).
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 30, "flip": "horizontal", "color": [0.6986416373362043, 0.39103013274436993, 0.7338256355090964], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 30, "flip": "none", "color": [0.7375466272024475, 0.7958785429353309, 0.9602750500929624], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n110\n110\n111\n\nPiece B:\n011\n011\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst4_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece E with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.2781238656332754, 0.3149691097007876, 0.8834243520527705]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.09541635884526178, 0.9752420367434649, 0.6631387179145616]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.4955604281106083, 0.23218544540889552, 0.750238147366625]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.2926298809515543, 0.23058311511659102, 0.3786033753419644]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [1, 2, 1, 3], "color": [0.6744683957180527, 0.765436016656263, 0.5757777482665812]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
4x4_inst21_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 2]], "angle": 60, "flip": "horizontal", "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281], "is_merged": true}, {"index": 0, "shape": [0, 3, 2, 4], "angle": 30, "flip": "none", "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1111\n0011\n0011\n0011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst13_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_6.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (2, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.7966424419178151, 0.9680914967906663, 0.866954291693426]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.29384131363027277, 0.3163325797949277, 0.007829642754902055]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2805251122858946, 0.9715538225079458, 0.3810974789090861]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 3, "w": 3.0, "h": 3.0, "label": "3x3", "piece": [1, 4, 2, 5], "color": [0.13663939469484443, 0.7631849020052232, 0.6462586504062603]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.08091420612656075, 0.9562651224873678, 0.23051757819828445]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 2, 4], "color": [0.9400983497113293, 0.32605090347507637, 0.5045925067978794]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n111\n111\n111\n\nPiece E:\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
4x4_inst10_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x,y) = (2, 4).
Step 2: Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its upper-left corner at (x,y) = (0, 3).
Step 3: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).
Step 4: Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).
Step 5: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_5.png"], "instructions": ["", "Place piece D with its upper-left corner at (x,y) = (2, 4).", "Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 1)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 2, 4], "angle": 0, "flip": "none", "color": [0.7227327947376154, 0.03867259473351192, 0.7187065902508578], "is_merged": false}, {"index": 2, "shape": [0, 1, 0, 2], "angle": 30, "flip": "vertical", "color": [0.6583796654906042, 0.6756935160824654, 0.35383825296178073], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 2], "angle": 90, "flip": "none", "color": [0.985913636595184, 0.05054811512912383, 0.006039335896045883], "is_merged": false}, {"index": 4, "shape": [[1, 3, 0, 2], [1, 2, 2, 4]], "angle": 30, "flip": "none", "color": [0.25836663280757977, 0.2609931063406825, 0.8704001126195765], "is_merged": false}, {"index": 1, "shape": [2, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.7647943845442875, 0.521793038303051, 0.22931721031735863], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1111\n1100\n\nPiece D:\n11\n\nPiece E:\n1100\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst20_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Step 4: Place piece C with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "cell_center": [7.446152422706633, 6.0]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "cell_center": [2.4820508075688776, 6.0]}, {"index": 3, "angle": 30, "orig_width": 4, "orig_height": 1, "w": 3.964101615137755, "h": 2.8660254037844384, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523], "cell_center": [7.446152422706633, 2.0]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "cell_center": [2.4820508075688776, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n111\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst16_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (3, 4).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "valid": true, "config": [{"index": 2, "shape": [[0, 2, 0, 1], [2, 4, 0, 3]], "angle": 90, "flip": "none", "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795], "is_merged": false}, {"index": 1, "shape": [2, 4, 3, 4], "angle": 90, "flip": "none", "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 4], "angle": 30, "flip": "none", "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1100\n1100\n1111\n\nPiece C:\n1100\n1100\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst12_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_step/4x4_inst12perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_step/4x4_inst12perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_step/4x4_inst12perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_step/4x4_inst12perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_step/4x4_inst12perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.8799540670390662, 0.016815702542142485, 0.6851494150554925], "cell_center": [2.5, 6.348076211353315]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.6933282349034623, 0.28464064197742567, 0.5984440934517744], "cell_center": [7.5, 6.348076211353315]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.8269286759639897, 0.28853959708119414, 0.11506735623330777], "cell_center": [2.5, 2.1160254037844384]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.49483518787283254, 0.25660426038958584, 0.4007459306539174], "cell_center": [7.5, 2.1160254037844384]}], "variant": "perturbed_step"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst30_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 1, 3], "angle": 90, "flip": "none", "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [0, 1, 0, 3]], "angle": 30, "flip": "none", "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "is_merged": false}, {"index": 3, "shape": [3, 4, 1, 4], "angle": 0, "flip": "none", "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "horizontal", "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1000\n1000\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n111\n\nPiece E:\n0001\n0001\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst30_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 60, "flip": "horizontal", "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n110\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst12_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).
Step 2: Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3).
Step 3: Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 60, "flip": "none", "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 1], "angle": 90, "flip": "horizontal", "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868], "is_merged": true}, {"index": 2, "shape": [[1, 3, 0, 2], [0, 1, 1, 3]], "angle": 90, "flip": "none", "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n110\n111\n001\n\nPiece C:\n001\n111\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst11_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "horizontal", "color": [0.20466808994905894, 0.704066164831489, 0.6231877093078216], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 60, "flip": "none", "color": [0.10167857717644269, 0.8327584618892119, 0.8500740367164027], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n001\n001\n111\n\nPiece B:\n100\n100\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst9_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/perturbed_part/4x4_inst9perturbed_part_assembly_step_7.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (2, 3).", "Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 1).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1)."], "results": ["", "", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.726034657723742, 0.14100632109447608, 0.1515951180124674]}, {"index": 6, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.778064233634106, 0.49491432744069963, 0.1366699960458858]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 1, 2], "color": [0.08568095338134385, 0.6682948586606138, 0.6055837889275328]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.3767840683317317, 0.9804349782325034, 0.6211477157651492]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 3, 4], "color": [0.6391948573912559, 0.6949802608182306, 0.21433155875468102]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [1, 4, 0, 1], "color": [0.32195261495336813, 0.6322591244083937, 0.7762269388570919]}, {"index": 5, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.28340804127686015, 0.9232672116663543, 0.8311037648416407]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n\nPiece C:\n1\n1\n1\n\nPiece D:\n11\n\nPiece E:\n11\n11\n\nPiece F:\n111\n\nPiece G:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
3x3_inst29_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst29/assembly/3x3_inst29assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/assembly/3x3_inst29assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/assembly/3x3_inst29assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/assembly/3x3_inst29assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.16908974540263644, 0.9028171146233334, 0.20691211710600244], "cell_center": [2.049038105676658, 5.049038105676658]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.45969448450814654, 0.03567904341063466, 0.6125989178735066], "cell_center": [2.049038105676658, 1.6830127018922192]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5587780227736063, 0.37341366971430356, 0.25392528265228476], "cell_center": [6.147114317029974, 5.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst35_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst35/irregular_assembly/4x4_inst35invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst35/irregular_assembly/4x4_inst35invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst35/irregular_assembly/4x4_inst35invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst35/irregular_assembly/4x4_inst35invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst35/irregular_assembly/4x4_inst35invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", " Flip piece D horizontally. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 2, "shape": [1, 3, 1, 2], "angle": 90, "flip": "none", "color": [0.6248973146304716, 0.19456100377421137, 0.7615477279269885], "is_merged": false}, {"index": 1, "shape": [1, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.828332628276821, 0.3568437652207792, 0.07499970601291073], "is_merged": false}, {"index": 0, "shape": [0, 1, 0, 4], "angle": 90, "flip": "none", "color": [0.5370430119950892, 0.9674495663481948, 0.06812209327812946], "is_merged": false}, {"index": 3, "shape": [[3, 4, 1, 4], [1, 3, 2, 4]], "angle": 0, "flip": "horizontal", "color": [0.3003864702913007, 0.9202383693433634, 0.08263462112700326], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n1\n\nPiece B:\n1\n1\n1\n\nPiece C:\n11\n\nPiece D:\n0111\n1100\n1100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst19_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x, y) = (1, 1).
Step 2: Place piece B with its upper-left corner at (x, y) = (1, 3).
Step 3: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_4.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (1, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.8916148044641335, 0.3781423287870871, 0.36352922300777135], "cell_center": [4.5, 1.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8415274483290549, 0.46286374035661404, 0.8797592115225641], "cell_center": [4.5, 4.5]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3223902645479415, 0.8258414522110806, 0.3821764742442382], "cell_center": [1.5, 1.5]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.4978586459293345, 0.5976559765313394, 0.14086452934263438], "cell_center": [1.5, 4.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst21_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Place piece C with its upper-left corner at (x, y) = (1, 2).
Step 3: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.6165348490517608, 0.47248907820449537, 0.17394439876786527], "cell_center": [1.6830127018922196, 6.147114317029974]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.5750109852621413, 0.4718251861047962, 0.07260160357926093], "cell_center": [1.6830127018922196, 2.049038105676658]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.6140362933411411, 0.9726156360309749, 0.23541658483033545], "cell_center": [5.049038105676659, 6.147114317029974]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst3_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_step/3x3_inst3perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_step/3x3_inst3perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_step/3x3_inst3perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_step/3x3_inst3perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_step/3x3_inst3perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.16349340438282878, 0.21139582589822659, 0.2570028333453004], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst0_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "cell_center": [2.049038105676658, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "cell_center": [6.147114317029974, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.8422134984480056, 0.15250547228228883, 0.5324273953128456], "cell_center": [2.049038105676658, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst67_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "horizontal", "color": [0.011555386923828292, 0.38856667577712833, 0.5580544451581476], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.610168984685911, 0.8861242806116434, 0.5519982870011023], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n0111\n1100\n1100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst53_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 4).", "Place piece A with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 4, 0, 4], [0, 2, 1, 4]], "angle": 30, "flip": "none", "color": [0.5703411072949541, 0.4675093349253865, 0.059971239841069], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.6171011853051268, 0.4159916646382219, 0.32416928134320555], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11110\n11110\n00111\n00111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst17_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1)."], "valid": true, "config": [{"index": 2, "shape": [[1, 3, 1, 3], [0, 1, 2, 3]], "angle": 0, "flip": "none", "color": [0.5019930741412741, 0.012559332865545225, 0.17639361210978133], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 2], "angle": 90, "flip": "none", "color": [0.5781587086361871, 0.8308911842343512, 0.6376093319739924], "is_merged": true}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "none", "color": [0.3661900859965067, 0.7558139235341418, 0.8335971471271846], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n110\n\nPiece C:\n11\n11\n01\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst14_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_6.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.5631914090172505, 0.5804703370467916, 0.4790988214748605], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.15000823947344966, 0.4439607975953732, 0.1370434408981498], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.6561140073467281, 0.4764433888300178, 0.7238357704859639], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25169887858646867, 0.6011267349617215, 0.9995531297392487], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.8928397408510584, 0.20487579654854826, 0.908916065600491], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.23171741259592205, 0.12354035634812421, 0.9975313433534191], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst18_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece F with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Step 3: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 5: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 6: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_6.png"], "instructions": ["", "Place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 5, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001], "cell_center": [10.0, 1.8660254037844386]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638], "cell_center": [2.0, 1.8660254037844386]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175], "cell_center": [6.0, 1.8660254037844386]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714], "cell_center": [6.0, 5.598076211353316]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483], "cell_center": [2.0, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005], "cell_center": [10.0, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n111\n\nPiece F:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst24_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
Step 2: Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).
Step 3: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).
Step 4: Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 90, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "is_merged": false}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n110\n110\n111\n\nPiece C:\n1\n1\n\nPiece D:\n100\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst9_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 3).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 1).", "Place piece E with its upper-left corner at (x,y) = (1, 4)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 3, 4], "angle": 30, "flip": "none", "color": [0.08568095338134385, 0.6682948586606138, 0.6055837889275328], "is_merged": false}, {"index": 2, "shape": [1, 3, 2, 4], "angle": 30, "flip": "none", "color": [0.32195261495336813, 0.6322591244083937, 0.7762269388570919], "is_merged": false}, {"index": 1, "shape": [3, 4, 1, 4], "angle": 30, "flip": "none", "color": [0.6391948573912559, 0.6949802608182306, 0.21433155875468102], "is_merged": true}, {"index": 0, "shape": [1, 4, 0, 1], "angle": 90, "flip": "none", "color": [0.3767840683317317, 0.9804349782325034, 0.6211477157651492], "is_merged": false}, {"index": 4, "shape": [[1, 3, 1, 2], [0, 1, 0, 3]], "angle": 0, "flip": "none", "color": [0.726034657723742, 0.14100632109447608, 0.1515951180124674], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n010\n010\n111\n\nPiece C:\n11\n11\n\nPiece D:\n1\n\nPiece E:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst1_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 0).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_step/3x3_inst1perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_step/3x3_inst1perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_step/3x3_inst1perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_step/3x3_inst1perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_step/3x3_inst1perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 0).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "Over board", "Over board", "", "Over board"], "valid": false, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.14881909049605957, 0.9309150666944223, 0.2473442019032891], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.256800880301729, 0.03751904073714318, 0.9621217613176958], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.4502474416941842, 0.8486047097331468, 0.005901795236425311], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.6560169554382161, 0.08892499875961357, 0.2746181042425252], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst18_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 4: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_4.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.010600729886533378, 0.8500375523210303, 0.41713905454049915]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst40_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 2).
Step 2: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 2).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "vertical", "color": [0.6182029536479532, 0.1028217441783712, 0.6005490533698828], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 90, "flip": "none", "color": [0.5687910254987621, 0.5142377944845191, 0.5258868534366733], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst23_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).
Step 2: Place piece D with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
Step 5: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.33940213919128803, 0.15148877406439698, 0.5222835237729154]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.16858591960978841, 0.08544656496515068, 0.11494367118197413]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.6294248924659861, 0.3328326929596823, 0.09034406811739082]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.9963442161344365, 0.11387330077903723, 0.2799037066005946]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.02981754658528879, 0.27867823105972955, 0.046516018756367794]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
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