| {"width": 1254, "height": 1254, "grid_rows": 200, "grid_cols": 200, "square_left": 125.0, "square_top": 125.0, "square_size": 1004.0, "num_regions": 10, "question": "How many separated regions are inside the image? A region is a maximal area filled with one continuous fill. Boundaries between regions may appear as continuous lines OR as a chain of small individual markers \u2014 discrete dots, footprints, dashes, or short segments aligned along a curve \u2014 that you must visually link together to recognize as a single boundary. Two locations belong to the same region if you can travel between them without crossing such a boundary (continuous or chained). Count every distinct region and report the total as a positive integer. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 10, "difficulty": "medium", "region_seed_cells": [[199, 74], [21, 4], [108, 97], [33, 185], [49, 68], [113, 3], [181, 127], [131, 160], [175, 3], [3, 113]], "region_cell_counts": [74251, 80287, 99834, 140057, 110665, 106165, 110475, 125225, 74962, 86095], "region_adjacency": [[0, 2], [0, 5], [0, 6], [0, 8], [1, 4], [1, 5], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 7], [3, 9], [4, 5], [4, 9], [5, 8], [6, 7]], "image": "images/counting_regions_00000.png"} | |
| {"width": 1254, "height": 1254, "grid_rows": 200, "grid_cols": 200, "square_left": 125.0, "square_top": 125.0, "square_size": 1004.0, "num_regions": 12, "question": "How many separated regions are inside the image? A region is a maximal area filled with one continuous fill. Boundaries between regions may appear as continuous lines OR as a chain of small individual markers \u2014 discrete dots, footprints, dashes, or short segments aligned along a curve \u2014 that you must visually link together to recognize as a single boundary. Two locations belong to the same region if you can travel between them without crossing such a boundary (continuous or chained). Count every distinct region and report the total as a positive integer. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 12, "difficulty": "hard", "region_seed_cells": [[118, 113], [82, 50], [175, 46], [13, 58], [53, 170], [196, 105], [45, 117], [46, 0], [178, 192], [110, 192], [144, 5], [6, 196]], "region_cell_counts": [107644, 90017, 70137, 60871, 74055, 98974, 110114, 72037, 91826, 87191, 78872, 66278], "region_adjacency": [[0, 1], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [1, 3], [1, 6], [1, 7], [1, 10], [2, 5], [2, 10], [3, 6], [3, 7], [4, 6], [4, 9], [4, 11], [5, 8], [5, 10], [6, 11], [7, 10], [8, 9]], "image": "images/counting_regions_00001.png"} | |
| {"width": 1254, "height": 1254, "grid_rows": 200, "grid_cols": 200, "square_left": 125.0, "square_top": 125.0, "square_size": 1004.0, "num_regions": 15, "question": "How many separated regions are inside the image? A region is a maximal area filled with one continuous fill. Boundaries between regions may appear as continuous lines OR as a chain of small individual markers \u2014 discrete dots, footprints, dashes, or short segments aligned along a curve \u2014 that you must visually link together to recognize as a single boundary. Two locations belong to the same region if you can travel between them without crossing such a boundary (continuous or chained). Count every distinct region and report the total as a positive integer. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 15, "difficulty": "hard", "region_seed_cells": [[46, 134], [106, 26], [10, 80], [135, 80], [27, 198], [57, 69], [184, 194], [15, 18], [92, 129], [152, 6], [100, 176], [163, 119], [199, 27], [199, 74], [47, 154]], "region_cell_counts": [59115, 63143, 63169, 70499, 55611, 74488, 64501, 87475, 72985, 62554, 98562, 87154, 47120, 50242, 51398], "region_adjacency": [[0, 2], [0, 4], [0, 5], [0, 8], [0, 14], [1, 5], [1, 7], [1, 9], [2, 5], [2, 7], [3, 5], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [4, 14], [5, 7], [5, 8], [5, 9], [6, 10], [6, 11], [8, 10], [8, 14], [9, 12], [10, 11], [10, 14], [11, 13], [12, 13]], "image": "images/counting_regions_00002.png"} | |
| {"width": 1254, "height": 1254, "grid_rows": 200, "grid_cols": 200, "square_left": 125.0, "square_top": 125.0, "square_size": 1004.0, "num_regions": 18, "question": "How many separated regions are inside the image? A region is a maximal area filled with one continuous fill. Boundaries between regions may appear as continuous lines OR as a chain of small individual markers \u2014 discrete dots, footprints, dashes, or short segments aligned along a curve \u2014 that you must visually link together to recognize as a single boundary. Two locations belong to the same region if you can travel between them without crossing such a boundary (continuous or chained). Count every distinct region and report the total as a positive integer. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 18, "difficulty": "hard", "region_seed_cells": [[129, 183], [199, 19], [165, 99], [85, 94], [196, 133], [43, 184], [96, 147], [0, 35], [156, 40], [0, 111], [53, 45], [104, 9], [1, 154], [32, 2], [175, 179], [53, 141], [112, 59], [142, 141]], "region_cell_counts": [49542, 49619, 59811, 61799, 41901, 56407, 58257, 50999, 72110, 69684, 47373, 71734, 44532, 43735, 48309, 51149, 74918, 56137], "region_adjacency": [[0, 6], [0, 14], [0, 17], [1, 2], [1, 8], [2, 4], [2, 8], [2, 16], [2, 17], [3, 6], [3, 9], [3, 10], [3, 15], [3, 16], [3, 17], [4, 14], [4, 17], [5, 6], [5, 12], [5, 15], [6, 15], [6, 17], [7, 9], [7, 10], [7, 13], [8, 11], [8, 16], [9, 10], [9, 12], [9, 15], [10, 11], [10, 13], [10, 16], [11, 13], [11, 16], [12, 15], [14, 17], [16, 17]], "image": "images/counting_regions_00003.png"} | |
| {"width": 1254, "height": 1254, "grid_rows": 200, "grid_cols": 200, "square_left": 125.0, "square_top": 125.0, "square_size": 1004.0, "num_regions": 20, "question": "How many separated regions are inside the image? A region is a maximal area filled with one continuous fill. Boundaries between regions may appear as continuous lines OR as a chain of small individual markers \u2014 discrete dots, footprints, dashes, or short segments aligned along a curve \u2014 that you must visually link together to recognize as a single boundary. Two locations belong to the same region if you can travel between them without crossing such a boundary (continuous or chained). Count every distinct region and report the total as a positive integer. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 20, "difficulty": "hard", "region_seed_cells": [[96, 38], [161, 47], [39, 84], [45, 148], [124, 168], [2, 130], [96, 134], [182, 120], [29, 31], [31, 193], [167, 180], [155, 1], [197, 11], [74, 183], [134, 112], [196, 70], [118, 74], [64, 6], [78, 97], [2, 62]], "region_cell_counts": [68165, 53951, 53663, 47695, 72486, 39787, 54164, 57307, 50313, 49792, 63259, 37212, 31919, 48205, 58095, 35318, 48515, 37963, 52838, 47369], "region_adjacency": [[0, 1], [0, 11], [0, 16], [0, 17], [0, 18], [0, 19], [1, 11], [1, 12], [1, 14], [1, 15], [1, 16], [2, 3], [2, 5], [2, 18], [2, 19], [3, 5], [3, 6], [3, 9], [3, 13], [3, 18], [4, 6], [4, 7], [4, 10], [4, 13], [4, 14], [5, 9], [5, 19], [6, 13], [6, 14], [6, 18], [7, 10], [7, 14], [7, 15], [8, 17], [8, 19], [9, 13], [11, 12], [12, 15], [14, 15], [14, 16], [14, 18], [16, 18], [17, 19], [18, 19]], "image": "images/counting_regions_00004.png"} | |