diff_sorted_id stringclasses 105
values | problem_statement stringlengths 778 1.74k | problem_type stringclasses 11
values | problem_category stringclasses 5
values | relative_diff_score stringclasses 35
values | opt_solution stringlengths 24 474 | opt_solution_cost stringlengths 1 4 | opt_solution_compute_t stringlengths 14 20 | solution_depth stringclasses 40
values | max_successor_states stringclasses 51
values | num_vars_per_state stringclasses 47
values | is_feasible_args stringlengths 43 1.24k | is_correct_args stringlengths 43 1.26k | A*_args stringlengths 46 1.27k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
82 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[2, 13], [2, 12], [3, 12], [4, 11], [5, 11], [6, 12], [7, 11], [8, 11], [9, 10], [9, 9], [9, 8], [9, 7], [9, 6], [9, 5], [9, 4], [8, 4], [8, 3], [8, 2], [8, 1], [8, 0]] | 20 | 0.03277468681335449 | 20 | 8 | 2 | ["[[1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0,... | ["[[1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0,... | ["[[1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0,... |
82 | Given 7 labeled water jugs with capacities 52, 55, 84, 135, 136, 47, 139, 76 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 292, 325, 496, 516 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the a... | water_jug | subset_sum | 6 | [["+", 52, 4], ["+", 139, 4], ["+", 139, 4], ["+", 139, 4], ["+", 47, 4], ["+", 135, 3], ["+", 135, 3], ["+", 139, 3], ["-", 52, 3], ["+", 139, 3], ["+", 139, 2], ["+", 139, 2], ["+", 47, 2], ["+", 135, 1], ["+", 136, 1], ["-", 55, 1], ["+", 76, 1]] | 17 | 0.049492597579956055 | 17 | 64 | 3 | [[52, 55, 84, 135, 136, 47, 139, 76], [292, 325, 496, 516]] | [[52, 55, 84, 135, 136, 47, 139, 76], [292, 325, 496, 516]] | ["[52, 55, 84, 135, 136, 47, 139, 76]", "[292, 325, 496, 516]"] |
83 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [82, 79, 51, 82, 63, 80, 79, 51, 82, 63, 99, 39, 63, 99, 51, 82, 99, 63, 39, 31, 16, 50, 5, 41, 50, 5, 41, 45, 67, 79, 80, 50, 45, 41] | 34 | 4.1595001220703125 | 34 | 4 | 15 | [[[79, 82, 80, 67, 45], [51, "_", 63, 41, 5], [39, 99, 31, 16, 50]]] | [[[79, 82, 80, 67, 45], [51, "_", 63, 41, 5], [39, 99, 31, 16, 50]]] | ["[[79, 82, 80, 67, 45], [51, '_', 63, 41, 5], [39, 99, 31, 16, 50]]"] |
83 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left", "up-left"] | 14 | 0.2462632656097412 | 14 | 4 | 25 | [[["u", "r", "a", "n", "e"], ["s", "l", "r", "i", "s"], ["a", "i", "_", "e", "e"], ["b", "o", "k", "b", "l"], ["s", "k", "r", "f", "f"]]] | [[["u", "r", "a", "n", "e"], ["s", "l", "r", "i", "s"], ["a", "i", "_", "e", "e"], ["b", "o", "k", "b", "l"], ["s", "k", "r", "f", "f"]], ["rane", "sures", "liber", "bikol", "skaff"]] | ["[['u', 'r', 'a', 'n', 'e'], ['s', 'l', 'r', 'i', 's'], ['a', 'i', '_', 'e', 'e'], ['b', 'o', 'k', 'b', 'l'], ['s', 'k', 'r', 'f', 'f']]", "['rane', 'sures', 'liber', 'bikol', 'skaff']"] |
83 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 14 | ["X", "D", "N", "P", "K", "T", "N", "R", "K"] | 9 | 0.12111306190490723 | 9 | 14 | 17 | [[[0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, ... | [[[0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, ... | ["[[0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0,... |
83 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 5, 22, 10, 4, 26, 26, 31, 13, 30, 37, 14, 14, 38, 9, 30, 7, 16, 21, 37, 4, 24, 10, 41, 13, 16, 3, 40, 24, 117, 34, 7, 11, 14, 28, 37, 21, 32, 2, 15, 5, 13, 3, 28, 31, 22, 30, 32, 38, 25, 10, 4, 30], such that the sum ... | coin_exchange | subset_sum | 34 | [40, 32, 4, 31, 4, 117, 34, 32, 4, 21, 21, 31, 28, 12] | 36 | 0.06167340278625488 | 14 | 53 | 53 | [[12, 5, 22, 10, 4, 26, 26, 31, 13, 30, 37, 14, 14, 38, 9, 30, 7, 16, 21, 37, 4, 24, 10, 41, 13, 16, 3, 40, 24, 117, 34, 7, 11, 14, 28, 37, 21, 32, 2, 15, 5, 13, 3, 28, 31, 22, 30, 32, 38, 25, 10, 4, 30]] | [[12, 5, 22, 10, 4, 26, 26, 31, 13, 30, 37, 14, 14, 38, 9, 30, 7, 16, 21, 37, 4, 24, 10, 41, 13, 16, 3, 40, 24, 117, 34, 7, 11, 14, 28, 37, 21, 32, 2, 15, 5, 13, 3, 28, 31, 22, 30, 32, 38, 25, 10, 4, 30], {"10": 7, "2": 2, "14": 12, "15": 8, "13": 10, "9": 1, "38": 17, "117": 2, "16": 13, "25": 11, "31": 3, "32": 2, "2... | ["[12, 5, 22, 10, 4, 26, 26, 31, 13, 30, 37, 14, 14, 38, 9, 30, 7, 16, 21, 37, 4, 24, 10, 41, 13, 16, 3, 40, 24, 117, 34, 7, 11, 14, 28, 37, 21, 32, 2, 15, 5, 13, 3, 28, 31, 22, 30, 32, 38, 25, 10, 4, 30]", "{10: 7, 2: 2, 14: 12, 15: 8, 13: 10, 9: 1, 38: 17, 117: 2, 16: 13, 25: 11, 31: 3, 32: 2, 22: 10, 7: 4, 12: 3, 4:... |
83 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 2], [0, 2]] | 29 | 281.29705452919006 | 29 | 6 | 18 | [[["Red", "Green", "Blue", "Blue", "Blue", "Red"], ["Red", "Red", "Green", "Blue", "Green", "Blue"], ["Red", "Red", "Green", "Green", "Blue", "Green"]], 9] | [[["Red", "Green", "Blue", "Blue", "Blue", "Red"], ["Red", "Red", "Green", "Blue", "Green", "Blue"], ["Red", "Red", "Green", "Green", "Blue", "Green"]], 9] | ["[['Red', 'Green', 'Blue', 'Blue', 'Blue', 'Red'], ['Red', 'Red', 'Green', 'Blue', 'Green', 'Blue'], ['Red', 'Red', 'Green', 'Green', 'Blue', 'Green']]", "9"] |
83 | We have a 4x4 numerical grid, with numbers ranging from 36 to 86 (36 included in the range but 86 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 13 | [[0, 1, 39], [0, 3, 51], [1, 0, 40], [1, 1, 41], [2, 1, 55], [3, 0, 56]] | 705 | 0.23045659065246582 | 6 | 50 | 16 | ["[['38', '', '50', ''], ['', '', '64', '67'], ['54', '', '71', '79'], ['', '59', '89', '90']]", 36, 91] | ["[['38', '', '50', ''], ['', '', '64', '67'], ['54', '', '71', '79'], ['', '59', '89', '90']]", 36, 91] | ["[['38', '', '50', ''], ['', '', '64', '67'], ['54', '', '71', '79'], ['', '59', '89', '90']]", "36", "91"] |
83 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 43 to 84. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 240, 226, None for columns 1 to 2 respectively, and the sums of rows must be None, 255, 268, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[0, 0, 43], [0, 2, 44], [1, 0, 52], [1, 1, 62], [1, 2, 73], [2, 0, 49], [2, 1, 80], [3, 0, 46], [3, 1, 47], [3, 2, 45], [3, 3, 48]] | 912 | 105.51012396812439 | 11 | 31 | 16 | ["[['', '51', '', '65'], ['', '', '', '68'], ['', '', '64', '75'], ['', '', '', '']]", 4, 43, 84] | ["[['', '51', '', '65'], ['', '', '', '68'], ['', '', '64', '75'], ['', '', '', '']]", 43, 84, [1, 3], [1, 3], [240, 226], [255, 268], 264] | ["[['', '51', '', '65'], ['', '', '', '68'], ['', '', '64', '75'], ['', '', '', '']]", "43", "84", "[None, 240, 226, None]", "[None, 255, 268, None]", "264"] |
83 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[5, 8], [5, 8], [6, 8], [1, 4], [6, 4], [6, 11], [7, 11], [7, 8], [1, 0], [1, 11], [3, 0], [6, 0], [6, 11], [9, 6], [9, 4], [9, 11], [1, 10], [1, 6], [1, 8], [9, 1], [9, 8], [9, 4], [7, 9], [5, 9], [5, 6], [5, 9], [5, 0], [3, 1], [3, 1], [3, 1], [3, 11], [3, 4], [3, 4], [7, 3], [7, 6], [7, 3], [5, 1], [0, 3], [0, 3], ... | 228 | 0.21515893936157227 | 43 | 132 | 42 | [[[], ["Black", "Green", "White", "Pink", "Yellow", "Blue", "Red"], [], ["Green", "Red", "Red", "Red", "White", "Black", "Black"], [], ["Blue", "Blue", "Pink", "Yellow", "Pink", "Green", "Red"], ["Blue", "Black", "White", "Green", "White", "Yellow", "Yellow"], ["White", "Blue", "Pink", "Green", "Yellow", "Green", "Pink... | [[[], ["Black", "Green", "White", "Pink", "Yellow", "Blue", "Red"], [], ["Green", "Red", "Red", "Red", "White", "Black", "Black"], [], ["Blue", "Blue", "Pink", "Yellow", "Pink", "Green", "Red"], ["Blue", "Black", "White", "Green", "White", "Yellow", "Yellow"], ["White", "Blue", "Pink", "Green", "Yellow", "Green", "Pink... | ["[[], ['Black', 'Green', 'White', 'Pink', 'Yellow', 'Blue', 'Red'], [], ['Green', 'Red', 'Red', 'Red', 'White', 'Black', 'Black'], [], ['Blue', 'Blue', 'Pink', 'Yellow', 'Pink', 'Green', 'Red'], ['Blue', 'Black', 'White', 'Green', 'White', 'Yellow', 'Yellow'], ['White', 'Blue', 'Pink', 'Green', 'Yellow', 'Green', 'Pin... |
83 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 13) to his destination workshop at index (5, 1), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[2, 13], [2, 12], [3, 12], [4, 12], [4, 11], [5, 11], [5, 10], [6, 10], [6, 9], [6, 8], [6, 7], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1]] | 198 | 0.028166532516479492 | 18 | 4 | 4 | [[["x", "x", "14", "x", "3", "x", "18", "x", "4", "4", "x", "x", "16", "x"], ["x", "x", "1", "15", "x", "18", "x", "18", "x", "x", "x", "x", "14", "x"], ["x", "x", "7", "14", "x", "x", "16", "x", "x", "x", "x", "5", "19", "15"], ["x", "13", "18", "x", "17", "x", "6", "8", "x", "8", "x", "x", "13", "x"], ["12", "x", "15... | [[["x", "x", "14", "x", "3", "x", "18", "x", "4", "4", "x", "x", "16", "x"], ["x", "x", "1", "15", "x", "18", "x", "18", "x", "x", "x", "x", "14", "x"], ["x", "x", "7", "14", "x", "x", "16", "x", "x", "x", "x", "5", "19", "15"], ["x", "13", "18", "x", "17", "x", "6", "8", "x", "8", "x", "x", "13", "x"], ["12", "x", "15... | ["[['x', 'x', '14', 'x', '3', 'x', '18', 'x', '4', '4', 'x', 'x', '16', 'x'], ['x', 'x', '1', '15', 'x', '18', 'x', '18', 'x', 'x', 'x', 'x', '14', 'x'], ['x', 'x', '7', '14', 'x', 'x', '16', 'x', 'x', 'x', 'x', '5', '19', '15'], ['x', '13', '18', 'x', '17', 'x', '6', '8', 'x', '8', 'x', 'x', '13', 'x'], ['12', 'x', '1... |
83 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[13, 10], [12, 9], [11, 8], [10, 7], [9, 6], [9, 5], [8, 5], [8, 4], [8, 3], [8, 2], [8, 1], [8, 0], [7, 0], [6, 0], [5, 0], [4, 0]] | 16 | 0.0652778148651123 | 16 | 8 | 2 | ["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1], [0, 1, 1,... | ["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1], [0, 1, 1,... | ["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1], [0, 1, 1,... |
83 | Given 7 labeled water jugs with capacities 19, 42, 18, 127, 106, 32, 22, 137 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 245, 252, 264, 314 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the a... | water_jug | subset_sum | 6 | [["+", 22, 4], ["+", 137, 4], ["+", 18, 4], ["+", 137, 4], ["+", 127, 3], ["+", 137, 3], ["+", 106, 2], ["+", 127, 2], ["+", 19, 2], ["+", 127, 1], ["-", 19, 1], ["+", 137, 1]] | 12 | 0.036943674087524414 | 12 | 64 | 3 | [[19, 42, 18, 127, 106, 32, 22, 137], [245, 252, 264, 314]] | [[19, 42, 18, 127, 106, 32, 22, 137], [245, 252, 264, 314]] | ["[19, 42, 18, 127, 106, 32, 22, 137]", "[245, 252, 264, 314]"] |
84 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [96, 85, 60, 96, 76, 29, 85, 60, 96, 76, 89, 72, 37, 42, 82, 12, 80, 85, 60, 89, 72, 27, 76, 72, 27, 37, 29, 27, 72, 76, 37, 29, 27, 60, 85, 82, 12, 55, 42, 12, 55, 42] | 42 | 31.574211835861206 | 42 | 4 | 15 | [[[85, 96, 29, 80, 12], [60, "_", 76, 42, 82], [27, 89, 72, 37, 55]]] | [[[85, 96, 29, 80, 12], [60, "_", 76, 42, 82], [27, 89, 72, 37, 55]]] | ["[[85, 96, 29, 80, 12], [60, '_', 76, 42, 82], [27, 89, 72, 37, 55]]"] |
84 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["up-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 18 | 0.3263390064239502 | 18 | 4 | 25 | [[["e", "r", "p", "t", "o"], ["s", "t", "r", "k", "r"], ["e", "a", "_", "a", "i"], ["d", "o", "n", "s", "a"], ["d", "e", "s", "e", "x"]]] | [[["e", "r", "p", "t", "o"], ["s", "t", "r", "k", "r"], ["e", "a", "_", "a", "i"], ["d", "o", "n", "s", "a"], ["d", "e", "s", "e", "x"]], ["roto", "serer", "tapas", "dinka", "desex"]] | ["[['e', 'r', 'p', 't', 'o'], ['s', 't', 'r', 'k', 'r'], ['e', 'a', '_', 'a', 'i'], ['d', 'o', 'n', 's', 'a'], ['d', 'e', 's', 'e', 'x']]", "['roto', 'serer', 'tapas', 'dinka', 'desex']"] |
84 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 14 | ["T", "Q", "H", "S", "K", "P", "L", "K", "A", "H"] | 10 | 0.10328006744384766 | 10 | 14 | 17 | [[[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, ... | [[[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, ... | ["[[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1,... |
84 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [17, 4, 35, 10, 42, 11, 10, 11, 2, 14, 29, 31, 33, 3, 38, 4, 32, 9, 19, 14, 4, 39, 6, 36, 31, 25, 40, 8, 33, 31, 11, 34, 18, 2, 32, 40, 4, 16, 1, 36, 37, 3, 33, 20, 10, 8, 9, 20, 14, 35, 36, 22, 35, 4], such that the sum o... | coin_exchange | subset_sum | 35 | [29, 31, 31, 31, 35, 32, 35, 35, 32, 6, 9, 9, 39, 36, 34, 2] | 61 | 0.06626677513122559 | 16 | 54 | 54 | [[17, 4, 35, 10, 42, 11, 10, 11, 2, 14, 29, 31, 33, 3, 38, 4, 32, 9, 19, 14, 4, 39, 6, 36, 31, 25, 40, 8, 33, 31, 11, 34, 18, 2, 32, 40, 4, 16, 1, 36, 37, 3, 33, 20, 10, 8, 9, 20, 14, 35, 36, 22, 35, 4]] | [[17, 4, 35, 10, 42, 11, 10, 11, 2, 14, 29, 31, 33, 3, 38, 4, 32, 9, 19, 14, 4, 39, 6, 36, 31, 25, 40, 8, 33, 31, 11, 34, 18, 2, 32, 40, 4, 16, 1, 36, 37, 3, 33, 20, 10, 8, 9, 20, 14, 35, 36, 22, 35, 4], {"37": 11, "10": 3, "36": 8, "32": 3, "3": 1, "18": 16, "14": 5, "35": 5, "16": 15, "8": 5, "42": 20, "29": 4, "6": ... | ["[17, 4, 35, 10, 42, 11, 10, 11, 2, 14, 29, 31, 33, 3, 38, 4, 32, 9, 19, 14, 4, 39, 6, 36, 31, 25, 40, 8, 33, 31, 11, 34, 18, 2, 32, 40, 4, 16, 1, 36, 37, 3, 33, 20, 10, 8, 9, 20, 14, 35, 36, 22, 35, 4]", "{37: 11, 10: 3, 36: 8, 32: 3, 3: 1, 18: 16, 14: 5, 35: 5, 16: 15, 8: 5, 42: 20, 29: 4, 6: 1, 25: 9, 11: 4, 20: 15... |
84 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[2, 1], [2, 0], [2, 1], [2, 0], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2]] | 33 | 137.44458413124084 | 33 | 6 | 18 | [[["Green", "Red", "Green", "Green", "Blue", "Green"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"], ["Blue", "Red", "Blue", "Red", "Red", "Green"]], 9] | [[["Green", "Red", "Green", "Green", "Blue", "Green"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"], ["Blue", "Red", "Blue", "Red", "Red", "Green"]], 9] | ["[['Green', 'Red', 'Green', 'Green', 'Blue', 'Green'], ['Blue', 'Blue', 'Blue', 'Red', 'Red', 'Green'], ['Blue', 'Red', 'Blue', 'Red', 'Red', 'Green']]", "9"] |
84 | We have a 4x4 numerical grid, with numbers ranging from 23 to 73 (23 included in the range but 73 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 13 | [[0, 2, 51], [1, 2, 50], [1, 3, 52], [2, 0, 40], [2, 1, 48], [2, 3, 53], [3, 0, 39]] | 729 | 0.5444209575653076 | 7 | 50 | 16 | ["[['91', '57', '', '45'], ['41', '49', '', ''], ['', '', '49', ''], ['', '46', '47', '73']]", 39, 94] | ["[['91', '57', '', '45'], ['41', '49', '', ''], ['', '', '49', ''], ['', '46', '47', '73']]", 39, 94] | ["[['91', '57', '', '45'], ['41', '49', '', ''], ['', '', '49', ''], ['', '46', '47', '73']]", "39", "94"] |
84 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 37 to 83. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 277, 204, None for columns 1 to 2 respectively, and the sums of rows must be None, 253, 221, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[1, 0, 38], [1, 3, 79], [2, 0, 39], [2, 3, 76], [3, 0, 64], [3, 1, 80], [3, 2, 63], [3, 3, 37]] | 928 | 1.0334880352020264 | 8 | 31 | 16 | ["[['42', '53', '43', '72'], ['', '82', '54', ''], ['', '62', '44', ''], ['', '', '', '']]", 4, 37, 83] | ["[['42', '53', '43', '72'], ['', '82', '54', ''], ['', '62', '44', ''], ['', '', '', '']]", 37, 83, [1, 3], [1, 3], [277, 204], [253, 221], 252] | ["[['42', '53', '43', '72'], ['', '82', '54', ''], ['', '62', '44', ''], ['', '', '', '']]", "37", "83", "[None, 277, 204, None]", "[None, 253, 221, None]", "252"] |
84 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[7, 10], [9, 10], [8, 1], [8, 3], [11, 3], [11, 10], [11, 10], [11, 1], [11, 2], [11, 0], [9, 3], [9, 3], [9, 11], [9, 2], [9, 1], [7, 9], [7, 11], [7, 11], [4, 11], [4, 2], [4, 9], [4, 11], [4, 1], [4, 3], [7, 9], [7, 4], [7, 9], [6, 7], [6, 1], [6, 7], [6, 3], [6, 7], [6, 10], [0, 9], [6, 1], [8, 6], [8, 6], [8, 6],... | 210 | 3.1606807708740234 | 45 | 132 | 42 | [[[], [], [], [], ["Pink", "Red", "Green", "Pink", "White", "Blue", "Yellow"], [], ["Yellow", "White", "Yellow", "Blue", "Yellow", "Black", "White"], ["Black", "Green", "Pink", "Pink", "Green", "Yellow", "Green"], ["White", "Blue", "Red", "Red", "Red", "Yellow", "Black"], ["Black", "Blue", "Blue", "Pink", "Red", "White... | [[[], [], [], [], ["Pink", "Red", "Green", "Pink", "White", "Blue", "Yellow"], [], ["Yellow", "White", "Yellow", "Blue", "Yellow", "Black", "White"], ["Black", "Green", "Pink", "Pink", "Green", "Yellow", "Green"], ["White", "Blue", "Red", "Red", "Red", "Yellow", "Black"], ["Black", "Blue", "Blue", "Pink", "Red", "White... | ["[[], [], [], [], ['Pink', 'Red', 'Green', 'Pink', 'White', 'Blue', 'Yellow'], [], ['Yellow', 'White', 'Yellow', 'Blue', 'Yellow', 'Black', 'White'], ['Black', 'Green', 'Pink', 'Pink', 'Green', 'Yellow', 'Green'], ['White', 'Blue', 'Red', 'Red', 'Red', 'Yellow', 'Black'], ['Black', 'Blue', 'Blue', 'Pink', 'Red', 'Whit... |
84 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (9, 10) to his destination workshop at index (2, 3), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[9, 10], [8, 10], [7, 10], [6, 10], [6, 9], [6, 8], [6, 7], [5, 7], [4, 7], [3, 7], [3, 6], [3, 5], [2, 5], [2, 4], [2, 3]] | 131 | 0.028569698333740234 | 15 | 4 | 4 | [[["x", "10", "16", "12", "x", "x", "x", "x", "18", "18", "10", "x", "x", "19"], ["7", "x", "x", "11", "5", "13", "6", "x", "x", "x", "x", "x", "8", "14"], ["x", "15", "6", "20", "4", "9", "16", "9", "16", "x", "11", "x", "x", "9"], ["1", "16", "x", "x", "x", "6", "15", "1", "10", "10", "9", "4", "x", "4"], ["x", "x", ... | [[["x", "10", "16", "12", "x", "x", "x", "x", "18", "18", "10", "x", "x", "19"], ["7", "x", "x", "11", "5", "13", "6", "x", "x", "x", "x", "x", "8", "14"], ["x", "15", "6", "20", "4", "9", "16", "9", "16", "x", "11", "x", "x", "9"], ["1", "16", "x", "x", "x", "6", "15", "1", "10", "10", "9", "4", "x", "4"], ["x", "x", ... | ["[['x', '10', '16', '12', 'x', 'x', 'x', 'x', '18', '18', '10', 'x', 'x', '19'], ['7', 'x', 'x', '11', '5', '13', '6', 'x', 'x', 'x', 'x', 'x', '8', '14'], ['x', '15', '6', '20', '4', '9', '16', '9', '16', 'x', '11', 'x', 'x', '9'], ['1', '16', 'x', 'x', 'x', '6', '15', '1', '10', '10', '9', '4', 'x', '4'], ['x', 'x',... |
84 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[9, 0], [8, 1], [7, 2], [6, 3], [5, 4], [5, 5], [5, 6], [4, 6], [3, 6], [3, 7], [3, 8], [3, 9], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [3, 13]] | 18 | 0.028172016143798828 | 18 | 8 | 2 | ["[[0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 0,... | ["[[0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 0,... | ["[[0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 0,... |
84 | Given 7 labeled water jugs with capacities 82, 91, 135, 11, 12, 19, 143, 60 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 231, 288, 342, 410 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the am... | water_jug | subset_sum | 6 | [["+", 82, 4], ["+", 91, 4], ["+", 91, 4], ["+", 135, 4], ["+", 11, 4], ["+", 60, 3], ["+", 135, 3], ["+", 12, 3], ["+", 135, 3], ["+", 60, 2], ["+", 82, 2], ["+", 11, 2], ["+", 135, 2], ["+", 91, 1], ["-", 11, 1], ["+", 60, 1], ["+", 91, 1]] | 17 | 0.05072736740112305 | 17 | 64 | 3 | [[82, 91, 135, 11, 12, 19, 143, 60], [231, 288, 342, 410]] | [[82, 91, 135, 11, 12, 19, 143, 60], [231, 288, 342, 410]] | ["[82, 91, 135, 11, 12, 19, 143, 60]", "[231, 288, 342, 410]"] |
85 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [26, 39, 51, 7, 43, 23, 91, 26, 27, 63, 26, 91, 23, 27, 91, 23, 27, 51, 39, 91, 51, 43, 89, 17, 68, 27, 43, 89, 17, 68, 27, 17, 7, 39, 89, 43, 17, 7, 39, 69, 68, 27] | 42 | 43.326194763183594 | 42 | 4 | 15 | [[[93, 26, 39, 51, 69], [27, "_", 43, 7, 89], [63, 91, 23, 68, 17]]] | [[[93, 26, 39, 51, 69], [27, "_", 43, 7, 89], [63, 91, 23, 68, 17]]] | ["[[93, 26, 39, 51, 69], [27, '_', 43, 7, 89], [63, 91, 23, 68, 17]]"] |
85 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-right", "up-left"] | 22 | 1.548938512802124 | 22 | 4 | 25 | [[["c", "s", "n", "i", "p"], ["s", "o", "o", "r", "n"], ["c", "u", "i", "e", "_"], ["a", "n", "t", "b", "e"], ["p", "e", "r", "t", "a"]]] | [[["c", "s", "n", "i", "p"], ["s", "o", "o", "r", "n"], ["c", "u", "i", "e", "_"], ["a", "n", "t", "b", "e"], ["p", "e", "r", "t", "a"]], ["snip", "scoon", "cuber", "artie", "penta"]] | ["[['c', 's', 'n', 'i', 'p'], ['s', 'o', 'o', 'r', 'n'], ['c', 'u', 'i', 'e', '_'], ['a', 'n', 't', 'b', 'e'], ['p', 'e', 'r', 't', 'a']]", "['snip', 'scoon', 'cuber', 'artie', 'penta']"] |
85 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 14 | ["Y", "I", "S", "D", "H", "V", "X", "W", "X", "G", "H"] | 11 | 0.025726318359375 | 11 | 14 | 17 | [[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, ... | [[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, ... | ["[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1,... |
85 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [38, 36, 40, 31, 39, 29, 36, 31, 16, 14, 16, 45, 40, 45, 257, 8, 39, 16, 2, 41, 9, 26, 22, 24], such that the sum of the chosen coins adds up to 452. Each coin in the list is unique and can only be used once. Also coins ca... | coin_exchange | subset_sum | 15 | [29, 39, 36, 39, 36, 257, 16] | 35 | 0.03696179389953613 | 7 | 24 | 24 | [[38, 36, 40, 31, 39, 29, 36, 31, 16, 14, 16, 45, 40, 45, 257, 8, 39, 16, 2, 41, 9, 26, 22, 24]] | [[38, 36, 40, 31, 39, 29, 36, 31, 16, 14, 16, 45, 40, 45, 257, 8, 39, 16, 2, 41, 9, 26, 22, 24], {"9": 6, "14": 9, "24": 8, "26": 12, "16": 6, "45": 14, "8": 3, "22": 8, "38": 9, "40": 14, "31": 9, "257": 11, "36": 2, "2": 1, "41": 6, "29": 6, "39": 4}, 452] | ["[38, 36, 40, 31, 39, 29, 36, 31, 16, 14, 16, 45, 40, 45, 257, 8, 39, 16, 2, 41, 9, 26, 22, 24]", "{9: 6, 14: 9, 24: 8, 26: 12, 16: 6, 45: 14, 8: 3, 22: 8, 38: 9, 40: 14, 31: 9, 257: 11, 36: 2, 2: 1, 41: 6, 29: 6, 39: 4}", "452"] |
85 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[1, 0], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 0], [1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [1, 2]] | 36 | 402.36865186691284 | 36 | 6 | 18 | [[["Blue", "Green", "Red", "Red", "Blue", "Red"], ["Green", "Blue", "Green", "Blue", "Red", "Green"], ["Blue", "Red", "Green", "Green", "Blue", "Red"]], 9] | [[["Blue", "Green", "Red", "Red", "Blue", "Red"], ["Green", "Blue", "Green", "Blue", "Red", "Green"], ["Blue", "Red", "Green", "Green", "Blue", "Red"]], 9] | ["[['Blue', 'Green', 'Red', 'Red', 'Blue', 'Red'], ['Green', 'Blue', 'Green', 'Blue', 'Red', 'Green'], ['Blue', 'Red', 'Green', 'Green', 'Blue', 'Red']]", "9"] |
85 | We have a 4x4 numerical grid, with numbers ranging from 17 to 67 (17 included in the range but 67 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 14 | [[0, 1, 58], [0, 3, 39], [1, 2, 69], [2, 1, 70], [2, 3, 76], [3, 1, 74], [3, 3, 77]] | 778 | 30.918853044509888 | 7 | 50 | 16 | ["[['71', '', '57', ''], ['67', '68', '', '73'], ['51', '', '72', ''], ['50', '', '75', '']]", 39, 94] | ["[['71', '', '57', ''], ['67', '68', '', '73'], ['51', '', '72', ''], ['50', '', '75', '']]", 39, 94] | ["[['71', '', '57', ''], ['67', '68', '', '73'], ['51', '', '72', ''], ['50', '', '75', '']]", "39", "94"] |
85 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 37 to 83. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 252, 238, None for columns 1 to 2 respectively, and the sums of rows must be None, 221, 257, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 0, 37], [0, 1, 38], [1, 1, 77], [1, 3, 61], [2, 0, 41], [2, 3, 82], [3, 0, 40], [3, 2, 55]] | 909 | 0.9668257236480713 | 8 | 31 | 16 | ["[['', '', '80', '72'], ['44', '', '39', ''], ['', '70', '64', ''], ['', '67', '', '42']]", 4, 37, 83] | ["[['', '', '80', '72'], ['44', '', '39', ''], ['', '70', '64', ''], ['', '67', '', '42']]", 37, 83, [1, 3], [1, 3], [252, 238], [221, 257], 221] | ["[['', '', '80', '72'], ['44', '', '39', ''], ['', '70', '64', ''], ['', '67', '', '42']]", "37", "83", "[None, 252, 238, None]", "[None, 221, 257, None]", "221"] |
85 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[0, 7], [0, 11], [3, 7], [9, 7], [9, 11], [0, 2], [4, 2], [9, 2], [3, 1], [6, 1], [6, 2], [4, 5], [4, 11], [4, 7], [0, 8], [9, 1], [9, 1], [9, 11], [9, 1], [3, 9], [6, 9], [0, 9], [0, 9], [10, 5], [0, 7], [10, 0], [10, 7], [10, 5], [10, 1], [10, 11], [3, 5], [3, 0], [3, 5], [4, 9], [4, 9], [4, 5], [3, 2], [10, 2], [6,... | 228 | 6.149892091751099 | 44 | 132 | 42 | [[["Pink", "Red", "Black", "Green", "Yellow", "Yellow", "Pink"], [], [], ["Pink", "White", "Yellow", "Blue", "Green", "Blue", "Black"], ["Black", "Blue", "Red", "Pink", "Yellow", "Yellow", "Blue"], [], ["White", "Black", "Yellow", "Green", "Red", "Green", "Green"], [], [], ["Pink", "Red", "Black", "White", "White", "Re... | [[["Pink", "Red", "Black", "Green", "Yellow", "Yellow", "Pink"], [], [], ["Pink", "White", "Yellow", "Blue", "Green", "Blue", "Black"], ["Black", "Blue", "Red", "Pink", "Yellow", "Yellow", "Blue"], [], ["White", "Black", "Yellow", "Green", "Red", "Green", "Green"], [], [], ["Pink", "Red", "Black", "White", "White", "Re... | ["[['Pink', 'Red', 'Black', 'Green', 'Yellow', 'Yellow', 'Pink'], [], [], ['Pink', 'White', 'Yellow', 'Blue', 'Green', 'Blue', 'Black'], ['Black', 'Blue', 'Red', 'Pink', 'Yellow', 'Yellow', 'Blue'], [], ['White', 'Black', 'Yellow', 'Green', 'Red', 'Green', 'Green'], [], [], ['Pink', 'Red', 'Black', 'White', 'White', 'R... |
85 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (10, 12) to his destination workshop at index (4, 3), indexing from 0. Ben's car can mo... | traffic | pathfinding | 6 | [[10, 12], [10, 11], [10, 10], [10, 9], [10, 8], [10, 7], [9, 7], [8, 7], [7, 7], [6, 7], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [4, 3]] | 140 | 0.026478052139282227 | 16 | 4 | 4 | [[["5", "10", "x", "x", "x", "16", "x", "x", "x", "16", "x", "10", "8", "x"], ["1", "x", "13", "x", "7", "x", "x", "x", "10", "3", "3", "13", "18", "11"], ["14", "x", "x", "x", "9", "16", "16", "15", "x", "x", "15", "x", "4", "4"], ["15", "x", "3", "x", "x", "17", "x", "16", "10", "9", "x", "6", "16", "17"], ["12", "8"... | [[["5", "10", "x", "x", "x", "16", "x", "x", "x", "16", "x", "10", "8", "x"], ["1", "x", "13", "x", "7", "x", "x", "x", "10", "3", "3", "13", "18", "11"], ["14", "x", "x", "x", "9", "16", "16", "15", "x", "x", "15", "x", "4", "4"], ["15", "x", "3", "x", "x", "17", "x", "16", "10", "9", "x", "6", "16", "17"], ["12", "8"... | ["[['5', '10', 'x', 'x', 'x', '16', 'x', 'x', 'x', '16', 'x', '10', '8', 'x'], ['1', 'x', '13', 'x', '7', 'x', 'x', 'x', '10', '3', '3', '13', '18', '11'], ['14', 'x', 'x', 'x', '9', '16', '16', '15', 'x', 'x', '15', 'x', '4', '4'], ['15', 'x', '3', 'x', 'x', '17', 'x', '16', '10', '9', 'x', '6', '16', '17'], ['12', '8... |
85 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[1, 3], [2, 3], [3, 3], [4, 4], [5, 4], [5, 5], [5, 6], [5, 7], [6, 8], [6, 9], [7, 10], [8, 10], [9, 10], [10, 10], [11, 11], [12, 11]] | 16 | 0.030063152313232422 | 16 | 8 | 2 | ["[[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0,... | ["[[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0,... | ["[[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0,... |
85 | Given 7 labeled water jugs with capacities 67, 98, 66, 59, 37, 61, 128, 92 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 308, 309, 387, 433 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo... | water_jug | subset_sum | 6 | [["+", 59, 4], ["+", 128, 4], ["+", 128, 4], ["+", 59, 4], ["+", 59, 4], ["+", 98, 3], ["+", 128, 3], ["+", 128, 3], ["-", 59, 3], ["+", 92, 3], ["+", 59, 2], ["+", 92, 2], ["+", 92, 2], ["+", 66, 2], ["+", 59, 1], ["+", 92, 1], ["+", 98, 1], ["+", 59, 1]] | 18 | 0.08887290954589844 | 18 | 64 | 3 | [[67, 98, 66, 59, 37, 61, 128, 92], [308, 309, 387, 433]] | [[67, 98, 66, 59, 37, 61, 128, 92], [308, 309, 387, 433]] | ["[67, 98, 66, 59, 37, 61, 128, 92]", "[308, 309, 387, 433]"] |
86 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [82, 21, 14, 82, 21, 37, 72, 83, 53, 43, 20, 54, 43, 21, 82, 43, 21, 20, 71, 88, 98, 71, 54, 21, 20, 53, 83, 82, 43, 14] | 30 | 1.5921499729156494 | 30 | 4 | 15 | [[[88, 71, 83, 72, 37], [98, 43, 53, "_", 82], [24, 20, 54, 14, 21]]] | [[[88, 71, 83, 72, 37], [98, 43, 53, "_", 82], [24, 20, 54, 14, 21]]] | ["[[88, 71, 83, 72, 37], [98, 43, 53, '_', 82], [24, 20, 54, 14, 21]]"] |
86 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "up-left", "up-left"] | 24 | 0.686600923538208 | 24 | 4 | 25 | [[["y", "c", "a", "r", "d"], ["s", "u", "l", "c", "a"], ["v", "h", "_", "n", "o"], ["s", "e", "l", "s", "m"], ["b", "i", "u", "h", "y"]]] | [[["y", "c", "a", "r", "d"], ["s", "u", "l", "c", "a"], ["v", "h", "_", "n", "o"], ["s", "e", "l", "s", "m"], ["b", "i", "u", "h", "y"]], ["card", "sylva", "shune", "solum", "bichy"]] | ["[['y', 'c', 'a', 'r', 'd'], ['s', 'u', 'l', 'c', 'a'], ['v', 'h', '_', 'n', 'o'], ['s', 'e', 'l', 's', 'm'], ['b', 'i', 'u', 'h', 'y']]", "['card', 'sylva', 'shune', 'solum', 'bichy']"] |
86 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["G", "O", "P", "N", "Y", "Z", "P", "T", "Y"] | 9 | 0.05178332328796387 | 9 | 15 | 18 | [[[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0,... | [[[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0,... | ["[[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0... |
86 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [31, 8, 22, 27, 2, 25, 2, 8, 49, 26, 65, 6, 37, 49, 15, 21, 27, 5, 34, 28, 47, 15, 7, 42, 32, 20, 34, 48, 39, 7, 13], such that the sum of the chosen coins adds up to 490. Each coin in the list is unique and can only be us... | coin_exchange | subset_sum | 16 | [7, 7, 27, 37, 22, 27, 2, 5, 47, 42, 26, 2, 65, 48, 49, 49, 28] | 94 | 0.05118918418884277 | 17 | 31 | 31 | [[31, 8, 22, 27, 2, 25, 2, 8, 49, 26, 65, 6, 37, 49, 15, 21, 27, 5, 34, 28, 47, 15, 7, 42, 32, 20, 34, 48, 39, 7, 13]] | [[31, 8, 22, 27, 2, 25, 2, 8, 49, 26, 65, 6, 37, 49, 15, 21, 27, 5, 34, 28, 47, 15, 7, 42, 32, 20, 34, 48, 39, 7, 13], {"7": 1, "65": 16, "21": 18, "25": 18, "15": 14, "31": 15, "6": 2, "37": 2, "5": 1, "22": 1, "8": 7, "26": 2, "2": 1, "32": 8, "27": 2, "13": 8, "39": 17, "28": 11, "47": 6, "42": 10, "34": 15, "20": 8... | ["[31, 8, 22, 27, 2, 25, 2, 8, 49, 26, 65, 6, 37, 49, 15, 21, 27, 5, 34, 28, 47, 15, 7, 42, 32, 20, 34, 48, 39, 7, 13]", "{7: 1, 65: 16, 21: 18, 25: 18, 15: 14, 31: 15, 6: 2, 37: 2, 5: 1, 22: 1, 8: 7, 26: 2, 2: 1, 32: 8, 27: 2, 13: 8, 39: 17, 28: 11, 47: 6, 42: 10, 34: 15, 20: 8, 48: 11, 49: 13}", "490"] |
86 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 1], [0, 1], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [1, 0], [1, 2], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1]] | 34 | 154.73638343811035 | 34 | 6 | 18 | [[["Red", "Red", "Blue", "Red", "Blue", "Green"], ["Green", "Red", "Green", "Green", "Blue", "Blue"], ["Red", "Green", "Blue", "Red", "Blue", "Green"]], 9] | [[["Red", "Red", "Blue", "Red", "Blue", "Green"], ["Green", "Red", "Green", "Green", "Blue", "Blue"], ["Red", "Green", "Blue", "Red", "Blue", "Green"]], 9] | ["[['Red', 'Red', 'Blue', 'Red', 'Blue', 'Green'], ['Green', 'Red', 'Green', 'Green', 'Blue', 'Blue'], ['Red', 'Green', 'Blue', 'Red', 'Blue', 'Green']]", "9"] |
86 | We have a 4x4 numerical grid, with numbers ranging from 6 to 56 (6 included in the range but 56 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid cell... | consecutive_grid | underdetermined_system | 14 | [[0, 2, 29], [0, 3, 28], [1, 0, 43], [1, 3, 55], [2, 1, 44], [3, 0, 30], [3, 1, 31]] | 686 | 0.6507663726806641 | 7 | 50 | 16 | ["[['81', '52', '', ''], ['', '50', '53', ''], ['42', '', '54', '74'], ['', '', '56', '77']]", 28, 83] | ["[['81', '52', '', ''], ['', '50', '53', ''], ['42', '', '54', '74'], ['', '', '56', '77']]", 28, 83] | ["[['81', '52', '', ''], ['', '50', '53', ''], ['42', '', '54', '74'], ['', '', '56', '77']]", "28", "83"] |
86 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 37 to 83. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 214, 240, None for columns 1 to 2 respectively, and the sums of rows must be None, 213, 197, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 0, 37], [1, 0, 40], [1, 3, 62], [2, 1, 38], [2, 2, 43], [3, 0, 49], [3, 1, 78], [3, 3, 39]] | 864 | 4.137092590332031 | 8 | 31 | 16 | ["[['', '48', '64', '67'], ['', '50', '61', ''], ['42', '', '', '74'], ['', '', '72', '']]", 4, 37, 83] | ["[['', '48', '64', '67'], ['', '50', '61', ''], ['42', '', '', '74'], ['', '', '72', '']]", 37, 83, [1, 3], [1, 3], [214, 240], [213, 197], 215] | ["[['', '48', '64', '67'], ['', '50', '61', ''], ['42', '', '', '74'], ['', '', '72', '']]", "37", "83", "[None, 214, 240, None]", "[None, 213, 197, None]", "215"] |
86 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[3, 5], [7, 5], [2, 1], [2, 10], [2, 11], [8, 10], [8, 10], [8, 5], [3, 6], [7, 6], [2, 9], [4, 11], [4, 1], [4, 9], [4, 11], [4, 5], [4, 11], [7, 1], [7, 10], [7, 1], [7, 6], [7, 5], [8, 7], [8, 5], [3, 8], [3, 6], [7, 8], [0, 7], [0, 7], [0, 10], [0, 1], [0, 7], [0, 7], [3, 8], [3, 11], [2, 6], [2, 6], [0, 11], [2, ... | 263 | 3.3329944610595703 | 43 | 132 | 42 | [[["Black", "Black", "Yellow", "Blue", "Black", "Black", "Green"], [], ["Blue", "Yellow", "Green", "Black", "White", "White", "Blue"], ["Red", "White", "Pink", "White", "Pink", "Green", "Pink"], ["Green", "Blue", "Black", "Green", "Red", "Green", "Yellow"], [], [], ["Red", "White", "Blue", "Yellow", "Blue", "White", "R... | [[["Black", "Black", "Yellow", "Blue", "Black", "Black", "Green"], [], ["Blue", "Yellow", "Green", "Black", "White", "White", "Blue"], ["Red", "White", "Pink", "White", "Pink", "Green", "Pink"], ["Green", "Blue", "Black", "Green", "Red", "Green", "Yellow"], [], [], ["Red", "White", "Blue", "Yellow", "Blue", "White", "R... | ["[['Black', 'Black', 'Yellow', 'Blue', 'Black', 'Black', 'Green'], [], ['Blue', 'Yellow', 'Green', 'Black', 'White', 'White', 'Blue'], ['Red', 'White', 'Pink', 'White', 'Pink', 'Green', 'Pink'], ['Green', 'Blue', 'Black', 'Green', 'Red', 'Green', 'Yellow'], [], [], ['Red', 'White', 'Blue', 'Yellow', 'Blue', 'White', '... |
86 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 0) to his destination workshop at index (5, 12), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[3, 0], [2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [6, 5], [6, 6], [6, 7], [7, 7], [7, 8], [7, 9], [6, 9], [6, 10], [5, 10], [5, 11], [5, 12]] | 189 | 0.02854442596435547 | 21 | 4 | 4 | [[["x", "x", "11", "16", "x", "x", "x", "x", "4", "x", "14", "5", "x", "x"], ["3", "1", "13", "x", "x", "14", "11", "x", "x", "15", "12", "15", "x", "x"], ["17", "15", "17", "10", "11", "x", "7", "1", "1", "14", "x", "9", "x", "x"], ["8", "x", "x", "13", "2", "12", "x", "8", "x", "x", "9", "13", "19", "5"], ["4", "x", ... | [[["x", "x", "11", "16", "x", "x", "x", "x", "4", "x", "14", "5", "x", "x"], ["3", "1", "13", "x", "x", "14", "11", "x", "x", "15", "12", "15", "x", "x"], ["17", "15", "17", "10", "11", "x", "7", "1", "1", "14", "x", "9", "x", "x"], ["8", "x", "x", "13", "2", "12", "x", "8", "x", "x", "9", "13", "19", "5"], ["4", "x", ... | ["[['x', 'x', '11', '16', 'x', 'x', 'x', 'x', '4', 'x', '14', '5', 'x', 'x'], ['3', '1', '13', 'x', 'x', '14', '11', 'x', 'x', '15', '12', '15', 'x', 'x'], ['17', '15', '17', '10', '11', 'x', '7', '1', '1', '14', 'x', '9', 'x', 'x'], ['8', 'x', 'x', '13', '2', '12', 'x', '8', 'x', 'x', '9', '13', '19', '5'], ['4', 'x',... |
86 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 8], [1, 9], [2, 9], [2, 10], [3, 11], [4, 11], [5, 12], [6, 12], [7, 13], [8, 13], [9, 13], [10, 13], [11, 13], [12, 13], [13, 12]] | 20 | 0.022798776626586914 | 20 | 8 | 2 | ["[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1,... | ["[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1,... | ["[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1,... |
86 | Given 7 labeled water jugs with capacities 87, 13, 27, 106, 18, 91, 17, 138 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 205, 365, 391, 414 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the am... | water_jug | subset_sum | 6 | [["+", 138, 4], ["+", 138, 4], ["+", 138, 4], ["+", 106, 3], ["+", 138, 3], ["+", 138, 3], ["-", 18, 3], ["+", 27, 3], ["+", 138, 2], ["+", 138, 2], ["-", 17, 2], ["+", 106, 2], ["+", 87, 1], ["+", 91, 1], ["+", 27, 1]] | 15 | 0.04750704765319824 | 15 | 64 | 3 | [[87, 13, 27, 106, 18, 91, 17, 138], [205, 365, 391, 414]] | [[87, 13, 27, 106, 18, 91, 17, 138], [205, 365, 391, 414]] | ["[87, 13, 27, 106, 18, 91, 17, 138]", "[205, 365, 391, 414]"] |
87 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [96, 100, 75, 43, 58, 84, 27, 74, 52, 77, 84, 58, 94, 96, 100, 75, 43, 60, 74, 27, 60, 74, 29, 43, 74, 60, 58, 84, 77, 52] | 30 | 0.9509561061859131 | 30 | 4 | 15 | [[["_", 94, 43, 58, 77], [96, 100, 75, 84, 52], [50, 29, 60, 27, 74]]] | [[["_", 94, 43, 58, 77], [96, 100, 75, 84, 52], [50, 29, 60, 27, 74]]] | ["[['_', 94, 43, 58, 77], [96, 100, 75, 84, 52], [50, 29, 60, 27, 74]]"] |
87 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-right", "up-left", "up-left... | 26 | 3.2265894412994385 | 26 | 4 | 25 | [[["e", "e", "l", "h", "o"], ["m", "r", "t", "u", "n"], ["p", "e", "_", "c", "i"], ["t", "c", "l", "h", "p"], ["m", "u", "i", "g", "a"]]] | [[["e", "e", "l", "h", "o"], ["m", "r", "t", "u", "n"], ["p", "e", "_", "c", "i"], ["t", "c", "l", "h", "p"], ["m", "u", "i", "g", "a"]], ["echo", "metin", "perch", "tulip", "mulga"]] | ["[['e', 'e', 'l', 'h', 'o'], ['m', 'r', 't', 'u', 'n'], ['p', 'e', '_', 'c', 'i'], ['t', 'c', 'l', 'h', 'p'], ['m', 'u', 'i', 'g', 'a']]", "['echo', 'metin', 'perch', 'tulip', 'mulga']"] |
87 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["E", "L", "P", "A", "G", "P", "A"] | 7 | 0.03984355926513672 | 7 | 15 | 18 | [[[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,... | [[[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,... | ["[[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0... |
87 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [25, 41, 34, 19, 19, 36, 37, 13, 28, 26, 181, 7, 14, 6, 29, 36, 33, 7, 8, 43, 19, 9, 3, 2, 18, 40, 43, 22, 23, 21], such that the sum of the chosen coins adds up to 449. Each coin in the list is unique and can only be used... | coin_exchange | subset_sum | 17 | [13, 21, 41, 43, 181, 40, 43, 6, 33, 28] | 48 | 0.04537367820739746 | 10 | 30 | 30 | [[25, 41, 34, 19, 19, 36, 37, 13, 28, 26, 181, 7, 14, 6, 29, 36, 33, 7, 8, 43, 19, 9, 3, 2, 18, 40, 43, 22, 23, 21]] | [[25, 41, 34, 19, 19, 36, 37, 13, 28, 26, 181, 7, 14, 6, 29, 36, 33, 7, 8, 43, 19, 9, 3, 2, 18, 40, 43, 22, 23, 21], {"21": 5, "26": 13, "36": 8, "28": 8, "34": 12, "3": 2, "6": 2, "23": 10, "2": 2, "9": 5, "41": 4, "29": 19, "7": 6, "18": 18, "43": 2, "8": 7, "181": 9, "25": 10, "33": 8, "14": 13, "13": 1, "22": 13, "... | ["[25, 41, 34, 19, 19, 36, 37, 13, 28, 26, 181, 7, 14, 6, 29, 36, 33, 7, 8, 43, 19, 9, 3, 2, 18, 40, 43, 22, 23, 21]", "{21: 5, 26: 13, 36: 8, 28: 8, 34: 12, 3: 2, 6: 2, 23: 10, 2: 2, 9: 5, 41: 4, 29: 19, 7: 6, 18: 18, 43: 2, 8: 7, 181: 9, 25: 10, 33: 8, 14: 13, 13: 1, 22: 13, 40: 7, 37: 11, 19: 11}", "449"] |
87 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 2], [1, 2], [0, 2], [0, 1], [0, 1], [2, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2]] | 35 | 125.82809782028198 | 35 | 6 | 18 | [[["Blue", "Green", "Red", "Red", "Blue", "Green"], ["Blue", "Red", "Green", "Green", "Green", "Red"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"]], 9] | [[["Blue", "Green", "Red", "Red", "Blue", "Green"], ["Blue", "Red", "Green", "Green", "Green", "Red"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"]], 9] | ["[['Blue', 'Green', 'Red', 'Red', 'Blue', 'Green'], ['Blue', 'Red', 'Green', 'Green', 'Green', 'Red'], ['Blue', 'Blue', 'Blue', 'Red', 'Red', 'Green']]", "9"] |
87 | We have a 4x4 numerical grid, with numbers ranging from 14 to 64 (14 included in the range but 64 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 14 | [[0, 0, 17], [0, 2, 39], [1, 0, 18], [1, 1, 40], [1, 3, 57], [2, 0, 19], [2, 1, 41], [3, 0, 20]] | 580 | 30.668219327926636 | 8 | 50 | 16 | ["[['', '38', '', '56'], ['', '', '55', ''], ['', '', '61', '65'], ['', '59', '64', '67']]", 17, 72] | ["[['', '38', '', '56'], ['', '', '55', ''], ['', '', '61', '65'], ['', '59', '64', '67']]", 17, 72] | ["[['', '38', '', '56'], ['', '', '55', ''], ['', '', '61', '65'], ['', '59', '64', '67']]", "17", "72"] |
87 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 37 to 83. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 258, 247, None for columns 1 to 2 respectively, and the sums of rows must be None, 233, 237, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[1, 1, 64], [1, 2, 53], [1, 3, 60], [2, 1, 80], [2, 2, 65], [3, 0, 40], [3, 1, 38], [3, 3, 37]] | 931 | 4.630835771560669 | 8 | 31 | 16 | ["[['72', '76', '68', '69'], ['56', '', '', ''], ['49', '', '', '43'], ['', '', '61', '']]", 4, 37, 83] | ["[['72', '76', '68', '69'], ['56', '', '', ''], ['49', '', '', '43'], ['', '', '61', '']]", 37, 83, [1, 3], [1, 3], [258, 247], [233, 237], 242] | ["[['72', '76', '68', '69'], ['56', '', '', ''], ['49', '', '', '43'], ['', '', '61', '']]", "37", "83", "[None, 258, 247, None]", "[None, 233, 237, None]", "242"] |
87 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[0, 3], [0, 11], [5, 11], [0, 7], [0, 9], [0, 11], [4, 7], [1, 10], [2, 10], [2, 7], [4, 0], [5, 10], [8, 10], [1, 6], [1, 6], [1, 3], [1, 10], [2, 6], [2, 7], [5, 6], [5, 7], [5, 7], [9, 5], [2, 3], [2, 9], [2, 3], [4, 11], [4, 2], [4, 11], [4, 11], [8, 3], [8, 10], [8, 2], [8, 0], [1, 5], [1, 5], [8, 1], [4, 0], [9,... | 319 | 183.4848072528839 | 45 | 132 | 42 | [[["Black", "Blue", "Pink", "Green", "Blue", "Red", "Red"], ["Yellow", "White", "White", "Black", "Yellow", "Green", "Green"], ["Yellow", "Pink", "White", "Pink", "Black", "Red", "Black"], [], ["Pink", "Red", "Blue", "White", "Blue", "Blue", "Red"], ["Blue", "Yellow", "White", "Pink", "Pink", "Green", "Green"], [], [],... | [[["Black", "Blue", "Pink", "Green", "Blue", "Red", "Red"], ["Yellow", "White", "White", "Black", "Yellow", "Green", "Green"], ["Yellow", "Pink", "White", "Pink", "Black", "Red", "Black"], [], ["Pink", "Red", "Blue", "White", "Blue", "Blue", "Red"], ["Blue", "Yellow", "White", "Pink", "Pink", "Green", "Green"], [], [],... | ["[['Black', 'Blue', 'Pink', 'Green', 'Blue', 'Red', 'Red'], ['Yellow', 'White', 'White', 'Black', 'Yellow', 'Green', 'Green'], ['Yellow', 'Pink', 'White', 'Pink', 'Black', 'Red', 'Black'], [], ['Pink', 'Red', 'Blue', 'White', 'Blue', 'Blue', 'Red'], ['Blue', 'Yellow', 'White', 'Pink', 'Pink', 'Green', 'Green'], [], []... |
87 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 0) to his destination workshop at index (6, 12), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[3, 0], [3, 1], [2, 1], [2, 2], [2, 3], [3, 3], [4, 3], [4, 4], [4, 5], [4, 6], [4, 7], [4, 8], [5, 8], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12]] | 146 | 0.027922391891479492 | 18 | 4 | 4 | [[["x", "6", "19", "13", "x", "16", "11", "6", "14", "15", "7", "x", "x", "x"], ["x", "6", "16", "15", "x", "19", "16", "18", "x", "8", "10", "x", "x", "x"], ["x", "5", "10", "14", "2", "x", "x", "x", "11", "x", "11", "x", "x", "x"], ["6", "13", "15", "10", "x", "x", "x", "x", "19", "x", "x", "x", "2", "x"], ["x", "15"... | [[["x", "6", "19", "13", "x", "16", "11", "6", "14", "15", "7", "x", "x", "x"], ["x", "6", "16", "15", "x", "19", "16", "18", "x", "8", "10", "x", "x", "x"], ["x", "5", "10", "14", "2", "x", "x", "x", "11", "x", "11", "x", "x", "x"], ["6", "13", "15", "10", "x", "x", "x", "x", "19", "x", "x", "x", "2", "x"], ["x", "15"... | ["[['x', '6', '19', '13', 'x', '16', '11', '6', '14', '15', '7', 'x', 'x', 'x'], ['x', '6', '16', '15', 'x', '19', '16', '18', 'x', '8', '10', 'x', 'x', 'x'], ['x', '5', '10', '14', '2', 'x', 'x', 'x', '11', 'x', '11', 'x', 'x', 'x'], ['6', '13', '15', '10', 'x', 'x', 'x', 'x', '19', 'x', 'x', 'x', '2', 'x'], ['x', '15... |
87 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[0, 11], [1, 10], [2, 9], [3, 8], [4, 7], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [8, 5], [9, 5], [10, 5], [10, 4], [10, 3], [10, 2], [11, 2], [12, 2]] | 18 | 0.022104978561401367 | 18 | 8 | 2 | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1,... | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1,... | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1,... |
87 | Given 7 labeled water jugs with capacities 36, 95, 47, 149, 58, 96, 81, 148 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 252, 307, 412, 431 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the am... | water_jug | subset_sum | 6 | [["+", 58, 4], ["+", 96, 4], ["+", 149, 4], ["+", 81, 4], ["+", 47, 4], ["+", 148, 3], ["+", 148, 3], ["+", 58, 3], ["+", 58, 3], ["+", 148, 2], ["+", 148, 2], ["-", 36, 2], ["+", 47, 2], ["+", 81, 1], ["+", 148, 1], ["-", 58, 1], ["+", 81, 1]] | 17 | 0.04282355308532715 | 17 | 64 | 3 | [[36, 95, 47, 149, 58, 96, 81, 148], [252, 307, 412, 431]] | [[36, 95, 47, 149, 58, 96, 81, 148], [252, 307, 412, 431]] | ["[36, 95, 47, 149, 58, 96, 81, 148]", "[252, 307, 412, 431]"] |
88 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [12, 55, 91, 27, 18, 67, 55, 12, 26, 65, 68, 54, 40, 55, 12, 26, 65, 70, 74, 91, 67, 18, 27, 67, 26, 65, 55, 12, 18, 26, 65, 55, 54, 40] | 34 | 2.9298317432403564 | 34 | 4 | 15 | [[[98, 74, 70, 26, 65], [91, 55, 12, "_", 68], [27, 18, 67, 40, 54]]] | [[[98, 74, 70, 26, 65], [91, 55, 12, "_", 68], [27, 18, 67, 40, 54]]] | ["[[98, 74, 70, 26, 65], [91, 55, 12, '_', 68], [27, 18, 67, 40, 54]]"] |
88 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 22 | 0.5754249095916748 | 22 | 4 | 25 | [[["g", "f", "t", "i", "m"], ["a", "l", "a", "a", "e"], ["n", "s", "_", "i", "e"], ["f", "p", "o", "k", "y"], ["z", "o", "r", "a", "r"]]] | [[["g", "f", "t", "i", "m"], ["a", "l", "a", "a", "e"], ["n", "s", "_", "i", "e"], ["f", "p", "o", "k", "y"], ["z", "o", "r", "a", "r"]], ["frim", "agate", "askip", "floey", "zonar"]] | ["[['g', 'f', 't', 'i', 'm'], ['a', 'l', 'a', 'a', 'e'], ['n', 's', '_', 'i', 'e'], ['f', 'p', 'o', 'k', 'y'], ['z', 'o', 'r', 'a', 'r']]", "['frim', 'agate', 'askip', 'floey', 'zonar']"] |
88 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["A", "O", "X", "M", "J", "F", "Y", "M", "J"] | 9 | 0.0450282096862793 | 9 | 15 | 18 | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,... | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,... | ["[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0... |
88 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [21, 31, 30, 31, 10, 17, 13, 35, 12, 2, 16, 40, 23, 10, 29, 13, 23, 2, 9, 5, 107, 46, 23, 11, 42, 9, 46, 28, 44, 22, 106, 10], such that the sum of the chosen coins adds up to 465. Each coin in the list is unique and can o... | coin_exchange | subset_sum | 18 | [10, 35, 10, 107, 106, 46, 44, 42, 40, 16, 2, 5, 2] | 105 | 0.05189323425292969 | 13 | 32 | 32 | [[21, 31, 30, 31, 10, 17, 13, 35, 12, 2, 16, 40, 23, 10, 29, 13, 23, 2, 9, 5, 107, 46, 23, 11, 42, 9, 46, 28, 44, 22, 106, 10]] | [[21, 31, 30, 31, 10, 17, 13, 35, 12, 2, 16, 40, 23, 10, 29, 13, 23, 2, 9, 5, 107, 46, 23, 11, 42, 9, 46, 28, 44, 22, 106, 10], {"13": 9, "106": 19, "28": 20, "44": 14, "9": 6, "35": 6, "22": 19, "46": 17, "11": 7, "40": 12, "17": 15, "10": 4, "12": 6, "30": 20, "2": 2, "23": 11, "42": 10, "16": 1, "107": 11, "21": 12,... | ["[21, 31, 30, 31, 10, 17, 13, 35, 12, 2, 16, 40, 23, 10, 29, 13, 23, 2, 9, 5, 107, 46, 23, 11, 42, 9, 46, 28, 44, 22, 106, 10]", "{13: 9, 106: 19, 28: 20, 44: 14, 9: 6, 35: 6, 22: 19, 46: 17, 11: 7, 40: 12, 17: 15, 10: 4, 12: 6, 30: 20, 2: 2, 23: 11, 42: 10, 16: 1, 107: 11, 21: 12, 5: 3, 31: 13, 29: 20}", "465"] |
88 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 2], [0, 1], [0, 2], [0, 1], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [1, 2], [0, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [1, 2]] | 38 | 564.8052530288696 | 38 | 6 | 18 | [[["Blue", "Green", "Red", "Green", "Green", "Red"], ["Green", "Blue", "Red", "Blue", "Blue", "Red"], ["Red", "Green", "Blue", "Blue", "Green", "Red"]], 9] | [[["Blue", "Green", "Red", "Green", "Green", "Red"], ["Green", "Blue", "Red", "Blue", "Blue", "Red"], ["Red", "Green", "Blue", "Blue", "Green", "Red"]], 9] | ["[['Blue', 'Green', 'Red', 'Green', 'Green', 'Red'], ['Green', 'Blue', 'Red', 'Blue', 'Blue', 'Red'], ['Red', 'Green', 'Blue', 'Blue', 'Green', 'Red']]", "9"] |
88 | We have a 4x4 numerical grid, with numbers ranging from 30 to 80 (30 included in the range but 80 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 15 | [[0, 1, 52], [0, 3, 71], [1, 3, 72], [2, 0, 28], [2, 1, 55], [2, 3, 73], [3, 0, 27], [3, 1, 56]] | 787 | 19.980714321136475 | 8 | 50 | 16 | ["[['51', '', '68', ''], ['50', '54', '69', ''], ['', '', '70', ''], ['', '', '76', '77']]", 27, 82] | ["[['51', '', '68', ''], ['50', '54', '69', ''], ['', '', '70', ''], ['', '', '76', '77']]", 27, 82] | ["[['51', '', '68', ''], ['50', '54', '69', ''], ['', '', '70', ''], ['', '', '76', '77']]", "27", "82"] |
88 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 68. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 183, 202, None for columns 1 to 2 respectively, and the sums of rows must be None, 190, 154, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 2, 40], [0, 3, 23], [1, 0, 24], [1, 1, 46], [1, 3, 57], [2, 1, 67], [3, 0, 30], [3, 1, 22], [3, 2, 66]] | 639 | 497.1962370872498 | 9 | 31 | 16 | ["[['27', '48', '', ''], ['', '', '63', ''], ['28', '', '33', '26'], ['', '', '', '39']]", 4, 22, 68] | ["[['27', '48', '', ''], ['', '', '63', ''], ['28', '', '33', '26'], ['', '', '', '39']]", 22, 68, [1, 3], [1, 3], [183, 202], [190, 154], 183] | ["[['27', '48', '', ''], ['', '', '63', ''], ['28', '', '33', '26'], ['', '', '', '39']]", "22", "68", "[None, 183, 202, None]", "[None, 190, 154, None]", "183"] |
88 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[0, 5], [4, 5], [0, 11], [0, 7], [4, 10], [4, 11], [4, 11], [2, 6], [8, 9], [8, 5], [8, 6], [8, 11], [8, 5], [2, 9], [2, 11], [2, 10], [2, 6], [2, 9], [3, 10], [3, 7], [3, 10], [3, 10], [3, 9], [3, 7], [3, 10], [1, 3], [8, 3], [1, 6], [1, 7], [1, 9], [1, 11], [1, 7], [4, 6], [4, 6], [0, 3], [0, 9], [8, 7], [0, 3], [0,... | 270 | 1.9822285175323486 | 42 | 132 | 42 | [[["Yellow", "Green", "White", "Pink", "Black", "Pink", "Pink"], ["Pink", "Red", "White", "Black", "Green", "White", "Pink"], ["Red", "Black", "Green", "Blue", "Red", "Black", "Yellow"], ["Blue", "White", "Blue", "Blue", "Black", "White", "Blue"], ["Yellow", "Blue", "Green", "Green", "Red", "Red", "Yellow"], [], [], []... | [[["Yellow", "Green", "White", "Pink", "Black", "Pink", "Pink"], ["Pink", "Red", "White", "Black", "Green", "White", "Pink"], ["Red", "Black", "Green", "Blue", "Red", "Black", "Yellow"], ["Blue", "White", "Blue", "Blue", "Black", "White", "Blue"], ["Yellow", "Blue", "Green", "Green", "Red", "Red", "Yellow"], [], [], []... | ["[['Yellow', 'Green', 'White', 'Pink', 'Black', 'Pink', 'Pink'], ['Pink', 'Red', 'White', 'Black', 'Green', 'White', 'Pink'], ['Red', 'Black', 'Green', 'Blue', 'Red', 'Black', 'Yellow'], ['Blue', 'White', 'Blue', 'Blue', 'Black', 'White', 'Blue'], ['Yellow', 'Blue', 'Green', 'Green', 'Red', 'Red', 'Yellow'], [], [], [... |
88 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 1) to his destination workshop at index (5, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[3, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5], [3, 5], [3, 6], [3, 7], [2, 7], [2, 8], [2, 9], [2, 10], [3, 10], [3, 11], [4, 11], [4, 12], [5, 12], [6, 12], [5, 12], [5, 13]] | 122 | 0.027570009231567383 | 21 | 4 | 4 | [[["x", "7", "x", "13", "8", "2", "15", "2", "5", "15", "6", "4", "7", "x"], ["x", "6", "19", "17", "5", "13", "15", "2", "11", "5", "x", "x", "9", "8"], ["16", "12", "10", "7", "8", "19", "19", "9", "5", "10", "2", "x", "x", "12"], ["x", "1", "19", "20", "x", "3", "4", "18", "x", "x", "10", "1", "12", "2"], ["x", "1",... | [[["x", "7", "x", "13", "8", "2", "15", "2", "5", "15", "6", "4", "7", "x"], ["x", "6", "19", "17", "5", "13", "15", "2", "11", "5", "x", "x", "9", "8"], ["16", "12", "10", "7", "8", "19", "19", "9", "5", "10", "2", "x", "x", "12"], ["x", "1", "19", "20", "x", "3", "4", "18", "x", "x", "10", "1", "12", "2"], ["x", "1",... | ["[['x', '7', 'x', '13', '8', '2', '15', '2', '5', '15', '6', '4', '7', 'x'], ['x', '6', '19', '17', '5', '13', '15', '2', '11', '5', 'x', 'x', '9', '8'], ['16', '12', '10', '7', '8', '19', '19', '9', '5', '10', '2', 'x', 'x', '12'], ['x', '1', '19', '20', 'x', '3', '4', '18', 'x', 'x', '10', '1', '12', '2'], ['x', '1'... |
88 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[0, 11], [1, 11], [2, 11], [3, 10], [4, 9], [4, 8], [4, 7], [4, 6], [4, 5], [5, 5], [6, 4], [7, 3], [8, 3], [9, 3], [9, 2], [9, 1]] | 16 | 0.023496627807617188 | 16 | 8 | 2 | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1,... | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1,... | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1,... |
88 | Given 7 labeled water jugs with capacities 95, 111, 144, 57, 13, 58, 12 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 226, 271, 331, 394 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount... | water_jug | subset_sum | 6 | [["+", 95, 4], ["+", 144, 4], ["+", 57, 4], ["-", 13, 4], ["+", 111, 4], ["+", 58, 3], ["+", 144, 3], ["+", 13, 3], ["+", 58, 3], ["+", 58, 3], ["+", 57, 2], ["+", 58, 2], ["+", 144, 2], ["+", 12, 2], ["+", 57, 1], ["+", 58, 1], ["+", 111, 1]] | 17 | 0.051752328872680664 | 17 | 56 | 3 | [[95, 111, 144, 57, 13, 58, 12], [226, 271, 331, 394]] | [[95, 111, 144, 57, 13, 58, 12], [226, 271, 331, 394]] | ["[95, 111, 144, 57, 13, 58, 12]", "[226, 271, 331, 394]"] |
89 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [54, 55, 31, 54, 32, 15, 55, 32, 15, 63, 65, 21, 20, 45, 96, 29, 54, 15, 63, 65, 36, 71, 45, 96, 29, 20, 21, 54, 20, 21, 54, 36, 71, 45, 96, 54, 45, 71, 65, 63, 32, 31] | 42 | 37.91888380050659 | 42 | 4 | 15 | [[[71, 36, 63, 32, 15], [20, 21, 65, "_", 54], [45, 96, 29, 31, 55]]] | [[[71, 36, 63, 32, 15], [20, 21, 65, "_", 54], [45, 96, 29, 31, 55]]] | ["[[71, 36, 63, 32, 15], [20, 21, 65, '_', 54], [45, 96, 29, 31, 55]]"] |
89 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-right", "up-right", "up-left", "down-left", "up-left"] | 24 | 1.2028648853302002 | 24 | 4 | 25 | [[["a", "f", "w", "g", "e"], ["p", "f", "l", "m", "y"], ["o", "o", "a", "r", "a"], ["g", "a", "m", "e", "t"], ["p", "u", "_", "f", "y"]]] | [[["a", "f", "w", "g", "e"], ["p", "f", "l", "m", "y"], ["o", "o", "a", "r", "a"], ["g", "a", "m", "e", "t"], ["p", "u", "_", "f", "y"]], ["fage", "palay", "mowra", "gemot", "puffy"]] | ["[['a', 'f', 'w', 'g', 'e'], ['p', 'f', 'l', 'm', 'y'], ['o', 'o', 'a', 'r', 'a'], ['g', 'a', 'm', 'e', 't'], ['p', 'u', '_', 'f', 'y']]", "['fage', 'palay', 'mowra', 'gemot', 'puffy']"] |
89 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["B", "E", "J", "I", "Q", "K", "I", "Q"] | 8 | 0.2261185646057129 | 8 | 15 | 18 | [[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,... | [[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,... | ["[[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1... |
89 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [27, 23, 11, 23, 6, 197, 7, 21, 2, 22, 12, 38, 15, 32, 5, 19, 6, 28, 31, 31, 10, 10, 28, 24, 41, 6, 39, 16, 11, 37, 23, 7, 2], such that the sum of the chosen coins adds up to 445. Each coin in the list is unique and can o... | coin_exchange | subset_sum | 19 | [38, 24, 22, 2, 7, 15, 37, 28, 197, 28, 41, 6] | 72 | 0.04321479797363281 | 12 | 33 | 33 | [[27, 23, 11, 23, 6, 197, 7, 21, 2, 22, 12, 38, 15, 32, 5, 19, 6, 28, 31, 31, 10, 10, 28, 24, 41, 6, 39, 16, 11, 37, 23, 7, 2]] | [[27, 23, 11, 23, 6, 197, 7, 21, 2, 22, 12, 38, 15, 32, 5, 19, 6, 28, 31, 31, 10, 10, 28, 24, 41, 6, 39, 16, 11, 37, 23, 7, 2], {"41": 14, "23": 15, "31": 19, "21": 18, "22": 2, "6": 3, "11": 5, "12": 11, "37": 10, "7": 2, "32": 19, "28": 10, "16": 12, "2": 2, "197": 7, "39": 18, "19": 18, "15": 4, "10": 9, "5": 4, "27... | ["[27, 23, 11, 23, 6, 197, 7, 21, 2, 22, 12, 38, 15, 32, 5, 19, 6, 28, 31, 31, 10, 10, 28, 24, 41, 6, 39, 16, 11, 37, 23, 7, 2]", "{41: 14, 23: 15, 31: 19, 21: 18, 22: 2, 6: 3, 11: 5, 12: 11, 37: 10, 7: 2, 32: 19, 28: 10, 16: 12, 2: 2, 197: 7, 39: 18, 19: 18, 15: 4, 10: 9, 5: 4, 27: 10, 38: 3, 24: 5}", "445"] |
89 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[1, 2], [1, 0], [1, 2], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 2], [1, 2]] | 33 | 59.62572884559631 | 33 | 6 | 18 | [[["Blue", "Green", "Blue", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Red", "Red", "Green", "Red"]], 9] | [[["Blue", "Green", "Blue", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Red", "Red", "Green", "Red"]], 9] | ["[['Blue', 'Green', 'Blue', 'Red', 'Red', 'Green'], ['Blue', 'Green', 'Blue', 'Blue', 'Red', 'Green'], ['Blue', 'Green', 'Red', 'Red', 'Green', 'Red']]", "9"] |
89 | We have a 4x4 numerical grid, with numbers ranging from 10 to 60 (10 included in the range but 60 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 15 | [[0, 2, 31], [0, 3, 30], [1, 2, 59], [1, 3, 60], [2, 1, 51], [2, 2, 61], [3, 1, 49], [3, 2, 63]] | 681 | 21.286011219024658 | 8 | 50 | 16 | ["[['62', '58', '', ''], ['56', '57', '', ''], ['50', '', '', '74'], ['48', '', '', '78']]", 30, 85] | ["[['62', '58', '', ''], ['56', '57', '', ''], ['50', '', '', '74'], ['48', '', '', '78']]", 30, 85] | ["[['62', '58', '', ''], ['56', '57', '', ''], ['50', '', '', '74'], ['48', '', '', '78']]", "30", "85"] |
89 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 68. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 187, 186, None for columns 1 to 2 respectively, and the sums of rows must be None, 139, 178, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 23], [0, 1, 38], [0, 2, 30], [0, 3, 67], [1, 1, 47], [2, 2, 66], [2, 3, 53], [3, 1, 65], [3, 2, 63]] | 678 | 413.0599796772003 | 9 | 36 | 16 | ["[['', '', '', ''], ['24', '', '27', '41'], ['22', '37', '', ''], ['29', '', '', '46']]", 4, 22, 68] | ["[['', '', '', ''], ['24', '', '27', '41'], ['22', '37', '', ''], ['29', '', '', '46']]", 22, 68, [1, 3], [1, 3], [187, 186], [139, 178], 160] | ["[['', '', '', ''], ['24', '', '27', '41'], ['22', '37', '', ''], ['29', '', '', '46']]", "22", "68", "[None, 187, 186, None]", "[None, 139, 178, None]", "160"] |
89 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[1, 7], [1, 2], [9, 2], [1, 0], [1, 10], [1, 0], [5, 10], [5, 0], [5, 11], [5, 7], [8, 7], [8, 7], [8, 2], [4, 2], [4, 10], [4, 11], [4, 1], [4, 2], [4, 2], [5, 1], [5, 11], [5, 1], [8, 7], [8, 5], [8, 7], [9, 5], [9, 5], [9, 11], [9, 8], [9, 8], [9, 5], [3, 9], [3, 11], [3, 9], [3, 5], [3, 11], [3, 5], [4, 1], [10, 8... | 317 | 39.28877377510071 | 46 | 132 | 42 | [[[], ["Blue", "Yellow", "Pink", "Green", "Pink", "Red", "Red"], [], ["Pink", "White", "Pink", "Black", "White", "Black", "Pink"], ["Yellow", "Green", "White", "Red", "Yellow", "Yellow", "Red"], ["Green", "Pink", "White", "Blue", "Red", "White", "Red"], [], [], ["Blue", "Blue", "Yellow", "Blue", "Black", "Blue", "Green... | [[[], ["Blue", "Yellow", "Pink", "Green", "Pink", "Red", "Red"], [], ["Pink", "White", "Pink", "Black", "White", "Black", "Pink"], ["Yellow", "Green", "White", "Red", "Yellow", "Yellow", "Red"], ["Green", "Pink", "White", "Blue", "Red", "White", "Red"], [], [], ["Blue", "Blue", "Yellow", "Blue", "Black", "Blue", "Green... | ["[[], ['Blue', 'Yellow', 'Pink', 'Green', 'Pink', 'Red', 'Red'], [], ['Pink', 'White', 'Pink', 'Black', 'White', 'Black', 'Pink'], ['Yellow', 'Green', 'White', 'Red', 'Yellow', 'Yellow', 'Red'], ['Green', 'Pink', 'White', 'Blue', 'Red', 'White', 'Red'], [], [], ['Blue', 'Blue', 'Yellow', 'Blue', 'Black', 'Blue', 'Gree... |
89 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 13) to his destination workshop at index (4, 0), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[3, 13], [4, 13], [5, 13], [5, 12], [6, 12], [6, 11], [6, 10], [6, 9], [5, 9], [5, 8], [5, 7], [5, 6], [4, 6], [4, 5], [4, 4], [4, 3], [3, 3], [3, 2], [3, 1], [3, 0], [4, 0]] | 189 | 0.029392480850219727 | 21 | 4 | 4 | [[["x", "x", "x", "7", "11", "16", "13", "19", "15", "x", "19", "x", "x", "16"], ["9", "x", "14", "x", "7", "3", "x", "x", "17", "9", "x", "x", "x", "19"], ["x", "11", "6", "18", "x", "19", "4", "x", "x", "x", "19", "12", "4", "17"], ["5", "12", "15", "3", "x", "x", "x", "x", "7", "x", "11", "17", "20", "20"], ["6", "x... | [[["x", "x", "x", "7", "11", "16", "13", "19", "15", "x", "19", "x", "x", "16"], ["9", "x", "14", "x", "7", "3", "x", "x", "17", "9", "x", "x", "x", "19"], ["x", "11", "6", "18", "x", "19", "4", "x", "x", "x", "19", "12", "4", "17"], ["5", "12", "15", "3", "x", "x", "x", "x", "7", "x", "11", "17", "20", "20"], ["6", "x... | ["[['x', 'x', 'x', '7', '11', '16', '13', '19', '15', 'x', '19', 'x', 'x', '16'], ['9', 'x', '14', 'x', '7', '3', 'x', 'x', '17', '9', 'x', 'x', 'x', '19'], ['x', '11', '6', '18', 'x', '19', '4', 'x', 'x', 'x', '19', '12', '4', '17'], ['5', '12', '15', '3', 'x', 'x', 'x', 'x', '7', 'x', '11', '17', '20', '20'], ['6', '... |
89 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[13, 7], [12, 6], [11, 5], [11, 4], [10, 4], [9, 4], [8, 4], [7, 4], [6, 3], [5, 3], [4, 3], [3, 2], [3, 1], [2, 1], [1, 1], [0, 1], [0, 0]] | 17 | 0.02617049217224121 | 17 | 8 | 2 | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1,... | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1,... | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1,... |
89 | Given 7 labeled water jugs with capacities 30, 26, 116, 76, 98, 48, 46, 45 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 201, 269, 315, 333 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo... | water_jug | subset_sum | 6 | [["+", 76, 4], ["+", 116, 4], ["+", 45, 4], ["+", 48, 4], ["+", 48, 4], ["+", 76, 3], ["+", 98, 3], ["+", 45, 3], ["+", 48, 3], ["+", 48, 3], ["+", 76, 2], ["+", 76, 2], ["+", 98, 2], ["-", 26, 2], ["+", 45, 2], ["+", 116, 1], ["-", 76, 1], ["+", 45, 1], ["+", 116, 1]] | 19 | 0.04046440124511719 | 19 | 64 | 3 | [[30, 26, 116, 76, 98, 48, 46, 45], [201, 269, 315, 333]] | [[30, 26, 116, 76, 98, 48, 46, 45], [201, 269, 315, 333]] | ["[30, 26, 116, 76, 98, 48, 46, 45]", "[201, 269, 315, 333]"] |
90 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 8 | [28, 79, 74, 96, 24, 25, 79, 74, 96, 79, 25, 24, 79, 84, 59, 88, 72, 96, 74, 25, 24, 19, 51, 79, 71, 59, 88, 72, 96, 74, 72, 88, 84, 71, 59, 80, 79, 51] | 38 | 19.18411660194397 | 38 | 4 | 15 | [[[88, 59, 84, 71, 80], [72, 79, 74, 96, 51], ["_", 28, 25, 24, 19]]] | [[[88, 59, 84, 71, 80], [72, 79, 74, 96, 51], ["_", 28, 25, 24, 19]]] | ["[[88, 59, 84, 71, 80], [72, 79, 74, 96, 51], ['_', 28, 25, 24, 19]]"] |
90 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["up-left", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "down-right", "up-right", "up-left", "up-right", "up-left", "down-left", "up-left"] | 20 | 0.5282673835754395 | 20 | 4 | 25 | [[["a", "s", "i", "u", "r"], ["m", "z", "n", "k", "y"], ["g", "i", "o", "i", "l"], ["l", "o", "g", "i", "a"], ["u", "r", "_", "a", "n"]]] | [[["a", "s", "i", "u", "r"], ["m", "z", "n", "k", "y"], ["g", "i", "o", "i", "l"], ["l", "o", "g", "i", "a"], ["u", "r", "_", "a", "n"]], ["sour", "mangy", "kizil", "logia", "urian"]] | ["[['a', 's', 'i', 'u', 'r'], ['m', 'z', 'n', 'k', 'y'], ['g', 'i', 'o', 'i', 'l'], ['l', 'o', 'g', 'i', 'a'], ['u', 'r', '_', 'a', 'n']]", "['sour', 'mangy', 'kizil', 'logia', 'urian']"] |
90 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["F", "B", "T", "R", "G", "C", "R", "G"] | 8 | 0.05848503112792969 | 8 | 15 | 18 | [[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1,... | [[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1,... | ["[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1... |
90 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [45, 45, 40, 38, 26, 3, 3, 21, 3, 35, 24, 9, 43, 10, 19, 5, 21, 36, 15, 18, 13, 33, 42, 34, 6, 20, 38, 25, 42, 19, 32, 9, 31, 4, 4, 25, 30, 8], such that the sum of the chosen coins adds up to 453. Each coin in the list is... | coin_exchange | subset_sum | 20 | [9, 9, 19, 45, 42, 38, 45, 42, 34, 26, 33, 43, 38, 30] | 74 | 0.07263016700744629 | 14 | 38 | 38 | [[45, 45, 40, 38, 26, 3, 3, 21, 3, 35, 24, 9, 43, 10, 19, 5, 21, 36, 15, 18, 13, 33, 42, 34, 6, 20, 38, 25, 42, 19, 32, 9, 31, 4, 4, 25, 30, 8]] | [[45, 45, 40, 38, 26, 3, 3, 21, 3, 35, 24, 9, 43, 10, 19, 5, 21, 36, 15, 18, 13, 33, 42, 34, 6, 20, 38, 25, 42, 19, 32, 9, 31, 4, 4, 25, 30, 8], {"13": 7, "9": 1, "38": 9, "19": 4, "31": 18, "25": 18, "40": 13, "4": 2, "15": 8, "45": 2, "10": 10, "20": 18, "5": 3, "35": 12, "30": 8, "8": 5, "21": 5, "43": 12, "32": 10,... | ["[45, 45, 40, 38, 26, 3, 3, 21, 3, 35, 24, 9, 43, 10, 19, 5, 21, 36, 15, 18, 13, 33, 42, 34, 6, 20, 38, 25, 42, 19, 32, 9, 31, 4, 4, 25, 30, 8]", "{13: 7, 9: 1, 38: 9, 19: 4, 31: 18, 25: 18, 40: 13, 4: 2, 15: 8, 45: 2, 10: 10, 20: 18, 5: 3, 35: 12, 30: 8, 8: 5, 21: 5, 43: 12, 32: 10, 6: 2, 24: 18, 3: 2, 33: 7, 42: 4, ... |
90 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 1], [0, 1], [2, 0], [2, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 2], [1, 0], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0]] | 28 | 211.78803420066833 | 28 | 6 | 18 | [[["Green", "Green", "Red", "Green", "Red", "Red"], ["Green", "Red", "Blue", "Blue", "Red", "Blue"], ["Blue", "Green", "Blue", "Blue", "Red", "Green"]], 9] | [[["Green", "Green", "Red", "Green", "Red", "Red"], ["Green", "Red", "Blue", "Blue", "Red", "Blue"], ["Blue", "Green", "Blue", "Blue", "Red", "Green"]], 9] | ["[['Green', 'Green', 'Red', 'Green', 'Red', 'Red'], ['Green', 'Red', 'Blue', 'Blue', 'Red', 'Blue'], ['Blue', 'Green', 'Blue', 'Blue', 'Red', 'Green']]", "9"] |
90 | We have a 4x4 numerical grid, with numbers ranging from 18 to 68 (18 included in the range but 68 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 15 | [[0, 3, 90], [1, 0, 46], [1, 2, 69], [2, 1, 66], [2, 2, 67], [2, 3, 68], [3, 0, 86], [3, 2, 43], [3, 3, 42]] | 787 | 36.04757237434387 | 9 | 50 | 16 | ["[['45', '60', '89', ''], ['', '65', '', '84'], ['55', '', '', ''], ['', '85', '', '']]", 42, 97] | ["[['45', '60', '89', ''], ['', '65', '', '84'], ['55', '', '', ''], ['', '85', '', '']]", 42, 97] | ["[['45', '60', '89', ''], ['', '65', '', '84'], ['55', '', '', ''], ['', '85', '', '']]", "42", "97"] |
90 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 68. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 143, 170, None for columns 1 to 2 respectively, and the sums of rows must be None, 211, 161, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 22], [0, 1, 23], [0, 3, 27], [1, 2, 59], [2, 0, 24], [2, 1, 29], [2, 2, 46], [3, 0, 31], [3, 2, 33]] | 614 | 16.494971752166748 | 9 | 36 | 16 | ["[['', '', '32', ''], ['37', '61', '', '54'], ['', '', '', '62'], ['', '30', '', '44']]", 4, 22, 68] | ["[['', '', '32', ''], ['37', '61', '', '54'], ['', '', '', '62'], ['', '30', '', '44']]", 22, 68, [1, 3], [1, 3], [143, 170], [211, 161], 146] | ["[['', '', '32', ''], ['37', '61', '', '54'], ['', '', '', '62'], ['', '30', '', '44']]", "22", "68", "[None, 143, 170, None]", "[None, 211, 161, None]", "146"] |
90 | In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 6 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 4 | [[3, 2], [3, 2], [3, 4], [5, 4], [9, 4], [0, 1], [7, 1], [7, 8], [7, 8], [6, 4], [6, 8], [6, 4], [0, 10], [0, 11], [5, 8], [5, 8], [5, 10], [7, 2], [7, 2], [7, 10], [7, 4], [3, 7], [5, 7], [5, 2], [6, 7], [6, 2], [3, 1], [3, 1], [0, 7], [0, 7], [3, 7], [0, 3], [0, 1], [6, 0], [9, 0], [9, 0], [9, 3], [9, 3], [9, 0], [9,... | 226 | 9.712183237075806 | 46 | 132 | 42 | [[["Pink", "Black", "Red", "White", "White", "Black", "Pink"], [], [], ["Green", "Green", "Blue", "White", "Pink", "Pink", "White"], [], ["Blue", "Yellow", "Yellow", "Black", "White", "Green", "Red"], ["Blue", "Yellow", "Blue", "White", "Green", "Red", "Pink"], ["Pink", "Yellow", "Yellow", "Green", "Green", "Black", "B... | [[["Pink", "Black", "Red", "White", "White", "Black", "Pink"], [], [], ["Green", "Green", "Blue", "White", "Pink", "Pink", "White"], [], ["Blue", "Yellow", "Yellow", "Black", "White", "Green", "Red"], ["Blue", "Yellow", "Blue", "White", "Green", "Red", "Pink"], ["Pink", "Yellow", "Yellow", "Green", "Green", "Black", "B... | ["[['Pink', 'Black', 'Red', 'White', 'White', 'Black', 'Pink'], [], [], ['Green', 'Green', 'Blue', 'White', 'Pink', 'Pink', 'White'], [], ['Blue', 'Yellow', 'Yellow', 'Black', 'White', 'Green', 'Red'], ['Blue', 'Yellow', 'Blue', 'White', 'Green', 'Red', 'Pink'], ['Pink', 'Yellow', 'Yellow', 'Green', 'Green', 'Black', '... |
90 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (6, 0) to his destination workshop at index (4, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 6 | [[6, 0], [5, 0], [5, 1], [5, 2], [6, 2], [7, 2], [6, 2], [6, 3], [6, 4], [6, 5], [5, 5], [5, 6], [5, 7], [5, 8], [4, 8], [4, 9], [4, 10], [3, 10], [3, 11], [3, 12], [3, 13], [4, 13]] | 144 | 0.032550811767578125 | 22 | 4 | 4 | [[["x", "x", "x", "x", "x", "x", "x", "x", "x", "15", "x", "x", "19", "1"], ["x", "12", "x", "19", "x", "x", "13", "x", "14", "13", "8", "x", "1", "6"], ["x", "17", "x", "19", "5", "4", "x", "x", "12", "x", "x", "10", "14", "x"], ["x", "18", "x", "1", "x", "14", "x", "x", "12", "x", "11", "4", "4", "7"], ["2", "15", "x... | [[["x", "x", "x", "x", "x", "x", "x", "x", "x", "15", "x", "x", "19", "1"], ["x", "12", "x", "19", "x", "x", "13", "x", "14", "13", "8", "x", "1", "6"], ["x", "17", "x", "19", "5", "4", "x", "x", "12", "x", "x", "10", "14", "x"], ["x", "18", "x", "1", "x", "14", "x", "x", "12", "x", "11", "4", "4", "7"], ["2", "15", "x... | ["[['x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', '15', 'x', 'x', '19', '1'], ['x', '12', 'x', '19', 'x', 'x', '13', 'x', '14', '13', '8', 'x', '1', '6'], ['x', '17', 'x', '19', '5', '4', 'x', 'x', '12', 'x', 'x', '10', '14', 'x'], ['x', '18', 'x', '1', 'x', '14', 'x', 'x', '12', 'x', '11', '4', '4', '7'], ['2', '15', '... |
90 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 14 | [[12, 11], [11, 11], [10, 11], [9, 11], [8, 11], [7, 11], [6, 10], [5, 9], [4, 8], [3, 8], [2, 7], [1, 7], [0, 7], [0, 6], [0, 5], [0, 4]] | 16 | 0.030002355575561523 | 16 | 8 | 2 | ["[[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0,... | ["[[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0,... | ["[[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0,... |
90 | Given 7 labeled water jugs with capacities 88, 125, 100, 62, 134, 89, 33, 133 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 306, 407, 457, 518 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the ... | water_jug | subset_sum | 6 | [["+", 125, 4], ["+", 125, 4], ["+", 134, 4], ["+", 134, 4], ["+", 89, 3], ["+", 100, 3], ["+", 134, 3], ["+", 134, 3], ["+", 133, 2], ["+", 133, 2], ["+", 133, 2], ["-", 125, 2], ["+", 133, 2], ["+", 89, 1], ["+", 125, 1], ["-", 33, 1], ["+", 125, 1]] | 17 | 0.05500078201293945 | 17 | 64 | 3 | [[88, 125, 100, 62, 134, 89, 33, 133], [306, 407, 457, 518]] | [[88, 125, 100, 62, 134, 89, 33, 133], [306, 407, 457, 518]] | ["[88, 125, 100, 62, 134, 89, 33, 133]", "[306, 407, 457, 518]"] |
91 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [19, 44, 51, 18, 10, 6, 28, 57, 68, 58, 69, 68, 58, 69, 44, 51, 18, 10, 6, 28, 57, 58, 68, 44, 51, 18, 10, 6] | 28 | 0.08781838417053223 | 28 | 4 | 18 | [[[93, 81, 68, 57, 28, 6], [55, 54, 58, 69, 38, 10], [21, "_", 19, 44, 51, 18]]] | [[[93, 81, 68, 57, 28, 6], [55, 54, 58, 69, 38, 10], [21, "_", 19, 44, 51, 18]]] | ["[[93, 81, 68, 57, 28, 6], [55, 54, 58, 69, 38, 10], [21, '_', 19, 44, 51, 18]]"] |
91 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 4 | ["down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "up-left"] | 24 | 0.4025259017944336 | 24 | 4 | 30 | [[["t", "p", "c", "p", "o", "y"], ["s", "e", "o", "t", "k", "s"], ["p", "i", "w", "t", "_", "l"], ["s", "n", "a", "y", "h", "a"], ["c", "a", "e", "c", "p", "n"]]] | [[["t", "p", "c", "p", "o", "y"], ["s", "e", "o", "t", "k", "s"], ["p", "i", "w", "t", "_", "l"], ["s", "n", "a", "y", "h", "a"], ["c", "a", "e", "c", "p", "n"]], ["peppy", "stocky", "pistol", "swathe", "cancan"]] | ["[['t', 'p', 'c', 'p', 'o', 'y'], ['s', 'e', 'o', 't', 'k', 's'], ['p', 'i', 'w', 't', '_', 'l'], ['s', 'n', 'a', 'y', 'h', 'a'], ['c', 'a', 'e', 'c', 'p', 'n']]", "['peppy', 'stocky', 'pistol', 'swathe', 'cancan']"] |
91 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 15 | ["A", "H", "D", "G", "T", "O", "F", "O", "M", "G"] | 10 | 0.059241533279418945 | 10 | 15 | 18 | [[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,... | [[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,... | ["[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1... |
91 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [36, 40, 17, 7, 15, 23, 18, 26, 29, 24, 15, 43, 13, 12, 31, 33, 30, 31, 26, 37, 14, 31, 43, 25, 30, 7, 37, 27, 221, 13, 26, 21], such that the sum of the chosen coins adds up to 445. Each coin in the list is unique and can... | coin_exchange | subset_sum | 21 | [17, 33, 37, 37, 30, 221, 40, 30] | 39 | 0.04606795310974121 | 8 | 32 | 32 | [[36, 40, 17, 7, 15, 23, 18, 26, 29, 24, 15, 43, 13, 12, 31, 33, 30, 31, 26, 37, 14, 31, 43, 25, 30, 7, 37, 27, 221, 13, 26, 21]] | [[36, 40, 17, 7, 15, 23, 18, 26, 29, 24, 15, 43, 13, 12, 31, 33, 30, 31, 26, 37, 14, 31, 43, 25, 30, 7, 37, 27, 221, 13, 26, 21], {"36": 14, "27": 19, "21": 6, "13": 8, "23": 17, "26": 17, "15": 6, "25": 7, "31": 20, "30": 5, "18": 14, "12": 6, "37": 2, "221": 18, "14": 13, "24": 10, "33": 4, "43": 11, "29": 18, "40": ... | ["[36, 40, 17, 7, 15, 23, 18, 26, 29, 24, 15, 43, 13, 12, 31, 33, 30, 31, 26, 37, 14, 31, 43, 25, 30, 7, 37, 27, 221, 13, 26, 21]", "{36: 14, 27: 19, 21: 6, 13: 8, 23: 17, 26: 17, 15: 6, 25: 7, 31: 20, 30: 5, 18: 14, 12: 6, 37: 2, 221: 18, 14: 13, 24: 10, 33: 4, 43: 11, 29: 18, 40: 1, 7: 6, 17: 2}", "445"] |
91 | The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 10 | [[0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [0, 2], [0, 2], [1, 2], [1, 0], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [0, 1]] | 32 | 75.25922632217407 | 32 | 6 | 18 | [[["Red", "Green", "Blue", "Red", "Blue", "Blue"], ["Red", "Blue", "Green", "Green", "Blue", "Red"], ["Green", "Green", "Red", "Blue", "Green", "Red"]], 9] | [[["Red", "Green", "Blue", "Red", "Blue", "Blue"], ["Red", "Blue", "Green", "Green", "Blue", "Red"], ["Green", "Green", "Red", "Blue", "Green", "Red"]], 9] | ["[['Red', 'Green', 'Blue', 'Red', 'Blue', 'Blue'], ['Red', 'Blue', 'Green', 'Green', 'Blue', 'Red'], ['Green', 'Green', 'Red', 'Blue', 'Green', 'Red']]", "9"] |
91 | We have a 4x4 numerical grid, with numbers ranging from 10 to 65 (10 included in the range but 65 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 11 | [[0, 0, 18], [0, 1, 19], [0, 3, 39], [1, 0, 17], [1, 1, 20], [1, 3, 40], [2, 1, 21], [3, 1, 22], [3, 2, 23]] | 410 | 5.110289812088013 | 9 | 55 | 16 | ["[['', '', '38', ''], ['', '', '33', ''], ['16', '', '28', '47'], ['14', '', '', '52']]", 14, 69] | ["[['', '', '38', ''], ['', '', '33', ''], ['16', '', '28', '47'], ['14', '', '', '52']]", 14, 69] | ["[['', '', '38', ''], ['', '', '33', ''], ['16', '', '28', '47'], ['14', '', '', '52']]", "14", "69"] |
91 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 68. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 177, 192, None for columns 1 to 2 respectively, and the sums of rows must be None, 217, 193, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 1, 48], [0, 2, 31], [0, 3, 23], [1, 0, 56], [1, 3, 66], [2, 0, 33], [2, 2, 67], [3, 0, 27], [3, 3, 22]] | 712 | 5.191744089126587 | 9 | 36 | 16 | ["[['62', '', '', ''], ['', '35', '60', ''], ['', '39', '', '54'], ['', '55', '34', '']]", 4, 22, 68] | ["[['62', '', '', ''], ['', '35', '60', ''], ['', '39', '', '54'], ['', '55', '34', '']]", 22, 68, [1, 3], [1, 3], [177, 192], [217, 193], 149] | ["[['62', '', '', ''], ['', '35', '60', ''], ['', '39', '', '54'], ['', '55', '34', '']]", "22", "68", "[None, 177, 192, None]", "[None, 217, 193, None]", "149"] |
91 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 2) to his destination workshop at index (8, 14), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[5, 2], [4, 2], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [4, 6], [4, 7], [5, 7], [5, 8], [5, 9], [6, 9], [6, 10], [6, 11], [7, 11], [7, 12], [7, 13], [7, 14], [8, 14]] | 182 | 0.028976917266845703 | 20 | 4 | 4 | [[["x", "x", "12", "x", "18", "3", "2", "15", "6", "11", "13", "x", "7", "17", "x"], ["13", "x", "20", "13", "5", "2", "x", "x", "10", "12", "19", "19", "16", "x", "17"], ["12", "12", "7", "x", "x", "x", "9", "x", "x", "10", "10", "18", "4", "x", "x"], ["x", "14", "3", "13", "9", "2", "19", "19", "x", "x", "x", "4", "x... | [[["x", "x", "12", "x", "18", "3", "2", "15", "6", "11", "13", "x", "7", "17", "x"], ["13", "x", "20", "13", "5", "2", "x", "x", "10", "12", "19", "19", "16", "x", "17"], ["12", "12", "7", "x", "x", "x", "9", "x", "x", "10", "10", "18", "4", "x", "x"], ["x", "14", "3", "13", "9", "2", "19", "19", "x", "x", "x", "4", "x... | ["[['x', 'x', '12', 'x', '18', '3', '2', '15', '6', '11', '13', 'x', '7', '17', 'x'], ['13', 'x', '20', '13', '5', '2', 'x', 'x', '10', '12', '19', '19', '16', 'x', '17'], ['12', '12', '7', 'x', 'x', 'x', '9', 'x', 'x', '10', '10', '18', '4', 'x', 'x'], ['x', '14', '3', '13', '9', '2', '19', '19', 'x', 'x', 'x', '4', '... |
91 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 15 | [[14, 2], [13, 2], [12, 2], [11, 3], [10, 4], [9, 4], [8, 4], [7, 4], [6, 4], [6, 5], [5, 6], [4, 6], [4, 7], [3, 8], [2, 8], [1, 9]] | 16 | 0.03218722343444824 | 16 | 8 | 2 | ["[[0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1... | ["[[0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1... | ["[[0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1... |
91 | Given 9 labeled water jugs with capacities 51, 75, 112, 122, 54, 129, 31, 127, 113 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 338, 431, 493, 550 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed... | water_jug | subset_sum | 7 | [["+", 75, 4], ["+", 112, 4], ["+", 112, 4], ["+", 122, 4], ["+", 129, 4], ["+", 112, 3], ["+", 127, 3], ["+", 127, 3], ["+", 127, 3], ["+", 51, 2], ["+", 122, 2], ["+", 129, 2], ["+", 129, 2], ["+", 112, 1], ["+", 113, 1], ["+", 113, 1]] | 16 | 0.05792498588562012 | 16 | 72 | 3 | [[51, 75, 112, 122, 54, 129, 31, 127, 113], [338, 431, 493, 550]] | [[51, 75, 112, 122, 54, 129, 31, 127, 113], [338, 431, 493, 550]] | ["[51, 75, 112, 122, 54, 129, 31, 127, 113]", "[338, 431, 493, 550]"] |
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