{"puzzle": "aquarium", "row": 6, "column": 6, "level": "easy", "original_data": {"region": [[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 2], [3, 3, 4, 2, 2, 2], [3, 4, 4, 4, 4, 5], [3, 4, 3, 3, 3, 5], [3, 3, 3, 3, 5, 5]], "row_water_counts": [1, 4, 4, 5, 5, 4], "col_water_counts": [5, 4, 5, 5, 3, 1]}, "id": 0, "observation": {"region": [[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 2], [3, 3, 4, 2, 2, 2], [3, 4, 4, 4, 4, 5], [3, 4, 3, 3, 3, 5], [3, 3, 3, 3, 5, 5]], "row_water_counts": [1, 4, 4, 5, 5, 4], "col_water_counts": [5, 4, 5, 5, 3, 1]}, "answer": [["W", null, null, null, null, null], ["W", "W", "W", "W", null, null], [null, null, "W", "W", "W", "W"], ["W", "W", "W", "W", "W", null], ["W", "W", "W", "W", "W", null], ["W", "W", "W", "W", null, null]], "idx": 0, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_0.png", "answer_image": "figs/aquarium_0_answer.png"} {"puzzle": "aquarium", "row": 6, "column": 6, "level": "normal", "original_data": {"region": [[0, 0, 1, 1, 2, 2], [0, 3, 1, 1, 1, 1], [3, 3, 1, 1, 4, 1], [5, 5, 4, 4, 4, 1], [5, 6, 7, 7, 4, 4], [6, 6, 8, 8, 8, 8]], "row_water_counts": [4, 2, 2, 5, 5, 4], "col_water_counts": [5, 4, 3, 3, 4, 3]}, "id": 1, "observation": {"region": [[0, 0, 1, 1, 2, 2], [0, 3, 1, 1, 1, 1], [3, 3, 1, 1, 4, 1], [5, 5, 4, 4, 4, 1], [5, 6, 7, 7, 4, 4], [6, 6, 8, 8, 8, 8]], "row_water_counts": [4, 2, 2, 5, 5, 4], "col_water_counts": [5, 4, 3, 3, 4, 3]}, "answer": [["W", "W", null, null, "W", "W"], ["W", "W", null, null, null, null], ["W", "W", null, null, null, null], ["W", "W", "W", "W", "W", null], ["W", null, "W", "W", "W", "W"], [null, null, "W", "W", "W", "W"]], "idx": 1, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_1.png", "answer_image": "figs/aquarium_1_answer.png"} {"puzzle": "aquarium", "row": 6, "column": 6, "level": "hard", "original_data": {"region": [[0, 1, 2, 3, 3, 4], [5, 6, 2, 7, 7, 4], [5, 2, 2, 8, 7, 9], [10, 10, 11, 12, 13, 9], [14, 14, 11, 12, 13, 15], [16, 17, 17, 13, 13, 15]], "row_water_counts": [1, 1, 4, 2, 4, 2], "col_water_counts": [3, 5, 2, 2, 1, 1]}, "id": 2, "observation": {"region": [[0, 1, 2, 3, 3, 4], [5, 6, 2, 7, 7, 4], [5, 2, 2, 8, 7, 9], [10, 10, 11, 12, 13, 9], [14, 14, 11, 12, 13, 15], [16, 17, 17, 13, 13, 15]], "row_water_counts": [1, 1, 4, 2, 4, 2], "col_water_counts": [3, 5, 2, 2, 1, 1]}, "answer": [[null, "W", null, null, null, null], [null, "W", null, null, null, null], [null, "W", "W", "W", "W", null], ["W", "W", null, null, null, null], ["W", "W", "W", "W", null, null], ["W", null, null, null, null, "W"]], "idx": 2, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_2.png", "answer_image": "figs/aquarium_2_answer.png"} {"puzzle": "aquarium", "row": 10, "column": 10, "level": "easy", "original_data": {"region": [[0, 0, 0, 0, 0, 0, 1, 1, 2, 2], [3, 3, 0, 0, 0, 0, 4, 1, 2, 2], [5, 3, 3, 0, 0, 4, 4, 1, 2, 2], [5, 5, 5, 0, 0, 0, 1, 1, 2, 2], [5, 6, 0, 0, 1, 1, 1, 2, 2, 2], [5, 6, 6, 6, 6, 7, 1, 2, 2, 2], [5, 5, 8, 8, 7, 7, 9, 9, 9, 2], [10, 10, 8, 8, 11, 11, 11, 9, 9, 2], [10, 8, 8, 12, 12, 12, 9, 9, 2, 2], [10, 10, 8, 8, 9, 9, 9, 13, 13, 2]], "row_water_counts": [6, 7, 7, 8, 6, 6, 2, 6, 8, 8], "col_water_counts": [9, 7, 6, 7, 9, 8, 8, 4, 3, 3]}, "id": 3, "observation": {"region": [[0, 0, 0, 0, 0, 0, 1, 1, 2, 2], [3, 3, 0, 0, 0, 0, 4, 1, 2, 2], [5, 3, 3, 0, 0, 4, 4, 1, 2, 2], [5, 5, 5, 0, 0, 0, 1, 1, 2, 2], [5, 6, 0, 0, 1, 1, 1, 2, 2, 2], [5, 6, 6, 6, 6, 7, 1, 2, 2, 2], [5, 5, 8, 8, 7, 7, 9, 9, 9, 2], [10, 10, 8, 8, 11, 11, 11, 9, 9, 2], [10, 8, 8, 12, 12, 12, 9, 9, 2, 2], [10, 10, 8, 8, 9, 9, 9, 13, 13, 2]], "row_water_counts": [6, 7, 7, 8, 6, 6, 2, 6, 8, 8], "col_water_counts": [9, 7, 6, 7, 9, 8, 8, 4, 3, 3]}, "answer": [["W", "W", "W", "W", "W", "W", null, null, null, null], ["W", "W", "W", "W", "W", "W", "W", null, null, null], ["W", "W", "W", "W", "W", "W", "W", null, null, null], ["W", "W", "W", "W", "W", "W", "W", "W", null, null], ["W", null, "W", "W", "W", "W", "W", null, null, null], ["W", "W", "W", "W", "W", null, "W", null, null, null], ["W", "W", null, null, null, null, null, null, null, null], [null, null, null, null, "W", "W", "W", "W", "W", "W"], ["W", null, null, "W", "W", "W", "W", "W", "W", "W"], ["W", "W", null, null, "W", "W", "W", "W", "W", "W"]], "idx": 3, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_3.png", "answer_image": "figs/aquarium_3_answer.png"} {"puzzle": "aquarium", "row": 10, "column": 10, "level": "normal", "original_data": {"region": [[0, 0, 0, 1, 1, 1, 1, 1, 2, 2], [0, 3, 4, 1, 5, 5, 5, 6, 6, 2], [0, 3, 4, 1, 1, 1, 5, 5, 2, 2], [0, 3, 4, 1, 7, 7, 7, 7, 8, 2], [0, 3, 4, 4, 4, 9, 9, 10, 8, 8], [3, 3, 4, 9, 9, 9, 10, 10, 8, 8], [3, 11, 9, 9, 10, 10, 10, 12, 13, 8], [14, 11, 11, 10, 10, 10, 12, 12, 13, 15], [14, 11, 16, 16, 16, 12, 12, 17, 18, 15], [14, 11, 16, 19, 19, 19, 19, 17, 18, 15]], "row_water_counts": [5, 3, 3, 7, 1, 1, 5, 6, 3, 2], "col_water_counts": [3, 2, 2, 6, 4, 5, 4, 4, 4, 2]}, "id": 4, "observation": {"region": [[0, 0, 0, 1, 1, 1, 1, 1, 2, 2], [0, 3, 4, 1, 5, 5, 5, 6, 6, 2], [0, 3, 4, 1, 1, 1, 5, 5, 2, 2], [0, 3, 4, 1, 7, 7, 7, 7, 8, 2], [0, 3, 4, 4, 4, 9, 9, 10, 8, 8], [3, 3, 4, 9, 9, 9, 10, 10, 8, 8], [3, 11, 9, 9, 10, 10, 10, 12, 13, 8], [14, 11, 11, 10, 10, 10, 12, 12, 13, 15], [14, 11, 16, 16, 16, 12, 12, 17, 18, 15], [14, 11, 16, 19, 19, 19, 19, 17, 18, 15]], "row_water_counts": [5, 3, 3, 7, 1, 1, 5, 6, 3, 2], "col_water_counts": [3, 2, 2, 6, 4, 5, 4, 4, 4, 2]}, "answer": [[null, null, null, "W", "W", "W", "W", "W", null, null], [null, null, null, "W", null, null, null, "W", "W", null], [null, null, null, "W", "W", "W", null, null, null, null], ["W", null, null, "W", "W", "W", "W", "W", null, "W"], ["W", null, null, null, null, null, null, null, null, null], [null, null, "W", null, null, null, null, null, null, null], ["W", null, "W", "W", null, null, null, null, "W", "W"], [null, null, null, "W", "W", "W", "W", "W", "W", null], [null, "W", null, null, null, "W", "W", null, null, null], [null, "W", null, null, null, null, null, null, "W", null]], "idx": 4, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_4.png", "answer_image": "figs/aquarium_4_answer.png"} {"puzzle": "aquarium", "row": 10, "column": 10, "level": "hard", "original_data": {"region": [[0, 1, 2, 2, 3, 4, 5, 5, 5, 6], [0, 1, 7, 2, 3, 4, 8, 8, 8, 6], [9, 9, 7, 2, 4, 4, 4, 10, 11, 11], [12, 7, 7, 13, 14, 15, 10, 10, 10, 10], [12, 16, 16, 13, 17, 15, 18, 18, 19, 19], [20, 16, 16, 17, 17, 21, 18, 18, 19, 22], [20, 20, 23, 24, 24, 21, 18, 25, 25, 22], [20, 23, 23, 26, 27, 28, 29, 29, 29, 30], [20, 23, 23, 26, 27, 28, 28, 30, 29, 30], [31, 31, 23, 23, 32, 32, 32, 30, 30, 30]], "row_water_counts": [3, 4, 5, 7, 1, 3, 4, 3, 1, 4], "col_water_counts": [1, 4, 3, 2, 2, 2, 5, 5, 8, 3]}, "id": 5, "observation": {"region": [[0, 1, 2, 2, 3, 4, 5, 5, 5, 6], [0, 1, 7, 2, 3, 4, 8, 8, 8, 6], [9, 9, 7, 2, 4, 4, 4, 10, 11, 11], [12, 7, 7, 13, 14, 15, 10, 10, 10, 10], [12, 16, 16, 13, 17, 15, 18, 18, 19, 19], [20, 16, 16, 17, 17, 21, 18, 18, 19, 22], [20, 20, 23, 24, 24, 21, 18, 25, 25, 22], [20, 23, 23, 26, 27, 28, 29, 29, 29, 30], [20, 23, 23, 26, 27, 28, 28, 30, 29, 30], [31, 31, 23, 23, 32, 32, 32, 30, 30, 30]], "row_water_counts": [3, 4, 5, 7, 1, 3, 4, 3, 1, 4], "col_water_counts": [1, 4, 3, 2, 2, 2, 5, 5, 8, 3]}, "answer": [[null, null, null, null, null, null, "W", "W", "W", null], [null, "W", null, null, null, null, "W", "W", "W", null], [null, null, null, null, "W", "W", "W", null, "W", "W"], [null, "W", "W", null, "W", null, "W", "W", "W", "W"], [null, null, null, "W", null, null, null, null, null, null], [null, "W", "W", null, null, null, null, null, "W", null], [null, null, null, null, null, "W", null, "W", "W", "W"], [null, null, null, null, null, null, "W", "W", "W", null], [null, null, null, null, null, null, null, null, "W", null], ["W", "W", "W", "W", null, null, null, null, null, null]], "idx": 5, "rules": "**Core Rules:**\nFill some cells as water so that:\n1. Each region is either empty or filled up to one consistent water level.\n2. If a cell in a region is water, then all cells of that region below it are also water.\n3. Row clues indicate exactly how many water cells are in each row.\n4. Column clues indicate exactly how many water cells are in each column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `region`: region ID grid as list of lists.\n - `row_water_counts`: list from top row to bottom row.\n - `col_water_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'W'` for water cells and `None` for non-water cells.", "ref_observation": {"region": [[0, 0, 0, 1, 1, 1], [0, 2, 2, 3, 3, 1], [0, 0, 2, 2, 3, 1], [4, 0, 0, 3, 3, 3], [4, 5, 5, 5, 5, 3], [4, 4, 5, 5, 5, 5]], "row_water_counts": [3, 1, 5, 2, 1, 4], "col_water_counts": [1, 2, 3, 3, 2, 5]}, "image": "figs/aquarium_5.png", "answer_image": "figs/aquarium_5_answer.png"} {"puzzle": "binairo", "row": 6, "column": 6, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null], ["B", null, null, "W", null, "B"], [null, null, null, null, null, null], [null, null, null, null, "W", null], [null, "W", "W", null, null, "B"], [null, "W", null, "B", null, null]]}, "id": 6, "observation": {"data": [[null, null, null, null, null, null], ["B", null, null, "W", null, "B"], [null, null, null, null, null, null], [null, null, null, null, "W", null], [null, "W", "W", null, null, "B"], [null, "W", null, "B", null, null]]}, "answer": [["W", "B", "B", "W", "B", "W"], ["B", "W", "B", "W", "W", "B"], ["W", "B", "W", "B", "B", "W"], ["W", "B", "B", "W", "W", "B"], ["B", "W", "W", "B", "W", "B"], ["B", "W", "W", "B", "B", "W"]], "idx": 6, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_6.png", "answer_image": "figs/binairo_6_answer.png"} {"puzzle": "binairo", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null], ["W", null, null, null, "W", null], [null, null, "B", null, null, null], ["W", null, null, "W", null, "W"], [null, null, null, null, null, null], ["B", null, null, "W", null, "B"]]}, "id": 7, "observation": {"data": [[null, null, null, null, null, null], ["W", null, null, null, "W", null], [null, null, "B", null, null, null], ["W", null, null, "W", null, "W"], [null, null, null, null, null, null], ["B", null, null, "W", null, "B"]]}, "answer": [["W", "B", "W", "B", "B", "W"], ["W", "B", "W", "B", "W", "B"], ["B", "W", "B", "W", "B", "W"], ["W", "B", "B", "W", "B", "W"], ["B", "W", "W", "B", "W", "B"], ["B", "W", "B", "W", "W", "B"]], "idx": 7, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_7.png", "answer_image": "figs/binairo_7_answer.png"} {"puzzle": "binairo", "row": 8, "column": 8, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, null], [null, null, null, "W", "W", null, null, "B"], ["W", null, "B", null, null, "W", "W", null], ["W", null, null, null, null, "W", null, null], [null, null, null, "B", null, null, null, null], [null, null, "W", null, null, null, "B", null], [null, null, null, null, null, null, null, "B"], [null, null, "W", null, "W", "W", null, null]]}, "id": 8, "observation": {"data": [[null, null, null, null, null, null, null, null], [null, null, null, "W", "W", null, null, "B"], ["W", null, "B", null, null, "W", "W", null], ["W", null, null, null, null, "W", null, null], [null, null, null, "B", null, null, null, null], [null, null, "W", null, null, null, "B", null], [null, null, null, null, null, null, null, "B"], [null, null, "W", null, "W", "W", null, null]]}, "answer": [["B", "W", "W", "B", "W", "B", "B", "W"], ["B", "W", "B", "W", "W", "B", "W", "B"], ["W", "B", "B", "W", "B", "W", "W", "B"], ["W", "B", "W", "B", "B", "W", "B", "W"], ["B", "W", "B", "B", "W", "B", "W", "W"], ["W", "B", "W", "W", "B", "W", "B", "B"], ["W", "W", "B", "W", "B", "B", "W", "B"], ["B", "B", "W", "B", "W", "W", "B", "W"]], "idx": 8, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_8.png", "answer_image": "figs/binairo_8_answer.png"} {"puzzle": "binairo", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[null, null, null, null, null, "W", null, null], ["B", null, "B", null, null, null, null, "B"], ["W", null, null, "W", null, null, null, null], [null, "B", null, null, null, null, null, null], [null, "B", "B", null, null, null, "W", null], [null, null, null, null, null, "B", null, "B"], ["W", null, "B", null, null, null, null, "W"], [null, null, null, "W", null, null, null, null]]}, "id": 9, "observation": {"data": [[null, null, null, null, null, "W", null, null], ["B", null, "B", null, null, null, null, "B"], ["W", null, null, "W", null, null, null, null], [null, "B", null, null, null, null, null, null], [null, "B", "B", null, null, null, "W", null], [null, null, null, null, null, "B", null, "B"], ["W", null, "B", null, null, null, null, "W"], [null, null, null, "W", null, null, null, null]]}, "answer": [["W", "B", "W", "B", "B", "W", "B", "W"], ["B", "W", "B", "W", "W", "B", "W", "B"], ["W", "W", "B", "W", "B", "B", "W", "B"], ["B", "B", "W", "B", "W", "W", "B", "W"], ["W", "B", "B", "W", "B", "W", "W", "B"], ["B", "W", "W", "B", "W", "B", "W", "B"], ["W", "W", "B", "B", "W", "B", "B", "W"], ["B", "B", "W", "W", "B", "W", "B", "W"]], "idx": 9, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_9.png", "answer_image": "figs/binairo_9_answer.png"} {"puzzle": "binairo", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, "W", null, "W", "B", null, null, "W", null], ["B", null, "W", null, null, null, null, "B", null, null], [null, null, null, "B", null, null, "W", null, null, null], ["B", "B", null, null, null, "B", null, null, null, null], [null, null, null, "B", null, null, null, null, null, null], [null, null, null, null, null, null, null, "W", null, "W"], [null, "B", null, "B", null, "B", null, null, null, null], [null, null, "W", null, null, null, "B", null, "W", null], ["B", null, null, null, null, null, null, "B", null, null], ["B", null, null, "B", null, "W", null, null, null, null]]}, "id": 10, "observation": {"data": [[null, null, "W", null, "W", "B", null, null, "W", null], ["B", null, "W", null, null, null, null, "B", null, null], [null, null, null, "B", null, null, "W", null, null, null], ["B", "B", null, null, null, "B", null, null, null, null], [null, null, null, "B", null, null, null, null, null, null], [null, null, null, null, null, null, null, "W", null, "W"], [null, "B", null, "B", null, "B", null, null, null, null], [null, null, "W", null, null, null, "B", null, "W", null], ["B", null, null, null, null, null, null, "B", null, null], ["B", null, null, "B", null, "W", null, null, null, null]]}, "answer": [["W", "B", "W", "B", "W", "B", "W", "B", "W", "B"], ["B", "B", "W", "W", "B", "W", "B", "B", "W", "W"], ["W", "W", "B", "B", "W", "B", "W", "W", "B", "B"], ["B", "B", "W", "W", "B", "B", "W", "W", "B", "W"], ["W", "W", "B", "B", "W", "W", "B", "B", "W", "B"], ["B", "W", "B", "W", "B", "W", "B", "W", "B", "W"], ["W", "B", "W", "B", "W", "B", "W", "W", "B", "B"], ["W", "B", "W", "W", "B", "W", "B", "B", "W", "B"], ["B", "W", "B", "W", "B", "B", "W", "B", "W", "W"], ["B", "W", "B", "B", "W", "W", "B", "W", "B", "W"]], "idx": 10, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_10.png", "answer_image": "figs/binairo_10_answer.png"} {"puzzle": "binairo", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, null, null, null, "W", null, null, null, null], ["W", null, "W", null, null, "W", null, "W", null, null], [null, "B", null, null, null, null, null, "W", null, "W"], ["B", null, null, null, "W", null, null, null, null, null], [null, null, null, null, null, null, null, null, null, "W"], [null, null, "W", "W", null, null, null, null, null, null], ["W", null, null, null, "B", null, null, null, null, null], ["W", "B", null, null, null, null, "W", "B", null, null], [null, null, null, null, "B", null, null, null, null, null], [null, "B", null, "W", null, null, "W", "B", null, null]]}, "id": 11, "observation": {"data": [[null, null, null, null, null, "W", null, null, null, null], ["W", null, "W", null, null, "W", null, "W", null, null], [null, "B", null, null, null, null, null, "W", null, "W"], ["B", null, null, null, "W", null, null, null, null, null], [null, null, null, null, null, null, null, null, null, "W"], [null, null, "W", "W", null, null, null, null, null, null], ["W", null, null, null, "B", null, null, null, null, null], ["W", "B", null, null, null, null, "W", "B", null, null], [null, null, null, null, "B", null, null, null, null, null], [null, "B", null, "W", null, null, "W", "B", null, null]]}, "answer": [["B", "W", "B", "B", "W", "W", "B", "B", "W", "W"], ["W", "B", "W", "B", "W", "W", "B", "W", "B", "B"], ["W", "B", "B", "W", "B", "B", "W", "W", "B", "W"], ["B", "W", "W", "B", "W", "W", "B", "B", "W", "B"], ["W", "W", "B", "B", "W", "B", "W", "B", "B", "W"], ["B", "B", "W", "W", "B", "W", "B", "W", "W", "B"], ["W", "W", "B", "W", "B", "B", "W", "W", "B", "B"], ["W", "B", "W", "B", "W", "B", "W", "B", "B", "W"], ["B", "W", "B", "W", "B", "W", "B", "W", "W", "B"], ["B", "B", "W", "W", "B", "B", "W", "B", "W", "W"]], "idx": 11, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. All rows are pairwise different, and all columns are pairwise different.\n4. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [[null, null, null, null, "W", null], [null, null, null, null, "W", null], [null, "W", "B", null, null, "W"], ["B", null, "B", null, null, "B"], [null, null, null, null, null, null], ["W", null, null, "W", null, "W"]]}, "image": "figs/binairo_11.png", "answer_image": "figs/binairo_11_answer.png"} {"puzzle": "binairoplus", "row": 6, "column": 6, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null], ["W", null, null, null, null, "B"], [null, "B", null, null, "W", null], [null, "W", null, null, "W", null], [null, null, null, null, null, null], ["W", null, null, null, null, "W"]], "horizontal": {"0.0,0.5": "x", "0.0,4.5": "="}, "vertical": {"2.5,0.0": "=", "2.5,5.0": "x", "3.5,2.0": "x", "3.5,3.0": "="}}, "id": 12, "observation": {"data": [[null, null, null, null, null, null], ["W", null, null, null, null, "B"], [null, "B", null, null, "W", null], [null, "W", null, null, "W", null], [null, null, null, null, null, null], ["W", null, null, null, null, "W"]], "horizontal": {"(0.0,0.5)": "x", "(0.0,4.5)": "="}, "vertical": {"(2.5,0.0)": "=", "(2.5,5.0)": "x", "(3.5,2.0)": "x", "(3.5,3.0)": "="}}, "answer": [["B", "W", "B", "B", "W", "W"], ["W", "W", "B", "W", "B", "B"], ["B", "B", "W", "B", "W", "W"], ["B", "W", "B", "W", "W", "B"], ["W", "B", "W", "W", "B", "B"], ["W", "B", "W", "B", "B", "W"]], "idx": 12, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_12.png", "answer_image": "figs/binairoplus_12_answer.png"} {"puzzle": "binairoplus", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[null, "B", "B", "W", "W", null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, "W", "W", "B", "B", null]], "horizontal": {"1.0,2.5": "="}, "vertical": {"0.5,5.0": "x", "2.5,2.0": "x", "2.5,4.0": "=", "2.5,5.0": "=", "3.5,0.0": "x", "4.5,0.0": "x"}}, "id": 13, "observation": {"data": [[null, "B", "B", "W", "W", null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, null, null, null, null, null], [null, "W", "W", "B", "B", null]], "horizontal": {"(1.0,2.5)": "="}, "vertical": {"(0.5,5.0)": "x", "(2.5,2.0)": "x", "(2.5,4.0)": "=", "(2.5,5.0)": "=", "(3.5,0.0)": "x", "(4.5,0.0)": "x"}}, "answer": [["W", "B", "B", "W", "W", "B"], ["B", "B", "W", "W", "B", "W"], ["W", "W", "B", "B", "W", "B"], ["B", "W", "W", "B", "W", "B"], ["W", "B", "B", "W", "B", "W"], ["B", "W", "W", "B", "B", "W"]], "idx": 13, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_13.png", "answer_image": "figs/binairoplus_13_answer.png"} {"puzzle": "binairoplus", "row": 8, "column": 8, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, "B", null, null, "W", null, null], [null, null, null, "W", "B", null, null, null], [null, "W", null, null, null, null, "B", null], [null, "B", null, null, null, null, "B", null], ["W", "W", null, null, null, null, "W", "B"], [null, "B", null, null, null, null, "W", null]], "horizontal": {}, "vertical": {"1.5,1.0": "=", "1.5,6.0": "x", "2.5,1.0": "x", "2.5,6.0": "=", "4.5,2.0": "=", "4.5,3.0": "x", "4.5,4.0": "x", "4.5,5.0": "=", "6.5,3.0": "=", "6.5,4.0": "="}}, "id": 14, "observation": {"data": [[null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, "B", null, null, "W", null, null], [null, null, null, "W", "B", null, null, null], [null, "W", null, null, null, null, "B", null], [null, "B", null, null, null, null, "B", null], ["W", "W", null, null, null, null, "W", "B"], [null, "B", null, null, null, null, "W", null]], "horizontal": {}, "vertical": {"(1.5,1.0)": "=", "(1.5,6.0)": "x", "(2.5,1.0)": "x", "(2.5,6.0)": "=", "(4.5,2.0)": "=", "(4.5,3.0)": "x", "(4.5,4.0)": "x", "(4.5,5.0)": "=", "(6.5,3.0)": "=", "(6.5,4.0)": "="}}, "answer": [["W", "B", "B", "W", "B", "W", "B", "W"], ["B", "W", "W", "B", "W", "B", "B", "W"], ["B", "W", "B", "W", "B", "W", "W", "B"], ["W", "B", "B", "W", "B", "B", "W", "W"], ["B", "W", "W", "B", "W", "W", "B", "B"], ["B", "B", "W", "W", "B", "W", "B", "W"], ["W", "W", "B", "B", "W", "B", "W", "B"], ["W", "B", "W", "B", "W", "B", "W", "B"]], "idx": 14, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_14.png", "answer_image": "figs/binairoplus_14_answer.png"} {"puzzle": "binairoplus", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[null, "B", null, null, null, null, "W", null], [null, "B", null, null, null, null, "W", null], [null, null, "B", null, null, "B", null, null], [null, null, null, null, null, null, null, null], [null, null, null, "W", "B", null, null, null], ["W", null, null, null, null, null, null, "W"], [null, null, null, "B", "W", null, null, null], [null, "W", null, null, null, null, "B", null]], "horizontal": {"5.0,1.5": "="}, "vertical": {"0.5,4.0": "=", "1.5,0.0": "x", "2.5,6.0": "x", "3.5,2.0": "=", "5.5,5.0": "="}}, "id": 15, "observation": {"data": [[null, "B", null, null, null, null, "W", null], [null, "B", null, null, null, null, "W", null], [null, null, "B", null, null, "B", null, null], [null, null, null, null, null, null, null, null], [null, null, null, "W", "B", null, null, null], ["W", null, null, null, null, null, null, "W"], [null, null, null, "B", "W", null, null, null], [null, "W", null, null, null, null, "B", null]], "horizontal": {"(5.0,1.5)": "="}, "vertical": {"(0.5,4.0)": "=", "(1.5,0.0)": "x", "(2.5,6.0)": "x", "(3.5,2.0)": "=", "(5.5,5.0)": "="}}, "answer": [["W", "B", "B", "W", "B", "W", "W", "B"], ["B", "B", "W", "W", "B", "W", "W", "B"], ["W", "W", "B", "B", "W", "B", "B", "W"], ["B", "W", "W", "B", "W", "B", "W", "B"], ["B", "B", "W", "W", "B", "W", "B", "W"], ["W", "B", "B", "W", "W", "B", "B", "W"], ["W", "W", "B", "B", "W", "B", "W", "B"], ["B", "W", "W", "B", "B", "W", "B", "W"]], "idx": 15, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_15.png", "answer_image": "figs/binairoplus_15_answer.png"} {"puzzle": "binairoplus", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, null, null, null], [null, null, "W", null, "B", "W", null, "B", null, null], [null, "B", null, null, null, null, null, null, "B", null], ["B", null, null, null, null, null, null, null, null, "B"], [null, null, "W", null, null, null, null, "W", null, null], [null, null, "B", null, null, null, null, "W", null, null], ["W", null, null, null, null, null, null, null, null, "W"], [null, "W", null, null, null, null, null, null, "W", null], [null, null, "W", null, "W", "B", null, "B", null, null], [null, null, null, null, null, null, null, null, null, null]], "horizontal": {"0.0,2.5": "x", "0.0,6.5": "x", "1.0,0.5": "=", "1.0,8.5": "=", "2.0,3.5": "=", "2.0,5.5": "=", "5.0,3.5": "x", "5.0,5.5": "x", "6.0,3.5": "x", "6.0,5.5": "x", "9.0,1.5": "x", "9.0,3.5": "x", "9.0,5.5": "=", "9.0,7.5": "="}, "vertical": {"0.5,3.0": "x", "0.5,6.0": "x", "2.5,4.0": "=", "2.5,5.0": "=", "4.5,3.0": "x", "4.5,6.0": "=", "5.5,1.0": "=", "5.5,8.0": "=", "7.5,0.0": "x", "7.5,9.0": "="}}, "id": 16, "observation": {"data": [[null, null, null, null, null, null, null, null, null, null], [null, null, "W", null, "B", "W", null, "B", null, null], [null, "B", null, null, null, null, null, null, "B", null], ["B", null, null, null, null, null, null, null, null, "B"], [null, null, "W", null, null, null, null, "W", null, null], [null, null, "B", null, null, null, null, "W", null, null], ["W", null, null, null, null, null, null, null, null, "W"], [null, "W", null, null, null, null, null, null, "W", null], [null, null, "W", null, "W", "B", null, "B", null, null], [null, null, null, null, null, null, null, null, null, null]], "horizontal": {"(0.0,2.5)": "x", "(0.0,6.5)": "x", "(1.0,0.5)": "=", "(1.0,8.5)": "=", "(2.0,3.5)": "=", "(2.0,5.5)": "=", "(5.0,3.5)": "x", "(5.0,5.5)": "x", "(6.0,3.5)": "x", "(6.0,5.5)": "x", "(9.0,1.5)": "x", "(9.0,3.5)": "x", "(9.0,5.5)": "=", "(9.0,7.5)": "="}, "vertical": {"(0.5,3.0)": "x", "(0.5,6.0)": "x", "(2.5,4.0)": "=", "(2.5,5.0)": "=", "(4.5,3.0)": "x", "(4.5,6.0)": "=", "(5.5,1.0)": "=", "(5.5,8.0)": "=", "(7.5,0.0)": "x", "(7.5,9.0)": "="}}, "answer": [["W", "W", "B", "W", "W", "B", "B", "W", "B", "B"], ["B", "B", "W", "B", "B", "W", "W", "B", "W", "W"], ["W", "B", "B", "W", "W", "B", "B", "W", "B", "W"], ["B", "W", "W", "B", "W", "B", "W", "B", "W", "B"], ["B", "W", "W", "B", "B", "W", "B", "W", "W", "B"], ["W", "B", "B", "W", "B", "W", "B", "W", "B", "W"], ["W", "B", "W", "B", "W", "B", "W", "B", "B", "W"], ["B", "W", "B", "W", "B", "W", "B", "W", "W", "B"], ["W", "B", "W", "B", "W", "B", "W", "B", "W", "B"], ["B", "W", "B", "W", "B", "W", "W", "B", "B", "W"]], "idx": 16, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_16.png", "answer_image": "figs/binairoplus_16_answer.png"} {"puzzle": "binairoplus", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, "B", null, null, null, null, null, null, null], ["B", null, null, null, null, null, "B", null, null, null], ["W", null, null, null, null, "B", "W", null, null, "W"], ["W", null, null, null, null, null, null, null, null, "B"], [null, null, null, null, "B", null, null, null, null, null], [null, null, null, null, null, "B", null, null, null, null], ["W", null, null, null, null, null, null, null, null, "B"], ["B", null, null, "B", "W", null, null, null, null, "W"], [null, null, null, "B", null, null, null, null, null, "W"], [null, null, null, null, null, null, null, "B", null, null]], "horizontal": {"0.0,7.5": "=", "1.0,7.5": "x", "4.0,0.5": "=", "4.0,6.5": "x", "4.0,8.5": "=", "9.0,1.5": "x"}, "vertical": {"0.5,3.0": "x", "0.5,5.0": "x", "1.5,3.0": "=", "1.5,7.0": "=", "2.5,2.0": "=", "3.5,3.0": "x", "5.5,3.0": "x", "5.5,8.0": "=", "6.5,8.0": "x"}}, "id": 17, "observation": {"data": [[null, null, "B", null, null, null, null, null, null, null], ["B", null, null, null, null, null, "B", null, null, null], ["W", null, null, null, null, "B", "W", null, null, "W"], ["W", null, null, null, null, null, null, null, null, "B"], [null, null, null, null, "B", null, null, null, null, null], [null, null, null, null, null, "B", null, null, null, null], ["W", null, null, null, null, null, null, null, null, "B"], ["B", null, null, "B", "W", null, null, null, null, "W"], [null, null, null, "B", null, null, null, null, null, "W"], [null, null, null, null, null, null, null, "B", null, null]], "horizontal": {"(0.0,7.5)": "=", "(1.0,7.5)": "x", "(4.0,0.5)": "=", "(4.0,6.5)": "x", "(4.0,8.5)": "=", "(9.0,1.5)": "x"}, "vertical": {"(0.5,3.0)": "x", "(0.5,5.0)": "x", "(1.5,3.0)": "=", "(1.5,7.0)": "=", "(2.5,2.0)": "=", "(3.5,3.0)": "x", "(5.5,3.0)": "x", "(5.5,8.0)": "=", "(6.5,8.0)": "x"}}, "answer": [["W", "W", "B", "B", "W", "B", "B", "W", "W", "B"], ["B", "B", "W", "W", "B", "W", "B", "B", "W", "W"], ["W", "B", "B", "W", "W", "B", "W", "B", "B", "W"], ["W", "W", "B", "B", "W", "W", "B", "W", "B", "B"], ["B", "B", "W", "W", "B", "B", "W", "B", "W", "W"], ["B", "W", "W", "B", "W", "B", "W", "W", "B", "B"], ["W", "W", "B", "W", "B", "W", "B", "W", "B", "B"], ["B", "B", "W", "B", "W", "B", "W", "B", "W", "W"], ["W", "B", "W", "B", "B", "W", "B", "W", "B", "W"], ["B", "W", "B", "W", "B", "W", "W", "B", "W", "B"]], "idx": 17, "rules": "**Core Rules:**\nFill every cell with `B` or `W` so that:\n1. Each row and each column contain the same number of black and white cells.\n2. No row or column has three consecutive cells of the same color.\n3. A `=` constraint means the two adjacent cells are the same color.\n4. A `x` constraint means the two adjacent cells are different colors.\n5. Given cells must stay fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `data`: initial grid as list of lists using `'B'`, `'W'`, or `None`.\n - `horizontal`: dict `{'(row, col+0.5)': '=' or 'x'}` for constraints between left-right neighbors.\n - `vertical`: dict `{'(row+0.5, col)': '=' or 'x'}` for constraints between up-down neighbors.\n4. **Answer:** full solved grid as list of lists using `'B'` / `'W'`.", "ref_observation": {"data": [["W", null, null, null, null, null], ["W", null, null, null, null, null], [null, "W", null, "B", null, null], [null, null, "B", null, "W", null], [null, null, null, null, null, "W"], [null, null, null, null, null, "W"]], "horizontal": {"(2.0,4.5)": "=", "(3.0,0.5)": "x"}, "vertical": {"(0.5,1.0)": "=", "(0.5,3.0)": "=", "(2.5,0.0)": "=", "(2.5,5.0)": "x", "(4.5,2.0)": "=", "(4.5,4.0)": "="}}, "image": "figs/binairoplus_17.png", "answer_image": "figs/binairoplus_17_answer.png"} {"puzzle": "futoshiki", "row": 4, "column": 4, "level": "easy", "original_data": {"data": [[null, null, null, null], [null, null, null, null], [null, null, null, null], [null, null, null, null]], "horizontal": {"0.0,1.5": "<", "0.0,2.5": ">"}, "vertical": {"1.5,1.0": "v", "2.5,0.0": "v", "2.5,1.0": "v", "2.5,3.0": "v"}}, "id": 18, "observation": {"data": [[null, null, null, null], [null, null, null, null], [null, null, null, null], [null, null, null, null]], "horizontal": {"(0,1.5)": "<", "(0,2.5)": ">"}, "vertical": {"(1.5,1)": "v", "(2.5,0)": "v", "(2.5,1)": "v", "(2.5,3)": "v"}}, "answer": [[4, 1, 3, 2], [3, 4, 2, 1], [2, 3, 1, 4], [1, 2, 4, 3]], "idx": 18, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_18.png", "answer_image": "figs/futoshiki_18_answer.png"} {"puzzle": "futoshiki", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[null, null, null, 1, 5], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null]], "horizontal": {"0.0,0.5": ">", "0.0,1.5": ">", "1.0,0.5": "<", "2.0,1.5": "<", "2.0,3.5": "<", "3.0,0.5": "<"}, "vertical": {"2.5,3.0": "v", "3.5,4.0": "v"}}, "id": 19, "observation": {"data": [[null, null, null, 1, 5], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null]], "horizontal": {"(0,0.5)": ">", "(0,1.5)": ">", "(1,0.5)": "<", "(2,1.5)": "<", "(2,3.5)": "<", "(3,0.5)": "<"}, "vertical": {"(2.5,3)": "v", "(3.5,4)": "v"}}, "answer": [[4, 3, 2, 1, 5], [3, 4, 1, 5, 2], [2, 1, 5, 3, 4], [1, 5, 4, 2, 3], [5, 2, 3, 4, 1]], "idx": 19, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_19.png", "answer_image": "figs/futoshiki_19_answer.png"} {"puzzle": "futoshiki", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, null, null], [null, 3, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null]], "horizontal": {"0.0,0.5": ">", "0.0,3.5": "<", "1.0,0.5": "<", "1.0,2.5": "<", "3.0,1.5": "<", "3.0,2.5": ">", "4.0,1.5": "<"}, "vertical": {"1.5,0.0": "v", "2.5,2.0": "v"}}, "id": 20, "observation": {"data": [[null, null, null, null, null], [null, 3, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null]], "horizontal": {"(0,0.5)": ">", "(0,3.5)": "<", "(1,0.5)": "<", "(1,2.5)": "<", "(3,1.5)": "<", "(3,2.5)": ">", "(4,1.5)": "<"}, "vertical": {"(1.5,0)": "v", "(2.5,2)": "v"}}, "answer": [[5, 4, 2, 1, 3], [2, 3, 1, 5, 4], [1, 5, 4, 3, 2], [4, 1, 3, 2, 5], [3, 2, 5, 4, 1]], "idx": 20, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_20.png", "answer_image": "figs/futoshiki_20_answer.png"} {"puzzle": "futoshiki", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [1, null, null, null, null], [5, null, null, null, null]], "horizontal": {"0.0,0.5": "<", "0.0,1.5": "<", "2.0,1.5": "<", "2.0,3.5": ">", "4.0,3.5": ">"}, "vertical": {"0.5,1.0": "^", "1.5,0.0": "^", "1.5,4.0": "^", "2.5,2.0": "^", "3.5,3.0": "^"}}, "id": 21, "observation": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [1, null, null, null, null], [5, null, null, null, null]], "horizontal": {"(0,0.5)": "<", "(0,1.5)": "<", "(2,1.5)": "<", "(2,3.5)": ">", "(4,3.5)": ">"}, "vertical": {"(0.5,1)": "^", "(1.5,0)": "^", "(1.5,4)": "^", "(2.5,2)": "^", "(3.5,3)": "^"}}, "answer": [[2, 3, 5, 1, 4], [3, 5, 1, 4, 2], [4, 1, 2, 5, 3], [1, 4, 3, 2, 5], [5, 2, 4, 3, 1]], "idx": 21, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_21.png", "answer_image": "figs/futoshiki_21_answer.png"} {"puzzle": "futoshiki", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 7, null, null, null], [null, null, 4, null, null, null, 7]], "horizontal": {"0.0,1.5": "<", "0.0,3.5": ">", "1.0,3.5": ">", "4.0,0.5": ">", "4.0,5.5": ">", "6.0,2.5": "<", "6.0,3.5": ">", "6.0,4.5": ">"}, "vertical": {"0.5,1.0": "v", "0.5,2.0": "^", "0.5,5.0": "^", "1.5,6.0": "^", "2.5,2.0": "^", "2.5,6.0": "^", "4.5,1.0": "v", "4.5,2.0": "v", "4.5,6.0": "v", "5.5,2.0": "v", "4.5,5.0": "^", "5.5,0.0": "^"}}, "id": 22, "observation": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 7, null, null, null], [null, null, 4, null, null, null, 7]], "horizontal": {"(0,1.5)": "<", "(0,3.5)": ">", "(1,3.5)": ">", "(4,0.5)": ">", "(4,5.5)": ">", "(6,2.5)": "<", "(6,3.5)": ">", "(6,4.5)": ">"}, "vertical": {"(0.5,1)": "v", "(0.5,2)": "^", "(0.5,5)": "^", "(1.5,6)": "^", "(2.5,2)": "^", "(2.5,6)": "^", "(4.5,1)": "v", "(4.5,2)": "v", "(4.5,6)": "v", "(5.5,2)": "v", "(4.5,5)": "^", "(5.5,0)": "^"}}, "answer": [[7, 2, 3, 6, 5, 4, 1], [5, 1, 6, 3, 2, 7, 4], [3, 7, 1, 4, 6, 2, 5], [4, 5, 2, 1, 7, 3, 6], [6, 4, 7, 2, 1, 5, 3], [1, 3, 5, 7, 4, 6, 2], [2, 6, 4, 5, 3, 1, 7]], "idx": 22, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_22.png", "answer_image": "figs/futoshiki_22_answer.png"} {"puzzle": "futoshiki", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, 4, null, null, null, 6, null], [null, null, null, null, null, null, null], [null, null, 4, null, null, null, 6], [null, null, null, null, null, null, 4], [null, null, 3, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null]], "horizontal": {"0.0,0.5": ">", "0.0,3.5": "<", "1.0,1.5": ">", "2.0,0.5": "<", "3.0,0.5": ">", "3.0,1.5": ">", "5.0,0.5": ">", "5.0,1.5": ">", "5.0,4.5": "<", "5.0,5.5": "<"}, "vertical": {"1.5,6.0": "v", "2.5,2.0": "v", "4.5,4.0": "^"}}, "id": 23, "observation": {"data": [[null, 4, null, null, null, 6, null], [null, null, null, null, null, null, null], [null, null, 4, null, null, null, 6], [null, null, null, null, null, null, 4], [null, null, 3, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null]], "horizontal": {"(0,0.5)": ">", "(0,3.5)": "<", "(1,1.5)": ">", "(2,0.5)": "<", "(3,0.5)": ">", "(3,1.5)": ">", "(5,0.5)": ">", "(5,1.5)": ">", "(5,4.5)": "<", "(5,5.5)": "<"}, "vertical": {"(1.5,6)": "v", "(2.5,2)": "v", "(4.5,4)": "^"}}, "answer": [[5, 4, 7, 2, 3, 6, 1], [3, 6, 5, 1, 4, 2, 7], [1, 2, 4, 5, 7, 3, 6], [7, 5, 2, 3, 6, 1, 4], [4, 7, 3, 6, 1, 5, 2], [6, 3, 1, 7, 2, 4, 5], [2, 1, 6, 4, 5, 7, 3]], "idx": 23, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_23.png", "answer_image": "figs/futoshiki_23_answer.png"} {"puzzle": "futoshiki", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, 4, null, null]], "horizontal": {"0.0,1.5": ">", "0.0,3.5": ">", "0.0,5.5": ">", "1.0,0.5": ">", "1.0,2.5": ">", "1.0,3.5": ">", "2.0,3.5": ">", "3.0,3.5": ">", "3.0,5.5": ">", "4.0,0.5": ">", "4.0,1.5": "<", "4.0,3.5": ">", "4.0,4.5": ">", "5.0,2.5": ">", "6.0,1.5": "<"}, "vertical": {"0.5,0.0": "v", "0.5,4.0": "v", "0.5,1.0": "^", "1.5,6.0": "v", "2.5,1.0": "v", "2.5,2.0": "v", "3.5,0.0": "v", "3.5,1.0": "v", "4.5,1.0": "v", "4.5,5.0": "v", "5.5,5.0": "^", "5.5,6.0": "^"}}, "id": 24, "observation": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, 4, null, null]], "horizontal": {"(0,1.5)": ">", "(0,3.5)": ">", "(0,5.5)": ">", "(1,0.5)": ">", "(1,2.5)": ">", "(1,3.5)": ">", "(2,3.5)": ">", "(3,3.5)": ">", "(3,5.5)": ">", "(4,0.5)": ">", "(4,1.5)": "<", "(4,3.5)": ">", "(4,4.5)": ">", "(5,2.5)": ">", "(6,1.5)": "<"}, "vertical": {"(0.5,0)": "v", "(0.5,4)": "v", "(0.5,1)": "^", "(1.5,6)": "v", "(2.5,1)": "v", "(2.5,2)": "v", "(3.5,0)": "v", "(3.5,1)": "v", "(4.5,1)": "v", "(4.5,5)": "v", "(5.5,5)": "^", "(5.5,6)": "^"}}, "answer": [[7, 4, 1, 5, 3, 6, 2], [6, 5, 4, 3, 2, 1, 7], [1, 7, 3, 6, 5, 2, 4], [5, 6, 2, 4, 1, 7, 3], [3, 2, 5, 7, 6, 4, 1], [4, 1, 6, 2, 7, 3, 5], [2, 3, 7, 1, 4, 5, 6]], "idx": 24, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_24.png", "answer_image": "figs/futoshiki_24_answer.png"} {"puzzle": "futoshiki", "row": 9, "column": 9, "level": "easy", "original_data": {"data": [[null, null, 8, null, null, null, 4, null, null], [1, null, null, null, null, null, null, null, 2], [null, null, null, null, null, null, null, null, null], [6, null, 3, null, null, 8, null, null, null], [null, null, 4, null, null, 1, null, null, null], [null, null, null, null, null, null, null, 4, 5], [null, null, null, null, null, null, 6, null, 9], [null, null, 7, null, null, null, 2, 6, null], [null, null, null, null, null, null, null, null, null]], "horizontal": {"1.0,5.5": "<", "2.0,1.5": ">", "2.0,7.5": "<", "3.0,4.5": "<", "3.0,7.5": "<", "4.0,6.5": ">", "5.0,5.5": "<", "6.0,0.5": "<", "6.0,3.5": "<", "7.0,0.5": "<", "7.0,1.5": ">", "8.0,6.5": ">"}, "vertical": {"0.5,8.0": "v", "1.5,1.0": "v", "0.5,2.0": "^", "0.5,4.0": "^", "2.5,2.0": "v", "2.5,6.0": "v", "2.5,7.0": "v", "2.5,0.0": "^", "3.5,0.0": "v", "2.5,5.0": "^", "3.5,3.0": "^", "4.5,1.0": "^", "4.5,2.0": "^", "4.5,8.0": "^", "6.5,5.0": "v"}}, "id": 25, "observation": {"data": [[null, null, 8, null, null, null, 4, null, null], [1, null, null, null, null, null, null, null, 2], [null, null, null, null, null, null, null, null, null], [6, null, 3, null, null, 8, null, null, null], [null, null, 4, null, null, 1, null, null, null], [null, null, null, null, null, null, null, 4, 5], [null, null, null, null, null, null, 6, null, 9], [null, null, 7, null, null, null, 2, 6, null], [null, null, null, null, null, null, null, null, null]], "horizontal": {"(1,5.5)": "<", "(2,1.5)": ">", "(2,7.5)": "<", "(3,4.5)": "<", "(3,7.5)": "<", "(4,6.5)": ">", "(5,5.5)": "<", "(6,0.5)": "<", "(6,3.5)": "<", "(7,0.5)": "<", "(7,1.5)": ">", "(8,6.5)": ">"}, "vertical": {"(0.5,8)": "v", "(1.5,1)": "v", "(0.5,2)": "^", "(0.5,4)": "^", "(2.5,2)": "v", "(2.5,6)": "v", "(2.5,7)": "v", "(2.5,0)": "^", "(3.5,0)": "v", "(2.5,5)": "^", "(3.5,3)": "^", "(4.5,1)": "^", "(4.5,2)": "^", "(4.5,8)": "^", "(6.5,5)": "v"}}, "answer": [[7, 1, 8, 2, 3, 5, 4, 9, 6], [1, 7, 9, 3, 4, 6, 8, 5, 2], [2, 6, 5, 1, 9, 4, 3, 7, 8], [6, 9, 3, 5, 7, 8, 1, 2, 4], [5, 2, 4, 7, 6, 1, 9, 8, 3], [9, 3, 6, 8, 1, 2, 7, 4, 5], [3, 5, 2, 4, 8, 7, 6, 1, 9], [4, 8, 7, 9, 5, 3, 2, 6, 1], [8, 4, 1, 6, 2, 9, 5, 3, 7]], "idx": 25, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_25.png", "answer_image": "figs/futoshiki_25_answer.png"} {"puzzle": "futoshiki", "row": 9, "column": 9, "level": "normal", "original_data": {"data": [[8, 3, null, null, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 5, null, null], [null, null, null, null, null, null, null, null, 3], [null, null, null, null, null, null, null, null, null]], "horizontal": {"0.0,2.5": ">", "0.0,3.5": ">", "1.0,0.5": "<", "1.0,6.5": ">", "2.0,2.5": "<", "3.0,1.5": "<", "3.0,2.5": "<", "3.0,6.5": ">", "4.0,1.5": ">", "4.0,3.5": "<", "4.0,7.5": ">", "5.0,2.5": "<", "5.0,5.5": ">", "5.0,7.5": ">", "6.0,5.5": ">", "8.0,0.5": ">", "8.0,3.5": ">", "8.0,6.5": "<", "8.0,7.5": "<"}, "vertical": {"0.5,2.0": "^", "0.5,6.0": "^", "0.5,8.0": "^", "1.5,6.0": "^", "2.5,6.0": "v", "1.5,8.0": "^", "2.5,0.0": "^", "3.5,0.0": "v", "2.5,1.0": "^", "2.5,4.0": "^", "3.5,4.0": "v", "2.5,7.0": "^", "3.5,7.0": "v", "2.5,8.0": "^", "3.5,3.0": "^", "4.5,1.0": "^", "5.5,0.0": "^", "5.5,1.0": "^", "5.5,7.0": "^", "6.5,0.0": "^", "6.5,2.0": "^", "6.5,5.0": "^", "6.5,7.0": "^", "7.5,7.0": "v", "7.5,6.0": "^"}}, "id": 26, "observation": {"data": [[8, 3, null, null, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 5, null, null], [null, null, null, null, null, null, null, null, 3], [null, null, null, null, null, null, null, null, null]], "horizontal": {"(0,2.5)": ">", "(0,3.5)": ">", "(1,0.5)": "<", "(1,6.5)": ">", "(2,2.5)": "<", "(3,1.5)": "<", "(3,2.5)": "<", "(3,6.5)": ">", "(4,1.5)": ">", "(4,3.5)": "<", "(4,7.5)": ">", "(5,2.5)": "<", "(5,5.5)": ">", "(5,7.5)": ">", "(6,5.5)": ">", "(8,0.5)": ">", "(8,3.5)": ">", "(8,6.5)": "<", "(8,7.5)": "<"}, "vertical": {"(0.5,2)": "^", "(0.5,6)": "^", "(0.5,8)": "^", "(1.5,6)": "^", "(2.5,6)": "v", "(1.5,8)": "^", "(2.5,0)": "^", "(3.5,0)": "v", "(2.5,1)": "^", "(2.5,4)": "^", "(3.5,4)": "v", "(2.5,7)": "^", "(3.5,7)": "v", "(2.5,8)": "^", "(3.5,3)": "^", "(4.5,1)": "^", "(5.5,0)": "^", "(5.5,1)": "^", "(5.5,7)": "^", "(6.5,0)": "^", "(6.5,2)": "^", "(6.5,5)": "^", "(6.5,7)": "^", "(7.5,7)": "v", "(7.5,6)": "^"}}, "answer": [[8, 3, 7, 5, 2, 6, 1, 9, 4], [2, 6, 9, 8, 3, 4, 7, 1, 5], [7, 1, 4, 9, 5, 3, 8, 2, 6], [9, 2, 3, 4, 8, 1, 6, 5, 7], [5, 4, 2, 6, 7, 8, 9, 3, 1], [1, 8, 6, 7, 9, 5, 3, 4, 2], [3, 9, 1, 2, 4, 7, 5, 6, 8], [4, 7, 5, 1, 6, 9, 2, 8, 3], [6, 5, 8, 3, 1, 2, 4, 7, 9]], "idx": 26, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_26.png", "answer_image": "figs/futoshiki_26_answer.png"} {"puzzle": "futoshiki", "row": 9, "column": 9, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 8, null, null], [null, null, 6, null, 3, null, null, null, null], [null, null, null, null, null, null, 5, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, 5, null, 8, 6], [null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, null]], "horizontal": {"0.0,0.5": ">", "0.0,3.5": ">", "1.0,3.5": ">", "2.0,3.5": "<", "3.0,0.5": "<", "3.0,2.5": ">", "3.0,3.5": ">", "3.0,4.5": ">", "4.0,5.5": ">", "5.0,0.5": ">", "6.0,5.5": "<", "7.0,1.5": "<", "7.0,3.5": "<", "8.0,4.5": ">", "8.0,6.5": ">", "8.0,7.5": ">"}, "vertical": {"1.5,0.0": "v", "0.5,2.0": "^", "0.5,4.0": "^", "0.5,7.0": "^", "0.5,8.0": "^", "1.5,2.0": "^", "1.5,7.0": "^", "2.5,0.0": "^", "3.5,3.0": "v", "2.5,7.0": "^", "4.5,2.0": "v", "4.5,4.0": "v", "3.5,6.0": "^", "3.5,7.0": "^", "4.5,8.0": "v", "4.5,7.0": "^", "5.5,4.0": "^", "6.5,8.0": "v", "7.5,0.0": "v", "7.5,8.0": "v", "7.5,1.0": "^"}}, "id": 27, "observation": {"data": [[null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 8, null, null], [null, null, 6, null, 3, null, null, null, null], [null, null, null, null, null, null, 5, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, 5, null, 8, 6], [null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, null]], "horizontal": {"(0,0.5)": ">", "(0,3.5)": ">", "(1,3.5)": ">", "(2,3.5)": "<", "(3,0.5)": "<", "(3,2.5)": ">", "(3,3.5)": ">", "(3,4.5)": ">", "(4,5.5)": ">", "(5,0.5)": ">", "(6,5.5)": "<", "(7,1.5)": "<", "(7,3.5)": "<", "(8,4.5)": ">", "(8,6.5)": ">", "(8,7.5)": ">"}, "vertical": {"(1.5,0)": "v", "(0.5,2)": "^", "(0.5,4)": "^", "(0.5,7)": "^", "(0.5,8)": "^", "(1.5,2)": "^", "(1.5,7)": "^", "(2.5,0)": "^", "(3.5,3)": "v", "(2.5,7)": "^", "(4.5,2)": "v", "(4.5,4)": "v", "(3.5,6)": "^", "(3.5,7)": "^", "(4.5,8)": "v", "(4.5,7)": "^", "(5.5,4)": "^", "(6.5,8)": "v", "(7.5,0)": "v", "(7.5,8)": "v", "(7.5,1)": "^"}}, "answer": [[8, 7, 3, 6, 5, 9, 4, 1, 2], [6, 1, 4, 9, 7, 3, 8, 2, 5], [4, 9, 6, 2, 3, 7, 1, 5, 8], [7, 8, 9, 4, 2, 1, 5, 6, 3], [1, 2, 5, 3, 4, 8, 6, 7, 9], [9, 4, 2, 7, 1, 5, 3, 8, 6], [2, 5, 1, 8, 6, 4, 9, 3, 7], [5, 3, 7, 1, 8, 6, 2, 9, 4], [3, 6, 8, 5, 9, 2, 7, 4, 1]], "idx": 27, "rules": "**Core Rules:**\nThe numbers are from 1 to the size of the grid (e.g. 1..5 for a 5x5 puzzle).\nEach row and column must contain each number exactly once.\nThe numbers must satisfy all inequality signs.\n\n**Coordinates & Output:**\n1. Cell centers are at integer coordinates `(row, col)`.\n2. Horizontal inequalities are stored at `(row, col+0.5)` with symbols `<` or `>`.\n3. Vertical inequalities are stored at `(row+0.5, col)` with symbols `^` or `v`.\n4. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n5. **Observation:** a dictionary with:\n - `data`: `N x N` 2D list (givens are ints, empty cells are `None`)\n - `horizontal`: dict `{'(row, col+0.5)': '<' or '>'}`\n - `vertical`: dict `{'(row+0.5, col)': '^' or 'v'}`\n6. **Answer:** full solved `N x N` 2D list.", "ref_observation": {"data": [[null, null, null, 4], [null, null, null, null], [null, null, 2, null], [3, null, null, 1]], "horizontal": {}, "vertical": {"(0.5,2)": "^", "(1.5,1)": "^"}}, "image": "figs/futoshiki_27.png", "answer_image": "figs/futoshiki_27_answer.png"} {"puzzle": "hashi", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, 2, null, 3, null, 1, null], [2, null, null, null, null, null, null], [null, null, null, null, 4, null, 4], [null, null, null, null, null, null, null], [null, 1, null, null, null, null, null], [null, null, null, null, 2, null, null], [3, null, null, 3, null, null, 3]]}, "id": 28, "observation": {"data": [[null, 2, null, 3, null, 1, null], [2, null, null, null, null, null, null], [null, null, null, null, 4, null, 4], [null, null, null, null, null, null, null], [null, 1, null, null, null, null, null], [null, null, null, null, 2, null, null], [3, null, null, 3, null, null, 3]]}, "answer": {"((0, 1),(0, 3))": 1, "((0, 1),(4, 1))": 1, "((0, 3),(0, 5))": 1, "((0, 3),(6, 3))": 1, "((1, 0),(6, 0))": 2, "((2, 4),(2, 6))": 2, "((2, 4),(5, 4))": 2, "((2, 6),(6, 6))": 2, "((6, 0),(6, 3))": 1, "((6, 3),(6, 6))": 1}, "idx": 28, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_28.png", "answer_image": "figs/hashi_28_answer.png"} {"puzzle": "hashi", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, 1, null, null, null, null, 3], [2, null, null, 1, null, 2, null], [null, null, null, null, null, null, 3], [5, null, null, null, null, 3, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, 3, null, null, 2]]}, "id": 29, "observation": {"data": [[null, 1, null, null, null, null, 3], [2, null, null, 1, null, 2, null], [null, null, null, null, null, null, 3], [5, null, null, null, null, 3, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, 3, null, null, 2]]}, "answer": {"((0, 1),(0, 6))": 1, "((0, 6),(2, 6))": 2, "((1, 0),(3, 0))": 2, "((1, 3),(1, 5))": 1, "((1, 5),(3, 5))": 1, "((2, 6),(4, 6))": 1, "((3, 0),(3, 5))": 1, "((3, 0),(6, 0))": 2, "((3, 5),(5, 5))": 1, "((4, 6),(6, 6))": 1, "((5, 2),(5, 5))": 1, "((6, 0),(6, 3))": 2, "((6, 3),(6, 6))": 1}, "idx": 29, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_29.png", "answer_image": "figs/hashi_29_answer.png"} {"puzzle": "hashi", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[2, null, null, null, null, null, 2], [null, null, null, null, null, null, null], [null, 1, null, null, null, null, 2], [null, null, null, null, null, null, null], [5, null, null, null, null, null, 3], [null, null, null, null, null, null, null], [4, null, null, null, 3, null, 2]]}, "id": 30, "observation": {"data": [[2, null, null, null, null, null, 2], [null, null, null, null, null, null, null], [null, 1, null, null, null, null, 2], [null, null, null, null, null, null, null], [5, null, null, null, null, null, 3], [null, null, null, null, null, null, null], [4, null, null, null, 3, null, 2]]}, "answer": {"((0, 0),(0, 6))": 1, "((0, 0),(4, 0))": 1, "((0, 6),(2, 6))": 1, "((2, 1),(2, 6))": 1, "((4, 0),(4, 6))": 2, "((4, 0),(6, 0))": 2, "((4, 6),(6, 6))": 1, "((6, 0),(6, 4))": 2, "((6, 4),(6, 6))": 1}, "idx": 30, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_30.png", "answer_image": "figs/hashi_30_answer.png"} {"puzzle": "hashi", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, 2, null, null, null, null, null, null, 3], [1, null, null, 1, null, null, null, 3, null, null], [null, null, null, null, null, null, null, null, null, null], [3, null, 4, null, null, null, null, 3, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, 1, null, null, null], [5, null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [4, null, null, 3, null, null, 1, null, null, 2], [null, null, null, null, null, null, null, null, 1, null]]}, "id": 31, "observation": {"data": [[null, null, 2, null, null, null, null, null, null, 3], [1, null, null, 1, null, null, null, 3, null, null], [null, null, null, null, null, null, null, null, null, null], [3, null, 4, null, null, null, null, 3, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, 1, null, null, null], [5, null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [4, null, null, 3, null, null, 1, null, null, 2], [null, null, null, null, null, null, null, null, 1, null]]}, "answer": {"((0, 2),(0, 9))": 1, "((0, 2),(3, 2))": 1, "((0, 9),(8, 9))": 2, "((1, 0),(3, 0))": 1, "((1, 3),(1, 7))": 1, "((1, 7),(3, 7))": 2, "((3, 0),(3, 2))": 1, "((3, 0),(6, 0))": 1, "((3, 2),(3, 7))": 1, "((3, 2),(5, 2))": 1, "((5, 2),(5, 6))": 1, "((6, 0),(6, 8))": 2, "((6, 0),(8, 0))": 2, "((6, 8),(9, 8))": 1, "((8, 0),(8, 3))": 2, "((8, 3),(8, 6))": 1}, "idx": 31, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_31.png", "answer_image": "figs/hashi_31_answer.png"} {"puzzle": "hashi", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, 3, null, 6, null, null, null, null, null, 4], [null, null, null, null, null, 2, null, null, null, null], [null, null, null, null, null, null, null, 3, null, 5], [null, 4, null, 6, null, 5, null, null, null, null], [null, null, null, null, null, null, null, null, null, 3], [1, null, null, 2, null, null, null, 1, null, null], [null, 5, null, null, null, 5, null, null, null, 4], [null, null, null, null, null, null, null, 2, null, null], [null, 3, null, 1, null, null, null, null, null, 1], [2, null, null, null, null, 4, null, 4, null, null]]}, "id": 32, "observation": {"data": [[null, 3, null, 6, null, null, null, null, null, 4], [null, null, null, null, null, 2, null, null, null, null], [null, null, null, null, null, null, null, 3, null, 5], [null, 4, null, 6, null, 5, null, null, null, null], [null, null, null, null, null, null, null, null, null, 3], [1, null, null, 2, null, null, null, 1, null, null], [null, 5, null, null, null, 5, null, null, null, 4], [null, null, null, null, null, null, null, 2, null, null], [null, 3, null, 1, null, null, null, null, null, 1], [2, null, null, null, null, 4, null, 4, null, null]]}, "answer": {"((0, 1),(0, 3))": 2, "((0, 1),(3, 1))": 1, "((0, 3),(0, 9))": 2, "((0, 3),(3, 3))": 2, "((0, 9),(2, 9))": 2, "((1, 5),(3, 5))": 2, "((2, 7),(2, 9))": 2, "((2, 7),(5, 7))": 1, "((2, 9),(4, 9))": 1, "((3, 1),(3, 3))": 1, "((3, 1),(6, 1))": 2, "((3, 3),(3, 5))": 1, "((3, 3),(5, 3))": 2, "((3, 5),(6, 5))": 2, "((4, 9),(6, 9))": 2, "((5, 0),(9, 0))": 1, "((6, 1),(6, 5))": 1, "((6, 1),(8, 1))": 2, "((6, 5),(6, 9))": 1, "((6, 5),(9, 5))": 1, "((6, 9),(8, 9))": 1, "((7, 7),(9, 7))": 2, "((8, 1),(8, 3))": 1, "((9, 0),(9, 5))": 1, "((9, 5),(9, 7))": 2}, "idx": 32, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_32.png", "answer_image": "figs/hashi_32_answer.png"} {"puzzle": "hashi", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, 3, null, null, null, null, null, null, 2], [2, null, null, null, null, null, null, null, null, null], [null, null, 4, null, null, 4, null, 2, null, null], [3, null, null, null, null, null, null, null, null, 4], [null, 1, null, 2, null, null, 2, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [3, null, null, 4, null, null, null, null, 2, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [2, null, null, null, null, null, null, null, null, 3]]}, "id": 33, "observation": {"data": [[null, null, 3, null, null, null, null, null, null, 2], [2, null, null, null, null, null, null, null, null, null], [null, null, 4, null, null, 4, null, 2, null, null], [3, null, null, null, null, null, null, null, null, 4], [null, 1, null, 2, null, null, 2, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [3, null, null, 4, null, null, null, null, 2, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [2, null, null, null, null, null, null, null, null, 3]]}, "answer": {"((0, 2),(0, 9))": 1, "((0, 2),(2, 2))": 2, "((0, 9),(3, 9))": 1, "((1, 0),(3, 0))": 2, "((2, 2),(2, 5))": 2, "((2, 5),(2, 7))": 2, "((3, 0),(3, 9))": 1, "((3, 9),(9, 9))": 2, "((4, 1),(4, 3))": 1, "((4, 3),(6, 3))": 1, "((4, 6),(4, 8))": 2, "((4, 8),(6, 8))": 1, "((6, 0),(6, 3))": 2, "((6, 0),(9, 0))": 1, "((6, 3),(6, 8))": 1, "((9, 0),(9, 9))": 1}, "idx": 33, "rules": "**Core Rules:**\nConnect numbered islands with bridges so that:\n1. Bridges are straight and orthogonal, connecting two distinct islands.\n2. Bridges cannot cross other bridges or pass through islands.\n3. At most two bridges may connect the same pair of islands.\n4. The number on each island equals the total number of incident bridges.\n5. All islands must belong to one connected network.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: island layout as `N x N` 2D list (`int` for islands, `None` otherwise).\n4. **Answer:** dictionary `{((r1, c1), (r2, c2)): count}` where `count` is `1` or `2`.", "ref_observation": {"data": [[4, null, null, null, 3, null, 2], [null, null, 1, null, null, 3, null], [null, null, null, null, null, null, 3], [6, null, null, null, null, 5, null], [null, null, null, null, null, null, 2], [null, null, 1, null, null, 2, null], [4, null, null, null, null, null, 2]]}, "image": "figs/hashi_33.png", "answer_image": "figs/hashi_33_answer.png"} {"puzzle": "heyawake", "row": 6, "column": 6, "level": "easy", "original_data": {"region": [[0, 0, 0, 1, 2, 2], [3, 3, 4, 1, 5, 6], [3, 3, 4, 7, 5, 6], [3, 3, 8, 8, 5, 6], [3, 3, 8, 8, 9, 9], [3, 3, 10, 10, 10, 10]], "data": [[null, null, null, null, 1, null], [3, null, 0, null, 1, null], [null, null, null, 1, null, null], [null, null, 1, null, null, null], [null, null, null, null, 1, null], [null, null, 1, null, null, null]]}, "id": 34, "observation": {"region": [[0, 0, 0, 1, 2, 2], [3, 3, 4, 1, 5, 6], [3, 3, 4, 7, 5, 6], [3, 3, 8, 8, 5, 6], [3, 3, 8, 8, 9, 9], [3, 3, 10, 10, 10, 10]], "data": [[null, null, null, null, 1, null], [3, null, 0, null, 1, null], [null, null, null, 1, null, null], [null, null, 1, null, null, null], [null, null, null, null, 1, null], [null, null, 1, null, null, null]]}, "answer": [[null, null, "B", null, null, "B"], [null, "B", null, null, "B", null], [null, null, null, "B", null, null], ["B", null, "B", null, null, "B"], [null, null, null, null, "B", null], ["B", null, "B", null, null, null]], "idx": 34, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_34.png", "answer_image": "figs/heyawake_34_answer.png"} {"puzzle": "heyawake", "row": 6, "column": 6, "level": "normal", "original_data": {"region": [[0, 0, 0, 0, 1, 1], [2, 3, 3, 3, 1, 1], [2, 4, 5, 5, 1, 1], [2, 4, 5, 5, 6, 6], [7, 7, 8, 8, 8, 9], [7, 7, 10, 10, 11, 9]], "data": [[1, null, null, null, 2, null], [null, null, null, null, null, null], [null, 0, null, null, null, null], [null, null, null, null, 0, null], [1, null, 1, null, null, 1], [null, null, null, null, null, null]]}, "id": 35, "observation": {"region": [[0, 0, 0, 0, 1, 1], [2, 3, 3, 3, 1, 1], [2, 4, 5, 5, 1, 1], [2, 4, 5, 5, 6, 6], [7, 7, 8, 8, 8, 9], [7, 7, 10, 10, 11, 9]], "data": [[1, null, null, null, 2, null], [null, null, null, null, null, null], [null, 0, null, null, null, null], [null, null, null, null, 0, null], [1, null, 1, null, null, 1], [null, null, null, null, null, null]]}, "answer": [[null, null, null, "B", null, "B"], [null, "B", null, null, null, null], [null, null, "B", null, null, "B"], ["B", null, null, "B", null, null], [null, null, null, null, "B", null], ["B", null, "B", null, null, "B"]], "idx": 35, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_35.png", "answer_image": "figs/heyawake_35_answer.png"} {"puzzle": "heyawake", "row": 6, "column": 6, "level": "hard", "original_data": {"region": [[0, 0, 0, 0, 0, 0], [1, 1, 2, 3, 3, 4], [1, 1, 5, 5, 6, 4], [1, 1, 7, 7, 7, 7], [8, 9, 9, 9, 9, 10], [11, 9, 9, 9, 9, 10]], "data": [[2, null, null, null, null, null], [null, null, 0, null, null, null], [null, null, 1, null, null, null], [null, null, 2, null, null, null], [1, 2, null, null, null, null], [null, null, null, null, null, null]]}, "id": 36, "observation": {"region": [[0, 0, 0, 0, 0, 0], [1, 1, 2, 3, 3, 4], [1, 1, 5, 5, 6, 4], [1, 1, 7, 7, 7, 7], [8, 9, 9, 9, 9, 10], [11, 9, 9, 9, 9, 10]], "data": [[2, null, null, null, null, null], [null, null, 0, null, null, null], [null, null, 1, null, null, null], [null, null, 2, null, null, null], [1, 2, null, null, null, null], [null, null, null, null, null, null]]}, "answer": [[null, null, "B", null, null, "B"], [null, "B", null, null, "B", null], [null, null, null, "B", null, null], [null, null, "B", null, null, "B"], ["B", null, null, null, "B", null], [null, null, "B", null, null, null]], "idx": 36, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_36.png", "answer_image": "figs/heyawake_36_answer.png"} {"puzzle": "heyawake", "row": 8, "column": 8, "level": "easy", "original_data": {"region": [[0, 1, 1, 2, 2, 2, 3, 4], [0, 5, 5, 2, 2, 2, 3, 4], [0, 5, 5, 6, 6, 7, 3, 4], [0, 8, 8, 6, 6, 9, 9, 4], [0, 8, 8, 6, 6, 9, 9, 10], [0, 11, 12, 12, 12, 12, 13, 10], [0, 11, 12, 12, 12, 12, 13, 10], [0, 14, 14, 15, 15, 15, 15, 15]], "data": [[1, 0, null, null, null, null, 1, 1], [null, null, null, null, null, null, null, null], [null, null, null, 2, null, 0, null, null], [null, 0, null, null, null, 0, null, null], [null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, null]]}, "id": 37, "observation": {"region": [[0, 1, 1, 2, 2, 2, 3, 4], [0, 5, 5, 2, 2, 2, 3, 4], [0, 5, 5, 6, 6, 7, 3, 4], [0, 8, 8, 6, 6, 9, 9, 4], [0, 8, 8, 6, 6, 9, 9, 10], [0, 11, 12, 12, 12, 12, 13, 10], [0, 11, 12, 12, 12, 12, 13, 10], [0, 14, 14, 15, 15, 15, 15, 15]], "data": [[1, 0, null, null, null, null, 1, 1], [null, null, null, null, null, null, null, null], [null, null, null, 2, null, 0, null, null], [null, 0, null, null, null, 0, null, null], [null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, null]]}, "answer": [[null, null, null, "B", null, null, null, "B"], [null, "B", null, null, null, "B", null, null], [null, null, "B", null, null, null, "B", null], ["B", null, null, null, "B", null, null, null], [null, null, null, "B", null, null, null, "B"], [null, "B", null, null, null, "B", null, null], [null, null, "B", null, null, null, "B", null], [null, "B", null, null, "B", null, null, null]], "idx": 37, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_37.png", "answer_image": "figs/heyawake_37_answer.png"} {"puzzle": "heyawake", "row": 8, "column": 8, "level": "normal", "original_data": {"region": [[0, 0, 1, 1, 2, 2, 2, 2], [0, 0, 3, 3, 3, 4, 5, 6], [7, 8, 3, 3, 3, 9, 9, 6], [7, 8, 3, 3, 3, 9, 9, 6], [7, 10, 10, 11, 12, 9, 9, 6], [7, 10, 10, 11, 12, 9, 9, 6], [13, 13, 13, 11, 12, 14, 14, 6], [13, 13, 13, 15, 15, 16, 16, 16]], "data": [[2, null, null, null, 0, null, null, null], [null, null, null, null, null, null, 1, null], [null, 0, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null], [null, 1, null, 2, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, null, null, 0, null, null]]}, "id": 38, "observation": {"region": [[0, 0, 1, 1, 2, 2, 2, 2], [0, 0, 3, 3, 3, 4, 5, 6], [7, 8, 3, 3, 3, 9, 9, 6], [7, 8, 3, 3, 3, 9, 9, 6], [7, 10, 10, 11, 12, 9, 9, 6], [7, 10, 10, 11, 12, 9, 9, 6], [13, 13, 13, 11, 12, 14, 14, 6], [13, 13, 13, 15, 15, 16, 16, 16]], "data": [[2, null, null, null, 0, null, null, null], [null, null, null, null, null, null, 1, null], [null, 0, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null], [null, 1, null, 2, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, null, null, null, null, 0, null, null]]}, "answer": [["B", null, null, "B", null, null, null, null], [null, "B", null, null, null, null, "B", null], [null, null, "B", null, null, "B", null, null], ["B", null, null, null, "B", null, null, null], [null, null, null, "B", null, null, null, "B"], [null, null, "B", null, null, "B", null, null], [null, "B", null, "B", null, null, "B", null], [null, null, null, null, "B", null, null, null]], "idx": 38, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_38.png", "answer_image": "figs/heyawake_38_answer.png"} {"puzzle": "heyawake", "row": 8, "column": 8, "level": "hard", "original_data": {"region": [[0, 1, 2, 2, 2, 3, 3, 3], [0, 1, 4, 5, 5, 3, 3, 3], [0, 6, 6, 5, 5, 7, 7, 8], [0, 6, 6, 9, 9, 10, 10, 8], [11, 6, 6, 9, 9, 10, 10, 8], [11, 12, 13, 9, 9, 14, 14, 8], [15, 15, 13, 9, 9, 14, 14, 8], [15, 15, 13, 9, 9, 14, 14, 8]], "data": [[0, null, null, null, null, 1, null, null], [null, null, 1, 0, null, null, null, null], [null, 1, null, null, null, null, null, 2], [null, null, null, 3, null, 0, null, null], [null, null, null, null, null, null, null, null], [null, null, 1, null, null, null, null, null], [1, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "id": 39, "observation": {"region": [[0, 1, 2, 2, 2, 3, 3, 3], [0, 1, 4, 5, 5, 3, 3, 3], [0, 6, 6, 5, 5, 7, 7, 8], [0, 6, 6, 9, 9, 10, 10, 8], [11, 6, 6, 9, 9, 10, 10, 8], [11, 12, 13, 9, 9, 14, 14, 8], [15, 15, 13, 9, 9, 14, 14, 8], [15, 15, 13, 9, 9, 14, 14, 8]], "data": [[0, null, null, null, null, 1, null, null], [null, null, 1, 0, null, null, null, null], [null, 1, null, null, null, null, null, 2], [null, null, null, 3, null, 0, null, null], [null, null, null, null, null, null, null, null], [null, null, 1, null, null, null, null, null], [1, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "answer": [[null, "B", null, null, "B", null, null, null], [null, null, "B", null, null, null, "B", null], [null, "B", null, null, null, "B", null, null], [null, null, null, "B", null, null, null, "B"], ["B", null, null, null, "B", null, null, null], [null, null, "B", null, null, null, "B", null], [null, "B", null, null, null, "B", null, null], [null, null, null, "B", null, null, null, "B"]], "idx": 39, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_39.png", "answer_image": "figs/heyawake_39_answer.png"} {"puzzle": "heyawake", "row": 10, "column": 10, "level": "easy", "original_data": {"region": [[0, 0, 0, 1, 2, 3, 3, 3, 4, 4], [0, 0, 0, 5, 2, 6, 6, 6, 4, 4], [7, 8, 8, 8, 2, 9, 10, 10, 11, 12], [7, 8, 8, 8, 2, 9, 10, 10, 11, 12], [13, 8, 8, 8, 2, 9, 10, 10, 14, 14], [15, 15, 16, 16, 17, 18, 18, 18, 14, 14], [19, 19, 16, 16, 17, 18, 18, 18, 20, 21], [19, 19, 16, 16, 22, 22, 22, 22, 23, 21], [24, 24, 24, 24, 22, 22, 22, 22, 23, 21], [24, 24, 24, 24, 25, 26, 26, 26, 23, 21]], "data": [[1, null, null, 1, 1, null, null, null, null, null], [null, null, null, null, null, 0, null, null, null, null], [0, null, null, null, null, null, null, null, 1, null], [null, null, null, null, null, null, null, null, null, null], [0, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [0, null, null, null, null, null, null, null, 1, null], [null, null, null, null, null, null, null, null, 0, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, 1, null, null, null, null]]}, "id": 40, "observation": {"region": [[0, 0, 0, 1, 2, 3, 3, 3, 4, 4], [0, 0, 0, 5, 2, 6, 6, 6, 4, 4], [7, 8, 8, 8, 2, 9, 10, 10, 11, 12], [7, 8, 8, 8, 2, 9, 10, 10, 11, 12], [13, 8, 8, 8, 2, 9, 10, 10, 14, 14], [15, 15, 16, 16, 17, 18, 18, 18, 14, 14], [19, 19, 16, 16, 17, 18, 18, 18, 20, 21], [19, 19, 16, 16, 22, 22, 22, 22, 23, 21], [24, 24, 24, 24, 22, 22, 22, 22, 23, 21], [24, 24, 24, 24, 25, 26, 26, 26, 23, 21]], "data": [[1, null, null, 1, 1, null, null, null, null, null], [null, null, null, null, null, 0, null, null, null, null], [0, null, null, null, null, null, null, null, 1, null], [null, null, null, null, null, null, null, null, null, null], [0, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [0, null, null, null, null, null, null, null, 1, null], [null, null, null, null, null, null, null, null, 0, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, 1, null, null, null, null]]}, "answer": [[null, null, null, "B", null, null, "B", null, null, null], ["B", null, null, null, "B", null, null, null, null, "B"], [null, null, "B", null, null, "B", null, "B", null, null], [null, null, null, "B", null, null, "B", null, "B", null], [null, "B", null, null, null, "B", null, null, null, null], ["B", null, null, null, "B", null, null, null, null, "B"], [null, null, null, "B", null, null, "B", null, "B", null], [null, null, "B", null, null, null, null, "B", null, null], [null, "B", null, null, null, "B", null, null, null, "B"], [null, null, null, null, "B", null, null, "B", null, null]], "idx": 40, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_40.png", "answer_image": "figs/heyawake_40_answer.png"} {"puzzle": "heyawake", "row": 10, "column": 10, "level": "normal", "original_data": {"region": [[0, 1, 2, 2, 2, 2, 3, 3, 4, 4], [0, 5, 5, 5, 6, 6, 3, 3, 4, 4], [0, 7, 7, 7, 8, 8, 3, 3, 9, 10], [0, 11, 12, 12, 8, 8, 13, 13, 9, 10], [0, 11, 12, 12, 8, 8, 13, 13, 9, 10], [0, 14, 14, 15, 15, 15, 15, 15, 15, 10], [0, 14, 14, 16, 16, 17, 18, 19, 19, 10], [0, 20, 20, 16, 16, 17, 18, 21, 21, 10], [0, 22, 23, 23, 23, 23, 23, 21, 21, 10], [0, 24, 24, 24, 24, 24, 24, 24, 24, 24]], "data": [[1, null, 1, null, null, null, 1, null, null, null], [null, null, null, null, 0, null, null, null, null, null], [null, null, null, null, null, null, null, null, 0, 3], [null, null, null, null, null, null, 2, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, 0, null, null, null, null], [null, 1, null, null, null, null, null, null, null, null], [null, 1, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "id": 41, "observation": {"region": [[0, 1, 2, 2, 2, 2, 3, 3, 4, 4], [0, 5, 5, 5, 6, 6, 3, 3, 4, 4], [0, 7, 7, 7, 8, 8, 3, 3, 9, 10], [0, 11, 12, 12, 8, 8, 13, 13, 9, 10], [0, 11, 12, 12, 8, 8, 13, 13, 9, 10], [0, 14, 14, 15, 15, 15, 15, 15, 15, 10], [0, 14, 14, 16, 16, 17, 18, 19, 19, 10], [0, 20, 20, 16, 16, 17, 18, 21, 21, 10], [0, 22, 23, 23, 23, 23, 23, 21, 21, 10], [0, 24, 24, 24, 24, 24, 24, 24, 24, 24]], "data": [[1, null, 1, null, null, null, 1, null, null, null], [null, null, null, null, 0, null, null, null, null, null], [null, null, null, null, null, null, null, null, 0, 3], [null, null, null, null, null, null, 2, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, 0, null, null, null, null], [null, 1, null, null, null, null, null, null, null, null], [null, 1, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "answer": [[null, "B", null, null, null, "B", null, null, null, null], [null, null, null, "B", null, null, null, null, "B", null], [null, null, "B", null, "B", null, null, "B", null, null], [null, "B", null, null, null, null, "B", null, null, "B"], ["B", null, null, "B", null, "B", null, "B", null, null], [null, "B", null, null, "B", null, null, null, null, "B"], [null, null, null, "B", null, null, "B", null, "B", null], [null, null, "B", null, "B", null, null, "B", null, null], [null, "B", null, null, null, "B", null, null, null, "B"], [null, null, null, "B", null, null, "B", null, null, null]], "idx": 41, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_41.png", "answer_image": "figs/heyawake_41_answer.png"} {"puzzle": "heyawake", "row": 10, "column": 10, "level": "hard", "original_data": {"region": [[0, 0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 0, 6, 6, 7, 7, 7, 4, 4, 5], [0, 0, 6, 6, 7, 7, 7, 4, 4, 5], [0, 0, 8, 8, 9, 9, 9, 4, 4, 10], [11, 12, 12, 13, 13, 13, 14, 14, 14, 10], [11, 12, 12, 13, 13, 13, 14, 14, 14, 15], [16, 16, 16, 13, 13, 13, 17, 17, 18, 15], [19, 19, 20, 21, 21, 22, 23, 24, 18, 15], [19, 19, 25, 25, 25, 22, 23, 26, 26, 15]], "data": [[null, null, null, null, 2, null, null, 3, null, 1], [null, null, null, null, null, null, null, null, null, null], [null, null, 2, null, 1, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, 1, null, null, null, null, null], [null, 2, null, 2, null, null, 1, null, null, null], [null, null, null, null, null, null, null, null, null, 0], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, 0, null, null], [null, null, null, null, null, null, null, 1, null, null]]}, "id": 42, "observation": {"region": [[0, 0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 0, 6, 6, 7, 7, 7, 4, 4, 5], [0, 0, 6, 6, 7, 7, 7, 4, 4, 5], [0, 0, 8, 8, 9, 9, 9, 4, 4, 10], [11, 12, 12, 13, 13, 13, 14, 14, 14, 10], [11, 12, 12, 13, 13, 13, 14, 14, 14, 15], [16, 16, 16, 13, 13, 13, 17, 17, 18, 15], [19, 19, 20, 21, 21, 22, 23, 24, 18, 15], [19, 19, 25, 25, 25, 22, 23, 26, 26, 15]], "data": [[null, null, null, null, 2, null, null, 3, null, 1], [null, null, null, null, null, null, null, null, null, null], [null, null, 2, null, 1, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, 1, null, null, null, null, null], [null, 2, null, 2, null, null, 1, null, null, null], [null, null, null, null, null, null, null, null, null, 0], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, 0, null, null], [null, null, null, null, null, null, null, 1, null, null]]}, "answer": [[null, null, null, null, "B", null, null, "B", null, null], [null, "B", null, null, null, "B", null, null, null, "B"], [null, null, "B", null, null, null, null, "B", null, null], [null, null, null, "B", null, null, "B", null, null, null], ["B", null, null, null, "B", null, null, null, "B", null], [null, null, "B", null, null, "B", null, null, null, "B"], [null, "B", null, null, "B", null, "B", null, null, null], [null, null, "B", null, null, null, null, "B", null, null], ["B", null, null, "B", null, "B", null, null, "B", null], [null, null, null, null, "B", null, null, "B", null, null]], "idx": 42, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. A numbered region contains exactly that many black cells.\n2. Black cells cannot touch orthogonally.\n3. Any uninterrupted straight white segment (row/column) cannot pass through more than 2 regions.\n4. All white cells are orthogonally connected.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: clue 2D list (`int` or `None`)\n4. **Answer:** `N x N` 2D list using `'B'` for black cells and `None` for white cells.", "ref_observation": {"region": [[0, 1, 1, 1, 2, 2], [3, 3, 3, 3, 2, 2], [4, 4, 5, 6, 6, 7], [8, 8, 8, 6, 6, 7], [8, 8, 8, 9, 10, 7], [8, 8, 8, 9, 11, 11]], "data": [[1, null, null, null, 1, null], [1, null, null, null, null, null], [null, null, 1, null, null, 1], [3, null, null, null, null, null], [null, null, null, null, 1, null], [null, null, null, null, null, null]]}, "image": "figs/heyawake_42.png", "answer_image": "figs/heyawake_42_answer.png"} {"puzzle": "hitori", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[1, 5, 3, 4, 1], [5, 3, 5, 3, 1], [3, 5, 4, 1, 5], [5, 1, 2, 3, 4], [2, 1, 1, 1, 3]]}, "id": 43, "observation": {"data": [[1, 5, 3, 4, 1], [5, 3, 5, 3, 1], [3, 5, 4, 1, 5], [5, 1, 2, 3, 4], [2, 1, 1, 1, 3]]}, "answer": [[null, null, null, null, "B"], ["B", null, null, "B", null], [null, "B", null, null, null], [null, null, null, null, null], [null, "B", null, "B", null]], "idx": 43, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_43.png", "answer_image": "figs/hitori_43_answer.png"} {"puzzle": "hitori", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[3, 4, 3, 1, 5], [4, 3, 5, 3, 1], [5, 2, 5, 4, 3], [3, 3, 4, 1, 2], [4, 5, 2, 3, 4]]}, "id": 44, "observation": {"data": [[3, 4, 3, 1, 5], [4, 3, 5, 3, 1], [5, 2, 5, 4, 3], [3, 3, 4, 1, 2], [4, 5, 2, 3, 4]]}, "answer": [["B", null, null, null, null], [null, null, null, "B", null], [null, null, "B", null, null], [null, "B", null, "B", null], ["B", null, null, null, null]], "idx": 44, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_44.png", "answer_image": "figs/hitori_44_answer.png"} {"puzzle": "hitori", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[3, 4, 3, 2, 3], [4, 3, 2, 3, 5], [1, 2, 3, 1, 4], [5, 3, 1, 4, 2], [2, 4, 4, 3, 3]]}, "id": 45, "observation": {"data": [[3, 4, 3, 2, 3], [4, 3, 2, 3, 5], [1, 2, 3, 1, 4], [5, 3, 1, 4, 2], [2, 4, 4, 3, 3]]}, "answer": [[null, null, "B", null, "B"], [null, "B", null, null, null], [null, null, null, "B", null], [null, null, null, null, null], [null, "B", null, "B", null]], "idx": 45, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_45.png", "answer_image": "figs/hitori_45_answer.png"} {"puzzle": "hitori", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[5, 1, 2, 8, 7, 1, 4, 9, 8, 9], [8, 2, 10, 4, 9, 3, 6, 9, 1, 8], [1, 7, 7, 8, 4, 4, 9, 2, 9, 5], [4, 6, 9, 4, 8, 2, 9, 3, 6, 8], [6, 9, 1, 7, 9, 8, 2, 2, 5, 3], [1, 6, 3, 9, 1, 3, 8, 7, 8, 4], [9, 5, 7, 10, 5, 1, 4, 10, 4, 1], [8, 3, 1, 6, 2, 9, 5, 1, 5, 9], [9, 4, 5, 10, 8, 9, 10, 8, 3, 1], [3, 5, 10, 1, 4, 7, 10, 1, 9, 3]]}, "id": 46, "observation": {"data": [[5, 1, 2, 8, 7, 1, 4, 9, 8, 9], [8, 2, 10, 4, 9, 3, 6, 9, 1, 8], [1, 7, 7, 8, 4, 4, 9, 2, 9, 5], [4, 6, 9, 4, 8, 2, 9, 3, 6, 8], [6, 9, 1, 7, 9, 8, 2, 2, 5, 3], [1, 6, 3, 9, 1, 3, 8, 7, 8, 4], [9, 5, 7, 10, 5, 1, 4, 10, 4, 1], [8, 3, 1, 6, 2, 9, 5, 1, 5, 9], [9, 4, 5, 10, 8, 9, 10, 8, 3, 1], [3, 5, 10, 1, 4, 7, 10, 1, 9, 3]]}, "answer": [[null, null, null, "B", null, "B", null, null, null, "B"], ["B", null, null, null, null, null, null, "B", null, null], [null, null, "B", null, "B", null, null, null, "B", null], [null, "B", null, "B", null, null, "B", null, null, "B"], [null, null, null, null, "B", null, null, "B", null, null], ["B", null, null, null, null, "B", null, null, "B", null], [null, "B", null, "B", null, null, "B", null, null, "B"], [null, null, "B", null, null, "B", null, null, "B", null], ["B", null, null, null, "B", null, "B", null, null, null], [null, null, "B", null, null, null, null, "B", null, "B"]], "idx": 46, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_46.png", "answer_image": "figs/hitori_46_answer.png"} {"puzzle": "hitori", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[1, 2, 5, 7, 3, 2, 1, 9, 4, 7], [2, 1, 7, 3, 5, 9, 8, 10, 6, 4], [4, 3, 4, 2, 4, 7, 1, 5, 9, 1], [4, 5, 9, 5, 2, 5, 3, 5, 7, 5], [3, 9, 7, 6, 7, 10, 4, 2, 4, 1], [10, 6, 1, 7, 4, 9, 2, 7, 10, 5], [7, 3, 3, 9, 3, 8, 10, 1, 1, 2], [10, 8, 6, 5, 1, 4, 5, 3, 2, 10], [8, 7, 2, 4, 8, 2, 9, 2, 3, 10], [5, 2, 10, 2, 9, 6, 4, 8, 4, 2]]}, "id": 47, "observation": {"data": [[1, 2, 5, 7, 3, 2, 1, 9, 4, 7], [2, 1, 7, 3, 5, 9, 8, 10, 6, 4], [4, 3, 4, 2, 4, 7, 1, 5, 9, 1], [4, 5, 9, 5, 2, 5, 3, 5, 7, 5], [3, 9, 7, 6, 7, 10, 4, 2, 4, 1], [10, 6, 1, 7, 4, 9, 2, 7, 10, 5], [7, 3, 3, 9, 3, 8, 10, 1, 1, 2], [10, 8, 6, 5, 1, 4, 5, 3, 2, 10], [8, 7, 2, 4, 8, 2, 9, 2, 3, 10], [5, 2, 10, 2, 9, 6, 4, 8, 4, 2]]}, "answer": [[null, "B", null, "B", null, null, "B", null, "B", null], [null, null, null, null, null, null, null, null, null, null], ["B", null, null, null, "B", null, null, null, null, "B"], [null, "B", null, "B", null, "B", null, "B", null, null], [null, null, "B", null, null, null, null, null, "B", null], ["B", null, null, "B", null, "B", null, null, null, "B"], [null, "B", null, null, "B", null, null, "B", null, null], [null, null, null, "B", null, null, null, null, null, "B"], ["B", null, null, null, null, "B", null, "B", null, null], [null, null, null, "B", null, null, "B", null, null, "B"]], "idx": 47, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_47.png", "answer_image": "figs/hitori_47_answer.png"} {"puzzle": "hitori", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[2, 8, 5, 7, 3, 2, 10, 5, 4, 1], [9, 2, 8, 2, 10, 1, 2, 7, 3, 2], [4, 9, 4, 1, 10, 3, 8, 4, 10, 2], [6, 1, 3, 6, 2, 6, 7, 9, 5, 6], [3, 1, 2, 6, 1, 10, 1, 4, 7, 8], [8, 6, 10, 2, 5, 10, 3, 10, 10, 9], [5, 5, 10, 10, 7, 6, 2, 8, 2, 3], [3, 2, 6, 10, 6, 7, 5, 6, 9, 3], [1, 10, 9, 1, 4, 5, 1, 2, 1, 7], [10, 3, 1, 8, 9, 9, 4, 3, 6, 5]]}, "id": 48, "observation": {"data": [[2, 8, 5, 7, 3, 2, 10, 5, 4, 1], [9, 2, 8, 2, 10, 1, 2, 7, 3, 2], [4, 9, 4, 1, 10, 3, 8, 4, 10, 2], [6, 1, 3, 6, 2, 6, 7, 9, 5, 6], [3, 1, 2, 6, 1, 10, 1, 4, 7, 8], [8, 6, 10, 2, 5, 10, 3, 10, 10, 9], [5, 5, 10, 10, 7, 6, 2, 8, 2, 3], [3, 2, 6, 10, 6, 7, 5, 6, 9, 3], [1, 10, 9, 1, 4, 5, 1, 2, 1, 7], [10, 3, 1, 8, 9, 9, 4, 3, 6, 5]]}, "answer": [[null, null, null, null, null, "B", null, "B", null, null], [null, "B", null, "B", null, null, null, null, null, "B"], ["B", null, null, null, "B", null, null, "B", null, null], [null, null, null, "B", null, "B", null, null, null, "B"], [null, "B", null, null, null, null, "B", null, null, null], [null, null, "B", null, null, "B", null, null, "B", null], [null, "B", null, "B", null, null, "B", null, null, "B"], ["B", null, null, null, "B", null, null, "B", null, null], [null, null, null, "B", null, null, "B", null, "B", null], [null, "B", null, null, null, "B", null, null, null, null]], "idx": 48, "rules": "**Core Rules:**\nShade some cells black so that:\n1. In every row, each unshaded number appears at most once.\n2. In every column, each unshaded number appears at most once.\n3. Black cells cannot touch orthogonally (up/down/left/right).\n4. All unshaded (white) cells must form one orthogonally connected group.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: full number board as a `N x N` list of lists.\n4. **Answer:** solved grid mask as a `N x N` 2D list with `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, 2, 3, 5, 5], [1, 3, 3, 2, 1], [2, 5, 1, 1, 3], [3, 2, 2, 1, 5], [2, 1, 5, 5, 2]]}, "image": "figs/hitori_48.png", "answer_image": "figs/hitori_48_answer.png"} {"puzzle": "jigsawsudoku", "row": 5, "column": 5, "level": "easy", "original_data": {"region": [[0, 0, 0, 1, 1], [0, 0, 1, 1, 2], [3, 3, 3, 1, 2], [3, 3, 2, 2, 2], [4, 4, 4, 4, 4]], "data": [[null, 5, null, null, 1], [null, null, null, 4, null], [null, null, null, null, null], [null, 2, null, null, null], [1, null, null, 2, null]]}, "id": 49, "observation": {"region": [[0, 0, 0, 1, 1], [0, 0, 1, 1, 2], [3, 3, 3, 1, 2], [3, 3, 2, 2, 2], [4, 4, 4, 4, 4]], "data": [[null, 5, null, null, 1], [null, null, null, 4, null], [null, null, null, null, null], [null, 2, null, null, null], [1, null, null, 2, null]]}, "answer": [[2, 5, 4, 3, 1], [3, 1, 2, 4, 5], [4, 3, 1, 5, 2], [5, 2, 3, 1, 4], [1, 4, 5, 2, 3]], "idx": 49, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_49.png", "answer_image": "figs/jigsawsudoku_49_answer.png"} {"puzzle": "jigsawsudoku", "row": 5, "column": 5, "level": "normal", "original_data": {"region": [[0, 1, 1, 1, 2], [0, 0, 0, 1, 2], [3, 3, 0, 1, 2], [3, 4, 4, 4, 2], [3, 3, 4, 4, 2]], "data": [[null, 5, null, null, null], [null, null, null, null, 3], [null, 4, null, 2, null], [5, null, null, null, null], [null, null, null, 5, null]]}, "id": 50, "observation": {"region": [[0, 1, 1, 1, 2], [0, 0, 0, 1, 2], [3, 3, 0, 1, 2], [3, 4, 4, 4, 2], [3, 3, 4, 4, 2]], "data": [[null, 5, null, null, null], [null, null, null, null, 3], [null, 4, null, 2, null], [5, null, null, null, null], [null, null, null, 5, null]]}, "answer": [[4, 5, 1, 3, 2], [2, 1, 5, 4, 3], [1, 4, 3, 2, 5], [5, 3, 2, 1, 4], [3, 2, 4, 5, 1]], "idx": 50, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_50.png", "answer_image": "figs/jigsawsudoku_50_answer.png"} {"puzzle": "jigsawsudoku", "row": 5, "column": 5, "level": "hard", "original_data": {"region": [[0, 0, 1, 1, 1], [0, 1, 1, 2, 2], [0, 2, 2, 2, 3], [0, 3, 3, 3, 3], [4, 4, 4, 4, 4]], "data": [[null, null, null, 2, null], [null, null, null, null, null], [null, 5, null, 1, null], [null, null, null, null, null], [null, 4, null, null, null]]}, "id": 51, "observation": {"region": [[0, 0, 1, 1, 1], [0, 1, 1, 2, 2], [0, 2, 2, 2, 3], [0, 3, 3, 3, 3], [4, 4, 4, 4, 4]], "data": [[null, null, null, 2, null], [null, null, null, null, null], [null, 5, null, 1, null], [null, null, null, null, null], [null, 4, null, null, null]]}, "answer": [[3, 1, 4, 2, 5], [5, 3, 1, 4, 2], [2, 5, 3, 1, 4], [4, 2, 5, 3, 1], [1, 4, 2, 5, 3]], "idx": 51, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_51.png", "answer_image": "figs/jigsawsudoku_51_answer.png"} {"puzzle": "jigsawsudoku", "row": 7, "column": 7, "level": "easy", "original_data": {"region": [[0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2, 4, 3], [0, 0, 1, 2, 4, 4, 3], [5, 5, 5, 5, 4, 4, 3], [5, 6, 6, 5, 6, 4, 3], [5, 6, 6, 6, 6, 4, 3]], "data": [[null, null, null, null, null, null, null], [1, 7, null, 2, null, null, 6], [2, null, null, 7, 6, null, null], [null, null, 5, null, 2, null, null], [null, null, 2, 3, null, null, 4], [5, null, null, 4, null, 3, 7], [null, null, null, null, null, null, null]]}, "id": 52, "observation": {"region": [[0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2, 4, 3], [0, 0, 1, 2, 4, 4, 3], [5, 5, 5, 5, 4, 4, 3], [5, 6, 6, 5, 6, 4, 3], [5, 6, 6, 6, 6, 4, 3]], "data": [[null, null, null, null, null, null, null], [1, 7, null, 2, null, null, 6], [2, null, null, 7, 6, null, null], [null, null, 5, null, 2, null, null], [null, null, 2, 3, null, null, 4], [5, null, null, 4, null, 3, 7], [null, null, null, null, null, null, null]]}, "answer": [[3, 5, 7, 6, 4, 2, 1], [1, 7, 4, 2, 3, 5, 6], [2, 3, 1, 7, 6, 4, 5], [4, 6, 5, 1, 2, 7, 3], [7, 1, 2, 3, 5, 6, 4], [5, 2, 6, 4, 1, 3, 7], [6, 4, 3, 5, 7, 1, 2]], "idx": 52, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_52.png", "answer_image": "figs/jigsawsudoku_52_answer.png"} {"puzzle": "jigsawsudoku", "row": 7, "column": 7, "level": "normal", "original_data": {"region": [[0, 0, 0, 0, 1, 1, 1], [0, 1, 1, 1, 1, 2, 2], [0, 3, 3, 2, 2, 2, 2], [0, 3, 3, 3, 2, 4, 4], [5, 3, 6, 3, 4, 4, 4], [5, 6, 6, 6, 6, 6, 4], [5, 5, 5, 5, 5, 6, 4]], "data": [[3, null, null, null, null, 5, null], [5, 6, null, null, null, null, null], [4, null, null, 7, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 4, null, null, 2], [null, null, null, null, null, 7, 5], [null, 5, null, null, null, null, 6]]}, "id": 53, "observation": {"region": [[0, 0, 0, 0, 1, 1, 1], [0, 1, 1, 1, 1, 2, 2], [0, 3, 3, 2, 2, 2, 2], [0, 3, 3, 3, 2, 4, 4], [5, 3, 6, 3, 4, 4, 4], [5, 6, 6, 6, 6, 6, 4], [5, 5, 5, 5, 5, 6, 4]], "data": [[3, null, null, null, null, 5, null], [5, 6, null, null, null, null, null], [4, null, null, 7, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 4, null, null, 2], [null, null, null, null, null, 7, 5], [null, 5, null, null, null, null, 6]]}, "answer": [[3, 2, 7, 6, 4, 5, 1], [5, 6, 3, 2, 7, 1, 4], [4, 1, 2, 7, 5, 6, 3], [1, 3, 6, 5, 2, 4, 7], [6, 7, 5, 4, 1, 3, 2], [2, 4, 1, 3, 6, 7, 5], [7, 5, 4, 1, 3, 2, 6]], "idx": 53, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_53.png", "answer_image": "figs/jigsawsudoku_53_answer.png"} {"puzzle": "jigsawsudoku", "row": 7, "column": 7, "level": "hard", "original_data": {"region": [[0, 1, 1, 1, 2, 2, 2], [0, 0, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 3, 2], [4, 4, 0, 5, 3, 3, 6], [4, 5, 5, 5, 3, 6, 6], [4, 4, 5, 3, 3, 3, 6], [4, 4, 5, 5, 6, 6, 6]], "data": [[null, null, 7, 6, null, null, null], [null, null, null, null, 6, null, null], [null, null, null, 1, null, null, 4], [null, null, null, null, null, null, null], [1, null, null, 5, null, null, null], [null, null, 6, null, null, null, null], [null, null, null, 7, 3, null, null]]}, "id": 54, "observation": {"region": [[0, 1, 1, 1, 2, 2, 2], [0, 0, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 3, 2], [4, 4, 0, 5, 3, 3, 6], [4, 5, 5, 5, 3, 6, 6], [4, 4, 5, 3, 3, 3, 6], [4, 4, 5, 5, 6, 6, 6]], "data": [[null, null, 7, 6, null, null, null], [null, null, null, null, 6, null, null], [null, null, null, 1, null, null, 4], [null, null, null, null, null, null, null], [1, null, null, 5, null, null, null], [null, null, 6, null, null, null, null], [null, null, null, 7, 3, null, null]]}, "answer": [[4, 5, 7, 6, 1, 2, 3], [2, 1, 4, 3, 6, 5, 7], [6, 7, 5, 1, 2, 3, 4], [7, 2, 3, 4, 5, 6, 1], [1, 3, 2, 5, 4, 7, 6], [3, 4, 6, 2, 7, 1, 5], [5, 6, 1, 7, 3, 4, 2]], "idx": 54, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_54.png", "answer_image": "figs/jigsawsudoku_54_answer.png"} {"puzzle": "jigsawsudoku", "row": 9, "column": 9, "level": "easy", "original_data": {"region": [[0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 1, 0, 1, 1, 3, 2, 2, 2], [0, 1, 1, 1, 3, 3, 3, 2, 2], [0, 0, 4, 4, 3, 3, 3, 2, 5], [4, 4, 4, 5, 5, 3, 3, 2, 5], [4, 4, 4, 6, 5, 5, 5, 5, 5], [7, 4, 7, 6, 6, 6, 6, 6, 6], [7, 7, 7, 6, 8, 8, 8, 8, 6], [7, 7, 7, 7, 8, 8, 8, 8, 8]], "data": [[null, null, null, 7, null, null, null, 5, null], [6, null, 8, 2, null, 5, null, null, 7], [null, null, null, null, 8, 9, null, null, 2], [null, null, 3, 9, null, null, null, 8, null], [7, null, null, null, 2, null, null, null, 6], [null, 1, null, null, null, 8, 5, null, null], [8, null, null, 3, 1, null, null, null, null], [1, null, null, 8, null, 3, 6, null, 9], [null, 3, null, null, null, 2, null, null, null]]}, "id": 55, "observation": {"region": [[0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 1, 0, 1, 1, 3, 2, 2, 2], [0, 1, 1, 1, 3, 3, 3, 2, 2], [0, 0, 4, 4, 3, 3, 3, 2, 5], [4, 4, 4, 5, 5, 3, 3, 2, 5], [4, 4, 4, 6, 5, 5, 5, 5, 5], [7, 4, 7, 6, 6, 6, 6, 6, 6], [7, 7, 7, 6, 8, 8, 8, 8, 6], [7, 7, 7, 7, 8, 8, 8, 8, 8]], "data": [[null, null, null, 7, null, null, null, 5, null], [6, null, 8, 2, null, 5, null, null, 7], [null, null, null, null, 8, 9, null, null, 2], [null, null, 3, 9, null, null, null, 8, null], [7, null, null, null, 2, null, null, null, 6], [null, 1, null, null, null, 8, 5, null, null], [8, null, null, 3, 1, null, null, null, null], [1, null, null, 8, null, 3, 6, null, 9], [null, 3, null, null, null, 2, null, null, null]]}, "answer": [[9, 2, 1, 7, 3, 6, 8, 5, 4], [6, 9, 8, 2, 4, 5, 1, 3, 7], [3, 5, 7, 1, 8, 9, 4, 6, 2], [5, 4, 3, 9, 6, 7, 2, 8, 1], [7, 8, 5, 4, 2, 1, 3, 9, 6], [2, 1, 4, 6, 9, 8, 5, 7, 3], [8, 6, 9, 3, 1, 4, 7, 2, 5], [1, 7, 2, 8, 5, 3, 6, 4, 9], [4, 3, 6, 5, 7, 2, 9, 1, 8]], "idx": 55, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_55.png", "answer_image": "figs/jigsawsudoku_55_answer.png"} {"puzzle": "jigsawsudoku", "row": 9, "column": 9, "level": "normal", "original_data": {"region": [[0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 0, 1, 1, 1, 1, 2], [3, 3, 3, 0, 1, 1, 4, 2, 2], [3, 3, 5, 4, 4, 4, 4, 4, 2], [3, 3, 5, 5, 4, 4, 4, 2, 2], [3, 3, 5, 6, 6, 6, 6, 7, 2], [5, 5, 5, 6, 6, 6, 7, 7, 7], [8, 8, 5, 5, 6, 6, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 7, 7]], "data": [[7, null, null, 2, 6, null, null, 3, null], [9, null, null, null, null, 1, null, null, null], [null, null, null, null, null, null, null, 1, 6], [null, null, 3, 7, null, null, null, 6, null], [2, null, null, null, null, null, null, null, 9], [null, 3, null, null, null, 5, 2, null, null], [5, 9, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, null, 5], [null, 6, null, null, 8, 7, null, null, 3]]}, "id": 56, "observation": {"region": [[0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 0, 1, 1, 1, 1, 2], [3, 3, 3, 0, 1, 1, 4, 2, 2], [3, 3, 5, 4, 4, 4, 4, 4, 2], [3, 3, 5, 5, 4, 4, 4, 2, 2], [3, 3, 5, 6, 6, 6, 6, 7, 2], [5, 5, 5, 6, 6, 6, 7, 7, 7], [8, 8, 5, 5, 6, 6, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 7, 7]], "data": [[7, null, null, 2, 6, null, null, 3, null], [9, null, null, null, null, 1, null, null, null], [null, null, null, null, null, null, null, 1, 6], [null, null, 3, 7, null, null, null, 6, null], [2, null, null, null, null, null, null, null, 9], [null, 3, null, null, null, 5, 2, null, null], [5, 9, null, null, null, null, null, null, null], [null, null, null, 1, null, null, null, null, 5], [null, 6, null, null, 8, 7, null, null, 3]]}, "answer": [[7, 1, 5, 2, 6, 9, 8, 3, 4], [9, 8, 6, 4, 5, 1, 3, 7, 2], [8, 7, 9, 3, 2, 4, 5, 1, 6], [1, 5, 3, 7, 9, 2, 4, 6, 8], [2, 4, 7, 6, 3, 8, 1, 5, 9], [6, 3, 4, 9, 1, 5, 2, 8, 7], [5, 9, 2, 8, 7, 3, 6, 4, 1], [3, 2, 8, 1, 4, 6, 7, 9, 5], [4, 6, 1, 5, 8, 7, 9, 2, 3]], "idx": 56, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_56.png", "answer_image": "figs/jigsawsudoku_56_answer.png"} {"puzzle": "jigsawsudoku", "row": 9, "column": 9, "level": "hard", "original_data": {"region": [[0, 0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3, 3], [4, 0, 0, 1, 1, 2, 2, 2, 3], [4, 0, 1, 1, 5, 5, 2, 3, 3], [4, 1, 1, 4, 5, 5, 5, 3, 6], [4, 4, 4, 4, 4, 5, 5, 3, 6], [7, 7, 7, 7, 6, 5, 5, 6, 6], [7, 7, 7, 7, 6, 6, 6, 6, 8], [7, 8, 8, 8, 8, 8, 8, 8, 8]], "data": [[null, null, null, null, 3, null, null, null, null], [8, null, 6, null, null, null, null, 1, 4], [null, null, 5, null, null, null, 8, 4, null], [null, null, 1, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, 3, null, null], [null, 7, 4, null, null, null, 1, null, null], [6, 2, null, null, null, null, 4, null, 5], [null, null, null, null, 1, null, null, null, null]]}, "id": 57, "observation": {"region": [[0, 0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3, 3], [4, 0, 0, 1, 1, 2, 2, 2, 3], [4, 0, 1, 1, 5, 5, 2, 3, 3], [4, 1, 1, 4, 5, 5, 5, 3, 6], [4, 4, 4, 4, 4, 5, 5, 3, 6], [7, 7, 7, 7, 6, 5, 5, 6, 6], [7, 7, 7, 7, 6, 6, 6, 6, 8], [7, 8, 8, 8, 8, 8, 8, 8, 8]], "data": [[null, null, null, null, 3, null, null, null, null], [8, null, 6, null, null, null, null, 1, 4], [null, null, 5, null, null, null, 8, 4, null], [null, null, 1, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, null], [null, null, 2, null, null, null, 3, null, null], [null, 7, 4, null, null, null, 1, null, null], [6, 2, null, null, null, null, 4, null, 5], [null, null, null, null, 1, null, null, null, null]]}, "answer": [[2, 4, 7, 8, 3, 1, 5, 6, 9], [8, 3, 6, 5, 2, 7, 9, 1, 4], [3, 1, 5, 7, 9, 6, 8, 4, 2], [7, 9, 1, 4, 6, 5, 2, 8, 3], [1, 6, 3, 9, 4, 2, 7, 5, 8], [4, 5, 2, 6, 8, 9, 3, 7, 1], [9, 7, 4, 3, 5, 8, 1, 2, 6], [6, 2, 8, 1, 7, 3, 4, 9, 5], [5, 8, 9, 2, 1, 4, 6, 3, 7]], "idx": 57, "rules": "**Core Rules:**\nFill the grid with numbers `1..N` so that:\n1. Each row contains each number exactly once.\n2. Each column contains each number exactly once.\n3. Each irregular region contains each number exactly once.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation:** dictionary with:\n - `region`: `N x N` region-ID 2D list\n - `data`: `N x N` givens 2D list (`int` or `None`)\n4. **Answer:** full solved `N x N` 2D list of numbers.", "ref_observation": {"region": [[0, 1, 1, 2, 2], [0, 1, 1, 2, 2], [0, 3, 1, 4, 2], [0, 3, 4, 4, 4], [0, 3, 3, 3, 4]], "data": [[null, 4, null, null, null], [null, null, 5, null, null], [2, null, 1, null, 5], [null, null, 2, null, null], [null, null, null, 2, null]]}, "image": "figs/jigsawsudoku_57.png", "answer_image": "figs/jigsawsudoku_57_answer.png"} {"puzzle": "kakurasu", "row": 4, "column": 4, "level": "easy", "original_data": {"row_sum": [7, 7, 6, 7], "col_sum": [7, 7, 6, 7]}, "id": 58, "observation": {"row_sum": [7, 7, 6, 7], "col_sum": [7, 7, 6, 7]}, "answer": [[null, null, "B", "B"], [null, null, "B", "B"], ["B", "B", "B", null], ["B", "B", null, "B"]], "idx": 58, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_58.png", "answer_image": "figs/kakurasu_58_answer.png"} {"puzzle": "kakurasu", "row": 4, "column": 4, "level": "hard", "original_data": {"row_sum": [1, 7, 2, 9], "col_sum": [3, 9, 4, 6]}, "id": 59, "observation": {"row_sum": [1, 7, 2, 9], "col_sum": [3, 9, 4, 6]}, "answer": [["B", null, null, null], ["B", "B", null, "B"], [null, "B", null, null], [null, "B", "B", "B"]], "idx": 59, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_59.png", "answer_image": "figs/kakurasu_59_answer.png"} {"puzzle": "kakurasu", "row": 5, "column": 5, "level": "easy", "original_data": {"row_sum": [6, 4, 9, 7, 11], "col_sum": [4, 9, 3, 7, 13]}, "id": 60, "observation": {"row_sum": [6, 4, 9, 7, 11], "col_sum": [4, 9, 3, 7, 13]}, "answer": [["B", null, null, null, "B"], [null, null, null, "B", null], ["B", null, "B", null, "B"], [null, "B", null, null, "B"], [null, "B", null, "B", "B"]], "idx": 60, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_60.png", "answer_image": "figs/kakurasu_60_answer.png"} {"puzzle": "kakurasu", "row": 5, "column": 5, "level": "hard", "original_data": {"row_sum": [8, 1, 8, 11, 9], "col_sum": [14, 4, 13, 3, 10]}, "id": 61, "observation": {"row_sum": [8, 1, 8, 11, 9], "col_sum": [14, 4, 13, 3, 10]}, "answer": [[null, null, "B", null, "B"], ["B", null, null, null, null], ["B", null, "B", "B", null], ["B", "B", "B", null, "B"], ["B", null, "B", null, "B"]], "idx": 61, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_61.png", "answer_image": "figs/kakurasu_61_answer.png"} {"puzzle": "kakurasu", "row": 6, "column": 6, "level": "easy", "original_data": {"row_sum": [11, 1, 8, 4, 3, 1], "col_sum": [8, 4, 5, 5, 1, 3]}, "id": 62, "observation": {"row_sum": [11, 1, 8, 4, 3, 1], "col_sum": [8, 4, 5, 5, 1, 3]}, "answer": [[null, "B", null, "B", "B", null], ["B", null, null, null, null, null], [null, "B", null, null, null, "B"], [null, null, null, "B", null, null], [null, null, "B", null, null, null], ["B", null, null, null, null, null]], "idx": 62, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_62.png", "answer_image": "figs/kakurasu_62_answer.png"} {"puzzle": "kakurasu", "row": 6, "column": 6, "level": "hard", "original_data": {"row_sum": [15, 15, 7, 12, 14, 12], "col_sum": [2, 13, 7, 11, 11, 18]}, "id": 63, "observation": {"row_sum": [15, 15, 7, 12, 14, 12], "col_sum": [2, 13, 7, 11, 11, 18]}, "answer": [[null, null, null, "B", "B", "B"], ["B", null, "B", null, "B", "B"], [null, "B", null, null, "B", null], [null, "B", null, "B", null, "B"], [null, null, "B", null, "B", "B"], [null, "B", null, "B", null, "B"]], "idx": 63, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_63.png", "answer_image": "figs/kakurasu_63_answer.png"} {"puzzle": "kakurasu", "row": 7, "column": 7, "level": "easy", "original_data": {"row_sum": [17, 24, 21, 19, 23, 24, 8], "col_sum": [20, 24, 21, 12, 16, 27, 14]}, "id": 64, "observation": {"row_sum": [17, 24, 21, 19, 23, 24, 8], "col_sum": [20, 24, 21, 12, 16, 27, 14]}, "answer": [[null, "B", "B", null, "B", null, "B"], ["B", "B", "B", null, "B", "B", "B"], ["B", "B", "B", "B", "B", "B", null], ["B", null, "B", "B", "B", "B", null], ["B", "B", "B", "B", null, "B", "B"], ["B", "B", "B", null, "B", "B", "B"], [null, "B", null, null, null, "B", null]], "idx": 64, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_64.png", "answer_image": "figs/kakurasu_64_answer.png"} {"puzzle": "kakurasu", "row": 7, "column": 7, "level": "hard", "original_data": {"row_sum": [1, 17, 9, 20, 23, 10, 11], "col_sum": [15, 13, 9, 22, 27, 9, 7]}, "id": 65, "observation": {"row_sum": [1, 17, 9, 20, 23, 10, 11], "col_sum": [15, 13, 9, 22, 27, 9, 7]}, "answer": [["B", null, null, null, null, null, null], [null, "B", "B", null, "B", null, "B"], ["B", null, "B", null, "B", null, null], [null, "B", "B", "B", "B", "B", null], ["B", null, null, "B", "B", "B", "B"], ["B", null, null, "B", "B", null, null], [null, "B", null, "B", "B", null, null]], "idx": 65, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_65.png", "answer_image": "figs/kakurasu_65_answer.png"} {"puzzle": "kakurasu", "row": 8, "column": 8, "level": "easy", "original_data": {"row_sum": [19, 19, 8, 11, 10, 7, 22, 3], "col_sum": [11, 19, 7, 10, 24, 14, 7, 4]}, "id": 66, "observation": {"row_sum": [19, 19, 8, 11, 10, 7, 22, 3], "col_sum": [11, 19, 7, 10, 24, 14, 7, 4]}, "answer": [["B", null, null, "B", null, "B", null, "B"], ["B", null, "B", "B", "B", "B", null, null], [null, null, null, null, null, null, null, "B"], [null, null, null, null, "B", "B", null, null], [null, "B", "B", null, "B", null, null, null], [null, "B", null, null, "B", null, null, null], [null, null, null, "B", "B", "B", "B", null], ["B", "B", null, null, null, null, null, null]], "idx": 66, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_66.png", "answer_image": "figs/kakurasu_66_answer.png"} {"puzzle": "kakurasu", "row": 8, "column": 8, "level": "hard", "original_data": {"row_sum": [9, 28, 11, 6, 16, 19, 13, 23], "col_sum": [26, 2, 14, 9, 13, 9, 28, 21]}, "id": 67, "observation": {"row_sum": [9, 28, 11, 6, 16, 19, 13, 23], "col_sum": [26, 2, 14, 9, 13, 9, 28, 21]}, "answer": [[null, null, null, "B", "B", null, null, null], [null, "B", null, null, "B", "B", "B", "B"], [null, null, null, null, "B", "B", null, null], [null, null, null, null, null, "B", null, null], ["B", null, null, null, null, null, "B", "B"], ["B", null, "B", null, null, null, "B", "B"], ["B", null, null, null, "B", null, "B", null], ["B", null, "B", "B", null, null, "B", "B"]], "idx": 67, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_67.png", "answer_image": "figs/kakurasu_67_answer.png"} {"puzzle": "kakurasu", "row": 9, "column": 9, "level": "easy", "original_data": {"row_sum": [9, 8, 18, 5, 5, 10, 15, 5, 25], "col_sum": [13, 18, 8, 19, 20, 16, 1, 14, 10]}, "id": 68, "observation": {"row_sum": [9, 8, 18, 5, 5, 10, 15, 5, 25], "col_sum": [13, 18, 8, 19, 20, 16, 1, 14, 10]}, "answer": [[null, "B", null, null, null, null, "B", null, null], [null, null, null, null, null, null, null, "B", null], ["B", null, null, null, null, null, null, "B", "B"], ["B", null, null, "B", null, null, null, null, null], [null, null, null, null, "B", null, null, null, null], ["B", null, null, "B", "B", null, null, null, null], [null, null, null, null, null, "B", null, null, "B"], [null, "B", "B", null, null, null, null, null, null], [null, "B", null, "B", "B", "B", null, "B", null]], "idx": 68, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_68.png", "answer_image": "figs/kakurasu_68_answer.png"} {"puzzle": "kakurasu", "row": 9, "column": 9, "level": "hard", "original_data": {"row_sum": [1, 22, 12, 12, 27, 11, 34, 16, 27], "col_sum": [43, 27, 35, 10, 10, 26, 14, 39, 9]}, "id": 69, "observation": {"row_sum": [1, 22, 12, 12, 27, 11, 34, 16, 27], "col_sum": [43, 27, 35, 10, 10, 26, 14, 39, 9]}, "answer": [["B", null, null, null, null, null, null, null, null], [null, null, "B", "B", null, "B", null, null, "B"], ["B", null, null, null, "B", "B", null, null, null], ["B", null, "B", null, null, null, null, "B", null], ["B", "B", "B", null, null, "B", "B", "B", null], ["B", "B", null, null, null, null, null, "B", null], ["B", "B", "B", null, "B", "B", null, "B", "B"], ["B", null, "B", "B", null, null, null, "B", null], ["B", "B", "B", null, null, "B", "B", "B", null]], "idx": 69, "rules": "**Core Rules:**\nFill some cells black so that:\n1. In each row, the sum of the column-weights of black cells equals the row target number.\n2. In each column, the sum of the row-weights of black cells equals the column target number.\n3. Column-weights are listed above the board (left-to-right), row-weights are listed left of the board (top-to-bottom).\n4. Cells are either black or non-black.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_sum`: row target sums from top row to bottom row.\n - `col_sum`: column target sums from left column to right column.\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_sum": [9, 5, 7, 3], "col_sum": [3, 6, 7, 4]}, "image": "figs/kakurasu_69.png", "answer_image": "figs/kakurasu_69_answer.png"} {"puzzle": "kurodoko", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, 3, null], [4, null, null, null, null], [null, 9, null, 6, null], [null, null, null, null, 5], [null, 7, null, null, null]]}, "id": 70, "observation": {"data": [[null, null, null, 3, null], [4, null, null, null, null], [null, 9, null, 6, null], [null, null, null, null, 5], [null, 7, null, null, null]]}, "answer": [["B", null, null, 3, "B"], [4, null, null, "B", null], [null, 9, null, 6, null], ["B", null, "B", null, 5], [null, 7, null, "B", null]], "idx": 70, "rules": "**Core Rules:**\nShade some cells black guided by number clues.\n1. Each clue number counts how many white cells are visible from that clue cell, including itself.\n2. Visibility extends orthogonally until blocked by a black cell or the grid border.\n3. Clue cells are always white and cannot be shaded black.\n4. All white cells must form one orthogonally connected group.\n5. Black cells cannot touch orthogonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` for clue cells, `None` otherwise).\n4. **Answer:** full solved `N x N` 2D list where black cells are `'B'`, initial clue numbers are kept, and other empty cells are `None`.", "ref_observation": {"data": [[null, null, null, 3, null], [4, null, null, null, null], [null, 9, null, 7, null], [null, null, null, null, 7], [null, 6, null, null, null]]}, "image": "figs/kurodoko_70.png", "answer_image": "figs/kurodoko_70_answer.png"} {"puzzle": "kurodoko", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, null, null, 9, null, null, null], [null, 5, null, null, null, null, 8], [null, null, null, 8, null, null, 10], [null, null, null, 9, null, null, null], [7, null, null, 9, null, null, null], [3, null, null, null, null, 3, null], [null, null, null, 4, null, null, null]]}, "id": 71, "observation": {"data": [[null, null, null, 9, null, null, null], [null, 5, null, null, null, null, 8], [null, null, null, 8, null, null, 10], [null, null, null, 9, null, null, null], [7, null, null, 9, null, null, null], [3, null, null, null, null, 3, null], [null, null, null, 4, null, null, null]]}, "answer": [[null, "B", null, 9, null, null, null], [null, 5, null, null, "B", null, 8], ["B", null, "B", 8, null, null, 10], [null, "B", null, 9, null, null, null], [7, null, null, 9, null, "B", null], [3, "B", null, "B", null, 3, null], ["B", null, null, 4, null, "B", null]], "idx": 71, "rules": "**Core Rules:**\nShade some cells black guided by number clues.\n1. Each clue number counts how many white cells are visible from that clue cell, including itself.\n2. Visibility extends orthogonally until blocked by a black cell or the grid border.\n3. Clue cells are always white and cannot be shaded black.\n4. All white cells must form one orthogonally connected group.\n5. Black cells cannot touch orthogonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` for clue cells, `None` otherwise).\n4. **Answer:** full solved `N x N` 2D list where black cells are `'B'`, initial clue numbers are kept, and other empty cells are `None`.", "ref_observation": {"data": [[null, null, null, 3, null], [4, null, null, null, null], [null, 9, null, 7, null], [null, null, null, null, 7], [null, 6, null, null, null]]}, "image": "figs/kurodoko_71.png", "answer_image": "figs/kurodoko_71_answer.png"} {"puzzle": "kurodoko", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, null, 5, null, null, null, 13, null, null, null], [null, null, null, null, null, null, null, null, null, 4], [null, 11, null, null, null, null, null, null, null, null], [null, null, 8, null, 11, null, 14, 6, null, null], [null, 11, null, null, null, null, null, null, 8, null], [null, 14, null, null, null, null, null, null, 17, null], [null, null, 8, 4, null, 12, null, 6, null, null], [null, null, null, null, null, null, null, null, 8, null], [11, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, 3, null, null]]}, "id": 72, "observation": {"data": [[null, null, 5, null, null, null, 13, null, null, null], [null, null, null, null, null, null, null, null, null, 4], [null, 11, null, null, null, null, null, null, null, null], [null, null, 8, null, 11, null, 14, 6, null, null], [null, 11, null, null, null, null, null, null, 8, null], [null, 14, null, null, null, null, null, null, 17, null], [null, null, 8, 4, null, 12, null, 6, null, null], [null, null, null, null, null, null, null, null, 8, null], [11, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, 3, null, null]]}, "answer": [[null, "B", 5, null, null, null, 13, "B", null, null], [null, null, "B", null, null, "B", null, null, "B", 4], [null, 11, null, null, null, null, null, "B", null, null], ["B", null, 8, "B", 11, null, 14, 6, null, null], [null, 11, null, null, null, null, null, "B", 8, "B"], [null, 14, null, null, null, null, null, null, 17, null], [null, "B", 8, 4, "B", 12, null, 6, null, null], ["B", null, null, "B", null, null, null, "B", 8, "B"], [11, null, null, null, null, null, null, null, null, null], [null, null, "B", 2, "B", null, "B", 3, null, "B"]], "idx": 72, "rules": "**Core Rules:**\nShade some cells black guided by number clues.\n1. Each clue number counts how many white cells are visible from that clue cell, including itself.\n2. Visibility extends orthogonally until blocked by a black cell or the grid border.\n3. Clue cells are always white and cannot be shaded black.\n4. All white cells must form one orthogonally connected group.\n5. Black cells cannot touch orthogonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` for clue cells, `None` otherwise).\n4. **Answer:** full solved `N x N` 2D list where black cells are `'B'`, initial clue numbers are kept, and other empty cells are `None`.", "ref_observation": {"data": [[null, null, null, 3, null], [4, null, null, null, null], [null, 9, null, 7, null], [null, null, null, null, 7], [null, 6, null, null, null]]}, "image": "figs/kurodoko_72.png", "answer_image": "figs/kurodoko_72_answer.png"} {"puzzle": "lightup", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, null, 2, null, null, null, null], [null, 1, -1, null, null, -1, null], [null, null, null, null, null, 0, -1], [null, null, null, null, null, null, null], [0, -1, null, null, null, null, null], [null, 1, null, null, 1, 2, null], [null, null, null, null, -1, null, null]]}, "id": 73, "observation": {"data": [[null, null, 2, null, null, null, null], [null, 1, -1, null, null, -1, null], [null, null, null, null, null, 0, -1], [null, null, null, null, null, null, null], [0, -1, null, null, null, null, null], [null, 1, null, null, 1, 2, null], [null, null, null, null, -1, null, null]]}, "answer": [[null, "B", null, "B", null, null, null], [null, null, null, null, null, null, "B"], ["B", null, null, null, null, null, null], [null, "B", null, null, null, null, null], [null, null, null, null, "B", null, null], [null, null, "B", null, null, null, "B"], ["B", null, null, null, null, "B", null]], "idx": 73, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_73.png", "answer_image": "figs/lightup_73_answer.png"} {"puzzle": "lightup", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[-1, null, -1, null, null, null, 1], [null, null, 2, null, null, null, null], [null, null, null, null, null, 1, 1], [null, null, null, 1, null, null, null], [1, -1, null, null, null, null, null], [null, null, null, null, -1, null, null], [0, null, null, null, 1, null, -1]]}, "id": 74, "observation": {"data": [[-1, null, -1, null, null, null, 1], [null, null, 2, null, null, null, null], [null, null, null, null, null, 1, 1], [null, null, null, 1, null, null, null], [1, -1, null, null, null, null, null], [null, null, null, null, -1, null, null], [0, null, null, null, 1, null, -1]]}, "answer": [[null, null, null, null, null, "B", null], [null, "B", null, "B", null, null, null], [null, null, null, null, "B", null, null], ["B", null, null, null, null, null, "B"], [null, null, null, "B", null, null, null], [null, "B", null, null, null, null, null], [null, null, "B", null, null, "B", null]], "idx": 74, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_74.png", "answer_image": "figs/lightup_74_answer.png"} {"puzzle": "lightup", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, null, 0, null, 1, null, null], [null, null, null, null, null, null, null], [2, null, null, null, null, null, 1], [null, null, null, null, null, null, null], [2, null, null, null, null, null, 0], [null, null, null, null, null, null, null], [null, null, 0, null, 0, null, null]]}, "id": 75, "observation": {"data": [[null, null, 0, null, 1, null, null], [null, null, null, null, null, null, null], [2, null, null, null, null, null, 1], [null, null, null, null, null, null, null], [2, null, null, null, null, null, 0], [null, null, null, null, null, null, null], [null, null, 0, null, 0, null, null]]}, "answer": [["B", null, null, null, null, "B", null], [null, null, null, null, null, null, "B"], [null, "B", null, null, null, null, null], ["B", null, null, null, null, null, null], [null, null, null, "B", null, null, null], ["B", null, null, null, null, null, null], [null, null, null, null, null, null, "B"]], "idx": 75, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_75.png", "answer_image": "figs/lightup_75_answer.png"} {"puzzle": "lightup", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, null, null, null], [null, 1, 3, null, -1, null, null, -1, -1, null], [null, -1, null, -1, null, null, null, null, 0, null], [null, null, null, null, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, -1, null], [null, -1, null, null, null, null, null, null, null, null], [null, null, 3, null, null, null, null, null, null, null], [null, -1, null, null, null, null, 1, null, -1, null], [null, 0, 1, null, null, 1, null, 1, 0, null], [null, null, null, null, null, null, null, null, null, null]]}, "id": 76, "observation": {"data": [[null, null, null, null, null, null, null, null, null, null], [null, 1, 3, null, -1, null, null, -1, -1, null], [null, -1, null, -1, null, null, null, null, 0, null], [null, null, null, null, null, null, null, 2, null, null], [null, null, null, null, null, null, null, null, -1, null], [null, -1, null, null, null, null, null, null, null, null], [null, null, 3, null, null, null, null, null, null, null], [null, -1, null, null, null, null, 1, null, -1, null], [null, 0, 1, null, null, 1, null, 1, 0, null], [null, null, null, null, null, null, null, null, null, null]]}, "answer": [[null, null, "B", null, null, null, null, null, null, null], ["B", null, null, "B", null, null, null, null, null, null], [null, null, "B", null, null, "B", null, null, null, null], [null, null, null, null, null, null, "B", null, null, "B"], [null, null, null, null, null, null, null, "B", null, null], [null, null, null, null, null, null, null, null, "B", null], [null, "B", null, "B", null, null, null, null, null, null], [null, null, "B", null, null, null, null, null, null, null], [null, null, null, null, null, null, "B", null, null, null], [null, null, null, null, "B", null, null, null, null, null]], "idx": 76, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_76.png", "answer_image": "figs/lightup_76_answer.png"} {"puzzle": "lightup", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[1, -1, null, null, null, null, null, null, null, -1], [null, 2, null, null, null, -1, null, null, 2, -1], [null, null, null, null, null, 0, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, 1, -1, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, 0, 2, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, -1, null, null, null, null, null], [-1, 2, null, null, 2, null, null, null, 1, null], [0, null, null, null, null, null, null, null, -1, 0]]}, "id": 77, "observation": {"data": [[1, -1, null, null, null, null, null, null, null, -1], [null, 2, null, null, null, -1, null, null, 2, -1], [null, null, null, null, null, 0, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, 1, -1, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, 0, 2, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, -1, null, null, null, null, null], [-1, 2, null, null, 2, null, null, null, 1, null], [0, null, null, null, null, null, null, null, -1, 0]]}, "answer": [[null, null, null, null, null, null, null, null, "B", null], ["B", null, "B", null, null, null, null, "B", null, null], [null, null, null, "B", null, null, null, null, null, null], [null, "B", null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, "B", null], [null, null, null, null, "B", null, null, null, null, "B"], [null, null, null, null, null, null, "B", null, null, null], [null, "B", null, null, null, null, null, null, "B", null], [null, null, "B", null, null, "B", null, null, null, null], [null, null, null, null, "B", null, null, null, null, null]], "idx": 77, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_77.png", "answer_image": "figs/lightup_77_answer.png"} {"puzzle": "lightup", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[1, null, null, null, null, 1, 1, null, null, -1], [null, 2, null, null, null, null, null, null, -1, null], [null, null, null, null, null, null, 0, null, null, null], [0, null, 1, null, null, null, null, null, null, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, 1], [null, null, null, null, null, null, null, 1, null, 2], [null, null, null, 1, null, null, null, null, null, null], [null, -1, null, null, null, null, null, null, 2, null], [-1, null, null, -1, -1, null, null, null, null, -1]]}, "id": 78, "observation": {"data": [[1, null, null, null, null, 1, 1, null, null, -1], [null, 2, null, null, null, null, null, null, -1, null], [null, null, null, null, null, null, 0, null, null, null], [0, null, 1, null, null, null, null, null, null, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, 1], [null, null, null, null, null, null, null, 1, null, 2], [null, null, null, 1, null, null, null, null, null, null], [null, -1, null, null, null, null, null, null, 2, null], [-1, null, null, -1, -1, null, null, null, null, -1]]}, "answer": [[null, null, "B", null, null, null, null, "B", null, null], ["B", null, null, null, null, "B", null, null, null, null], [null, "B", null, null, null, null, null, null, null, null], [null, null, null, "B", null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, "B"], ["B", null, null, null, null, null, null, null, null, null], [null, null, null, null, "B", null, null, null, "B", null], [null, null, "B", null, null, null, null, null, null, "B"], [null, null, null, null, null, null, null, "B", null, null], [null, "B", null, null, null, null, null, null, "B", null]], "idx": 78, "rules": "**Core Rules:**\nPlace light bulbs on white cells so that:\n1. Every white cell is illuminated by at least one bulb.\n2. A bulb illuminates along its row and column until blocked by a black cell.\n3. No bulb may illuminate another bulb.\n4. Numbered black cells indicate exactly how many orthogonally adjacent bulbs they must have.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list for board blocks (`None` / `-1` / `0..4`).\n4. **Answer:** `N x N` grid using `'B'` for bulb cells and `None` for non-bulb cells.", "ref_observation": {"data": [[null, null, -1, 1, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 2], [1, null, null, null, null, null, 0], [1, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, 1, -1, null, null]]}, "image": "figs/lightup_78.png", "answer_image": "figs/lightup_78_answer.png"} {"puzzle": "lits", "row": 6, "column": 6, "level": "normal", "original_data": {"data": [[0, 0, 0, 0, 0, 1], [2, 2, 0, 0, 3, 1], [2, 4, 4, 3, 3, 1], [2, 2, 4, 3, 3, 1], [1, 2, 4, 4, 3, 1], [1, 1, 1, 1, 1, 1]]}, "id": 79, "observation": {"data": [[0, 0, 0, 0, 0, 1], [2, 2, 0, 0, 3, 1], [2, 4, 4, 3, 3, 1], [2, 2, 4, 3, 3, 1], [1, 2, 4, 4, 3, 1], [1, 1, 1, 1, 1, 1]]}, "answer": [[null, "I", "I", "I", "I", null], ["L", "L", null, null, "T", null], ["L", null, "L", "T", "T", null], ["L", null, "L", null, "T", "L"], [null, null, "L", "L", null, "L"], [null, null, null, null, "L", "L"]], "idx": 79, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_79.png", "answer_image": "figs/lits_79_answer.png"} {"puzzle": "lits", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[0, 0, 1, 1, 1, 1], [0, 0, 2, 2, 3, 3], [0, 2, 2, 2, 3, 3], [4, 2, 5, 2, 2, 3], [4, 2, 5, 5, 2, 2], [4, 4, 5, 5, 5, 2]]}, "id": 80, "observation": {"data": [[0, 0, 1, 1, 1, 1], [0, 0, 2, 2, 3, 3], [0, 2, 2, 2, 3, 3], [4, 2, 5, 2, 2, 3], [4, 2, 5, 5, 2, 2], [4, 4, 5, 5, 5, 2]]}, "answer": [["T", null, "I", "I", "I", "I"], ["T", "T", "S", null, null, "T"], ["T", null, "S", "S", "T", "T"], ["L", null, null, "S", null, "T"], ["L", null, null, "T", null, null], ["L", "L", "T", "T", "T", null]], "idx": 80, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_80.png", "answer_image": "figs/lits_80_answer.png"} {"puzzle": "lits", "row": 8, "column": 8, "level": "normal", "original_data": {"data": [[0, 0, 0, 0, 0, 0, 1, 1], [0, 2, 2, 2, 2, 1, 1, 2], [3, 3, 4, 4, 2, 2, 2, 2], [3, 3, 4, 4, 2, 5, 6, 2], [7, 3, 4, 4, 5, 5, 6, 6], [7, 7, 7, 4, 5, 5, 6, 8], [7, 4, 4, 4, 4, 5, 8, 8], [7, 7, 7, 7, 4, 8, 8, 8]]}, "id": 81, "observation": {"data": [[0, 0, 0, 0, 0, 0, 1, 1], [0, 2, 2, 2, 2, 1, 1, 2], [3, 3, 4, 4, 2, 2, 2, 2], [3, 3, 4, 4, 2, 5, 6, 2], [7, 3, 4, 4, 5, 5, 6, 6], [7, 7, 7, 4, 5, 5, 6, 8], [7, 4, 4, 4, 4, 5, 8, 8], [7, 7, 7, 7, 4, 8, 8, 8]]}, "answer": [["I", "I", "I", "I", null, null, "S", "S"], [null, null, null, "L", "L", "S", "S", null], ["L", "L", null, null, "L", null, null, null], [null, "L", null, null, "L", null, "T", null], ["I", "L", null, null, "S", null, "T", "T"], ["I", null, null, "L", "S", "S", "T", null], ["I", "L", "L", "L", null, "S", null, "L"], ["I", null, null, null, null, "L", "L", "L"]], "idx": 81, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_81.png", "answer_image": "figs/lits_81_answer.png"} {"puzzle": "lits", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[0, 1, 1, 1, 1, 2, 2, 2], [0, 0, 1, 3, 1, 4, 4, 2], [0, 1, 1, 3, 3, 3, 4, 2], [0, 0, 0, 5, 3, 6, 4, 2], [7, 7, 0, 5, 5, 6, 6, 2], [7, 0, 0, 5, 5, 5, 6, 2], [7, 7, 8, 8, 8, 6, 6, 2], [8, 8, 8, 8, 8, 6, 6, 6]]}, "id": 82, "observation": {"data": [[0, 1, 1, 1, 1, 2, 2, 2], [0, 0, 1, 3, 1, 4, 4, 2], [0, 1, 1, 3, 3, 3, 4, 2], [0, 0, 0, 5, 3, 6, 4, 2], [7, 7, 0, 5, 5, 6, 6, 2], [7, 0, 0, 5, 5, 5, 6, 2], [7, 7, 8, 8, 8, 6, 6, 2], [8, 8, 8, 8, 8, 6, 6, 6]]}, "answer": [[null, "I", "I", "I", "I", null, null, null], [null, null, null, "S", null, "L", "L", null], [null, null, null, "S", "S", null, "L", null], [null, "L", "L", null, "S", null, "L", "I"], ["L", null, "L", null, "T", null, null, "I"], ["L", null, "L", "T", "T", "T", null, "I"], ["L", "L", null, null, null, "L", null, "I"], [null, "I", "I", "I", "I", "L", "L", "L"]], "idx": 82, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_82.png", "answer_image": "figs/lits_82_answer.png"} {"puzzle": "lits", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [2, 2, 0, 2, 2, 3, 3, 3, 3, 1], [2, 2, 2, 2, 4, 4, 4, 4, 3, 1], [5, 5, 5, 5, 4, 4, 6, 6, 1, 1], [7, 5, 7, 4, 4, 6, 6, 6, 6, 8], [7, 7, 7, 7, 4, 9, 9, 9, 9, 8], [7, 10, 7, 10, 10, 10, 10, 9, 8, 8], [7, 10, 10, 10, 11, 9, 9, 9, 12, 8], [7, 11, 11, 11, 11, 11, 12, 12, 12, 8], [13, 13, 13, 13, 11, 8, 8, 8, 8, 8]]}, "id": 83, "observation": {"data": [[0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [2, 2, 0, 2, 2, 3, 3, 3, 3, 1], [2, 2, 2, 2, 4, 4, 4, 4, 3, 1], [5, 5, 5, 5, 4, 4, 6, 6, 1, 1], [7, 5, 7, 4, 4, 6, 6, 6, 6, 8], [7, 7, 7, 7, 4, 9, 9, 9, 9, 8], [7, 10, 7, 10, 10, 10, 10, 9, 8, 8], [7, 10, 10, 10, 11, 9, 9, 9, 12, 8], [7, 11, 11, 11, 11, 11, 12, 12, 12, 8], [13, 13, 13, 13, 11, 8, 8, 8, 8, 8]]}, "answer": [["I", "I", "I", "I", null, null, null, null, null, null], [null, null, null, "S", "S", "I", "I", "I", "I", "L"], [null, null, "S", "S", null, null, null, null, null, "L"], ["T", "T", "T", null, "T", null, "S", "S", "L", "L"], [null, "T", null, "T", "T", "S", "S", null, null, "I"], ["L", "L", "L", null, "T", null, "T", "T", "T", "I"], ["L", null, null, "L", null, null, null, "T", null, "I"], [null, "L", "L", "L", "T", null, null, null, "L", "I"], [null, null, null, null, "T", "T", "L", "L", "L", null], ["I", "I", "I", "I", "T", null, null, null, null, null]], "idx": 83, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_83.png", "answer_image": "figs/lits_83_answer.png"} {"puzzle": "lits", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[0, 0, 1, 1, 1, 1, 1, 1, 2, 2], [0, 1, 1, 2, 2, 2, 2, 2, 2, 2], [0, 0, 2, 2, 3, 3, 4, 4, 4, 4], [5, 5, 5, 5, 3, 3, 4, 3, 3, 3], [5, 5, 5, 5, 3, 3, 3, 3, 3, 3], [5, 6, 6, 6, 7, 7, 7, 8, 8, 3], [5, 9, 9, 6, 6, 7, 7, 7, 8, 3], [5, 9, 9, 6, 6, 7, 10, 7, 8, 8], [5, 9, 11, 11, 11, 10, 10, 7, 8, 12], [9, 9, 9, 9, 11, 10, 10, 12, 12, 12]]}, "id": 84, "observation": {"data": [[0, 0, 1, 1, 1, 1, 1, 1, 2, 2], [0, 1, 1, 2, 2, 2, 2, 2, 2, 2], [0, 0, 2, 2, 3, 3, 4, 4, 4, 4], [5, 5, 5, 5, 3, 3, 4, 3, 3, 3], [5, 5, 5, 5, 3, 3, 3, 3, 3, 3], [5, 6, 6, 6, 7, 7, 7, 8, 8, 3], [5, 9, 9, 6, 6, 7, 7, 7, 8, 3], [5, 9, 9, 6, 6, 7, 10, 7, 8, 8], [5, 9, 11, 11, 11, 10, 10, 7, 8, 12], [9, 9, 9, 9, 11, 10, 10, 12, 12, 12]]}, "answer": [["L", "L", null, null, "I", "I", "I", "I", null, null], ["L", null, null, "S", "S", null, null, null, null, null], ["L", null, "S", "S", null, "S", "I", "I", "I", "I"], ["T", "T", "T", null, "S", "S", null, null, null, null], [null, "T", null, null, "S", null, null, null, null, null], [null, "L", "L", "L", "T", "T", "T", "L", "L", null], [null, "I", null, "L", null, "T", null, null, "L", null], [null, "I", null, null, null, null, "T", null, "L", null], [null, "I", "L", "L", "L", "T", "T", null, null, "L"], [null, "I", null, null, "L", null, "T", "L", "L", "L"]], "idx": 84, "rules": "**Core Rules:**\nShade cells so that:\n1. In every region, shaded cells form exactly one tetromino of size 4.\n2. Allowed tetromino types are `L`, `I`, `T`, `S` (`O` is forbidden because 2x2 shaded blocks are forbidden).\n3. Two orthogonally adjacent regions cannot use the same tetromino type (rotation/reflection counts as the same type).\n4. All shaded cells in the whole grid must be orthogonally connected.\n5. No 2x2 block can be fully shaded.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using one of `L/I/T/S` for shaded cells and `None` for non-shaded cells.", "ref_observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 3, 3, 1, 1], [2, 3, 3, 3, 3, 1], [2, 3, 4, 1, 1, 1], [2, 3, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3]]}, "image": "figs/lits_84.png", "answer_image": "figs/lits_84_answer.png"} {"puzzle": "masyu", "row": 6, "column": 6, "level": "easy", "original_data": {"data": [[null, null, null, "W", null, null], [null, "B", null, null, "W", null], [null, "W", null, null, null, null], [null, null, null, null, "W", "B"], ["W", "B", "W", null, null, "W"], [null, null, null, null, null, null]]}, "id": 85, "observation": {"data": [[null, null, null, "W", null, null], [null, "B", null, null, "W", null], [null, "W", null, null, null, null], [null, null, null, null, "W", "B"], ["W", "B", "W", null, null, "W"], [null, null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [2, 4], [2, 3], [1, 3], [1, 2], [1, 1], [2, 1], [3, 1], [4, 1], [4, 2], [4, 3], [3, 3], [3, 4], [3, 5], [4, 5], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 85, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_85.png", "answer_image": "figs/masyu_85_answer.png"} {"puzzle": "masyu", "row": 8, "column": 8, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, null], ["W", null, null, "W", null, null, "B", "W"], ["W", null, null, "W", null, null, "W", "W"], [null, null, null, "W", "B", "W", null, null], [null, null, "W", null, "W", null, "W", null], [null, null, "W", null, null, null, null, null], [null, null, "W", null, "W", null, "W", null], ["B", "W", null, null, null, "W", null, null]]}, "id": 86, "observation": {"data": [[null, null, null, null, null, null, null, null], ["W", null, null, "W", null, null, "B", "W"], ["W", null, null, "W", null, null, "W", "W"], [null, null, null, "W", "B", "W", null, null], [null, null, "W", null, "W", null, "W", null], [null, null, "W", null, null, null, null, null], [null, null, "W", null, "W", null, "W", null], ["B", "W", null, null, null, "W", null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [2, 7], [3, 7], [3, 6], [2, 6], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [2, 2], [2, 3], [2, 4], [2, 5], [3, 5], [4, 5], [4, 6], [4, 7], [5, 7], [5, 6], [6, 6], [7, 6], [7, 5], [7, 4], [7, 3], [7, 2], [7, 1], [7, 0], [6, 0], [5, 0], [4, 0], [4, 1], [4, 2], [4, 3], [5, 3], [5, 2], [5, 1], [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [5, 5], [5, 4], [4, 4], [3, 4], [3, 3], [3, 2], [3, 1], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 86, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_86.png", "answer_image": "figs/masyu_86_answer.png"} {"puzzle": "masyu", "row": 8, "column": 8, "level": "normal", "original_data": {"data": [[null, null, "W", null, null, null, "W", null], ["W", null, null, null, "W", null, null, "W"], ["B", null, null, null, null, null, null, null], [null, null, null, null, "W", null, null, "B"], [null, "W", null, "B", null, null, null, null], [null, null, null, null, "W", "W", null, null], [null, null, null, "B", "W", null, null, "W"], ["B", null, null, null, null, null, "W", null]]}, "id": 87, "observation": {"data": [[null, null, "W", null, null, null, "W", null], ["W", null, null, null, "W", null, null, "W"], ["B", null, null, null, null, null, null, null], [null, null, null, null, "W", null, null, "B"], [null, "W", null, "B", null, null, null, null], [null, null, null, null, "W", "W", null, null], [null, null, null, "B", "W", null, null, "W"], ["B", null, null, null, null, null, "W", null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [1, 3], [1, 4], [1, 5], [0, 5], [0, 6], [0, 7], [1, 7], [2, 7], [2, 6], [2, 5], [2, 4], [2, 3], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [7, 5], [6, 5], [5, 5], [4, 5], [4, 4], [5, 4], [6, 4], [7, 4], [7, 3], [7, 2], [7, 1], [7, 0], [6, 0], [5, 0], [5, 1], [6, 1], [6, 2], [6, 3], [5, 3], [4, 3], [4, 2], [4, 1], [4, 0], [3, 0], [3, 1], [3, 2], [2, 2], [2, 1], [2, 0], [1, 0], [0, 0]], "idx": 87, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_87.png", "answer_image": "figs/masyu_87_answer.png"} {"puzzle": "masyu", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, null, null], [null, "W", null, null, "W", null, "W", null], ["B", null, null, null, null, "W", "W", null], [null, null, "W", null, null, null, "W", null], [null, null, null, null, null, "B", null, "W"], [null, null, "W", "W", null, null, null, null], [null, "W", null, null, null, null, null, null], [null, null, null, null, "W", null, null, "B"]]}, "id": 88, "observation": {"data": [[null, null, null, null, null, null, null, null], [null, "W", null, null, "W", null, "W", null], ["B", null, null, null, null, "W", "W", null], [null, null, "W", null, null, null, "W", null], [null, null, null, null, null, "B", null, "W"], [null, null, "W", "W", null, null, null, null], [null, "W", null, null, null, null, null, null], [null, null, null, null, "W", null, null, "B"]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 7], [2, 6], [2, 5], [2, 4], [3, 4], [3, 5], [3, 6], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [7, 5], [7, 4], [7, 3], [6, 3], [6, 2], [7, 2], [7, 1], [6, 1], [5, 1], [5, 2], [5, 3], [5, 4], [6, 4], [6, 5], [5, 5], [4, 5], [4, 4], [4, 3], [3, 3], [3, 2], [3, 1], [4, 1], [4, 0], [3, 0], [2, 0], [2, 1], [2, 2], [1, 2], [1, 1], [1, 0], [0, 0]], "idx": 88, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_88.png", "answer_image": "figs/masyu_88_answer.png"} {"puzzle": "masyu", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [["B", null, null, null, null, "B", null, null, null, null], [null, null, "B", "W", null, null, null, null, "W", "W"], [null, null, null, null, "W", null, null, "W", "W", null], [null, null, "W", "W", null, null, null, null, null, null], ["W", null, null, "W", "B", "W", null, "W", null, null], ["W", null, "W", "B", null, "B", null, "W", null, "W"], [null, "W", null, null, "W", "W", null, null, null, null], [null, null, null, "W", null, "B", "W", null, null, null], ["W", null, "W", null, null, null, "W", null, null, "W"], ["B", null, null, null, null, null, null, null, null, null]]}, "id": 89, "observation": {"data": [["B", null, null, null, null, "B", null, null, null, null], [null, null, "B", "W", null, null, null, null, "W", "W"], [null, null, null, null, "W", null, null, "W", "W", null], [null, null, "W", "W", null, null, null, null, null, null], ["W", null, null, "W", "B", "W", null, "W", null, null], ["W", null, "W", "B", null, "B", null, "W", null, "W"], [null, "W", null, null, "W", "W", null, null, null, null], [null, null, null, "W", null, "B", "W", null, null, null], ["W", null, "W", null, null, null, "W", null, null, "W"], ["B", null, null, null, null, null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [1, 3], [1, 2], [2, 2], [3, 2], [4, 2], [4, 1], [5, 1], [5, 2], [5, 3], [4, 3], [3, 3], [2, 3], [2, 4], [2, 5], [1, 5], [0, 5], [0, 6], [0, 7], [1, 7], [2, 7], [3, 7], [3, 8], [2, 8], [1, 8], [0, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [6, 8], [7, 8], [7, 9], [8, 9], [9, 9], [9, 8], [9, 7], [9, 6], [9, 5], [9, 4], [9, 3], [9, 2], [9, 1], [9, 0], [8, 0], [7, 0], [7, 1], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [7, 7], [7, 6], [7, 5], [6, 5], [5, 5], [5, 6], [5, 7], [5, 8], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [5, 4], [6, 4], [7, 4], [7, 3], [7, 2], [6, 2], [6, 1], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [2, 1], [2, 0], [1, 0], [0, 0]], "idx": 89, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_89.png", "answer_image": "figs/masyu_89_answer.png"} {"puzzle": "masyu", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, null, null, null, null, null, null, "B", null, null], [null, "W", null, null, null, null, "B", null, null, "W"], [null, null, null, null, null, null, null, null, null, null], ["W", null, null, "B", null, null, "W", null, "W", null], [null, "B", null, "W", null, "W", null, null, null, null], [null, null, "B", null, null, null, "W", "W", null, "W"], [null, "W", null, null, null, "W", null, "W", null, null], [null, null, null, null, null, null, "W", null, "W", null], [null, null, null, null, "B", null, "W", "W", null, null], ["B", null, null, null, null, null, null, null, null, null]]}, "id": 90, "observation": {"data": [[null, null, null, null, null, null, null, "B", null, null], [null, "W", null, null, null, null, "B", null, null, "W"], [null, null, null, null, null, null, null, null, null, null], ["W", null, null, "B", null, null, "W", null, "W", null], [null, "B", null, "W", null, "W", null, null, null, null], [null, null, "B", null, null, null, "W", "W", null, "W"], [null, "W", null, null, null, "W", null, "W", null, null], [null, null, null, null, null, null, "W", null, "W", null], [null, null, null, null, "B", null, "W", "W", null, null], ["B", null, null, null, null, null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [1, 5], [1, 6], [2, 6], [3, 6], [4, 6], [4, 7], [3, 7], [2, 7], [1, 7], [0, 7], [0, 8], [0, 9], [1, 9], [2, 9], [2, 8], [3, 8], [4, 8], [4, 9], [5, 9], [6, 9], [7, 9], [7, 8], [7, 7], [7, 6], [7, 5], [8, 5], [8, 6], [8, 7], [8, 8], [9, 8], [9, 7], [9, 6], [9, 5], [9, 4], [9, 3], [9, 2], [9, 1], [9, 0], [8, 0], [7, 0], [7, 1], [6, 1], [5, 1], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1], [3, 1], [4, 1], [4, 2], [4, 3], [4, 4], [5, 4], [5, 3], [5, 2], [6, 2], [7, 2], [8, 2], [8, 3], [8, 4], [7, 4], [6, 4], [6, 5], [6, 6], [6, 7], [6, 8], [5, 8], [5, 7], [5, 6], [5, 5], [4, 5], [3, 5], [3, 4], [3, 3], [2, 3], [1, 3], [1, 2], [1, 1], [1, 0], [0, 0]], "idx": 90, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_90.png", "answer_image": "figs/masyu_90_answer.png"} {"puzzle": "masyu", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, "W", null, null, "W", "W", null, null, null, "B"], [null, null, null, null, null, null, null, null, null, null], ["B", null, null, "W", null, null, null, "W", null, null], [null, "W", null, null, "W", "W", null, null, null, "W"], [null, null, null, "W", null, null, null, null, null, null], [null, null, null, null, "W", null, "W", null, null, null], [null, "W", null, null, null, null, "W", null, "W", null], [null, "W", null, null, "B", null, null, null, null, null], ["W", null, null, null, null, "B", null, null, null, null], [null, null, null, null, null, null, null, "B", null, "B"]]}, "id": 91, "observation": {"data": [[null, "W", null, null, "W", "W", null, null, null, "B"], [null, null, null, null, null, null, null, null, null, null], ["B", null, null, "W", null, null, null, "W", null, null], [null, "W", null, null, "W", "W", null, null, null, "W"], [null, null, null, "W", null, null, null, null, null, null], [null, null, null, null, "W", null, "W", null, null, null], [null, "W", null, null, null, null, "W", null, "W", null], [null, "W", null, null, "B", null, null, null, null, null], ["W", null, null, null, null, "B", null, null, null, null], [null, null, null, null, null, null, null, "B", null, "B"]]}, "answer": [[0, 0], [0, 1], [0, 2], [1, 2], [1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [1, 6], [1, 7], [0, 7], [0, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [4, 8], [5, 8], [6, 8], [7, 8], [7, 9], [8, 9], [9, 9], [9, 8], [9, 7], [8, 7], [7, 7], [7, 6], [8, 6], [9, 6], [9, 5], [9, 4], [9, 3], [9, 2], [9, 1], [9, 0], [8, 0], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [3, 2], [4, 2], [5, 2], [5, 1], [6, 1], [7, 1], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [7, 5], [6, 5], [6, 6], [6, 7], [5, 7], [5, 6], [5, 5], [4, 5], [4, 4], [5, 4], [6, 4], [7, 4], [7, 3], [7, 2], [6, 2], [6, 3], [5, 3], [4, 3], [3, 3], [3, 4], [3, 5], [3, 6], [4, 6], [4, 7], [3, 7], [3, 8], [2, 8], [2, 7], [2, 6], [2, 5], [1, 5], [1, 4], [2, 4], [2, 3], [2, 2], [2, 1], [2, 0], [1, 0], [0, 0]], "idx": 91, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `W` (white circle): the loop goes straight through this circle, and it must turn at least once in the previous or next step.\n2. `B` (black circle): the loop turns at this circle, and goes straight in both the previous and next steps.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `N x N` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `N x N` 2D list; each entry is `None`, `'W'`, or `'B'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B", "W", null, null, "W", null], [null, null, null, "W", null, null], [null, "W", null, null, "W", null], [null, "W", "W", null, "W", null], [null, "W", null, null, null, "W"], [null, null, null, "W", "W", "B"]]}, "image": "figs/masyu_91.png", "answer_image": "figs/masyu_91_answer.png"} {"puzzle": "minesweeper", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[2, null, 2, 2, null], [null, 3, null, null, null], [3, null, null, 3, null], [null, null, null, 1, null], [3, null, null, 1, 1]]}, "id": 92, "observation": {"data": [[2, null, 2, 2, null], [null, 3, null, null, null], [3, null, null, 3, null], [null, null, null, 1, null], [3, null, null, 1, 1]]}, "answer": [[null, "F", null, null, null], ["F", null, "F", null, "F"], [null, null, null, null, null], ["F", "F", null, null, "F"], [null, "F", null, null, null]], "idx": 92, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_92.png", "answer_image": "figs/minesweeper_92_answer.png"} {"puzzle": "minesweeper", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[null, null, null, 1, null], [null, 1, 2, 3, 3], [null, 2, null, null, null], [null, null, null, null, null], [1, null, 2, null, 0]]}, "id": 93, "observation": {"data": [[null, null, null, 1, null], [null, 1, 2, 3, 3], [null, 2, null, null, null], [null, null, null, null, null], [1, null, 2, null, 0]]}, "answer": [[null, "F", null, null, "F"], [null, null, null, null, null], [null, null, null, "F", "F"], [null, "F", "F", null, null], [null, null, null, null, null]], "idx": 93, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_93.png", "answer_image": "figs/minesweeper_93_answer.png"} {"puzzle": "minesweeper", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[0, null, null, 3, null, 3, null], [null, null, 2, 3, null, null, null], [null, null, null, null, 1, null, 1], [1, null, null, 1, null, 2, null], [1, null, null, null, 1, null, 2], [null, null, null, 2, null, null, null], [null, 1, 0, null, null, null, 1]]}, "id": 94, "observation": {"data": [[0, null, null, 3, null, 3, null], [null, null, 2, 3, null, null, null], [null, null, null, null, 1, null, 1], [1, null, null, 1, null, 2, null], [1, null, null, null, 1, null, 2], [null, null, null, 2, null, null, null], [null, 1, 0, null, null, null, 1]]}, "answer": [[null, null, "F", null, "F", null, "F"], [null, null, null, null, "F", null, null], [null, "F", null, null, null, null, null], [null, null, null, null, null, null, "F"], [null, null, "F", null, null, "F", null], ["F", null, null, null, null, null, null], [null, null, null, null, "F", "F", null]], "idx": 94, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_94.png", "answer_image": "figs/minesweeper_94_answer.png"} {"puzzle": "minesweeper", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, 1, null, null, 3, null, null], [null, null, 1, null, 4, null, 2], [null, 3, 2, 2, null, null, null], [2, null, 1, null, null, null, null], [null, null, null, null, 1, null, 0], [null, null, null, 1, null, null, null], [2, null, 2, null, null, null, 1]]}, "id": 95, "observation": {"data": [[null, 1, null, null, 3, null, null], [null, null, 1, null, 4, null, 2], [null, 3, 2, 2, null, null, null], [2, null, 1, null, null, null, null], [null, null, null, null, 1, null, 0], [null, null, null, 1, null, null, null], [2, null, 2, null, null, null, 1]]}, "answer": [[null, null, null, null, null, "F", null], ["F", null, null, "F", null, "F", null], ["F", null, null, null, "F", null, null], [null, "F", null, null, null, null, null], [null, null, null, null, null, null, null], [null, "F", null, null, "F", null, null], [null, "F", null, null, null, "F", null]], "idx": 95, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_95.png", "answer_image": "figs/minesweeper_95_answer.png"} {"puzzle": "minesweeper", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, null, null, 2, null, null, null, null, null], [1, null, 1, null, null, null, 3, null, null, 1], [null, null, null, null, 2, null, null, 2, 2, null], [2, null, 2, null, null, 3, null, null, 0, null], [null, null, null, 2, 3, null, null, null, null, 1], [1, null, null, 2, null, 3, null, 1, null, 1], [null, 1, 1, null, null, null, 1, null, null, 2], [null, null, null, null, null, 2, null, 2, null, 1], [null, null, null, 2, 2, null, 3, null, null, 1], [null, 1, 1, 1, 1, null, null, 2, null, null]]}, "id": 96, "observation": {"data": [[null, null, null, null, 2, null, null, null, null, null], [1, null, 1, null, null, null, 3, null, null, 1], [null, null, null, null, 2, null, null, 2, 2, null], [2, null, 2, null, null, 3, null, null, 0, null], [null, null, null, 2, 3, null, null, null, null, 1], [1, null, null, 2, null, 3, null, 1, null, 1], [null, 1, 1, null, null, null, 1, null, null, 2], [null, null, null, null, null, 2, null, 2, null, 1], [null, null, null, 2, 2, null, 3, null, null, 1], [null, 1, 1, 1, 1, null, null, 2, null, null]]}, "answer": [["F", null, null, "F", null, "F", null, null, null, null], [null, null, null, null, null, null, null, "F", "F", null], [null, null, null, null, null, "F", null, null, null, null], [null, "F", null, null, "F", null, null, null, null, null], [null, "F", null, null, null, "F", null, null, null, null], [null, null, null, null, "F", null, null, null, "F", null], [null, null, null, "F", null, "F", null, null, null, null], ["F", null, null, null, "F", null, null, null, "F", null], [null, null, "F", null, null, null, null, "F", null, null], [null, null, null, null, null, "F", "F", null, null, null]], "idx": 96, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_96.png", "answer_image": "figs/minesweeper_96_answer.png"} {"puzzle": "minesweeper", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, 1, null, 1, null, 3, null, 3, null], [2, 3, null, null, null, 4, null, null, 3, null], [1, null, null, null, null, null, null, 3, 3, null], [null, null, null, 2, null, 4, null, null, null, null], [null, null, null, null, null, 1, 0, null, 2, null], [null, 2, null, null, null, 4, 2, 3, null, null], [null, 0, null, 2, null, null, null, null, null, null], [null, 1, null, null, null, null, null, null, null, 2], [1, null, 1, null, null, 4, null, 2, null, 2], [null, null, null, null, null, 2, null, null, null, 1]]}, "id": 97, "observation": {"data": [[null, null, 1, null, 1, null, 3, null, 3, null], [2, 3, null, null, null, 4, null, null, 3, null], [1, null, null, null, null, null, null, 3, 3, null], [null, null, null, 2, null, 4, null, null, null, null], [null, null, null, null, null, 1, 0, null, 2, null], [null, 2, null, null, null, 4, 2, 3, null, null], [null, 0, null, 2, null, null, null, null, null, null], [null, 1, null, null, null, null, null, null, null, 2], [1, null, 1, null, null, 4, null, 2, null, 2], [null, null, null, null, null, 2, null, null, null, 1]]}, "answer": [["F", null, null, null, null, "F", null, "F", null, null], [null, null, "F", null, null, null, null, "F", null, "F"], [null, "F", null, null, "F", "F", "F", null, null, null], [null, null, null, null, null, null, null, null, "F", null], ["F", "F", null, null, "F", null, null, null, null, null], [null, null, null, null, null, null, null, null, "F", null], [null, null, null, null, "F", "F", "F", null, "F", null], [null, null, null, null, "F", "F", null, null, "F", null], [null, "F", null, null, "F", null, null, null, null, null], [null, null, null, null, "F", null, null, null, "F", null]], "idx": 97, "rules": "**Core Rules:**\nFind which cells contain mines so that:\n1. Each numbered cell equals the number of adjacent mines in its 8-neighborhood.\n2. Cells without numbers have no direct numeric clue.\n3. Mines are represented by flagged cells in the answer.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: clue grid as list of lists (`None` means no shown number).\n4. **Answer:** same-sized grid using `'F'` for flagged mine cells and `None` for non-mine cells.", "ref_observation": {"data": [[1, 2, null, null, 0], [1, null, null, null, 1], [3, null, 4, 3, null], [null, null, null, 3, null], [null, 3, 2, null, null]]}, "image": "figs/minesweeper_97.png", "answer_image": "figs/minesweeper_97_answer.png"} {"puzzle": "mosaic", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[null, 4, null, null, 1], [null, null, 8, null, null], [null, 6, 9, null, 5], [null, null, 6, null, null], [1, null, null, null, 3]]}, "id": 98, "observation": {"data": [[null, 4, null, null, 1], [null, null, 8, null, null], [null, 6, 9, null, 5], [null, null, 6, null, null], [1, null, null, null, 3]]}, "answer": [[null, "B", "B", null, null], [null, "B", "B", "B", null], [null, "B", "B", "B", "B"], [null, "B", "B", "B", "B"], [null, null, null, null, "B"]], "idx": 98, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_98.png", "answer_image": "figs/mosaic_98_answer.png"} {"puzzle": "mosaic", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[null, null, null, 1, null], [null, 2, 3, 4, null], [null, 3, 6, 6, null], [null, 5, null, 8, null], [null, null, 6, null, null]]}, "id": 99, "observation": {"data": [[null, null, null, 1, null], [null, 2, 3, 4, null], [null, 3, 6, 6, null], [null, 5, null, 8, null], [null, null, 6, null, null]]}, "answer": [["B", null, null, null, null], [null, null, null, "B", null], [null, null, "B", "B", "B"], [null, "B", "B", "B", null], [null, "B", "B", "B", "B"]], "idx": 99, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_99.png", "answer_image": "figs/mosaic_99_answer.png"} {"puzzle": "mosaic", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, 4, 4, null, null, 1, null], [null, null, null, null, 3, null, null], [null, 9, 7, 4, 3, 5, null], [null, 6, null, 2, null, null, 5], [3, null, 5, null, null, 4, null], [null, null, null, null, 1, null, null], [3, null, null, 2, null, null, 1]]}, "id": 100, "observation": {"data": [[null, 4, 4, null, null, 1, null], [null, null, null, null, 3, null, null], [null, 9, 7, 4, 3, 5, null], [null, 6, null, 2, null, null, 5], [3, null, 5, null, null, 4, null], [null, null, null, null, 1, null, null], [3, null, null, 2, null, null, 1]]}, "answer": [["B", null, null, "B", null, null, null], ["B", "B", "B", "B", null, null, "B"], ["B", "B", "B", null, null, "B", "B"], ["B", "B", "B", null, null, "B", "B"], [null, null, null, null, null, null, "B"], [null, "B", "B", "B", null, null, "B"], ["B", "B", null, null, null, null, null]], "idx": 100, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_100.png", "answer_image": "figs/mosaic_100_answer.png"} {"puzzle": "mosaic", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, 2, null, 2, null, 5, null], [4, 5, 4, null, 6, 6, 3], [3, null, 5, null, 6, 6, null], [3, null, null, null, 5, 4, null], [3, null, 6, null, 5, 4, 4], [5, null, 6, null, 4, null, null], [null, 4, null, null, null, 3, 2]]}, "id": 101, "observation": {"data": [[null, 2, null, 2, null, 5, null], [4, 5, 4, null, 6, 6, 3], [3, null, 5, null, 6, 6, null], [3, null, null, null, 5, 4, null], [3, null, 6, null, 5, 4, 4], [5, null, 6, null, 4, null, null], [null, 4, null, null, null, 3, 2]]}, "answer": [["B", null, null, null, "B", "B", null], [null, "B", null, null, "B", "B", "B"], ["B", "B", "B", "B", "B", null, null], [null, null, null, "B", null, "B", "B"], [null, "B", "B", "B", null, null, "B"], ["B", "B", null, "B", null, "B", null], ["B", "B", null, null, "B", null, "B"]], "idx": 101, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_101.png", "answer_image": "figs/mosaic_101_answer.png"} {"puzzle": "mosaic", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[4, 5, null, null, null, null, 1, null, 2, null], [null, null, 7, null, null, 2, null, 3, null, null], [6, 8, 7, 6, null, null, 3, null, null, 1], [null, 6, null, 5, 4, null, null, null, null, null], [null, null, 6, 6, 4, null, 4, 6, null, null], [null, 4, 7, 6, null, null, 7, null, null, 3], [null, null, 9, 8, null, null, null, null, null, 3], [2, null, 8, 7, null, null, 6, 5, 6, null], [null, null, null, 5, null, 3, null, null, null, 2], [2, null, null, 2, 3, null, 3, null, null, 0]]}, "id": 102, "observation": {"data": [[4, 5, null, null, null, null, 1, null, 2, null], [null, null, 7, null, null, 2, null, 3, null, null], [6, 8, 7, 6, null, null, 3, null, null, 1], [null, 6, null, 5, 4, null, null, null, null, null], [null, null, 6, 6, 4, null, 4, 6, null, null], [null, 4, 7, 6, null, null, 7, null, null, 3], [null, null, 9, 8, null, null, null, null, null, 3], [2, null, 8, 7, null, null, 6, 5, 6, null], [null, null, null, 5, null, 3, null, null, null, 2], [2, null, null, 2, 3, null, 3, null, null, 0]]}, "answer": [["B", "B", "B", null, null, null, null, null, "B", null], ["B", "B", null, "B", "B", null, null, "B", null, null], ["B", "B", "B", "B", null, "B", null, "B", null, null], ["B", "B", "B", null, "B", null, null, null, "B", null], [null, null, null, "B", null, null, "B", "B", "B", "B"], [null, "B", "B", "B", "B", null, "B", "B", null, null], [null, "B", "B", "B", null, "B", "B", "B", null, "B"], [null, "B", "B", "B", "B", null, null, "B", "B", "B"], [null, null, "B", "B", null, "B", null, "B", null, null], ["B", "B", null, null, null, "B", null, null, null, null]], "idx": 102, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_102.png", "answer_image": "figs/mosaic_102_answer.png"} {"puzzle": "mosaic", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, 2, null, 3, 3, 3, null, 2, null], [null, 5, null, 4, null, 3, null, 2, null, null], [3, 5, 2, null, null, null, 3, 2, null, null], [null, null, 2, 2, 3, null, null, 2, 2, 2], [null, 4, 5, null, 4, null, null, null, 2, null], [null, 4, 5, null, null, null, 3, null, 3, 3], [null, null, 6, 6, null, 4, null, 3, 3, null], [null, 6, 6, null, null, 5, 2, 2, 3, null], [null, null, null, 7, null, null, null, 0, 3, null], [3, 5, 4, null, null, 4, 2, 0, null, null]]}, "id": 103, "observation": {"data": [[null, null, 2, null, 3, 3, 3, null, 2, null], [null, 5, null, 4, null, 3, null, 2, null, null], [3, 5, 2, null, null, null, 3, 2, null, null], [null, null, 2, 2, 3, null, null, 2, 2, 2], [null, 4, 5, null, 4, null, null, null, 2, null], [null, 4, 5, null, null, null, 3, null, 3, 3], [null, null, 6, 6, null, 4, null, 3, 3, null], [null, 6, 6, null, null, 5, 2, 2, 3, null], [null, null, null, 7, null, null, null, 0, 3, null], [3, 5, 4, null, null, 4, 2, 0, null, null]]}, "answer": [["B", null, "B", null, "B", "B", null, "B", null, null], ["B", null, "B", null, "B", null, null, "B", null, null], ["B", null, null, null, null, null, null, null, null, "B"], ["B", null, "B", null, null, "B", "B", null, null, null], [null, null, null, "B", null, "B", null, null, "B", null], [null, "B", "B", "B", null, null, "B", null, null, "B"], ["B", null, "B", null, "B", null, "B", null, "B", null], [null, "B", null, "B", "B", null, null, null, null, "B"], ["B", "B", "B", "B", "B", "B", null, null, null, "B"], ["B", null, "B", null, "B", "B", null, null, null, "B"]], "idx": 103, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Each numbered cell equals the count of black cells in its 3x3 neighborhood (including itself).\n2. Unnumbered cells have no direct numeric constraint.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[null, 4, 5, null, 1], [null, null, null, null, null], [1, null, null, null, 0], [2, null, null, 3, null], [null, null, 4, null, null]]}, "image": "figs/mosaic_103.png", "answer_image": "figs/mosaic_103_answer.png"} {"puzzle": "nonograms", "row": 5, "column": 5, "level": "normal", "original_data": {"row_black_runs": [[1], [3], [3], [4], [2]], "col_black_runs": [[2, 1], [1, 2], [4], [2], [1]]}, "id": 104, "observation": {"row_black_runs": [[1], [3], [3], [4], [2]], "col_black_runs": [[2, 1], [1, 2], [4], [2], [1]]}, "answer": [["B", null, null, null, null], ["B", "B", "B", null, null], [null, null, "B", "B", "B"], ["B", "B", "B", "B", null], [null, "B", "B", null, null]], "idx": 104, "rules": "**Core Rules:**\nFill some cells black so that:\n1. Each row matches its row clues: clue numbers are lengths of consecutive black-cell runs in that row.\n2. Each column matches its column clues: clue numbers are lengths of consecutive black-cell runs in that column.\n3. Multiple runs in one row/column must be separated by at least one non-black cell.\n4. Clue order is fixed (left-to-right for rows, top-to-bottom for columns).\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_black_runs`: list of row clues from top row to bottom row; each item is a list (possibly multiple numbers).\n - `col_black_runs`: list of column clues from left column to right column; each item is a list (possibly multiple numbers).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_black_runs": [[2], [3], [1], [2, 2], [1, 2]], "col_black_runs": [[4], [2, 2], [1], [2], [2]]}, "image": "figs/nonograms_104.png", "answer_image": "figs/nonograms_104_answer.png"} {"puzzle": "nonograms", "row": 10, "column": 10, "level": "normal", "original_data": {"row_black_runs": [[4, 2, 1], [1, 3], [1, 4], [4], [5], [1], [3, 1], [4, 2], [7], [7]], "col_black_runs": [[1], [2, 1], [1, 1, 3], [1, 4], [4], [5, 4], [5, 2], [4, 2], [3, 2], [1, 4]]}, "id": 105, "observation": {"row_black_runs": [[4, 2, 1], [1, 3], [1, 4], [4], [5], [1], [3, 1], [4, 2], [7], [7]], "col_black_runs": [[1], [2, 1], [1, 1, 3], [1, 4], [4], [5, 4], [5, 2], [4, 2], [3, 2], [1, 4]]}, "answer": [["B", "B", "B", "B", null, "B", "B", null, null, "B"], [null, "B", null, null, null, "B", "B", "B", null, null], [null, null, "B", null, null, "B", "B", "B", "B", null], [null, null, null, null, null, "B", "B", "B", "B", null], [null, null, null, null, null, "B", "B", "B", "B", "B"], [null, null, null, null, null, null, null, null, null, "B"], [null, null, null, "B", "B", "B", null, null, null, "B"], [null, null, "B", "B", "B", "B", null, null, "B", "B"], [null, null, "B", "B", "B", "B", "B", "B", "B", null], [null, "B", "B", "B", "B", "B", "B", "B", null, null]], "idx": 105, "rules": "**Core Rules:**\nFill some cells black so that:\n1. Each row matches its row clues: clue numbers are lengths of consecutive black-cell runs in that row.\n2. Each column matches its column clues: clue numbers are lengths of consecutive black-cell runs in that column.\n3. Multiple runs in one row/column must be separated by at least one non-black cell.\n4. Clue order is fixed (left-to-right for rows, top-to-bottom for columns).\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `row_black_runs`: list of row clues from top row to bottom row; each item is a list (possibly multiple numbers).\n - `col_black_runs`: list of column clues from left column to right column; each item is a list (possibly multiple numbers).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for non-black cells.", "ref_observation": {"row_black_runs": [[2], [3], [1], [2, 2], [1, 2]], "col_black_runs": [[4], [2, 2], [1], [2], [2]]}, "image": "figs/nonograms_105.png", "answer_image": "figs/nonograms_105_answer.png"} {"puzzle": "norinori", "row": 6, "column": 6, "level": "normal", "original_data": {"data": [[0, 1, 1, 1, 1, 2], [0, 3, 4, 1, 2, 2], [0, 3, 4, 5, 5, 2], [0, 3, 6, 5, 5, 2], [3, 3, 6, 6, 2, 2], [3, 7, 7, 7, 7, 2]]}, "id": 106, "observation": {"data": [[0, 1, 1, 1, 1, 2], [0, 3, 4, 1, 2, 2], [0, 3, 4, 5, 5, 2], [0, 3, 6, 5, 5, 2], [3, 3, 6, 6, 2, 2], [3, 7, 7, 7, 7, 2]]}, "answer": [["S", "S", null, null, "S", "S"], [null, null, "S", null, null, null], [null, null, "S", null, "S", null], ["S", "S", null, null, "S", null], [null, null, "S", "S", null, null], ["S", "S", null, null, "S", "S"]], "idx": 106, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_106.png", "answer_image": "figs/norinori_106_answer.png"} {"puzzle": "norinori", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 2, 3], [0, 1, 0, 4, 5, 5], [0, 0, 0, 4, 6, 5], [0, 0, 4, 4, 6, 6], [7, 7, 7, 7, 6, 6]]}, "id": 107, "observation": {"data": [[0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 2, 3], [0, 1, 0, 4, 5, 5], [0, 0, 0, 4, 6, 5], [0, 0, 4, 4, 6, 6], [7, 7, 7, 7, 6, 6]]}, "answer": [[null, null, "S", "S", null, "S"], [null, "S", null, null, null, "S"], [null, "S", null, "S", "S", null], [null, null, "S", null, null, "S"], ["S", null, "S", null, null, "S"], ["S", null, null, "S", "S", null]], "idx": 107, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_107.png", "answer_image": "figs/norinori_107_answer.png"} {"puzzle": "norinori", "row": 8, "column": 8, "level": "normal", "original_data": {"data": [[0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 4, 1, 5, 2, 2, 2], [0, 0, 4, 4, 5, 5, 5, 2], [0, 0, 4, 6, 6, 5, 7, 7], [0, 0, 5, 5, 5, 5, 5, 7], [8, 8, 9, 10, 5, 5, 11, 11], [8, 9, 9, 10, 5, 5, 5, 11], [9, 9, 9, 9, 5, 5, 12, 12]]}, "id": 108, "observation": {"data": [[0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 4, 1, 5, 2, 2, 2], [0, 0, 4, 4, 5, 5, 5, 2], [0, 0, 4, 6, 6, 5, 7, 7], [0, 0, 5, 5, 5, 5, 5, 7], [8, 8, 9, 10, 5, 5, 11, 11], [8, 9, 9, 10, 5, 5, 5, 11], [9, 9, 9, 9, 5, 5, 12, 12]]}, "answer": [["S", "S", null, "S", "S", null, "S", "S"], [null, null, "S", null, null, "S", null, null], [null, null, "S", null, null, "S", null, null], [null, null, null, "S", "S", null, "S", "S"], [null, "S", "S", null, null, null, null, null], ["S", null, null, "S", null, null, "S", "S"], ["S", null, null, "S", null, null, null, null], [null, "S", "S", null, null, null, "S", "S"]], "idx": 108, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_108.png", "answer_image": "figs/norinori_108_answer.png"} {"puzzle": "norinori", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[0, 0, 0, 0, 1, 1, 1, 1], [0, 2, 2, 0, 3, 3, 1, 1], [0, 4, 4, 0, 3, 1, 1, 5], [4, 4, 4, 6, 3, 3, 1, 5], [4, 4, 4, 6, 7, 7, 1, 5], [4, 8, 8, 7, 7, 7, 9, 10], [4, 11, 12, 12, 9, 9, 9, 10], [11, 11, 11, 12, 12, 12, 12, 10]]}, "id": 109, "observation": {"data": [[0, 0, 0, 0, 1, 1, 1, 1], [0, 2, 2, 0, 3, 3, 1, 1], [0, 4, 4, 0, 3, 1, 1, 5], [4, 4, 4, 6, 3, 3, 1, 5], [4, 4, 4, 6, 7, 7, 1, 5], [4, 8, 8, 7, 7, 7, 9, 10], [4, 11, 12, 12, 9, 9, 9, 10], [11, 11, 11, 12, 12, 12, 12, 10]]}, "answer": [[null, null, null, "S", "S", null, null, null], [null, "S", "S", null, null, "S", "S", null], ["S", null, null, null, null, null, null, "S"], ["S", null, null, "S", null, "S", null, "S"], [null, null, null, "S", null, "S", null, null], [null, "S", "S", null, "S", null, "S", "S"], ["S", null, null, null, "S", null, null, null], ["S", null, "S", "S", null, null, "S", "S"]], "idx": 109, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_109.png", "answer_image": "figs/norinori_109_answer.png"} {"puzzle": "norinori", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[0, 1, 1, 2, 2, 2, 3, 3, 4, 4], [0, 5, 1, 5, 6, 6, 6, 6, 7, 4], [0, 5, 5, 5, 5, 5, 6, 6, 7, 7], [5, 5, 5, 5, 5, 8, 8, 6, 6, 7], [9, 10, 10, 11, 11, 6, 6, 6, 6, 6], [9, 10, 10, 11, 11, 12, 6, 13, 14, 14], [9, 15, 15, 15, 11, 12, 13, 13, 13, 14], [16, 16, 15, 11, 11, 11, 17, 13, 13, 13], [16, 18, 18, 11, 19, 19, 17, 13, 20, 13], [18, 18, 18, 19, 19, 19, 13, 13, 20, 13]]}, "id": 110, "observation": {"data": [[0, 1, 1, 2, 2, 2, 3, 3, 4, 4], [0, 5, 1, 5, 6, 6, 6, 6, 7, 4], [0, 5, 5, 5, 5, 5, 6, 6, 7, 7], [5, 5, 5, 5, 5, 8, 8, 6, 6, 7], [9, 10, 10, 11, 11, 6, 6, 6, 6, 6], [9, 10, 10, 11, 11, 12, 6, 13, 14, 14], [9, 15, 15, 15, 11, 12, 13, 13, 13, 14], [16, 16, 15, 11, 11, 11, 17, 13, 13, 13], [16, 18, 18, 11, 19, 19, 17, 13, 20, 13], [18, 18, 18, 19, 19, 19, 13, 13, 20, 13]]}, "answer": [["S", "S", null, "S", "S", null, "S", "S", null, "S"], [null, null, "S", null, null, null, null, null, null, "S"], ["S", null, "S", null, null, null, null, "S", "S", null], ["S", null, null, null, null, "S", "S", null, null, "S"], [null, "S", "S", null, null, null, null, null, null, "S"], ["S", null, null, "S", null, "S", null, "S", "S", null], ["S", null, null, "S", null, "S", null, null, null, "S"], [null, "S", "S", null, "S", null, "S", null, null, "S"], ["S", null, null, null, "S", null, "S", null, "S", null], ["S", null, "S", "S", null, null, null, null, "S", null]], "idx": 110, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_110.png", "answer_image": "figs/norinori_110_answer.png"} {"puzzle": "norinori", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[0, 0, 0, 0, 1, 1, 1, 2, 3, 3], [4, 0, 0, 5, 6, 6, 1, 2, 2, 2], [4, 4, 5, 5, 6, 7, 2, 2, 2, 2], [4, 4, 5, 6, 6, 7, 8, 8, 2, 2], [9, 10, 10, 11, 7, 7, 8, 12, 12, 2], [9, 9, 9, 11, 11, 13, 8, 12, 12, 12], [9, 9, 9, 9, 11, 13, 14, 14, 15, 15], [16, 16, 16, 17, 13, 13, 14, 15, 15, 18], [19, 19, 16, 17, 18, 18, 14, 18, 18, 18], [19, 19, 16, 16, 18, 18, 18, 18, 18, 18]]}, "id": 111, "observation": {"data": [[0, 0, 0, 0, 1, 1, 1, 2, 3, 3], [4, 0, 0, 5, 6, 6, 1, 2, 2, 2], [4, 4, 5, 5, 6, 7, 2, 2, 2, 2], [4, 4, 5, 6, 6, 7, 8, 8, 2, 2], [9, 10, 10, 11, 7, 7, 8, 12, 12, 2], [9, 9, 9, 11, 11, 13, 8, 12, 12, 12], [9, 9, 9, 9, 11, 13, 14, 14, 15, 15], [16, 16, 16, 17, 13, 13, 14, 15, 15, 18], [19, 19, 16, 17, 18, 18, 14, 18, 18, 18], [19, 19, 16, 16, 18, 18, 18, 18, 18, 18]]}, "answer": [["S", null, null, "S", null, "S", "S", null, "S", "S"], ["S", null, null, "S", null, null, null, null, null, null], [null, "S", "S", null, null, "S", "S", null, null, null], [null, null, null, "S", "S", null, null, "S", "S", null], [null, "S", "S", null, null, "S", "S", null, null, null], [null, null, null, "S", "S", null, null, "S", null, "S"], [null, "S", "S", null, null, "S", null, "S", null, "S"], ["S", null, null, "S", null, "S", null, null, "S", null], ["S", null, null, "S", null, null, "S", null, "S", null], [null, "S", "S", null, null, null, "S", null, null, null]], "idx": 111, "rules": "**Core Rules:**\nShade some cells so that:\n1. Each region contains exactly 2 shaded cells.\n2. Every shaded cell belongs to a domino (two orthogonally adjacent shaded cells).\n3. Different dominoes cannot touch orthogonally (diagonal touching is allowed).\n4. Dominoes may cross region borders.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** a same-sized grid, using `'S'` for shaded cells and `None` for unshaded cells.", "ref_observation": {"data": [[0, 0, 1, 1, 1, 2], [0, 0, 0, 3, 3, 2], [0, 4, 0, 0, 3, 3], [4, 4, 5, 5, 7, 3], [4, 5, 5, 6, 7, 3], [4, 4, 5, 6, 7, 7]]}, "image": "figs/norinori_111.png", "answer_image": "figs/norinori_111_answer.png"} {"puzzle": "nurikabe", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[3, null, null, 3, null], [null, null, 1, null, null], [null, null, null, null, null], [null, 3, null, null, null], [null, null, null, null, null]]}, "id": 112, "observation": {"data": [[3, null, null, 3, null], [null, null, 1, null, null], [null, null, null, null, null], [null, 3, null, null, null], [null, null, null, null, null]]}, "answer": [[null, "B", "B", null, null], [null, "B", null, "B", null], [null, "B", "B", "B", "B"], ["B", null, null, null, "B"], ["B", "B", "B", "B", "B"]], "idx": 112, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_112.png", "answer_image": "figs/nurikabe_112_answer.png"} {"puzzle": "nurikabe", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null], [null, 2, null, null, null, 2, null], [2, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 6], [null, 1, null, null, null, 3, null], [null, null, null, null, null, null, null]]}, "id": 113, "observation": {"data": [[null, null, null, null, null, null, null], [null, 2, null, null, null, 2, null], [2, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 6], [null, 1, null, null, null, 3, null], [null, null, null, null, null, null, null]]}, "answer": [["B", "B", "B", "B", "B", "B", "B"], ["B", null, null, "B", null, null, "B"], [null, "B", "B", "B", "B", "B", "B"], [null, "B", null, null, null, null, null], ["B", "B", "B", "B", "B", "B", null], ["B", null, "B", null, null, null, "B"], ["B", "B", "B", "B", "B", "B", "B"]], "idx": 113, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_113.png", "answer_image": "figs/nurikabe_113_answer.png"} {"puzzle": "nurikabe", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, 1, null, null, 2, null, null, null, 3, null], [2, null, null, null, null, null, null, 3, null, null], [null, null, 2, null, null, null, null, null, null, 2], [null, 3, null, null, null, 3, null, null, 6, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "id": 114, "observation": {"data": [[1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, 1, null, null, 2, null, null, null, 3, null], [2, null, null, null, null, null, null, 3, null, null], [null, null, 2, null, null, null, null, null, null, 2], [null, 3, null, null, null, 3, null, null, 6, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "answer": [[null, "B", "B", "B", "B", "B", "B", "B", "B", "B"], ["B", null, null, null, null, null, null, "B", null, "B"], ["B", "B", "B", "B", "B", "B", "B", "B", null, "B"], ["B", null, "B", null, null, "B", null, "B", null, "B"], [null, "B", "B", "B", "B", "B", null, null, "B", null], [null, "B", null, null, "B", null, "B", "B", "B", null], ["B", null, "B", "B", "B", null, null, "B", null, "B"], ["B", null, "B", null, "B", "B", "B", "B", null, "B"], ["B", null, "B", null, "B", null, null, null, null, "B"], ["B", "B", "B", "B", "B", "B", "B", "B", "B", "B"]], "idx": 114, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_114.png", "answer_image": "figs/nurikabe_114_answer.png"} {"puzzle": "nurikabe", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[null, null, null, null, null], [null, null, null, 5, null], [null, null, null, null, 1], [null, null, null, null, null], [1, null, 3, null, null]]}, "id": 115, "observation": {"data": [[null, null, null, null, null], [null, null, null, 5, null], [null, null, null, null, 1], [null, null, null, null, null], [1, null, 3, null, null]]}, "answer": [["B", "B", "B", "B", "B"], ["B", null, null, null, "B"], ["B", null, null, "B", null], ["B", "B", "B", "B", "B"], [null, "B", null, null, null]], "idx": 115, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_115.png", "answer_image": "figs/nurikabe_115_answer.png"} {"puzzle": "nurikabe", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, 2, null], [null, null, 4, null, null, null, null], [null, 1, null, null, null, 4, null], [null, null, null, null, 4, null, null], [null, 1, null, null, null, null, null], [null, null, null, null, null, null, null]]}, "id": 116, "observation": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, 2, null], [null, null, 4, null, null, null, null], [null, 1, null, null, null, 4, null], [null, null, null, null, 4, null, null], [null, 1, null, null, null, null, null], [null, null, null, null, null, null, null]]}, "answer": [["B", "B", "B", "B", "B", "B", "B"], ["B", null, null, "B", null, null, "B"], ["B", "B", null, null, "B", "B", "B"], ["B", null, "B", "B", "B", null, null], ["B", "B", "B", null, null, "B", null], ["B", null, "B", null, null, "B", null], ["B", "B", "B", "B", "B", "B", "B"]], "idx": 116, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_116.png", "answer_image": "figs/nurikabe_116_answer.png"} {"puzzle": "nurikabe", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, 1, null, null, null, null, null, null, null], [null, null, null, 5, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, 1, null, null, null, null, null], [null, null, null, null, null, 9, null, null, null, 5], [6, null, null, 3, null, null, null, 8, null, null], [null, null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, 1, null, null]]}, "id": 117, "observation": {"data": [[null, null, 1, null, null, null, null, null, null, null], [null, null, null, 5, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, 1, null, null, null, null, null], [null, null, null, null, null, 9, null, null, null, 5], [6, null, null, 3, null, null, null, 8, null, null], [null, null, null, null, null, null, null, null, 3, null], [null, null, null, null, null, null, null, null, null, null], [1, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, 1, null, null]]}, "answer": [["B", "B", null, "B", "B", "B", "B", "B", "B", null], [null, "B", "B", null, "B", null, null, null, "B", null], [null, "B", null, null, "B", "B", null, null, "B", null], [null, "B", null, "B", null, "B", "B", null, "B", null], [null, "B", null, "B", "B", null, "B", null, "B", null], [null, "B", "B", null, "B", null, "B", null, "B", "B"], [null, "B", null, null, "B", null, "B", "B", null, "B"], ["B", "B", "B", "B", "B", null, null, "B", null, "B"], [null, "B", null, null, null, null, "B", "B", null, "B"], ["B", "B", "B", "B", "B", "B", "B", null, "B", "B"]], "idx": 117, "rules": "**Core Rules:**\nColor cells black or white so that:\n1. Black cells form one orthogonally connected group.\n2. No 2x2 block may be entirely black.\n3. Each numbered cell belongs to a white island whose size equals that number.\n4. Each white island contains exactly one numbered cell.\n5. Numbered cells are white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: number grid as list of lists (`None` means no given number).\n4. **Answer:** same-sized grid using `'B'` for black cells and `None` for white cells.", "ref_observation": {"data": [[1, null, null, null, null], [null, 1, null, null, 2], [null, null, null, null, null], [null, null, null, 3, null], [null, null, null, null, null]]}, "image": "figs/nurikabe_117.png", "answer_image": "figs/nurikabe_117_answer.png"} {"puzzle": "renzoku", "row": 4, "column": 4, "level": "easy", "original_data": {"data": [[null, null, null, null], [2, null, null, null], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 2.5], [0.5, 0.0], [0.5, 2.0], [1.0, 1.5], [1.5, 1.0], [1.5, 3.0], [2.0, 0.5], [2.0, 2.5], [2.5, 0.0], [2.5, 2.0], [3.0, 1.5]]}, "id": 118, "observation": {"data": [[null, null, null, null], [2, null, null, null], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 2.5], [0.5, 0.0], [0.5, 2.0], [1.0, 1.5], [1.5, 1.0], [1.5, 3.0], [2.0, 0.5], [2.0, 2.5], [2.5, 0.0], [2.5, 2.0], [3.0, 1.5]]}, "answer": [[1, 2, 4, 3], [2, 4, 3, 1], [4, 3, 1, 2], [3, 1, 2, 4]], "idx": 118, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_118.png", "answer_image": "figs/renzoku_118_answer.png"} {"puzzle": "renzoku", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, 2, 4], [null, null, null, null, null], [null, null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 2.5], [0.5, 1.0], [0.5, 4.0], [1.0, 1.5], [1.0, 2.5], [1.5, 2.0], [2.5, 0.0], [3.0, 2.5], [3.5, 3.0], [4.0, 1.5]]}, "id": 119, "observation": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, 2, 4], [null, null, null, null, null], [null, null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 2.5], [0.5, 1.0], [0.5, 4.0], [1.0, 1.5], [1.0, 2.5], [1.5, 2.0], [2.5, 0.0], [3.0, 2.5], [3.5, 3.0], [4.0, 1.5]]}, "answer": [[5, 4, 2, 1, 3], [1, 3, 4, 5, 2], [3, 1, 5, 2, 4], [2, 5, 3, 4, 1], [4, 2, 1, 3, 5]], "idx": 119, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_119.png", "answer_image": "figs/renzoku_119_answer.png"} {"puzzle": "renzoku", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, 4, null, null], [null, null, null, null, null], [null, null, null, null, null]], "adjacent": [[0.0, 1.5], [0.0, 3.5], [0.5, 1.0], [0.5, 3.0], [1.0, 2.5], [1.5, 3.0], [1.5, 4.0], [2.5, 0.0], [2.5, 1.0], [3.0, 0.5], [3.0, 1.5], [3.5, 2.0], [3.5, 3.0], [4.0, 0.5], [4.0, 2.5], [4.0, 3.5]]}, "id": 120, "observation": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, 4, null, null], [null, null, null, null, null], [null, null, null, null, null]], "adjacent": [[0.0, 1.5], [0.0, 3.5], [0.5, 1.0], [0.5, 3.0], [1.0, 2.5], [1.5, 3.0], [1.5, 4.0], [2.5, 0.0], [2.5, 1.0], [3.0, 0.5], [3.0, 1.5], [3.5, 2.0], [3.5, 3.0], [4.0, 0.5], [4.0, 2.5], [4.0, 3.5]]}, "answer": [[1, 4, 5, 3, 2], [3, 5, 1, 2, 4], [5, 2, 4, 1, 3], [4, 3, 2, 5, 1], [2, 1, 3, 4, 5]], "idx": 120, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_120.png", "answer_image": "figs/renzoku_120_answer.png"} {"puzzle": "renzoku", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, 5, null, null, null], [null, null, null, null, 5]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [0.0, 3.5], [0.5, 2.0], [0.5, 4.0], [1.0, 0.5], [1.0, 2.5], [1.5, 1.0], [1.5, 2.0], [2.5, 0.0], [2.5, 4.0], [3.0, 3.5], [3.5, 2.0], [3.5, 3.0], [4.0, 1.5], [4.0, 2.5]]}, "id": 121, "observation": {"data": [[null, null, null, null, null], [null, null, null, null, null], [null, null, null, null, null], [null, 5, null, null, null], [null, null, null, null, 5]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [0.0, 3.5], [0.5, 2.0], [0.5, 4.0], [1.0, 0.5], [1.0, 2.5], [1.5, 1.0], [1.5, 2.0], [2.5, 0.0], [2.5, 4.0], [3.0, 3.5], [3.5, 2.0], [3.5, 3.0], [4.0, 1.5], [4.0, 2.5]]}, "answer": [[5, 4, 3, 1, 2], [3, 2, 4, 5, 1], [1, 3, 5, 2, 4], [2, 5, 1, 4, 3], [4, 1, 2, 3, 5]], "idx": 121, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_121.png", "answer_image": "figs/renzoku_121_answer.png"} {"puzzle": "renzoku", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null], [null, null, 6, null, 1, null, null], [null, null, null, null, null, null, null], [4, null, null, null, 7, 1, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, 2, null, null]], "adjacent": [[0.0, 3.5], [0.5, 1.0], [0.5, 3.0], [0.5, 6.0], [1.5, 0.0], [2.0, 2.5], [2.5, 3.0], [3.0, 1.5], [3.0, 5.5], [3.5, 1.0], [3.5, 6.0], [4.0, 2.5], [4.0, 4.5], [4.5, 0.0], [4.5, 4.0], [5.0, 2.5], [5.0, 5.5], [5.5, 5.0], [5.5, 6.0], [6.0, 1.5], [6.0, 5.5]]}, "id": 122, "observation": {"data": [[null, null, null, null, null, null, null], [null, null, 6, null, 1, null, null], [null, null, null, null, null, null, null], [4, null, null, null, 7, 1, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, 2, null, null]], "adjacent": [[0.0, 3.5], [0.5, 1.0], [0.5, 3.0], [0.5, 6.0], [1.5, 0.0], [2.0, 2.5], [2.5, 3.0], [3.0, 1.5], [3.0, 5.5], [3.5, 1.0], [3.5, 6.0], [4.0, 2.5], [4.0, 4.5], [4.5, 0.0], [4.5, 4.0], [5.0, 2.5], [5.0, 5.5], [5.5, 5.0], [5.5, 6.0], [6.0, 1.5], [6.0, 5.5]]}, "answer": [[7, 1, 3, 5, 6, 2, 4], [5, 2, 6, 4, 1, 7, 3], [6, 4, 1, 2, 5, 3, 7], [4, 6, 5, 3, 7, 1, 2], [2, 5, 7, 6, 3, 4, 1], [3, 7, 2, 1, 4, 6, 5], [1, 3, 4, 7, 2, 5, 6]], "idx": 122, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_122.png", "answer_image": "figs/renzoku_122_answer.png"} {"puzzle": "renzoku", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [2, null, null, null, null, null, null], [null, null, 7, 2, null, null, null], [null, null, null, null, null, null, null]], "adjacent": [[0.0, 1.5], [0.5, 2.0], [0.5, 5.0], [1.5, 3.0], [1.5, 5.0], [1.5, 6.0], [2.0, 2.5], [3.0, 0.5], [3.0, 3.5], [3.0, 4.5], [3.5, 1.0], [3.5, 3.0], [3.5, 4.0], [3.5, 6.0], [4.0, 1.5], [4.0, 2.5], [4.0, 3.5], [5.0, 0.5], [6.0, 1.5]]}, "id": 123, "observation": {"data": [[null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [2, null, null, null, null, null, null], [null, null, 7, 2, null, null, null], [null, null, null, null, null, null, null]], "adjacent": [[0.0, 1.5], [0.5, 2.0], [0.5, 5.0], [1.5, 3.0], [1.5, 5.0], [1.5, 6.0], [2.0, 2.5], [3.0, 0.5], [3.0, 3.5], [3.0, 4.5], [3.5, 1.0], [3.5, 3.0], [3.5, 4.0], [3.5, 6.0], [4.0, 1.5], [4.0, 2.5], [4.0, 3.5], [5.0, 0.5], [6.0, 1.5]]}, "answer": [[5, 2, 3, 1, 6, 4, 7], [7, 4, 2, 6, 1, 3, 5], [3, 1, 6, 5, 7, 2, 4], [6, 7, 1, 3, 4, 5, 2], [2, 6, 5, 4, 3, 7, 1], [4, 3, 7, 2, 5, 1, 6], [1, 5, 4, 7, 2, 6, 3]], "idx": 123, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_123.png", "answer_image": "figs/renzoku_123_answer.png"} {"puzzle": "renzoku", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, null, 6, null, null, null, 4], [null, null, null, null, 1, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 6], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null]], "adjacent": [[0.0, 3.5], [0.5, 3.0], [1.0, 2.5], [2.0, 5.5], [2.5, 1.0], [3.0, 1.5], [3.5, 2.0], [3.5, 4.0], [4.0, 0.5], [4.0, 3.5], [4.0, 5.5], [4.5, 3.0], [5.0, 1.5], [5.0, 4.5], [6.0, 2.5]]}, "id": 124, "observation": {"data": [[null, null, 6, null, null, null, 4], [null, null, null, null, 1, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, 6], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null], [null, null, null, null, null, null, null]], "adjacent": [[0.0, 3.5], [0.5, 3.0], [1.0, 2.5], [2.0, 5.5], [2.5, 1.0], [3.0, 1.5], [3.5, 2.0], [3.5, 4.0], [4.0, 0.5], [4.0, 3.5], [4.0, 5.5], [4.5, 3.0], [5.0, 1.5], [5.0, 4.5], [6.0, 2.5]]}, "answer": [[5, 1, 6, 2, 3, 7, 4], [2, 6, 4, 3, 1, 5, 7], [6, 4, 7, 1, 5, 2, 3], [1, 3, 2, 5, 7, 4, 6], [4, 5, 3, 7, 6, 1, 2], [7, 2, 1, 6, 4, 3, 5], [3, 7, 5, 4, 2, 6, 1]], "idx": 124, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_124.png", "answer_image": "figs/renzoku_124_answer.png"} {"puzzle": "renzoku", "row": 9, "column": 9, "level": "easy", "original_data": {"data": [[2, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, 1, null, 9, null, null, 5, null, null], [null, null, null, null, null, null, null, null, null], [null, 2, null, 4, null, null, null, 3, 9], [null, null, null, null, null, null, null, null, null], [6, null, null, null, null, null, null, 4, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, 3]], "adjacent": [[0.0, 1.5], [0.0, 6.5], [0.0, 7.5], [0.5, 1.0], [0.5, 2.0], [0.5, 8.0], [1.0, 1.5], [1.0, 4.5], [1.5, 5.0], [1.5, 8.0], [2.0, 3.5], [2.0, 7.5], [2.5, 2.0], [3.0, 1.5], [3.0, 3.5], [3.0, 5.5], [3.0, 7.5], [3.5, 0.0], [3.5, 3.0], [3.5, 4.0], [4.5, 1.0], [4.5, 5.0], [4.5, 6.0], [5.0, 0.5], [5.0, 4.5], [6.0, 0.5], [6.0, 2.5], [6.0, 3.5], [6.5, 0.0], [6.5, 2.0], [6.5, 8.0], [7.0, 5.5], [7.0, 7.5], [7.5, 1.0], [7.5, 4.0], [7.5, 6.0], [8.0, 2.5]]}, "id": 125, "observation": {"data": [[2, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, 1, null, 9, null, null, 5, null, null], [null, null, null, null, null, null, null, null, null], [null, 2, null, 4, null, null, null, 3, 9], [null, null, null, null, null, null, null, null, null], [6, null, null, null, null, null, null, 4, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, 3]], "adjacent": [[0.0, 1.5], [0.0, 6.5], [0.0, 7.5], [0.5, 1.0], [0.5, 2.0], [0.5, 8.0], [1.0, 1.5], [1.0, 4.5], [1.5, 5.0], [1.5, 8.0], [2.0, 3.5], [2.0, 7.5], [2.5, 2.0], [3.0, 1.5], [3.0, 3.5], [3.0, 5.5], [3.0, 7.5], [3.5, 0.0], [3.5, 3.0], [3.5, 4.0], [4.5, 1.0], [4.5, 5.0], [4.5, 6.0], [5.0, 0.5], [5.0, 4.5], [6.0, 0.5], [6.0, 2.5], [6.0, 3.5], [6.5, 0.0], [6.5, 2.0], [6.5, 8.0], [7.0, 5.5], [7.0, 7.5], [7.5, 1.0], [7.5, 4.0], [7.5, 6.0], [8.0, 2.5]]}, "answer": [[2, 7, 8, 3, 9, 1, 6, 5, 4], [9, 6, 7, 1, 4, 3, 8, 2, 5], [3, 1, 4, 9, 8, 2, 5, 7, 6], [7, 4, 3, 5, 6, 8, 9, 1, 2], [8, 2, 6, 4, 7, 5, 1, 3, 9], [4, 3, 9, 7, 5, 6, 2, 8, 1], [6, 5, 1, 2, 3, 9, 7, 4, 8], [5, 9, 2, 8, 1, 4, 3, 6, 7], [1, 8, 5, 6, 2, 7, 4, 9, 3]], "idx": 125, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_125.png", "answer_image": "figs/renzoku_125_answer.png"} {"puzzle": "renzoku", "row": 9, "column": 9, "level": "normal", "original_data": {"data": [[null, null, null, null, null, 9, 6, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, 1, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, 4, null, 9, null, 6, 1, 8, null]], "adjacent": [[0.0, 3.5], [0.0, 7.5], [0.5, 2.0], [0.5, 4.0], [1.0, 0.5], [1.0, 3.5], [1.5, 0.0], [1.5, 1.0], [1.5, 5.0], [2.0, 3.5], [2.0, 4.5], [2.0, 7.5], [2.5, 7.0], [3.0, 3.5], [3.0, 5.5], [4.0, 5.5], [5.5, 0.0], [5.5, 1.0], [5.5, 2.0], [5.5, 3.0], [5.5, 5.0], [5.5, 7.0], [6.0, 5.5], [6.0, 6.5], [6.5, 8.0], [7.0, 1.5], [7.0, 3.5], [7.0, 5.5], [7.5, 2.0]]}, "id": 126, "observation": {"data": [[null, null, null, null, null, 9, 6, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, 2, null, null, null, 1, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, 4, null, 9, null, 6, 1, 8, null]], "adjacent": [[0.0, 3.5], [0.0, 7.5], [0.5, 2.0], [0.5, 4.0], [1.0, 0.5], [1.0, 3.5], [1.5, 0.0], [1.5, 1.0], [1.5, 5.0], [2.0, 3.5], [2.0, 4.5], [2.0, 7.5], [2.5, 7.0], [3.0, 3.5], [3.0, 5.5], [4.0, 5.5], [5.5, 0.0], [5.5, 1.0], [5.5, 2.0], [5.5, 3.0], [5.5, 5.0], [5.5, 7.0], [6.0, 5.5], [6.0, 6.5], [6.5, 8.0], [7.0, 1.5], [7.0, 3.5], [7.0, 5.5], [7.5, 2.0]]}, "answer": [[5, 1, 4, 8, 7, 9, 6, 2, 3], [8, 7, 3, 5, 6, 2, 4, 9, 1], [9, 6, 8, 1, 2, 3, 7, 5, 4], [6, 3, 5, 7, 8, 1, 2, 4, 9], [3, 5, 9, 2, 4, 7, 8, 1, 6], [1, 8, 6, 4, 9, 5, 3, 7, 2], [2, 9, 7, 3, 1, 4, 5, 6, 8], [4, 2, 1, 6, 5, 8, 9, 3, 7], [7, 4, 2, 9, 3, 6, 1, 8, 5]], "idx": 126, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_126.png", "answer_image": "figs/renzoku_126_answer.png"} {"puzzle": "renzoku", "row": 9, "column": 9, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, 5, null, 2], [null, null, 8, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, 3, null, null, null, null, null, null], [null, 6, null, null, null, null, 1, null, null], [null, null, null, null, null, null, 9, null, 5], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null]], "adjacent": [[0.0, 4.5], [0.5, 1.0], [0.5, 5.0], [1.0, 6.5], [1.5, 4.0], [2.0, 0.5], [2.0, 5.5], [2.5, 3.0], [3.0, 0.5], [3.0, 5.5], [3.5, 2.0], [3.5, 4.0], [4.0, 5.5], [4.5, 1.0], [6.0, 5.5], [6.5, 0.0], [6.5, 3.0], [6.5, 5.0], [6.5, 7.0], [7.0, 5.5], [7.0, 6.5], [7.0, 7.5], [8.0, 1.5], [8.0, 3.5], [8.0, 5.5], [8.0, 7.5]]}, "id": 127, "observation": {"data": [[null, null, null, null, null, null, 5, null, 2], [null, null, 8, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, 3, null, null, null, null, null, null], [null, 6, null, null, null, null, 1, null, null], [null, null, null, null, null, null, 9, null, 5], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null]], "adjacent": [[0.0, 4.5], [0.5, 1.0], [0.5, 5.0], [1.0, 6.5], [1.5, 4.0], [2.0, 0.5], [2.0, 5.5], [2.5, 3.0], [3.0, 0.5], [3.0, 5.5], [3.5, 2.0], [3.5, 4.0], [4.0, 5.5], [4.5, 1.0], [6.0, 5.5], [6.5, 0.0], [6.5, 3.0], [6.5, 5.0], [6.5, 7.0], [7.0, 5.5], [7.0, 6.5], [7.0, 7.5], [8.0, 1.5], [8.0, 3.5], [8.0, 5.5], [8.0, 7.5]]}, "answer": [[6, 4, 1, 3, 7, 8, 5, 9, 2], [1, 3, 8, 5, 2, 9, 7, 6, 4], [9, 8, 5, 7, 1, 3, 4, 2, 6], [2, 1, 3, 6, 4, 7, 8, 5, 9], [8, 6, 4, 9, 5, 2, 1, 3, 7], [3, 7, 2, 4, 8, 6, 9, 1, 5], [5, 9, 7, 2, 6, 4, 3, 8, 1], [4, 2, 9, 1, 3, 5, 6, 7, 8], [7, 5, 6, 8, 9, 1, 2, 4, 3]], "idx": 127, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Numbers are from `1` to grid size `N`.\n2. Each row and each column contains each number exactly once.\n3. A dot between two orthogonally adjacent cells means their values are consecutive.\n4. If no dot is between two orthogonally adjacent cells, their values are not consecutive.\n\n**Coordinates & Output:**\n1. Cell centers are integer coordinates `(row, col)` with top-left `(0, 0)`.\n2. Between-cell coordinates use `.5`:\n - Horizontal gap: `(row, col+0.5)`\n - Vertical gap: `(row+0.5, col)`\n3. **Observation** has two parts:\n - `data`: clue grid as list of lists with numbers or `None`.\n - `adjacent`: list of midpoint coordinates where a dot exists.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null], [null, null, null, 1], [null, null, null, null], [null, null, null, null]], "adjacent": [[0.0, 0.5], [0.0, 1.5], [1.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 2.5], [0.5, 0.0], [0.5, 1.0], [1.5, 0.0], [1.5, 1.0], [2.5, 2.0], [2.5, 3.0]]}, "image": "figs/renzoku_127.png", "answer_image": "figs/renzoku_127_answer.png"} {"puzzle": "shingoki", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [["B3", null, null, "B5", "W2", null], [null, null, null, null, "B3", null], ["B2", null, null, null, null, null], [null, null, null, null, null, null], [null, "B2", null, "B2", null, "B2"], ["B3", null, null, null, null, null]]}, "id": 128, "observation": {"data": [["B3", null, null, "B5", "W2", null], [null, null, null, null, "B3", null], ["B2", null, null, null, null, null], [null, null, null, null, null, null], [null, "B2", null, "B2", null, "B2"], ["B3", null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2], [3, 3], [2, 3], [1, 3], [0, 3], [0, 4], [0, 5], [1, 5], [1, 4], [2, 4], [3, 4], [3, 5], [4, 5], [4, 4], [5, 4], [5, 3], [4, 3], [4, 2], [5, 2], [5, 1], [5, 0], [4, 0], [4, 1], [3, 1], [3, 0], [2, 0], [2, 1], [1, 1], [1, 0], [0, 0]], "idx": 128, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_128.png", "answer_image": "figs/shingoki_128_answer.png"} {"puzzle": "shingoki", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, null, null, null], [null, null, null, "B3", "B3", "B2"], [null, null, "W2", null, null, null], [null, "W2", null, null, null, null], [null, null, null, null, null, "W2"], ["B7", null, null, null, "B2", null]]}, "id": 129, "observation": {"data": [[null, null, null, null, null, null], [null, null, null, "B3", "B3", "B2"], [null, null, "W2", null, null, null], [null, "W2", null, null, null, null], [null, null, null, null, null, "W2"], ["B7", null, null, null, "B2", null]]}, "answer": [[0, 0], [0, 1], [1, 1], [1, 2], [1, 3], [0, 3], [0, 4], [0, 5], [1, 5], [1, 4], [2, 4], [3, 4], [3, 5], [4, 5], [5, 5], [5, 4], [4, 4], [4, 3], [3, 3], [2, 3], [2, 2], [2, 1], [3, 1], [4, 1], [4, 2], [5, 2], [5, 1], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 129, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_129.png", "answer_image": "figs/shingoki_129_answer.png"} {"puzzle": "shingoki", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, null, null, "B2", "B2", null, null, null], [null, null, null, null, null, null, null, null], [null, null, "B2", null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, "W5", "W2", null, null, null, null, null], ["W7", null, null, "W2", null, "B2", "W2", "W7"], [null, null, null, null, null, null, "B3", null], [null, null, "B6", null, null, null, null, null]]}, "id": 130, "observation": {"data": [[null, null, null, "B2", "B2", null, null, null], [null, null, null, null, null, null, null, null], [null, null, "B2", null, null, null, null, null], [null, null, null, null, null, null, null, null], [null, "W5", "W2", null, null, null, null, null], ["W7", null, null, "W2", null, "B2", "W2", "W7"], [null, null, null, null, null, null, "B3", null], [null, null, "B6", null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [4, 2], [3, 2], [3, 3], [2, 3], [2, 2], [1, 2], [1, 3], [0, 3], [0, 4], [1, 4], [1, 5], [2, 5], [2, 4], [3, 4], [4, 4], [4, 3], [5, 3], [6, 3], [6, 4], [5, 4], [5, 5], [6, 5], [6, 6], [5, 6], [4, 6], [4, 5], [3, 5], [3, 6], [2, 6], [1, 6], [0, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [7, 5], [7, 4], [7, 3], [7, 2], [6, 2], [6, 1], [7, 1], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 130, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_130.png", "answer_image": "figs/shingoki_130_answer.png"} {"puzzle": "shingoki", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, null, "W3", null, null, null, null, null], [null, null, "B3", null, null, null, null, null], [null, null, null, null, "B2", null, "W3", null], [null, "W4", null, null, null, null, null, null], [null, null, null, null, "W2", "B3", null, "W6"], [null, null, null, null, "B5", null, "W2", null], ["B7", null, "B2", null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "id": 131, "observation": {"data": [[null, null, "W3", null, null, null, null, null], [null, null, "B3", null, null, null, null, null], [null, null, null, null, "B2", null, "W3", null], [null, "W4", null, null, null, null, null, null], [null, null, null, null, "W2", "B3", null, "W6"], [null, null, null, null, "B5", null, "W2", null], ["B7", null, "B2", null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [1, 3], [1, 4], [2, 4], [2, 3], [3, 3], [3, 2], [2, 2], [1, 2], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [5, 3], [5, 4], [4, 4], [3, 4], [3, 5], [3, 6], [2, 6], [1, 6], [0, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [6, 6], [5, 6], [4, 6], [4, 5], [5, 5], [6, 5], [6, 4], [7, 4], [7, 3], [6, 3], [6, 2], [7, 2], [7, 1], [6, 1], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 131, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_131.png", "answer_image": "figs/shingoki_131_answer.png"} {"puzzle": "shingoki", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[null, "B6", null, null, null, null, null, null], [null, null, null, null, "B5", null, null, "B8"], [null, null, null, null, null, null, null, null], ["W5", null, null, "B3", null, "W3", "W5", null], [null, null, null, null, "B4", null, null, null], [null, null, null, null, null, null, null, null], [null, "B6", null, null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "id": 132, "observation": {"data": [[null, "B6", null, null, null, null, null, null], [null, null, null, null, "B5", null, null, "B8"], [null, null, null, null, null, null, null, null], ["W5", null, null, "B3", null, "W3", "W5", null], [null, null, null, null, "B4", null, null, null], [null, null, null, null, null, null, null, null], [null, "B6", null, null, null, null, null, null], [null, null, null, null, null, null, null, null]]}, "answer": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [1, 5], [1, 6], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [6, 6], [5, 6], [4, 6], [3, 6], [2, 6], [2, 5], [3, 5], [4, 5], [5, 5], [5, 4], [5, 3], [4, 3], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [2, 2], [2, 3], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [6, 2], [6, 3], [6, 4], [7, 4], [7, 3], [7, 2], [7, 1], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1], [1, 1], [0, 1]], "idx": 132, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_132.png", "answer_image": "figs/shingoki_132_answer.png"} {"puzzle": "shingoki", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [["B6", null, null, "B7", null, null, null, null, "B2", "B2", null], [null, null, null, null, null, null, null, null, null, null, "W2"], [null, null, null, null, "W4", null, "W3", null, "B7", null, null], ["W5", "W2", null, null, null, null, null, null, null, "W2", null], [null, null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, "B2", null], [null, "B2", null, null, "B3", "B3", null, "B5", null, null, null], [null, null, null, null, null, null, null, null, null, null, null], [null, "B2", "B4", null, null, null, "B3", null, "B7", null, null], ["W2", null, null, "B3", null, null, null, null, null, "B2", "W2"], [null, null, "B2", null, null, null, "B2", "B2", null, null, null]]}, "id": 133, "observation": {"data": [["B6", null, null, "B7", null, null, null, null, "B2", "B2", null], [null, null, null, null, null, null, null, null, null, null, "W2"], [null, null, null, null, "W4", null, "W3", null, "B7", null, null], ["W5", "W2", null, null, null, null, null, null, null, "W2", null], [null, null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, "B2", null], [null, "B2", null, null, "B3", "B3", null, "B5", null, null, null], [null, null, null, null, null, null, null, null, null, null, null], [null, "B2", "B4", null, null, null, "B3", null, "B7", null, null], ["W2", null, null, "B3", null, null, null, null, null, "B2", "W2"], [null, null, "B2", null, null, null, "B2", "B2", null, null, null]]}, "answer": [[0, 0], [0, 1], [1, 1], [1, 2], [2, 2], [2, 1], [3, 1], [4, 1], [4, 2], [4, 3], [3, 3], [2, 3], [1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [1, 6], [2, 6], [3, 6], [3, 7], [4, 7], [5, 7], [6, 7], [6, 6], [6, 5], [5, 5], [5, 6], [4, 6], [4, 5], [3, 5], [2, 5], [1, 5], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [5, 3], [5, 2], [6, 2], [7, 2], [8, 2], [8, 3], [7, 3], [6, 3], [6, 4], [7, 4], [8, 4], [8, 5], [8, 6], [7, 6], [7, 7], [8, 7], [8, 8], [7, 8], [6, 8], [5, 8], [4, 8], [3, 8], [2, 8], [2, 7], [1, 7], [0, 7], [0, 8], [1, 8], [1, 9], [0, 9], [0, 10], [1, 10], [2, 10], [2, 9], [3, 9], [4, 9], [4, 10], [5, 10], [5, 9], [6, 9], [6, 10], [7, 10], [7, 9], [8, 9], [8, 10], [9, 10], [10, 10], [10, 9], [9, 9], [9, 8], [10, 8], [10, 7], [9, 7], [9, 6], [10, 6], [10, 5], [9, 5], [9, 4], [9, 3], [10, 3], [10, 2], [9, 2], [9, 1], [10, 1], [10, 0], [9, 0], [8, 0], [8, 1], [7, 1], [7, 0], [6, 0], [6, 1], [5, 1], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0]], "idx": 133, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_133.png", "answer_image": "figs/shingoki_133_answer.png"} {"puzzle": "shingoki", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, null, "W4", null, null, null, null, null, null, null, "B12"], [null, null, null, "B5", null, "B2", "B4", "B2", null, null, null], [null, null, null, null, null, "B3", null, null, null, null, null], [null, "B2", null, "B3", null, null, null, null, null, null, null], ["W3", null, null, "B3", null, null, null, null, "W2", null, null], [null, "B2", "B5", "B3", null, null, "B7", null, null, "W5", null], [null, null, null, null, null, "B3", null, null, "W2", null, null], [null, null, null, null, null, "B3", null, null, null, null, null], [null, null, null, null, null, "B3", null, null, null, "W2", "B3"], [null, "B2", null, null, null, null, null, "B4", null, null, null], [null, "W4", null, null, null, null, null, null, null, null, null]]}, "id": 134, "observation": {"data": [[null, null, "W4", null, null, null, null, null, null, null, "B12"], [null, null, null, "B5", null, "B2", "B4", "B2", null, null, null], [null, null, null, null, null, "B3", null, null, null, null, null], [null, "B2", null, "B3", null, null, null, null, null, null, null], ["W3", null, null, "B3", null, null, null, null, "W2", null, null], [null, "B2", "B5", "B3", null, null, "B7", null, null, "W5", null], [null, null, null, null, null, "B3", null, null, "W2", null, null], [null, null, null, null, null, "B3", null, null, null, null, null], [null, null, null, null, null, "B3", null, null, null, "W2", "B3"], [null, "B2", null, null, null, null, null, "B4", null, null, null], [null, "W4", null, null, null, null, null, null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [1, 5], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [7, 9], [7, 8], [8, 8], [8, 9], [8, 10], [9, 10], [9, 9], [10, 9], [10, 8], [9, 8], [9, 7], [8, 7], [7, 7], [6, 7], [6, 8], [6, 9], [5, 9], [4, 9], [3, 9], [2, 9], [1, 9], [1, 8], [2, 8], [2, 7], [1, 7], [1, 6], [2, 6], [3, 6], [4, 6], [4, 7], [3, 7], [3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [6, 6], [7, 6], [8, 6], [9, 6], [10, 6], [10, 5], [9, 5], [9, 4], [10, 4], [10, 3], [10, 2], [10, 1], [10, 0], [9, 0], [9, 1], [8, 1], [8, 0], [7, 0], [7, 1], [6, 1], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [2, 1], [2, 2], [3, 2], [4, 2], [4, 1], [5, 1], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [9, 3], [8, 3], [8, 4], [8, 5], [7, 5], [7, 4], [7, 3], [6, 3], [6, 4], [6, 5], [5, 5], [5, 4], [5, 3], [4, 3], [4, 4], [4, 5], [3, 5], [2, 5], [2, 4], [3, 4], [3, 3], [2, 3], [1, 3], [1, 2], [1, 1], [1, 0], [0, 0]], "idx": 134, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_134.png", "answer_image": "figs/shingoki_134_answer.png"} {"puzzle": "shingoki", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, "W9", null, null, null, null, null, null, null, null], [null, null, null, null, null, "W6", null, null, null, null, null], ["B4", "B2", null, "B4", null, "B3", null, null, null, null, null], [null, null, "B3", null, null, null, "B3", "W2", null, "W2", null], [null, null, null, null, null, null, null, null, null, null, null], ["B8", null, null, null, null, null, "B4", null, null, null, null], [null, "B3", null, null, null, null, "B4", null, null, null, "B4"], [null, null, null, null, null, "W3", null, null, null, null, "W3"], [null, null, "B2", null, null, null, null, null, null, "B2", null], [null, null, null, null, null, null, "W7", null, null, null, null], [null, null, null, null, null, null, "W9", null, null, null, null]]}, "id": 135, "observation": {"data": [[null, null, "W9", null, null, null, null, null, null, null, null], [null, null, null, null, null, "W6", null, null, null, null, null], ["B4", "B2", null, "B4", null, "B3", null, null, null, null, null], [null, null, "B3", null, null, null, "B3", "W2", null, "W2", null], [null, null, null, null, null, null, null, null, null, null, null], ["B8", null, null, null, null, null, "B4", null, null, null, null], [null, "B3", null, null, null, null, "B4", null, null, null, "B4"], [null, null, null, null, null, "W3", null, null, null, null, "W3"], [null, null, "B2", null, null, null, null, null, null, "B2", null], [null, null, null, null, null, null, "W7", null, null, null, null], [null, null, null, null, null, null, "W9", null, null, null, null]]}, "answer": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 9], [1, 10], [2, 10], [2, 9], [3, 9], [4, 9], [4, 8], [3, 8], [3, 7], [3, 6], [2, 6], [2, 7], [2, 8], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [2, 2], [3, 2], [3, 1], [4, 1], [4, 2], [4, 3], [3, 3], [2, 3], [2, 4], [2, 5], [3, 5], [3, 4], [4, 4], [4, 5], [4, 6], [5, 6], [5, 7], [5, 8], [5, 9], [6, 9], [6, 10], [7, 10], [8, 10], [9, 10], [9, 9], [10, 9], [10, 8], [10, 7], [10, 6], [10, 5], [10, 4], [10, 3], [10, 2], [10, 1], [10, 0], [9, 0], [8, 0], [7, 0], [7, 1], [6, 1], [6, 2], [6, 3], [7, 3], [7, 2], [8, 2], [8, 1], [9, 1], [9, 2], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7], [9, 8], [8, 8], [8, 9], [7, 9], [7, 8], [6, 8], [6, 7], [6, 6], [7, 6], [8, 6], [8, 5], [7, 5], [6, 5], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1], [1, 1], [1, 0], [0, 0]], "idx": 135, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nThe loop must pass through all clue circles, where:\n1. `Wk` (white circle): the loop goes straight through the circle.\n2. `Bk` (black circle): the loop turns at the circle.\n3. The number `k` is the sum of the lengths of the two straight segments extending from that circle.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)` on an `(N+1) x (N+1)` dot grid.\n2. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n3. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` 2D list; each entry is `None` or a clue token string like `'W3'` / `'B5'`.\n4. **Answer:** an ordered closed loop path as a list of dot coordinates, e.g.\n `[(0,0), (0,1), (1,1), ..., (0,0)]`.", "ref_observation": {"data": [["B5", "W3", null, null, null, null], [null, "B2", "B3", null, null, null], [null, null, null, "W4", null, null], [null, null, null, null, null, "W5"], ["W2", null, "B2", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/shingoki_135.png", "answer_image": "figs/shingoki_135_answer.png"} {"puzzle": "skyscrapers", "row": 4, "column": 4, "level": "easy", "original_data": {"U": [2, 1, 2, 2], "D": [3, 4, 1, 2], "L": [2, 1, 2, 2], "R": [3, 4, 1, 2]}, "id": 136, "observation": {"U": [2, 1, 2, 2], "D": [3, 4, 1, 2], "L": [2, 1, 2, 2], "R": [3, 4, 1, 2]}, "answer": [[1, 4, 3, 2], [4, 3, 2, 1], [3, 2, 1, 4], [2, 1, 4, 3]], "idx": 136, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_136.png", "answer_image": "figs/skyscrapers_136_answer.png"} {"puzzle": "skyscrapers", "row": 4, "column": 4, "level": "normal", "original_data": {"U": [null, null, null, null], "D": [null, null, null, null], "L": [null, null, 2, null], "R": [null, 1, null, 3]}, "id": 137, "observation": {"U": [null, null, null, null], "D": [null, null, null, null], "L": [null, null, 2, null], "R": [null, 1, null, 3]}, "answer": [[2, 3, 4, 1], [3, 2, 1, 4], [1, 4, 2, 3], [4, 1, 3, 2]], "idx": 137, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_137.png", "answer_image": "figs/skyscrapers_137_answer.png"} {"puzzle": "skyscrapers", "row": 4, "column": 4, "level": "hard", "original_data": {"U": [null, null, null, null], "D": [3, 2, null, null], "L": [null, null, null, null], "R": [3, 3, null, 2]}, "id": 138, "observation": {"U": [null, null, null, null], "D": [3, 2, null, null], "L": [null, null, null, null], "R": [3, 3, null, 2]}, "answer": [[4, 3, 1, 2], [2, 4, 3, 1], [3, 1, 2, 4], [1, 2, 4, 3]], "idx": 138, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_138.png", "answer_image": "figs/skyscrapers_138_answer.png"} {"puzzle": "skyscrapers", "row": 5, "column": 5, "level": "easy", "original_data": {"U": [1, 2, 4, 2, 3], "D": [2, 2, 1, 4, 3], "L": [1, 3, 3, 2, 2], "R": [4, 2, 1, 3, 2]}, "id": 139, "observation": {"U": [1, 2, 4, 2, 3], "D": [2, 2, 1, 4, 3], "L": [1, 3, 3, 2, 2], "R": [4, 2, 1, 3, 2]}, "answer": [[5, 4, 2, 3, 1], [2, 1, 3, 5, 4], [3, 2, 1, 4, 5], [1, 5, 4, 2, 3], [4, 3, 5, 1, 2]], "idx": 139, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_139.png", "answer_image": "figs/skyscrapers_139_answer.png"} {"puzzle": "skyscrapers", "row": 5, "column": 5, "level": "normal", "original_data": {"U": [null, 5, null, null, 3], "D": [2, null, 4, null, null], "L": [null, 4, null, null, null], "R": [3, null, null, null, 3]}, "id": 140, "observation": {"U": [null, 5, null, null, 3], "D": [2, null, 4, null, null], "L": [null, 4, null, null, null], "R": [3, null, null, null, 3]}, "answer": [[2, 1, 5, 4, 3], [1, 2, 3, 5, 4], [5, 3, 4, 2, 1], [3, 4, 2, 1, 5], [4, 5, 1, 3, 2]], "idx": 140, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_140.png", "answer_image": "figs/skyscrapers_140_answer.png"} {"puzzle": "skyscrapers", "row": 5, "column": 5, "level": "hard", "original_data": {"U": [3, 3, null, null, null], "D": [null, null, null, null, null], "L": [2, null, 1, null, null], "R": [null, null, 2, 2, null]}, "id": 141, "observation": {"U": [3, 3, null, null, null], "D": [null, null, null, null, null], "L": [2, null, 1, null, null], "R": [null, null, 2, 2, null]}, "answer": [[2, 1, 5, 4, 3], [3, 4, 1, 2, 5], [5, 3, 2, 1, 4], [4, 2, 3, 5, 1], [1, 5, 4, 3, 2]], "idx": 141, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_141.png", "answer_image": "figs/skyscrapers_141_answer.png"} {"puzzle": "skyscrapers", "row": 6, "column": 6, "level": "easy", "original_data": {"U": [1, 5, 4, 3, 2, 2], "D": [3, 1, 2, 3, 2, 4], "L": [1, 3, 4, 2, 3, 2], "R": [3, 1, 2, 3, 2, 4]}, "id": 142, "observation": {"U": [1, 5, 4, 3, 2, 2], "D": [3, 1, 2, 3, 2, 4], "L": [1, 3, 4, 2, 3, 2], "R": [3, 1, 2, 3, 2, 4]}, "answer": [[6, 2, 1, 3, 5, 4], [4, 1, 3, 5, 2, 6], [2, 3, 4, 6, 1, 5], [5, 4, 6, 1, 3, 2], [1, 5, 2, 4, 6, 3], [3, 6, 5, 2, 4, 1]], "idx": 142, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_142.png", "answer_image": "figs/skyscrapers_142_answer.png"} {"puzzle": "skyscrapers", "row": 6, "column": 6, "level": "normal", "original_data": {"U": [2, null, null, 1, null, 6], "D": [null, null, 2, 2, 3, null], "L": [4, null, 3, null, 2, null], "R": [null, null, null, null, null, null]}, "id": 143, "observation": {"U": [2, null, null, 1, null, 6], "D": [null, null, 2, 2, 3, null], "L": [4, null, 3, null, 2, null], "R": [null, null, null, null, null, null]}, "answer": [[2, 3, 4, 6, 5, 1], [6, 1, 5, 3, 4, 2], [1, 5, 2, 4, 6, 3], [5, 6, 3, 2, 1, 4], [4, 2, 6, 1, 3, 5], [3, 4, 1, 5, 2, 6]], "idx": 143, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_143.png", "answer_image": "figs/skyscrapers_143_answer.png"} {"puzzle": "skyscrapers", "row": 6, "column": 6, "level": "hard", "original_data": {"U": [2, null, 4, null, null, 2], "D": [null, 4, 3, null, 1, null], "L": [null, null, 4, null, 2, 3], "R": [3, 4, null, 3, null, null]}, "id": 144, "observation": {"U": [2, null, 4, null, null, 2], "D": [null, 4, 3, null, 1, null], "L": [null, null, 4, null, 2, 3], "R": [3, 4, null, 3, null, null]}, "answer": [[2, 6, 1, 3, 5, 4], [6, 2, 3, 5, 4, 1], [1, 4, 5, 6, 2, 3], [4, 5, 6, 1, 3, 2], [5, 3, 4, 2, 1, 6], [3, 1, 2, 4, 6, 5]], "idx": 144, "rules": "**Core Rules:**\nFill the `N x N` grid with building heights `1..N` so that:\n1. Each row contains each height exactly once.\n2. Each column contains each height exactly once.\n3. Side clues indicate how many buildings are visible from that direction.\n A taller building hides all shorter buildings behind it.\n\n**Coordinates & Output:**\n1. Cell coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. Side clue order is fixed:\n - `U` (top): left to right\n - `D` (bottom): left to right\n - `L` (left): top to bottom\n - `R` (right): top to bottom\n4. **Observation** has four parts:\n - `U`: top clues list\n - `D`: bottom clues list\n - `L`: left clues list\n - `R`: right clues list\n5. **Answer:** full solved `N x N` 2D list (list of lists) of integers.", "ref_observation": {"U": [1, 3, 2, 2], "D": [3, 2, 3, 1], "L": [1, 2, 2, 3], "R": [2, 2, 3, 1]}, "image": "figs/skyscrapers_144.png", "answer_image": "figs/skyscrapers_144_answer.png"} {"puzzle": "slant", "row": 5, "column": 5, "level": "easy", "original_data": {"data": [[null, null, 0, null, 0, null], [2, null, null, null, null, null], [null, null, 2, null, null, 2], [2, 2, null, 2, 1, null], [0, null, null, null, null, 0], [null, null, 0, null, 1, null]]}, "id": 145, "observation": {"data": [[null, null, 0, null, 0, null], [2, null, null, null, null, null], [null, null, 2, null, null, 2], [2, 2, null, 2, 1, null], [0, null, null, null, null, 0], [null, null, 0, null, 1, null]]}, "answer": [["/", "\\", "/", "\\", "/"], ["\\", "\\", "\\", "\\", "\\"], ["/", "/", "/", "/", "/"], ["\\", "\\", "\\", "\\", "/"], ["/", "/", "\\", "\\", "\\"]], "idx": 145, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_145.png", "answer_image": "figs/slant_145_answer.png"} {"puzzle": "slant", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, null, null, null], [null, 3, 2, 2, 1, null], [null, null, 3, null, 3, null], [1, 2, null, 2, null, 1], [1, null, 3, 2, null, 1], [null, null, 1, null, 1, null]]}, "id": 146, "observation": {"data": [[null, null, null, null, null, null], [null, 3, 2, 2, 1, null], [null, null, 3, null, 3, null], [1, 2, null, 2, null, 1], [1, null, 3, 2, null, 1], [null, null, 1, null, 1, null]]}, "answer": [["\\", "\\", "/", "\\", "\\"], ["/", "\\", "/", "\\", "/"], ["/", "\\", "\\", "\\", "\\"], ["/", "\\", "/", "/", "\\"], ["/", "\\", "\\", "\\", "\\"]], "idx": 146, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_146.png", "answer_image": "figs/slant_146_answer.png"} {"puzzle": "slant", "row": 7, "column": 7, "level": "easy", "original_data": {"data": [[null, 0, null, 1, 1, 1, 0, null], [null, null, null, null, 1, null, 3, 0], [null, 1, null, 3, null, null, 1, null], [1, null, null, null, 1, null, 3, null], [2, 2, null, null, 4, null, null, 2], [null, null, null, 1, null, null, null, null], [null, 2, null, 4, null, 2, 1, 1], [null, 0, null, null, null, null, null, 0]]}, "id": 147, "observation": {"data": [[null, 0, null, 1, 1, 1, 0, null], [null, null, null, null, 1, null, 3, 0], [null, 1, null, 3, null, null, 1, null], [1, null, null, null, 1, null, 3, null], [2, 2, null, null, 4, null, null, 2], [null, null, null, 1, null, null, null, null], [null, 2, null, 4, null, 2, 1, 1], [null, 0, null, null, null, null, null, 0]]}, "answer": [["\\", "/", "\\", "\\", "\\", "\\", "/"], ["/", "\\", "\\", "\\", "/", "\\", "\\"], ["/", "/", "/", "\\", "\\", "\\", "/"], ["/", "/", "/", "\\", "/", "\\", "\\"], ["\\", "\\", "/", "/", "\\", "\\", "/"], ["/", "\\", "\\", "/", "/", "/", "/"], ["/", "\\", "/", "\\", "\\", "\\", "/"]], "idx": 147, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_147.png", "answer_image": "figs/slant_147_answer.png"} {"puzzle": "slant", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[null, null, null, 1, 1, null, null, null], [null, 2, 1, 3, 2, 1, 3, null], [1, null, null, 2, 2, 2, null, null], [null, null, 1, null, null, 2, 1, null], [null, 1, null, null, 2, 2, null, null], [null, 2, 1, null, 3, 2, 3, null], [null, 2, 1, 2, null, 3, 1, null], [null, null, null, null, null, null, null, null]]}, "id": 148, "observation": {"data": [[null, null, null, 1, 1, null, null, null], [null, 2, 1, 3, 2, 1, 3, null], [1, null, null, 2, 2, 2, null, null], [null, null, 1, null, null, 2, 1, null], [null, 1, null, null, 2, 2, null, null], [null, 2, 1, null, 3, 2, 3, null], [null, 2, 1, 2, null, 3, 1, null], [null, null, null, null, null, null, null, null]]}, "answer": [["/", "/", "/", "/", "/", "\\", "/"], ["\\", "\\", "/", "\\", "\\", "\\", "\\"], ["\\", "/", "/", "\\", "\\", "\\", "\\"], ["/", "\\", "/", "\\", "\\", "\\", "/"], ["/", "/", "\\", "\\", "\\", "\\", "/"], ["/", "/", "/", "/", "\\", "\\", "\\"], ["\\", "\\", "/", "/", "/", "\\", "/"]], "idx": 148, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_148.png", "answer_image": "figs/slant_148_answer.png"} {"puzzle": "slant", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, null, 2, null, null, 1, null, null, null, 0], [null, 4, null, null, 1, 2, null, null, 1, null, null], [2, null, 3, null, 3, null, null, null, null, 3, null], [null, 2, null, null, 3, null, null, 4, null, 2, null], [null, null, null, 2, 2, null, 3, 2, 3, null, null], [2, null, null, 1, null, null, null, null, null, null, 1], [null, null, 1, 2, 2, 1, null, 2, 2, 2, null], [null, null, null, 2, 2, null, 2, null, 2, 3, null], [null, 2, null, null, null, null, 1, 2, 3, null, null], [0, null, 2, 1, null, 3, null, 3, 1, 1, null], [null, 1, null, 1, 0, null, null, null, 1, null, null]]}, "id": 149, "observation": {"data": [[null, null, null, 2, null, null, 1, null, null, null, 0], [null, 4, null, null, 1, 2, null, null, 1, null, null], [2, null, 3, null, 3, null, null, null, null, 3, null], [null, 2, null, null, 3, null, null, 4, null, 2, null], [null, null, null, 2, 2, null, 3, 2, 3, null, null], [2, null, null, 1, null, null, null, null, null, null, 1], [null, null, 1, 2, 2, 1, null, 2, 2, 2, null], [null, null, null, 2, 2, null, 2, null, 2, 3, null], [null, 2, null, null, null, null, 1, 2, 3, null, null], [0, null, 2, 1, null, 3, null, 3, 1, 1, null], [null, 1, null, 1, 0, null, null, null, 1, null, null]]}, "answer": [["\\", "/", "/", "\\", "\\", "\\", "\\", "/", "\\", "\\"], ["/", "\\", "/", "\\", "/", "/", "\\", "\\", "\\", "/"], ["\\", "\\", "\\", "\\", "\\", "\\", "\\", "/", "/", "/"], ["/", "/", "/", "/", "\\", "\\", "/", "\\", "/", "/"], ["/", "/", "/", "/", "\\", "/", "/", "\\", "\\", "/"], ["\\", "/", "\\", "/", "\\", "\\", "\\", "\\", "\\", "/"], ["\\", "\\", "\\", "/", "\\", "/", "\\", "\\", "\\", "/"], ["\\", "/", "\\", "/", "\\", "/", "\\", "\\", "\\", "\\"], ["\\", "/", "/", "\\", "\\", "/", "/", "/", "\\", "\\"], ["/", "/", "/", "/", "\\", "\\", "/", "\\", "\\", "/"]], "idx": 149, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_149.png", "answer_image": "figs/slant_149_answer.png"} {"puzzle": "slant", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, 1, null, null, null, null, null, null, null, null, null], [null, null, 3, 1, null, 1, 2, 3, null, 1, null], [1, 2, 3, null, null, null, 1, null, null, null, 1], [null, 1, 1, null, null, 1, 1, null, 1, 2, 1], [null, null, 1, null, 2, 2, null, null, 2, 1, null], [null, 1, null, null, null, null, 3, null, 2, null, null], [null, 3, 1, null, 3, null, null, 1, 2, null, 1], [1, 1, 2, 3, 1, 2, null, 1, null, 2, null], [1, null, 2, null, 3, null, null, null, 1, null, 1], [1, 2, null, 2, 1, 2, null, 2, 2, 2, 1], [null, 1, 1, null, null, null, null, null, 1, null, null]]}, "id": 150, "observation": {"data": [[null, 1, null, null, null, null, null, null, null, null, null], [null, null, 3, 1, null, 1, 2, 3, null, 1, null], [1, 2, 3, null, null, null, 1, null, null, null, 1], [null, 1, 1, null, null, 1, 1, null, 1, 2, 1], [null, null, 1, null, 2, 2, null, null, 2, 1, null], [null, 1, null, null, null, null, 3, null, 2, null, null], [null, 3, 1, null, 3, null, null, 1, 2, null, 1], [1, 1, 2, 3, 1, 2, null, 1, null, 2, null], [1, null, 2, null, 3, null, null, null, 1, null, 1], [1, 2, null, 2, 1, 2, null, 2, 2, 2, 1], [null, 1, 1, null, null, null, null, null, 1, null, null]]}, "answer": [["\\", "\\", "/", "\\", "/", "/", "\\", "/", "/", "\\"], ["/", "/", "/", "/", "\\", "/", "\\", "\\", "\\", "\\"], ["/", "/", "\\", "/", "/", "\\", "\\", "/", "/", "\\"], ["\\", "/", "/", "\\", "\\", "\\", "/", "\\", "/", "\\"], ["/", "\\", "/", "\\", "\\", "\\", "/", "\\", "/", "/"], ["/", "/", "\\", "\\", "/", "/", "/", "\\", "/", "/"], ["/", "\\", "\\", "\\", "\\", "\\", "\\", "\\", "/", "/"], ["/", "/", "/", "\\", "/", "/", "\\", "/", "\\", "\\"], ["/", "/", "/", "\\", "\\", "\\", "\\", "\\", "\\", "\\"], ["/", "/", "/", "\\", "/", "/", "\\", "\\", "\\", "\\"]], "idx": 150, "rules": "**Core Rules:**\nPlace exactly one diagonal in every cell (`/` or `\\\\`) so that:\n1. Each numbered dot has exactly that many incident diagonal segments.\n2. The drawn segments must not form any closed loop.\n\n**Coordinates & Output:**\n1. Dot coordinates use `(row, col)` on an `(N+1) x (N+1)` point grid.\n2. Cell coordinates use `(row, col)` on an `N x N` cell grid.\n3. Top-left is `(0, 0)`; `row` increases top-to-bottom, `col` increases left-to-right.\n4. **Observation** has one part:\n - `data`: `(N+1) x (N+1)` clue 2D list (`int` or `None`).\n5. **Answer:** `N x N` 2D list (list of lists) where each cell element is either `'/'` or `'\\\\'`.", "ref_observation": {"data": [[null, 1, 1, null, 1, 1], [null, null, null, 1, null, null], [1, 3, null, null, null, null], [2, null, null, 3, null, 1], [null, 2, null, 2, null, 0], [0, null, null, 0, null, null]]}, "image": "figs/slant_150.png", "answer_image": "figs/slant_150_answer.png"} {"puzzle": "slitherlink", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[null, null, null, 1, null], [2, null, 1, 1, null], [2, null, 2, null, null], [1, 2, 0, 2, null], [null, 3, 3, 3, null]]}, "id": 151, "observation": {"data": [[null, null, null, 1, null], [2, null, 1, 1, null], [2, null, 2, null, null], [1, 2, 0, 2, null], [null, 3, 3, 3, null]]}, "answer": [[3, 2], [3, 1], [2, 1], [1, 1], [0, 1], [0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [5, 1], [4, 1], [4, 2], [5, 2], [5, 3], [4, 3], [4, 4], [5, 4], [5, 5], [4, 5], [3, 5], [3, 4], [3, 3], [2, 3], [2, 4], [2, 5], [1, 5], [0, 5], [0, 4], [0, 3], [0, 2], [1, 2], [2, 2], [3, 2]], "idx": 151, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_151.png", "answer_image": "figs/slitherlink_151_answer.png"} {"puzzle": "slitherlink", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, 3, 2, null, null, null, 2, 2, 3, null], [null, null, null, null, null, null, 3, null, 3, null], [null, 3, 2, null, 3, 2, null, null, 2, null], [3, 2, 0, 2, null, null, null, null, null, 3], [2, null, 3, 2, 1, 3, null, null, null, 2], [3, 2, 2, null, null, null, 2, 1, 3, null], [1, 2, null, 2, null, null, 2, null, null, 2], [2, 2, 3, 1, 2, null, null, 2, 1, 3], [2, null, null, null, 2, 2, null, null, 1, 2], [null, 2, null, null, 1, null, null, null, null, 3]]}, "id": 152, "observation": {"data": [[null, 3, 2, null, null, null, 2, 2, 3, null], [null, null, null, null, null, null, 3, null, 3, null], [null, 3, 2, null, 3, 2, null, null, 2, null], [3, 2, 0, 2, null, null, null, null, null, 3], [2, null, 3, 2, 1, 3, null, null, null, 2], [3, 2, 2, null, null, null, 2, 1, 3, null], [1, 2, null, 2, null, null, 2, null, null, 2], [2, 2, 3, 1, 2, null, null, 2, 1, 3], [2, null, null, null, 2, 2, null, null, 1, 2], [null, 2, null, null, 1, null, null, null, null, 3]]}, "answer": [[3, 2], [2, 2], [2, 1], [2, 0], [1, 0], [0, 0], [0, 1], [1, 1], [1, 2], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [2, 7], [2, 6], [1, 6], [1, 5], [1, 4], [1, 3], [2, 3], [3, 3], [3, 4], [2, 4], [2, 5], [3, 5], [3, 6], [3, 7], [3, 8], [2, 8], [2, 9], [1, 9], [1, 8], [0, 8], [0, 9], [0, 10], [1, 10], [2, 10], [3, 10], [3, 9], [4, 9], [4, 10], [5, 10], [6, 10], [7, 10], [7, 9], [8, 9], [8, 10], [9, 10], [10, 10], [10, 9], [9, 9], [9, 8], [10, 8], [10, 7], [10, 6], [10, 5], [9, 5], [9, 6], [9, 7], [8, 7], [7, 7], [7, 8], [6, 8], [6, 9], [5, 9], [5, 8], [4, 8], [4, 7], [5, 7], [6, 7], [6, 6], [7, 6], [8, 6], [8, 5], [8, 4], [9, 4], [9, 3], [10, 3], [10, 2], [9, 2], [8, 2], [8, 3], [7, 3], [7, 2], [7, 1], [8, 1], [9, 1], [10, 1], [10, 0], [9, 0], [8, 0], [7, 0], [6, 0], [5, 0], [5, 1], [6, 1], [6, 2], [6, 3], [6, 4], [7, 4], [7, 5], [6, 5], [5, 5], [5, 6], [4, 6], [4, 5], [4, 4], [4, 3], [5, 3], [5, 2], [4, 2], [4, 1], [4, 0], [3, 0], [3, 1], [3, 2]], "idx": 152, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_152.png", "answer_image": "figs/slitherlink_152_answer.png"} {"puzzle": "slitherlink", "row": 5, "column": 5, "level": "hard", "original_data": {"data": [[3, 2, null, 2, null], [null, null, 2, null, null], [1, 2, 1, 3, 2], [2, 3, null, null, null], [null, 2, 3, 3, null]]}, "id": 153, "observation": {"data": [[3, 2, null, 2, null], [null, null, 2, null, null], [1, 2, 1, 3, 2], [2, 3, null, null, null], [null, 2, 3, 3, null]]}, "answer": [[3, 1], [3, 2], [4, 2], [5, 2], [5, 3], [4, 3], [4, 4], [5, 4], [5, 5], [4, 5], [3, 5], [2, 5], [1, 5], [0, 5], [0, 4], [1, 4], [2, 4], [3, 4], [3, 3], [2, 3], [1, 3], [0, 3], [0, 2], [1, 2], [2, 2], [2, 1], [1, 1], [0, 1], [0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [5, 1], [4, 1], [3, 1]], "idx": 153, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_153.png", "answer_image": "figs/slitherlink_153_answer.png"} {"puzzle": "slitherlink", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[null, null, null, null, null, null, null, null, 3, null], [3, null, 2, 2, null, null, null, null, 1, null], [null, null, 2, 3, 2, 0, null, null, 3, 2], [null, null, 1, null, null, 1, null, null, 2, 3], [1, null, null, 3, 3, 3, null, 3, 2, null], [null, 3, null, 2, null, null, null, 2, 2, null], [null, 1, null, 2, null, null, null, 1, 1, 2], [3, null, 2, null, null, null, null, 2, null, null], [null, null, 2, 3, null, null, 2, 1, null, null], [3, null, 2, 3, null, 1, 2, null, 3, null]]}, "id": 154, "observation": {"data": [[null, null, null, null, null, null, null, null, 3, null], [3, null, 2, 2, null, null, null, null, 1, null], [null, null, 2, 3, 2, 0, null, null, 3, 2], [null, null, 1, null, null, 1, null, null, 2, 3], [1, null, null, 3, 3, 3, null, 3, 2, null], [null, 3, null, 2, null, null, null, 2, 2, null], [null, 1, null, 2, null, null, null, 1, 1, 2], [3, null, 2, null, null, null, null, 2, null, null], [null, null, 2, 3, null, null, 2, 1, null, null], [3, null, 2, 3, null, 1, 2, null, 3, null]]}, "answer": [[2, 5], [2, 4], [3, 4], [3, 3], [2, 3], [1, 3], [1, 4], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 8], [0, 8], [0, 9], [1, 9], [1, 10], [2, 10], [2, 9], [2, 8], [3, 8], [3, 9], [3, 10], [4, 10], [4, 9], [4, 8], [4, 7], [5, 7], [5, 8], [5, 9], [5, 10], [6, 10], [6, 9], [6, 8], [6, 7], [6, 6], [7, 6], [7, 7], [8, 7], [8, 8], [8, 9], [7, 9], [7, 10], [8, 10], [9, 10], [10, 10], [10, 9], [9, 9], [9, 8], [10, 8], [10, 7], [9, 7], [9, 6], [8, 6], [8, 5], [9, 5], [10, 5], [10, 4], [10, 3], [9, 3], [9, 4], [8, 4], [8, 3], [8, 2], [9, 2], [10, 2], [10, 1], [10, 0], [9, 0], [9, 1], [8, 1], [8, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [6, 5], [6, 4], [6, 3], [6, 2], [5, 2], [5, 1], [6, 1], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1], [1, 1], [1, 0], [0, 0], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2], [3, 1], [4, 1], [4, 2], [4, 3], [5, 3], [5, 4], [4, 4], [4, 5], [5, 5], [5, 6], [4, 6], [3, 6], [3, 7], [2, 7], [2, 6], [1, 6], [1, 5], [2, 5]], "idx": 154, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_154.png", "answer_image": "figs/slitherlink_154_answer.png"} {"puzzle": "slitherlink", "row": 7, "column": 7, "level": "normal", "original_data": {"data": [[3, null, 1, null, null, null, null], [1, null, null, null, null, null, 2], [null, 3, 0, 2, null, null, 3], [null, null, 1, 2, null, null, 1], [null, 2, 3, null, 2, null, null], [null, null, 1, 1, 2, 2, null], [null, 3, 2, null, null, null, null]]}, "id": 155, "observation": {"data": [[3, null, 1, null, null, null, null], [1, null, null, null, null, null, 2], [null, 3, 0, 2, null, null, 3], [null, null, 1, 2, null, null, 1], [null, 2, 3, null, 2, null, null], [null, null, 1, 1, 2, 2, null], [null, 3, 2, null, null, null, null]]}, "answer": [[2, 2], [2, 1], [3, 1], [3, 2], [4, 2], [5, 2], [5, 3], [4, 3], [4, 4], [3, 4], [2, 4], [2, 3], [1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 6], [1, 5], [2, 5], [3, 5], [3, 6], [2, 6], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [7, 6], [7, 5], [6, 5], [6, 6], [5, 6], [4, 6], [4, 5], [5, 5], [5, 4], [6, 4], [7, 4], [7, 3], [7, 2], [6, 2], [6, 1], [7, 1], [7, 0], [6, 0], [5, 0], [5, 1], [4, 1], [4, 0], [3, 0], [2, 0], [1, 0], [0, 0], [0, 1], [1, 1], [1, 2], [2, 2]], "idx": 155, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_155.png", "answer_image": "figs/slitherlink_155_answer.png"} {"puzzle": "slitherlink", "row": 7, "column": 7, "level": "hard", "original_data": {"data": [[3, null, null, null, null, null, 3], [1, 2, 1, null, 1, 2, null], [2, 3, null, 2, null, null, 2], [3, null, null, 2, null, null, null], [null, 2, null, null, 3, null, 2], [null, null, null, 3, null, null, 3], [null, 2, null, 3, 2, 2, null]]}, "id": 156, "observation": {"data": [[3, null, null, null, null, null, 3], [1, 2, 1, null, 1, 2, null], [2, 3, null, 2, null, null, 2], [3, null, null, 2, null, null, null], [null, 2, null, null, 3, null, 2], [null, null, null, 3, null, null, 3], [null, 2, null, 3, 2, 2, null]]}, "answer": [[3, 0], [4, 0], [4, 1], [5, 1], [5, 2], [6, 2], [6, 1], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [6, 4], [6, 3], [5, 3], [5, 4], [4, 4], [4, 5], [5, 5], [6, 5], [7, 5], [7, 6], [7, 7], [6, 7], [6, 6], [5, 6], [5, 7], [4, 7], [3, 7], [3, 6], [3, 5], [2, 5], [2, 6], [2, 7], [1, 7], [0, 7], [0, 6], [1, 6], [1, 5], [0, 5], [0, 4], [0, 3], [0, 2], [0, 1], [0, 0], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [2, 4], [3, 4], [3, 3], [4, 3], [4, 2], [3, 2], [2, 2], [2, 1], [3, 1], [3, 0]], "idx": 156, "rules": "**Core Rules:**\nDraw lines between dots to form a single closed loop without crossings or branches.\nEach clue number indicates how many loop edges surround that cell.\n\n**Coordinates & Output:**\n1. Dot coordinates are integer `(row, col)`.\n2. Clue coordinates are half-integer cell centers `(row+0.5, col+0.5)`.\n3. Top-left is `(0, 0)`; `row` increases downward, `col` increases rightward.\n4. **Observation** has one part:\n - `data`: `N x N` clue 2D list (`int` or `None`).\n5. **Answer:** ordered list of loop-dot coordinates, e.g. `[(0,0), (0,1), ..., (0,0)]`.", "ref_observation": {"data": [[null, null, null, null, null], [2, null, 2, null, 2], [null, null, null, 3, 0], [null, null, 2, null, 2], [null, 1, null, null, null]]}, "image": "figs/slitherlink_156.png", "answer_image": "figs/slitherlink_156_answer.png"} {"puzzle": "starbattle1", "row": 5, "column": 5, "level": "normal", "original_data": {"data": [[0, 1, 1, 1, 1], [0, 0, 1, 1, 1], [2, 2, 3, 1, 1], [2, 3, 3, 4, 4], [3, 3, 3, 3, 4]]}, "id": 157, "observation": {"data": [[0, 1, 1, 1, 1], [0, 0, 1, 1, 1], [2, 2, 3, 1, 1], [2, 3, 3, 4, 4], [3, 3, 3, 3, 4]]}, "answer": [["S", null, null, null, null], [null, null, null, "S", null], [null, "S", null, null, null], [null, null, null, null, "S"], [null, null, "S", null, null]], "idx": 157, "rules": "**Core Rules (1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Each region contains exactly 1 star.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [2, 3, 3, 1, 4], [2, 3, 3, 1, 4], [2, 1, 1, 1, 4]]}, "image": "figs/starbattle1_157.png", "answer_image": "figs/starbattle1_157_answer.png"} {"puzzle": "starbattle1", "row": 6, "column": 6, "level": "normal", "original_data": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 0, 0, 1, 1], [2, 0, 0, 0, 1, 1], [2, 0, 3, 3, 3, 1], [2, 0, 3, 3, 3, 4], [2, 3, 3, 5, 5, 4]]}, "id": 158, "observation": {"data": [[0, 0, 0, 0, 1, 1], [2, 0, 0, 0, 1, 1], [2, 0, 0, 0, 1, 1], [2, 0, 3, 3, 3, 1], [2, 0, 3, 3, 3, 4], [2, 3, 3, 5, 5, 4]]}, "answer": [[null, "S", null, null, null, null], [null, null, null, null, "S", null], ["S", null, null, null, null, null], [null, null, "S", null, null, null], [null, null, null, null, null, "S"], [null, null, null, "S", null, null]], "idx": 158, "rules": "**Core Rules (1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Each region contains exactly 1 star.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [2, 3, 3, 1, 4], [2, 3, 3, 1, 4], [2, 1, 1, 1, 4]]}, "image": "figs/starbattle1_158.png", "answer_image": "figs/starbattle1_158_answer.png"} {"puzzle": "starbattle1", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[0, 0, 0, 0, 0, 1], [2, 2, 2, 0, 3, 1], [2, 4, 4, 3, 3, 1], [2, 4, 5, 3, 1, 1], [2, 5, 5, 3, 3, 1], [2, 2, 3, 3, 1, 1]]}, "id": 159, "observation": {"data": [[0, 0, 0, 0, 0, 1], [2, 2, 2, 0, 3, 1], [2, 4, 4, 3, 3, 1], [2, 4, 5, 3, 1, 1], [2, 5, 5, 3, 3, 1], [2, 2, 3, 3, 1, 1]]}, "answer": [[null, null, null, null, "S", null], ["S", null, null, null, null, null], [null, null, "S", null, null, null], [null, null, null, null, null, "S"], [null, "S", null, null, null, null], [null, null, null, "S", null, null]], "idx": 159, "rules": "**Core Rules (1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Each region contains exactly 1 star.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [2, 3, 3, 1, 4], [2, 3, 3, 1, 4], [2, 1, 1, 1, 4]]}, "image": "figs/starbattle1_159.png", "answer_image": "figs/starbattle1_159_answer.png"} {"puzzle": "starbattle1", "row": 8, "column": 8, "level": "normal", "original_data": {"data": [[0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1, 1, 2], [0, 0, 3, 3, 4, 4, 4, 2], [0, 0, 3, 3, 4, 4, 4, 2], [0, 5, 5, 3, 3, 4, 6, 6], [0, 0, 5, 5, 5, 5, 6, 6], [5, 0, 5, 5, 5, 5, 6, 6], [5, 5, 5, 5, 5, 7, 7, 7]]}, "id": 160, "observation": {"data": [[0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1, 1, 2], [0, 0, 3, 3, 4, 4, 4, 2], [0, 0, 3, 3, 4, 4, 4, 2], [0, 5, 5, 3, 3, 4, 6, 6], [0, 0, 5, 5, 5, 5, 6, 6], [5, 0, 5, 5, 5, 5, 6, 6], [5, 5, 5, 5, 5, 7, 7, 7]]}, "answer": [[null, null, "S", null, null, null, null, null], [null, null, null, null, null, null, null, "S"], [null, null, null, null, "S", null, null, null], [null, "S", null, null, null, null, null, null], [null, null, null, "S", null, null, null, null], [null, null, null, null, null, null, "S", null], ["S", null, null, null, null, null, null, null], [null, null, null, null, null, "S", null, null]], "idx": 160, "rules": "**Core Rules (1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Each region contains exactly 1 star.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [2, 3, 3, 1, 4], [2, 3, 3, 1, 4], [2, 1, 1, 1, 4]]}, "image": "figs/starbattle1_160.png", "answer_image": "figs/starbattle1_160_answer.png"} {"puzzle": "starbattle1", "row": 8, "column": 8, "level": "hard", "original_data": {"data": [[0, 0, 1, 1, 1, 1, 1, 2], [0, 0, 3, 3, 3, 1, 1, 2], [0, 3, 3, 4, 3, 3, 2, 2], [0, 3, 0, 4, 3, 2, 2, 5], [0, 0, 0, 4, 3, 3, 3, 5], [0, 4, 0, 4, 5, 5, 5, 5], [0, 4, 4, 4, 6, 6, 5, 7], [0, 0, 0, 0, 0, 0, 7, 7]]}, "id": 161, "observation": {"data": [[0, 0, 1, 1, 1, 1, 1, 2], [0, 0, 3, 3, 3, 1, 1, 2], [0, 3, 3, 4, 3, 3, 2, 2], [0, 3, 0, 4, 3, 2, 2, 5], [0, 0, 0, 4, 3, 3, 3, 5], [0, 4, 0, 4, 5, 5, 5, 5], [0, 4, 4, 4, 6, 6, 5, 7], [0, 0, 0, 0, 0, 0, 7, 7]]}, "answer": [[null, null, null, "S", null, null, null, null], ["S", null, null, null, null, null, null, null], [null, null, "S", null, null, null, null, null], [null, null, null, null, null, "S", null, null], [null, null, null, null, null, null, null, "S"], [null, "S", null, null, null, null, null, null], [null, null, null, null, "S", null, null, null], [null, null, null, null, null, null, "S", null]], "idx": 161, "rules": "**Core Rules (1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Each region contains exactly 1 star.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [2, 3, 3, 1, 4], [2, 3, 3, 1, 4], [2, 1, 1, 1, 4]]}, "image": "figs/starbattle1_161.png", "answer_image": "figs/starbattle1_161_answer.png"} {"puzzle": "starbattle2", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[0, 0, 0, 0, 1, 1, 2, 2, 2, 3], [4, 4, 4, 0, 1, 1, 2, 2, 3, 3], [4, 4, 4, 4, 4, 1, 2, 2, 3, 3], [5, 4, 4, 6, 6, 1, 3, 3, 3, 3], [5, 5, 6, 6, 6, 6, 3, 3, 3, 3], [5, 5, 6, 6, 6, 6, 6, 3, 3, 7], [5, 5, 6, 6, 6, 6, 8, 8, 8, 7], [9, 9, 6, 6, 6, 6, 8, 8, 8, 7], [9, 9, 9, 9, 6, 6, 8, 8, 8, 7], [9, 9, 9, 9, 9, 9, 7, 7, 7, 7]]}, "id": 162, "observation": {"data": [[0, 0, 0, 0, 1, 1, 2, 2, 2, 3], [4, 4, 4, 0, 1, 1, 2, 2, 3, 3], [4, 4, 4, 4, 4, 1, 2, 2, 3, 3], [5, 4, 4, 6, 6, 1, 3, 3, 3, 3], [5, 5, 6, 6, 6, 6, 3, 3, 3, 3], [5, 5, 6, 6, 6, 6, 6, 3, 3, 7], [5, 5, 6, 6, 6, 6, 8, 8, 8, 7], [9, 9, 6, 6, 6, 6, 8, 8, 8, 7], [9, 9, 9, 9, 6, 6, 8, 8, 8, 7], [9, 9, 9, 9, 9, 9, 7, 7, 7, 7]]}, "answer": [[null, "S", null, null, null, null, null, null, "S", null], [null, null, null, "S", null, "S", null, null, null, null], ["S", null, null, null, null, null, null, "S", null, null], [null, null, "S", null, null, "S", null, null, null, null], ["S", null, null, null, null, null, null, null, null, "S"], [null, null, null, "S", null, null, null, "S", null, null], [null, "S", null, null, null, null, null, null, null, "S"], [null, null, null, null, "S", null, "S", null, null, null], [null, null, "S", null, null, null, null, null, "S", null], [null, null, null, null, "S", null, "S", null, null, null]], "idx": 162, "rules": "**Core Rules (2-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 2 stars.\n2. Each column contains exactly 2 stars.\n3. Each region contains exactly 2 stars.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 1, 2, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 0, 4, 1, 1, 2, 2, 3, 3], [0, 0, 4, 4, 1, 1, 1, 1, 3, 3], [4, 4, 4, 4, 1, 1, 5, 5, 5, 3], [6, 6, 4, 4, 1, 1, 5, 5, 7, 7], [6, 8, 8, 8, 8, 1, 5, 5, 7, 7], [6, 6, 9, 9, 8, 1, 7, 7, 7, 7], [9, 6, 9, 9, 8, 1, 7, 7, 7, 7], [9, 9, 9, 9, 8, 1, 7, 7, 7, 7]]}, "image": "figs/starbattle2_162.png", "answer_image": "figs/starbattle2_162_answer.png"} {"puzzle": "starbattle2", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [[0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [2, 0, 0, 3, 3, 1, 1, 1, 1, 4], [2, 2, 2, 3, 3, 5, 5, 1, 4, 4], [6, 6, 2, 3, 5, 5, 5, 1, 4, 4], [6, 6, 3, 3, 3, 7, 1, 1, 1, 4], [6, 8, 8, 3, 7, 7, 9, 9, 1, 4], [6, 8, 8, 3, 7, 7, 9, 4, 4, 4], [6, 8, 8, 3, 7, 7, 9, 9, 4, 4], [6, 8, 8, 3, 7, 9, 9, 9, 9, 4], [6, 8, 8, 7, 7, 7, 7, 7, 9, 9]]}, "id": 163, "observation": {"data": [[0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [2, 0, 0, 3, 3, 1, 1, 1, 1, 4], [2, 2, 2, 3, 3, 5, 5, 1, 4, 4], [6, 6, 2, 3, 5, 5, 5, 1, 4, 4], [6, 6, 3, 3, 3, 7, 1, 1, 1, 4], [6, 8, 8, 3, 7, 7, 9, 9, 1, 4], [6, 8, 8, 3, 7, 7, 9, 4, 4, 4], [6, 8, 8, 3, 7, 7, 9, 9, 4, 4], [6, 8, 8, 3, 7, 9, 9, 9, 9, 4], [6, 8, 8, 7, 7, 7, 7, 7, 9, 9]]}, "answer": [[null, null, null, null, "S", null, "S", null, null, null], ["S", null, null, null, null, null, null, null, "S", null], [null, null, "S", null, null, null, "S", null, null, null], [null, null, null, null, "S", null, null, null, null, "S"], [null, "S", null, null, null, null, null, "S", null, null], [null, null, null, "S", null, "S", null, null, null, null], [null, "S", null, null, null, null, null, null, "S", null], [null, null, null, "S", null, "S", null, null, null, null], ["S", null, null, null, null, null, null, "S", null, null], [null, null, "S", null, null, null, null, null, null, "S"]], "idx": 163, "rules": "**Core Rules (2-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 2 stars.\n2. Each column contains exactly 2 stars.\n3. Each region contains exactly 2 stars.\n4. Stars cannot touch each other, including diagonally.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: region ID grid as `N x N` list of lists.\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [[0, 0, 0, 1, 2, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 0, 4, 1, 1, 2, 2, 3, 3], [0, 0, 4, 4, 1, 1, 1, 1, 3, 3], [4, 4, 4, 4, 1, 1, 5, 5, 5, 3], [6, 6, 4, 4, 1, 1, 5, 5, 7, 7], [6, 8, 8, 8, 8, 1, 5, 5, 7, 7], [6, 6, 9, 9, 8, 1, 7, 7, 7, 7], [9, 6, 9, 9, 8, 1, 7, 7, 7, 7], [9, 9, 9, 9, 8, 1, 7, 7, 7, 7]]}, "image": "figs/starbattle2_163.png", "answer_image": "figs/starbattle2_163_answer.png"} {"puzzle": "starbattlex", "row": 6, "column": 6, "level": "normal", "original_data": {"data": [[null, "B", null, null, "B", "B"], [null, null, null, null, "B", "B"], [null, "B", null, null, null, "B"], ["B", null, "B", null, null, null], [null, "B", null, null, null, null], [null, null, null, "B", null, "B"]]}, "id": 164, "observation": {"data": [[null, "B", null, null, "B", "B"], [null, null, null, null, "B", "B"], [null, "B", null, null, null, "B"], ["B", null, "B", null, null, null], [null, "B", null, null, null, null], [null, null, null, "B", null, "B"]]}, "answer": [[null, null, null, "S", null, null], ["S", null, null, null, null, null], [null, null, null, null, "S", null], [null, "S", null, null, null, null], [null, null, null, null, null, "S"], [null, null, "S", null, null, null]], "idx": 164, "rules": "**Core Rules (Shapeless, 1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Stars cannot touch each other, including diagonally.\n4. Black obstacle cells cannot contain stars.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: obstacle grid as `N x N` list of lists (`'B'` or `None`).\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [["B", "B", null, null, "B", null], [null, null, null, null, null, null], [null, null, null, null, "B", null], [null, null, null, null, null, "B"], ["B", "B", "B", null, "B", null], [null, "B", null, null, null, null]]}, "image": "figs/starbattlex_164.png", "answer_image": "figs/starbattlex_164_answer.png"} {"puzzle": "starbattlex", "row": 8, "column": 8, "level": "normal", "original_data": {"data": [["B", null, null, null, "B", null, null, "B"], ["B", "B", null, null, null, null, null, "B"], ["B", null, "B", "B", "B", null, "B", "B"], [null, null, null, null, null, null, null, null], ["B", null, "B", "B", null, null, null, "B"], ["B", null, "B", null, null, null, "B", "B"], ["B", null, null, "B", null, null, null, null], ["B", null, "B", "B", null, null, null, null]]}, "id": 165, "observation": {"data": [["B", null, null, null, "B", null, null, "B"], ["B", "B", null, null, null, null, null, "B"], ["B", null, "B", "B", "B", null, "B", "B"], [null, null, null, null, null, null, null, null], ["B", null, "B", "B", null, null, null, "B"], ["B", null, "B", null, null, null, "B", "B"], ["B", null, null, "B", null, null, null, null], ["B", null, "B", "B", null, null, null, null]]}, "answer": [[null, "S", null, null, null, null, null, null], [null, null, null, "S", null, null, null, null], [null, null, null, null, null, "S", null, null], ["S", null, null, null, null, null, null, null], [null, null, null, null, null, null, "S", null], [null, null, null, null, "S", null, null, null], [null, null, "S", null, null, null, null, null], [null, null, null, null, null, null, null, "S"]], "idx": 165, "rules": "**Core Rules (Shapeless, 1-Star):**\nPlace stars on the grid so that:\n1. Each row contains exactly 1 star.\n2. Each column contains exactly 1 star.\n3. Stars cannot touch each other, including diagonally.\n4. Black obstacle cells cannot contain stars.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has one part:\n - `data`: obstacle grid as `N x N` list of lists (`'B'` or `None`).\n4. **Answer:** same-sized grid using `'S'` for star cells and `None` for non-star cells.", "ref_observation": {"data": [["B", "B", null, null, "B", null], [null, null, null, null, null, null], [null, null, null, null, "B", null], [null, null, null, null, null, "B"], ["B", "B", "B", null, "B", null], [null, "B", null, null, null, null]]}, "image": "figs/starbattlex_165.png", "answer_image": "figs/starbattlex_165_answer.png"} {"puzzle": "stitches", "row": 5, "column": 5, "level": "normal", "original_data": {"region": [[0, 0, 1, 1, 0], [0, 0, 0, 0, 0], [0, 0, 2, 0, 0], [3, 2, 2, 3, 4], [3, 3, 3, 3, 4]], "row_stitch_counts": [2, 0, 4, 3, 3], "col_stitch_counts": [2, 1, 3, 2, 4]}, "id": 166, "observation": {"region": [[0, 0, 1, 1, 0], [0, 0, 0, 0, 0], [0, 0, 2, 0, 0], [3, 2, 2, 3, 4], [3, 3, 3, 3, 4]], "row_stitch_counts": [2, 0, 4, 3, 3], "col_stitch_counts": [2, 1, 3, 2, 4]}, "answer": [[[0, 3], [0, 4]], [[2, 0], [3, 0]], [[2, 1], [2, 2]], [[2, 4], [3, 4]], [[3, 2], [4, 2]], [[4, 3], [4, 4]]], "idx": 166, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_166.png", "answer_image": "figs/stitches_166_answer.png"} {"puzzle": "stitches", "row": 5, "column": 5, "level": "hard", "original_data": {"region": [[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [3, 0, 2, 2, 1], [3, 0, 2, 2, 2], [4, 4, 4, 4, 4]], "row_stitch_counts": [2, 3, 3, 3, 3], "col_stitch_counts": [4, 3, 2, 2, 3]}, "id": 167, "observation": {"region": [[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [3, 0, 2, 2, 1], [3, 0, 2, 2, 2], [4, 4, 4, 4, 4]], "row_stitch_counts": [2, 3, 3, 3, 3], "col_stitch_counts": [4, 3, 2, 2, 3]}, "answer": [[[0, 1], [0, 2]], [[1, 0], [2, 0]], [[1, 2], [1, 3]], [[2, 3], [2, 4]], [[3, 0], [4, 0]], [[3, 1], [4, 1]], [[3, 4], [4, 4]]], "idx": 167, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_167.png", "answer_image": "figs/stitches_167_answer.png"} {"puzzle": "stitches", "row": 7, "column": 7, "level": "normal", "original_data": {"region": [[0, 1, 1, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 2], [0, 0, 0, 0, 0, 0, 2], [3, 3, 0, 0, 2, 2, 2], [4, 3, 0, 0, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5], [4, 6, 6, 6, 6, 5, 5]], "row_stitch_counts": [1, 3, 2, 4, 5, 4, 3], "col_stitch_counts": [2, 3, 3, 3, 4, 4, 3]}, "id": 168, "observation": {"region": [[0, 1, 1, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 2], [0, 0, 0, 0, 0, 0, 2], [3, 3, 0, 0, 2, 2, 2], [4, 3, 0, 0, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5], [4, 6, 6, 6, 6, 5, 5]], "row_stitch_counts": [1, 3, 2, 4, 5, 4, 3], "col_stitch_counts": [2, 3, 3, 3, 4, 4, 3]}, "answer": [[[0, 6], [1, 6]], [[1, 3], [1, 4]], [[2, 5], [2, 6]], [[3, 0], [4, 0]], [[3, 1], [3, 2]], [[3, 5], [4, 5]], [[4, 2], [5, 2]], [[4, 3], [4, 4]], [[5, 1], [6, 1]], [[5, 3], [5, 4]], [[6, 4], [6, 5]]], "idx": 168, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_168.png", "answer_image": "figs/stitches_168_answer.png"} {"puzzle": "stitches", "row": 7, "column": 7, "level": "hard", "original_data": {"region": [[0, 0, 1, 1, 0, 2, 2], [0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 2, 3], [0, 0, 0, 0, 2, 2, 3], [4, 4, 4, 4, 3, 2, 3], [4, 5, 3, 3, 3, 3, 3], [5, 5, 3, 6, 6, 3, 3]], "row_stitch_counts": [2, 2, 0, 1, 4, 4, 3], "col_stitch_counts": [2, 4, 3, 3, 2, 2, 0]}, "id": 169, "observation": {"region": [[0, 0, 1, 1, 0, 2, 2], [0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 2, 3], [0, 0, 0, 0, 2, 2, 3], [4, 4, 4, 4, 3, 2, 3], [4, 5, 3, 3, 3, 3, 3], [5, 5, 3, 6, 6, 3, 3]], "row_stitch_counts": [2, 2, 0, 1, 4, 4, 3], "col_stitch_counts": [2, 4, 3, 3, 2, 2, 0]}, "answer": [[[0, 1], [0, 2]], [[1, 4], [1, 5]], [[3, 1], [4, 1]], [[4, 3], [5, 3]], [[4, 4], [4, 5]], [[5, 0], [6, 0]], [[5, 1], [5, 2]], [[6, 2], [6, 3]]], "idx": 169, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_169.png", "answer_image": "figs/stitches_169_answer.png"} {"puzzle": "stitches", "row": 10, "column": 10, "level": "normal", "original_data": {"region": [[0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [3, 3, 0, 1, 1, 1, 1, 1, 1, 2], [3, 3, 3, 4, 4, 2, 2, 2, 2, 2], [3, 3, 3, 3, 4, 4, 5, 5, 2, 2], [3, 3, 3, 3, 4, 4, 5, 2, 2, 6], [7, 3, 4, 4, 4, 8, 5, 8, 6, 6], [7, 3, 7, 8, 8, 8, 8, 8, 6, 6], [7, 7, 7, 7, 9, 9, 9, 8, 8, 6], [7, 9, 7, 9, 9, 6, 6, 6, 8, 6], [9, 9, 9, 9, 9, 9, 9, 6, 6, 6]], "row_stitch_counts": [1, 5, 5, 1, 7, 5, 6, 4, 4, 0], "col_stitch_counts": [2, 3, 3, 5, 5, 8, 4, 2, 4, 2]}, "id": 170, "observation": {"region": [[0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [3, 3, 0, 1, 1, 1, 1, 1, 1, 2], [3, 3, 3, 4, 4, 2, 2, 2, 2, 2], [3, 3, 3, 3, 4, 4, 5, 5, 2, 2], [3, 3, 3, 3, 4, 4, 5, 2, 2, 6], [7, 3, 4, 4, 4, 8, 5, 8, 6, 6], [7, 3, 7, 8, 8, 8, 8, 8, 6, 6], [7, 7, 7, 7, 9, 9, 9, 8, 8, 6], [7, 9, 7, 9, 9, 6, 6, 6, 8, 6], [9, 9, 9, 9, 9, 9, 9, 6, 6, 6]], "row_stitch_counts": [1, 5, 5, 1, 7, 5, 6, 4, 4, 0], "col_stitch_counts": [2, 3, 3, 5, 5, 8, 4, 2, 4, 2]}, "answer": [[[0, 5], [1, 5]], [[1, 1], [1, 2]], [[1, 3], [2, 3]], [[1, 8], [2, 8]], [[2, 4], [2, 5]], [[2, 6], [3, 6]], [[4, 3], [4, 4]], [[4, 5], [4, 6]], [[4, 7], [5, 7]], [[4, 8], [4, 9]], [[5, 2], [6, 2]], [[5, 4], [6, 4]], [[5, 5], [5, 6]], [[6, 0], [6, 1]], [[6, 3], [7, 3]], [[6, 5], [7, 5]], [[7, 8], [7, 9]], [[8, 0], [8, 1]], [[8, 4], [8, 5]]], "idx": 170, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_170.png", "answer_image": "figs/stitches_170_answer.png"} {"puzzle": "stitches", "row": 10, "column": 10, "level": "hard", "original_data": {"region": [[0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 2, 2, 2, 1, 1, 3, 1, 1], [0, 2, 2, 1, 1, 1, 3, 3, 1, 3], [2, 2, 4, 4, 4, 1, 1, 3, 3, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 5, 1, 6, 6, 1, 1, 1, 1], [5, 5, 5, 5, 6, 6, 1, 7, 1, 1], [5, 8, 8, 6, 6, 6, 1, 7, 1, 1], [5, 5, 6, 6, 6, 7, 7, 7, 7, 9], [5, 5, 5, 9, 9, 9, 9, 9, 9, 9]], "row_stitch_counts": [2, 6, 1, 2, 1, 4, 4, 6, 6, 4], "col_stitch_counts": [1, 5, 6, 6, 4, 5, 5, 2, 0, 2]}, "id": 171, "observation": {"region": [[0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 2, 2, 2, 1, 1, 3, 1, 1], [0, 2, 2, 1, 1, 1, 3, 3, 1, 3], [2, 2, 4, 4, 4, 1, 1, 3, 3, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 5, 1, 6, 6, 1, 1, 1, 1], [5, 5, 5, 5, 6, 6, 1, 7, 1, 1], [5, 8, 8, 6, 6, 6, 1, 7, 1, 1], [5, 5, 6, 6, 6, 7, 7, 7, 7, 9], [5, 5, 5, 9, 9, 9, 9, 9, 9, 9]], "row_stitch_counts": [2, 6, 1, 2, 1, 4, 4, 6, 6, 4], "col_stitch_counts": [1, 5, 6, 6, 4, 5, 5, 2, 0, 2]}, "answer": [[[0, 4], [0, 5]], [[1, 1], [1, 2]], [[1, 4], [1, 5]], [[1, 6], [1, 7]], [[2, 2], [3, 2]], [[3, 3], [4, 3]], [[5, 1], [6, 1]], [[5, 3], [6, 3]], [[5, 5], [5, 6]], [[6, 6], [6, 7]], [[7, 0], [7, 1]], [[7, 2], [7, 3]], [[7, 5], [8, 5]], [[7, 9], [8, 9]], [[8, 1], [8, 2]], [[8, 4], [9, 4]], [[8, 6], [9, 6]], [[9, 2], [9, 3]]], "idx": 171, "rules": "**Core Rules:**\nPlace stitches so that:\n1. Every pair of orthogonally adjacent cells from different regions is connected by exactly one stitch.\n2. A stitch connects two orthogonally adjacent holes.\n3. Two stitches cannot share a hole.\n4. Row and column clues give the exact number of used holes in each hole-row and hole-column.\n\n**Coordinates & Output:**\n1. Cell coordinates are integer `(row, col)` on an `N x N` grid, top-left is `(0, 0)`.\n2. Hole coordinates are integer `(row, col)` on an `N x N` hole grid aligned to cell centers.\n3. `row` increases downward, `col` increases rightward.\n4. **Observation** has three parts:\n - `region`: `N x N` region ID grid.\n - `row_stitch_counts`: length-`N` list of row clues (top to bottom).\n - `col_stitch_counts`: length-`N` list of column clues (left to right).\n5. **Answer:** list of stitches, where each stitch is `[(r1, c1), (r2, c2)]` and the two holes are orthogonally adjacent.", "ref_observation": {"region": [[0, 1, 1, 1, 2], [0, 1, 2, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 4, 3], [1, 1, 1, 4, 4]], "row_stitch_counts": [0, 4, 3, 2, 3], "col_stitch_counts": [1, 1, 3, 3, 4]}, "image": "figs/stitches_171.png", "answer_image": "figs/stitches_171_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "easy", "original_data": {"data": [[3, null, null, null, null, null, 4, null, null], [null, 4, 5, null, 2, 1, null, null, null], [1, null, null, null, 7, null, null, 2, 5], [null, null, null, null, null, 6, 3, 1, null], [null, null, null, 7, null, 9, null, null, null], [null, 1, 2, 3, null, null, null, null, null], [2, 5, null, null, 3, null, null, null, 9], [null, null, null, 9, 5, null, 2, 7, null], [null, null, 4, null, null, null, null, null, 8]]}, "id": 172, "observation": {"data": [[3, null, null, null, null, null, 4, null, null], [null, 4, 5, null, 2, 1, null, null, null], [1, null, null, null, 7, null, null, 2, 5], [null, null, null, null, null, 6, 3, 1, null], [null, null, null, 7, null, 9, null, null, null], [null, 1, 2, 3, null, null, null, null, null], [2, 5, null, null, 3, null, null, null, 9], [null, null, null, 9, 5, null, 2, 7, null], [null, null, 4, null, null, null, null, null, 8]], "unit": "3x3"}, "answer": [[3, 2, 7, 5, 9, 8, 4, 6, 1], [9, 4, 5, 6, 2, 1, 7, 8, 3], [1, 6, 8, 4, 7, 3, 9, 2, 5], [5, 7, 9, 2, 8, 6, 3, 1, 4], [4, 8, 3, 7, 1, 9, 6, 5, 2], [6, 1, 2, 3, 4, 5, 8, 9, 7], [2, 5, 6, 8, 3, 7, 1, 4, 9], [8, 3, 1, 9, 5, 4, 2, 7, 6], [7, 9, 4, 1, 6, 2, 5, 3, 8]], "idx": 172, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_172.png", "answer_image": "figs/sudoku_172_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "easy", "original_data": {"data": [[4, null, 3, null, null, 8, 9, null, 7], [2, null, null, null, null, 9, 3, 8, null], [null, null, null, null, 3, null, 1, null, null], [null, 5, 2, 1, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, 5, null, 4, 6, 7, null], [null, null, 6, null, 4, null, null, null, null], [null, 1, 7, 3, null, null, null, null, 9], [3, null, 4, 7, null, null, 2, null, 6]]}, "id": 173, "observation": {"data": [[4, null, 3, null, null, 8, 9, null, 7], [2, null, null, null, null, 9, 3, 8, null], [null, null, null, null, 3, null, 1, null, null], [null, 5, 2, 1, null, 6, null, null, null], [null, null, null, null, null, null, null, null, null], [null, null, null, 5, null, 4, 6, 7, null], [null, null, 6, null, 4, null, null, null, null], [null, 1, 7, 3, null, null, null, null, 9], [3, null, 4, 7, null, null, 2, null, 6]], "unit": "3x3"}, "answer": [[4, 6, 3, 2, 1, 8, 9, 5, 7], [2, 7, 1, 6, 5, 9, 3, 8, 4], [8, 9, 5, 4, 3, 7, 1, 6, 2], [7, 5, 2, 1, 8, 6, 4, 9, 3], [6, 4, 8, 9, 7, 3, 5, 2, 1], [1, 3, 9, 5, 2, 4, 6, 7, 8], [9, 2, 6, 8, 4, 1, 7, 3, 5], [5, 1, 7, 3, 6, 2, 8, 4, 9], [3, 8, 4, 7, 9, 5, 2, 1, 6]], "idx": 173, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_173.png", "answer_image": "figs/sudoku_173_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "normal", "original_data": {"data": [[null, null, null, null, null, 3, 6, 9, null], [null, null, null, null, null, 2, 4, null, 5], [null, null, 4, null, null, 9, null, 2, 1], [null, null, null, null, null, 7, 5, 6, 9], [null, null, null, null, 2, null, null, null, null], [9, 8, 5, 6, null, null, null, null, null], [2, 9, null, 3, null, null, 7, null, null], [6, null, 3, 5, null, null, null, null, null], [null, 4, 8, 2, null, null, null, null, null]]}, "id": 174, "observation": {"data": [[null, null, null, null, null, 3, 6, 9, null], [null, null, null, null, null, 2, 4, null, 5], [null, null, 4, null, null, 9, null, 2, 1], [null, null, null, null, null, 7, 5, 6, 9], [null, null, null, null, 2, null, null, null, null], [9, 8, 5, 6, null, null, null, null, null], [2, 9, null, 3, null, null, 7, null, null], [6, null, 3, 5, null, null, null, null, null], [null, 4, 8, 2, null, null, null, null, null]], "unit": "3x3"}, "answer": [[1, 2, 7, 4, 5, 3, 6, 9, 8], [3, 6, 9, 1, 8, 2, 4, 7, 5], [8, 5, 4, 7, 6, 9, 3, 2, 1], [4, 1, 2, 8, 3, 7, 5, 6, 9], [7, 3, 6, 9, 2, 5, 1, 8, 4], [9, 8, 5, 6, 1, 4, 2, 3, 7], [2, 9, 1, 3, 4, 8, 7, 5, 6], [6, 7, 3, 5, 9, 1, 8, 4, 2], [5, 4, 8, 2, 7, 6, 9, 1, 3]], "idx": 174, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_174.png", "answer_image": "figs/sudoku_174_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "normal", "original_data": {"data": [[null, null, null, 4, 2, null, 7, null, null], [null, 4, null, null, 8, 3, null, 1, null], [null, null, null, 6, 7, null, 3, null, null], [8, null, 7, null, null, 9, null, 5, null], [5, 2, 4, null, 1, null, null, 6, null], [null, 9, null, 5, null, null, null, 7, null], [6, null, 8, null, null, null, null, null, null], [null, 7, null, 1, 4, 2, null, null, null], [null, null, null, null, null, null, null, null, null]]}, "id": 175, "observation": {"data": [[null, null, null, 4, 2, null, 7, null, null], [null, 4, null, null, 8, 3, null, 1, null], [null, null, null, 6, 7, null, 3, null, null], [8, null, 7, null, null, 9, null, 5, null], [5, 2, 4, null, 1, null, null, 6, null], [null, 9, null, 5, null, null, null, 7, null], [6, null, 8, null, null, null, null, null, null], [null, 7, null, 1, 4, 2, null, null, null], [null, null, null, null, null, null, null, null, null]], "unit": "3x3"}, "answer": [[3, 5, 9, 4, 2, 1, 7, 8, 6], [7, 4, 6, 9, 8, 3, 2, 1, 5], [2, 8, 1, 6, 7, 5, 3, 4, 9], [8, 6, 7, 2, 3, 9, 4, 5, 1], [5, 2, 4, 7, 1, 8, 9, 6, 3], [1, 9, 3, 5, 6, 4, 8, 7, 2], [6, 1, 8, 3, 9, 7, 5, 2, 4], [9, 7, 5, 1, 4, 2, 6, 3, 8], [4, 3, 2, 8, 5, 6, 1, 9, 7]], "idx": 175, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_175.png", "answer_image": "figs/sudoku_175_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "hard", "original_data": {"data": [[8, 9, null, null, null, null, 2, null, null], [null, 1, null, null, 5, 9, null, null, null], [null, 7, 2, null, null, null, null, 4, null], [null, null, null, 8, 6, null, null, null, 9], [null, null, 5, 9, null, 7, 8, null, null], [9, null, null, null, 1, 2, null, null, null], [null, 3, null, null, null, null, 5, 7, null], [null, null, null, 7, 2, null, null, 9, null], [null, null, 8, null, null, null, null, 2, 1]]}, "id": 176, "observation": {"data": [[8, 9, null, null, null, null, 2, null, null], [null, 1, null, null, 5, 9, null, null, null], [null, 7, 2, null, null, null, null, 4, null], [null, null, null, 8, 6, null, null, null, 9], [null, null, 5, 9, null, 7, 8, null, null], [9, null, null, null, 1, 2, null, null, null], [null, 3, null, null, null, null, 5, 7, null], [null, null, null, 7, 2, null, null, 9, null], [null, null, 8, null, null, null, null, 2, 1]], "unit": "3x3"}, "answer": [[8, 9, 3, 4, 7, 6, 2, 1, 5], [6, 1, 4, 2, 5, 9, 3, 8, 7], [5, 7, 2, 1, 8, 3, 9, 4, 6], [3, 2, 7, 8, 6, 4, 1, 5, 9], [1, 4, 5, 9, 3, 7, 8, 6, 2], [9, 8, 6, 5, 1, 2, 7, 3, 4], [2, 3, 9, 6, 4, 1, 5, 7, 8], [4, 5, 1, 7, 2, 8, 6, 9, 3], [7, 6, 8, 3, 9, 5, 4, 2, 1]], "idx": 176, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_176.png", "answer_image": "figs/sudoku_176_answer.png"} {"puzzle": "sudoku", "row": 3, "column": 3, "level": "hard", "original_data": {"data": [[null, null, 8, null, null, null, null, null, null], [null, 3, null, null, null, null, 1, 7, null], [9, null, null, 4, 7, null, 5, null, 3], [null, 4, null, null, 1, null, null, null, null], [null, 1, null, 6, null, 8, null, 9, null], [null, null, null, null, 9, null, null, 2, null], [1, null, 6, null, 2, 7, null, null, 8], [null, 7, 3, null, null, null, null, 5, null], [null, null, null, null, null, null, 9, null, null]]}, "id": 177, "observation": {"data": [[null, null, 8, null, null, null, null, null, null], [null, 3, null, null, null, null, 1, 7, null], [9, null, null, 4, 7, null, 5, null, 3], [null, 4, null, null, 1, null, null, null, null], [null, 1, null, 6, null, 8, null, 9, null], [null, null, null, null, 9, null, null, 2, null], [1, null, 6, null, 2, 7, null, null, 8], [null, 7, 3, null, null, null, null, 5, null], [null, null, null, null, null, null, 9, null, null]], "unit": "3x3"}, "answer": [[7, 6, 8, 1, 3, 5, 2, 4, 9], [5, 3, 4, 2, 8, 9, 1, 7, 6], [9, 2, 1, 4, 7, 6, 5, 8, 3], [3, 4, 9, 7, 1, 2, 8, 6, 5], [2, 1, 7, 6, 5, 8, 3, 9, 4], [6, 8, 5, 3, 9, 4, 7, 2, 1], [1, 9, 6, 5, 2, 7, 4, 3, 8], [8, 7, 3, 9, 4, 1, 6, 5, 2], [4, 5, 2, 8, 6, 3, 9, 1, 7]], "idx": 177, "rules": "**Core Rules:**\nFill the grid with numbers so that:\n1. Every row contains each value `1..N` exactly once.\n2. Every column contains each value `1..N` exactly once.\n3. Every subgrid contains each value `1..N` exactly once.\n4. Subgrid size is configurable by unit `(r x c)`:\n - unit `3` means `3x3` subgrids (classic `9x9`).\n - unit `3x4` means `3x4` subgrids (grid size `12x12`).\n - unit `4x4` means `4x4` subgrids (grid size `16x16`).\n5. Given cells are fixed.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has two parts:\n - `data`: initial number grid as list of lists, using `None` for blank cells.\n - `unit`: subgrid shape string, e.g. `'3x3'`, `'3x4'`, `'4x4'`.\n4. **Answer:** full solved number grid as list of lists.", "ref_observation": {"data": [[null, null, 1, null, 3, 8, null, 5, null], [null, null, null, null, null, null, 7, 3, 8], [null, null, null, null, null, 5, null, null, 9], [9, 1, null, null, null, 7, 4, null, null], [null, null, 5, 6, null, 2, 3, null, null], [null, null, 3, 5, null, null, null, 8, 2], [3, null, null, 8, null, null, null, null, null], [1, 4, 7, null, null, null, null, null, null], [null, 5, null, 2, 4, null, 1, null, null]], "unit": "3x3"}, "image": "figs/sudoku_177.png", "answer_image": "figs/sudoku_177_answer.png"} {"puzzle": "tents", "row": 6, "column": 6, "level": "easy", "original_data": {"tree": [[null, "T", null, null, null, null], [null, null, "T", null, null, null], [null, null, null, null, null, "T"], [null, "T", null, null, null, null], [null, null, null, "T", null, null], [null, "T", null, null, null, "T"]], "row_tent_counts": [1, 2, 1, 0, 1, 2], "col_tent_counts": [2, 1, 1, 1, 1, 1]}, "id": 178, "observation": {"tree": [[null, "T", null, null, null, null], [null, null, "T", null, null, null], [null, null, null, null, null, "T"], [null, "T", null, null, null, null], [null, null, null, "T", null, null], [null, "T", null, null, null, "T"]], "row_tent_counts": [1, 2, 1, 0, 1, 2], "col_tent_counts": [2, 1, 1, 1, 1, 1]}, "answer": [["t", null, null, null, null, null], [null, null, null, "t", null, "t"], [null, "t", null, null, null, null], [null, null, null, null, null, null], [null, null, "t", null, null, null], ["t", null, null, null, "t", null]], "idx": 178, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_178.png", "answer_image": "figs/tents_178_answer.png"} {"puzzle": "tents", "row": 6, "column": 6, "level": "hard", "original_data": {"tree": [["T", null, null, null, null, null], [null, null, null, null, "T", null], ["T", null, null, null, null, null], [null, null, null, null, null, "T"], ["T", null, "T", null, null, "T"], [null, null, null, null, null, null]], "row_tent_counts": [1, 1, 1, 2, 1, 1], "col_tent_counts": [2, 1, 1, 1, 1, 1]}, "id": 179, "observation": {"tree": [["T", null, null, null, null, null], [null, null, null, null, "T", null], ["T", null, null, null, null, null], [null, null, null, null, null, "T"], ["T", null, "T", null, null, "T"], [null, null, null, null, null, null]], "row_tent_counts": [1, 1, 1, 2, 1, 1], "col_tent_counts": [2, 1, 1, 1, 1, 1]}, "answer": [[null, "t", null, null, null, null], [null, null, null, "t", null, null], [null, null, null, null, null, "t"], ["t", null, "t", null, null, null], [null, null, null, null, "t", null], ["t", null, null, null, null, null]], "idx": 179, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_179.png", "answer_image": "figs/tents_179_answer.png"} {"puzzle": "tents", "row": 8, "column": 8, "level": "easy", "original_data": {"tree": [[null, "T", null, null, null, null, null, "T"], [null, null, null, null, "T", null, null, null], ["T", null, null, null, null, null, null, null], [null, null, null, "T", null, null, null, null], [null, null, null, null, null, null, null, "T"], [null, null, "T", null, null, null, "T", null], [null, "T", "T", null, null, null, "T", null], [null, null, null, null, "T", null, null, null]], "row_tent_counts": [2, 1, 1, 2, 0, 2, 2, 2], "col_tent_counts": [2, 0, 3, 1, 1, 2, 1, 2]}, "id": 180, "observation": {"tree": [[null, "T", null, null, null, null, null, "T"], [null, null, null, null, "T", null, null, null], ["T", null, null, null, null, null, null, null], [null, null, null, "T", null, null, null, null], [null, null, null, null, null, null, null, "T"], [null, null, "T", null, null, null, "T", null], [null, "T", "T", null, null, null, "T", null], [null, null, null, null, "T", null, null, null]], "row_tent_counts": [2, 1, 1, 2, 0, 2, 2, 2], "col_tent_counts": [2, 0, 3, 1, 1, 2, 1, 2]}, "answer": [[null, null, "t", null, null, null, "t", null], ["t", null, null, null, null, null, null, null], [null, null, null, null, "t", null, null, null], [null, null, "t", null, null, null, null, "t"], [null, null, null, null, null, null, null, null], [null, null, null, "t", null, "t", null, null], ["t", null, null, null, null, null, null, "t"], [null, null, "t", null, null, "t", null, null]], "idx": 180, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_180.png", "answer_image": "figs/tents_180_answer.png"} {"puzzle": "tents", "row": 8, "column": 8, "level": "hard", "original_data": {"tree": [[null, null, "T", null, null, null, null, null], ["T", null, "T", null, null, null, null, "T"], [null, null, null, null, null, null, null, null], [null, "T", null, null, "T", null, null, null], [null, null, null, "T", null, null, null, "T"], [null, null, null, null, null, null, "T", null], [null, null, "T", null, null, "T", null, "T"], [null, null, null, null, null, null, null, null]], "row_tent_counts": [2, 1, 1, 3, 0, 3, 1, 1], "col_tent_counts": [1, 2, 1, 2, 0, 2, 0, 4]}, "id": 181, "observation": {"tree": [[null, null, "T", null, null, null, null, null], ["T", null, "T", null, null, null, null, "T"], [null, null, null, null, null, null, null, null], [null, "T", null, null, "T", null, null, null], [null, null, null, "T", null, null, null, "T"], [null, null, null, null, null, null, "T", null], [null, null, "T", null, null, "T", null, "T"], [null, null, null, null, null, null, null, null]], "row_tent_counts": [2, 1, 1, 3, 0, 3, 1, 1], "col_tent_counts": [1, 2, 1, 2, 0, 2, 0, 4]}, "answer": [[null, "t", null, null, null, null, null, "t"], [null, null, null, "t", null, null, null, null], ["t", null, null, null, null, null, null, null], [null, null, "t", null, null, "t", null, "t"], [null, null, null, null, null, null, null, null], [null, null, null, "t", null, "t", null, "t"], [null, "t", null, null, null, null, null, null], [null, null, null, null, null, null, null, "t"]], "idx": 181, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_181.png", "answer_image": "figs/tents_181_answer.png"} {"puzzle": "tents", "row": 10, "column": 10, "level": "easy", "original_data": {"tree": [["T", null, null, "T", null, "T", null, null, null, null], [null, null, null, null, null, null, null, null, "T", null], [null, "T", null, null, null, "T", null, null, null, null], [null, "T", null, null, null, null, null, null, null, "T"], [null, null, null, null, "T", "T", null, null, "T", null], [null, null, null, null, null, null, null, null, "T", null], [null, null, "T", "T", null, null, "T", null, null, null], [null, null, null, null, null, null, null, null, null, "T"], ["T", null, null, null, null, null, null, null, null, null], [null, null, null, null, "T", null, "T", null, null, "T"]], "row_tent_counts": [4, 0, 3, 0, 3, 2, 2, 2, 0, 4], "col_tent_counts": [1, 3, 1, 3, 1, 2, 3, 1, 2, 3]}, "id": 182, "observation": {"tree": [["T", null, null, "T", null, "T", null, null, null, null], [null, null, null, null, null, null, null, null, "T", null], [null, "T", null, null, null, "T", null, null, null, null], [null, "T", null, null, null, null, null, null, null, "T"], [null, null, null, null, "T", "T", null, null, "T", null], [null, null, null, null, null, null, null, null, "T", null], [null, null, "T", "T", null, null, "T", null, null, null], [null, null, null, null, null, null, null, null, null, "T"], ["T", null, null, null, null, null, null, null, null, null], [null, null, null, null, "T", null, "T", null, null, "T"]], "row_tent_counts": [4, 0, 3, 0, 3, 2, 2, 2, 0, 4], "col_tent_counts": [1, 3, 1, 3, 1, 2, 3, 1, 2, 3]}, "answer": [[null, "t", null, null, "t", null, "t", null, "t", null], [null, null, null, null, null, null, null, null, null, null], [null, null, "t", null, null, null, "t", null, null, "t"], [null, null, null, null, null, null, null, null, null, null], [null, "t", null, "t", null, null, null, null, null, "t"], [null, null, null, null, null, "t", null, "t", null, null], [null, "t", null, null, null, null, null, null, null, "t"], [null, null, null, "t", null, null, "t", null, null, null], [null, null, null, null, null, null, null, null, null, null], ["t", null, null, "t", null, "t", null, null, "t", null]], "idx": 182, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_182.png", "answer_image": "figs/tents_182_answer.png"} {"puzzle": "tents", "row": 10, "column": 10, "level": "hard", "original_data": {"tree": [[null, "T", null, null, null, "T", null, null, null, null], ["T", null, null, "T", null, null, null, null, null, null], [null, null, null, null, null, null, null, null, "T", null], [null, null, null, null, null, null, "T", null, "T", null], [null, null, null, null, null, null, null, null, null, null], ["T", null, null, "T", null, null, null, "T", "T", null], [null, null, null, null, "T", null, "T", null, null, null], [null, "T", null, null, null, null, null, "T", "T", null], [null, null, null, null, null, null, "T", null, null, null], [null, "T", null, "T", null, null, null, null, "T", null]], "row_tent_counts": [2, 1, 2, 1, 2, 2, 3, 2, 3, 2], "col_tent_counts": [3, 1, 1, 3, 1, 2, 2, 3, 0, 4]}, "id": 183, "observation": {"tree": [[null, "T", null, null, null, "T", null, null, null, null], ["T", null, null, "T", null, null, null, null, null, null], [null, null, null, null, null, null, null, null, "T", null], [null, null, null, null, null, null, "T", null, "T", null], [null, null, null, null, null, null, null, null, null, null], ["T", null, null, "T", null, null, null, "T", "T", null], [null, null, null, null, "T", null, "T", null, null, null], [null, "T", null, null, null, null, null, "T", "T", null], [null, null, null, null, null, null, "T", null, null, null], [null, "T", null, "T", null, null, null, null, "T", null]], "row_tent_counts": [2, 1, 2, 1, 2, 2, 3, 2, 3, 2], "col_tent_counts": [3, 1, 1, 3, 1, 2, 2, 3, 0, 4]}, "answer": [[null, null, "t", null, null, null, "t", null, null, null], [null, null, null, null, "t", null, null, null, null, null], ["t", null, null, null, null, null, null, "t", null, null], [null, null, null, null, null, null, null, null, null, "t"], [null, null, null, "t", null, null, "t", null, null, null], [null, "t", null, null, null, null, null, null, null, "t"], [null, null, null, "t", null, "t", null, "t", null, null], ["t", null, null, null, null, null, null, null, null, "t"], [null, null, null, "t", null, "t", null, "t", null, null], ["t", null, null, null, null, null, null, null, null, "t"]], "idx": 183, "rules": "**Core Rules:**\nPlace tents on empty cells so that:\n1. Each tent is orthogonally adjacent to exactly one tree.\n2. Each tree is paired with exactly one tent (1-to-1 pairing).\n3. Tents cannot touch each other, including diagonally.\n4. Row and column clues indicate exactly how many tents must be placed in that row/column.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases top-to-bottom, `col` increases left-to-right.\n3. **Observation** has three parts:\n - `tree`: list of lists using `'T'` for tree cells, else `None`.\n - `row_tent_counts`: list from top row to bottom row.\n - `col_tent_counts`: list from left column to right column.\n4. **Answer:** same-sized grid using `'t'` for tent cells and `None` for non-tent cells.", "ref_observation": {"tree": [[null, null, "T", null, null, "T"], [null, null, null, null, null, null], ["T", "T", null, null, null, null], [null, "T", null, null, null, null], [null, null, null, null, "T", null], [null, null, "T", null, null, null]], "row_tent_counts": [1, 2, 0, 3, 0, 1], "col_tent_counts": [1, 2, 1, 1, 1, 1]}, "image": "figs/tents_183.png", "answer_image": "figs/tents_183_answer.png"} {"puzzle": "yinyang", "row": 6, "column": 6, "level": "easy", "original_data": {"data": [[null, "W", null, null, null, null], [null, null, null, "W", null, null], [null, null, "B", "B", "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "id": 184, "observation": {"data": [[null, "W", null, null, null, null], [null, null, null, "W", null, null], [null, null, "B", "B", "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "answer": [["W", "W", "W", "B", "B", "B"], ["W", "B", "W", "W", "W", "B"], ["W", "B", "B", "B", "B", "B"], ["W", "B", "W", "W", "B", "W"], ["W", "B", "W", "B", "B", "W"], ["W", "W", "W", "W", "W", "W"]], "idx": 184, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_184.png", "answer_image": "figs/yinyang_184_answer.png"} {"puzzle": "yinyang", "row": 6, "column": 6, "level": "normal", "original_data": {"data": [[null, "B", null, null, null, null], [null, null, null, "B", null, null], [null, null, "B", null, null, null], [null, null, "B", "B", null, null], [null, null, null, null, "B", null], [null, "B", null, null, null, null]]}, "id": 185, "observation": {"data": [[null, "B", null, null, null, null], [null, null, null, "B", null, null], [null, null, "B", null, null, null], [null, null, "B", "B", null, null], [null, null, null, null, "B", null], [null, "B", null, null, null, null]]}, "answer": [["B", "B", "B", "W", "W", "W"], ["B", "W", "B", "B", "B", "W"], ["B", "W", "B", "W", "W", "W"], ["B", "W", "B", "B", "B", "W"], ["B", "W", "W", "W", "B", "W"], ["B", "B", "B", "W", "W", "W"]], "idx": 185, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_185.png", "answer_image": "figs/yinyang_185_answer.png"} {"puzzle": "yinyang", "row": 6, "column": 6, "level": "hard", "original_data": {"data": [[null, null, null, null, null, "W"], [null, null, "B", "W", null, null], [null, null, null, "W", "B", null], [null, null, "W", null, "W", null], [null, null, null, "B", null, null], [null, null, "B", null, null, null]]}, "id": 186, "observation": {"data": [[null, null, null, null, null, "W"], [null, null, "B", "W", null, null], [null, null, null, "W", "B", null], [null, null, "W", null, "W", null], [null, null, null, "B", null, null], [null, null, "B", null, null, null]]}, "answer": [["B", "B", "B", "B", "B", "W"], ["B", "W", "B", "W", "B", "W"], ["B", "W", "B", "W", "B", "W"], ["B", "W", "W", "W", "W", "W"], ["B", "W", "B", "B", "B", "W"], ["B", "B", "B", "W", "W", "W"]], "idx": 186, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_186.png", "answer_image": "figs/yinyang_186_answer.png"} {"puzzle": "yinyang", "row": 10, "column": 10, "level": "easy", "original_data": {"data": [[null, null, null, null, null, null, null, "W", null, null], [null, null, "W", null, null, null, null, "W", null, null], [null, "B", "W", null, "B", null, null, null, "B", null], [null, "B", null, "W", null, "B", "W", null, null, "B"], [null, null, "B", null, "W", "B", null, null, null, null], ["W", "W", null, "B", null, null, null, "W", null, null], [null, null, "B", null, "B", null, null, null, null, null], [null, "W", null, null, null, null, null, "W", null, null], [null, null, null, "W", null, null, "B", null, null, null], ["B", null, null, null, null, null, null, null, null, null]]}, "id": 187, "observation": {"data": [[null, null, null, null, null, null, null, "W", null, null], [null, null, "W", null, null, null, null, "W", null, null], [null, "B", "W", null, "B", null, null, null, "B", null], [null, "B", null, "W", null, "B", "W", null, null, "B"], [null, null, "B", null, "W", "B", null, null, null, null], ["W", "W", null, "B", null, null, null, "W", null, null], [null, null, "B", null, "B", null, null, null, null, null], [null, "W", null, null, null, null, null, "W", null, null], [null, null, null, "W", null, null, "B", null, null, null], ["B", null, null, null, null, null, null, null, null, null]]}, "answer": [["W", "W", "W", "W", "W", "W", "W", "W", "W", "W"], ["W", "B", "W", "B", "W", "B", "B", "W", "B", "W"], ["W", "B", "W", "B", "B", "B", "W", "W", "B", "W"], ["W", "B", "W", "W", "W", "B", "W", "B", "B", "B"], ["W", "B", "B", "B", "W", "B", "W", "W", "W", "B"], ["W", "W", "W", "B", "W", "B", "B", "W", "B", "B"], ["W", "B", "B", "B", "B", "B", "W", "W", "W", "B"], ["W", "W", "W", "B", "W", "B", "B", "W", "B", "B"], ["W", "B", "W", "W", "W", "W", "B", "W", "W", "B"], ["B", "B", "B", "B", "B", "B", "B", "B", "B", "B"]], "idx": 187, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_187.png", "answer_image": "figs/yinyang_187_answer.png"} {"puzzle": "yinyang", "row": 10, "column": 10, "level": "normal", "original_data": {"data": [[null, null, null, null, null, null, null, "W", null, null], [null, null, null, null, null, null, null, null, null, null], ["B", null, "B", null, "W", null, null, "W", null, null], [null, "B", null, null, null, null, "W", null, "W", null], [null, null, "B", null, "W", null, null, null, null, null], [null, "B", "W", null, null, "W", "B", "W", null, null], [null, null, "B", null, null, null, "W", null, null, null], [null, "B", null, "B", null, null, null, null, "W", null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "id": 188, "observation": {"data": [[null, null, null, null, null, null, null, "W", null, null], [null, null, null, null, null, null, null, null, null, null], ["B", null, "B", null, "W", null, null, "W", null, null], [null, "B", null, null, null, null, "W", null, "W", null], [null, null, "B", null, "W", null, null, null, null, null], [null, "B", "W", null, null, "W", "B", "W", null, null], [null, null, "B", null, null, null, "W", null, null, null], [null, "B", null, "B", null, null, null, null, "W", null], [null, null, null, null, null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "answer": [["B", "B", "B", "B", "B", "B", "B", "W", "W", "W"], ["B", "W", "W", "W", "W", "W", "B", "B", "B", "W"], ["B", "B", "B", "B", "W", "B", "B", "W", "B", "W"], ["W", "B", "W", "W", "W", "B", "W", "W", "W", "W"], ["W", "B", "B", "B", "W", "B", "B", "B", "B", "W"], ["W", "B", "W", "W", "W", "W", "B", "W", "B", "W"], ["W", "B", "B", "B", "B", "W", "W", "W", "B", "W"], ["W", "B", "W", "B", "W", "W", "B", "W", "W", "W"], ["W", "B", "W", "B", "B", "B", "B", "B", "B", "W"], ["W", "W", "W", "W", "W", "W", "W", "W", "W", "W"]], "idx": 188, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_188.png", "answer_image": "figs/yinyang_188_answer.png"} {"puzzle": "yinyang", "row": 10, "column": 10, "level": "hard", "original_data": {"data": [["W", null, "B", null, "W", null, null, null, null, null], [null, "B", null, null, null, "W", null, null, null, null], [null, null, "B", "B", null, null, null, null, "W", null], [null, "B", null, null, "B", null, null, null, null, null], [null, null, "B", null, null, null, null, null, null, null], [null, null, null, null, "W", "B", "B", null, null, null], [null, null, "W", null, null, null, null, null, null, null], [null, null, null, null, null, "W", null, "W", "W", null], [null, null, null, "W", null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "id": 189, "observation": {"data": [["W", null, "B", null, "W", null, null, null, null, null], [null, "B", null, null, null, "W", null, null, null, null], [null, null, "B", "B", null, null, null, null, "W", null], [null, "B", null, null, "B", null, null, null, null, null], [null, null, "B", null, null, null, null, null, null, null], [null, null, null, null, "W", "B", "B", null, null, null], [null, null, "W", null, null, null, null, null, null, null], [null, null, null, null, null, "W", null, "W", "W", null], [null, null, null, "W", null, null, null, null, null, null], [null, null, null, null, null, null, null, null, null, null]]}, "answer": [["W", "B", "B", "W", "W", "W", "W", "W", "W", "W"], ["W", "B", "W", "W", "B", "W", "B", "B", "B", "W"], ["W", "B", "B", "B", "B", "B", "B", "W", "W", "W"], ["W", "B", "W", "W", "B", "W", "W", "W", "B", "W"], ["W", "B", "B", "W", "B", "B", "W", "B", "B", "W"], ["W", "B", "W", "W", "W", "B", "B", "B", "W", "W"], ["W", "B", "W", "B", "B", "B", "W", "B", "B", "W"], ["W", "B", "W", "W", "B", "W", "W", "W", "W", "W"], ["W", "B", "B", "W", "B", "B", "B", "B", "B", "W"], ["W", "W", "W", "W", "W", "W", "W", "W", "W", "W"]], "idx": 189, "rules": "**Core Rules:**\nColor every cell either black (`B`) or white (`W`) so that:\n1. All black cells form one orthogonally connected region.\n2. All white cells form one orthogonally connected region.\n3. No 2x2 block can be all black or all white.\n\n**Coordinates & Output:**\n1. Coordinates use `(row, col)` with top-left as `(0, 0)`.\n2. `row` increases from top to bottom, `col` increases from left to right.\n3. **Observation** has one part:\n - `data`: `N x N` clue 2D list using `'B'`, `'W'`, or `None`.\n4. **Answer:** full `N x N` grid as a 2D list of `'B'` / `'W'`.", "ref_observation": {"data": [["B", null, null, null, null, null], [null, "B", null, "W", null, null], [null, "B", "W", null, "B", "B"], [null, "B", null, null, "B", null], [null, null, "W", null, null, null], [null, null, null, null, null, null]]}, "image": "figs/yinyang_189.png", "answer_image": "figs/yinyang_189_answer.png"}