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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
10 | 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 | 1 | ["up-right", "up-left", "down-left", "up-left"] | 4 | 0.1708054542541504 | 4 | 4 | 16 | [[["u", "k", "d", "x"], ["t", "e", "r", "b"], ["w", "a", "_", "i"], ["t", "e", "s", "t"]]] | [[["u", "k", "d", "x"], ["t", "e", "r", "b"], ["w", "a", "_", "i"], ["t", "e", "s", "t"]], ["kex", "turd", "wabi", "test"]] | ["[['u', 'k', 'd', 'x'], ['t', 'e', 'r', 'b'], ['w', 'a', '_', 'i'], ['t', 'e', 's', 't']]", "['kex', 'turd', 'wabi', 'test']"] |
10 | 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 | 10 | ["Q", "M", "O", "E", "X", "P", "V", "P", "W", "E"] | 10 | 0.03560161590576172 | 10 | 10 | 13 | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 0, 0, 0, 0]... | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 0, 0, 0, 0]... | ["[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 0, 0, 0, 0... |
10 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [6, 20, 15, 14, 23, 6, 8, 15, 11, 2, 16, 21, 17, 10, 23, 20, 21, 16, 13, 3, 7, 4, 9, 21, 7, 13, 10, 18, 11, 9, 13, 12, 15, 17, 2, 8, 18, 3, 16, 9, 3, 14, 23, 16], such that the sum of the chosen coins adds up to 236. Each ... | coin_exchange | subset_sum | 24 | [9, 9, 13, 13, 8, 6, 13, 8, 9, 17, 16, 17, 16, 6, 21, 16, 21, 16, 2] | 84 | 0.0525660514831543 | 19 | 44 | 44 | [[6, 20, 15, 14, 23, 6, 8, 15, 11, 2, 16, 21, 17, 10, 23, 20, 21, 16, 13, 3, 7, 4, 9, 21, 7, 13, 10, 18, 11, 9, 13, 12, 15, 17, 2, 8, 18, 3, 16, 9, 3, 14, 23, 16]] | [[6, 20, 15, 14, 23, 6, 8, 15, 11, 2, 16, 21, 17, 10, 23, 20, 21, 16, 13, 3, 7, 4, 9, 21, 7, 13, 10, 18, 11, 9, 13, 12, 15, 17, 2, 8, 18, 3, 16, 9, 3, 14, 23, 16], {"21": 11, "18": 16, "16": 6, "12": 5, "14": 11, "11": 8, "15": 11, "4": 3, "9": 2, "23": 14, "7": 5, "20": 12, "6": 2, "8": 3, "17": 6, "13": 3, "3": 3, "2... | ["[6, 20, 15, 14, 23, 6, 8, 15, 11, 2, 16, 21, 17, 10, 23, 20, 21, 16, 13, 3, 7, 4, 9, 21, 7, 13, 10, 18, 11, 9, 13, 12, 15, 17, 2, 8, 18, 3, 16, 9, 3, 14, 23, 16]", "{21: 11, 18: 16, 16: 6, 12: 5, 14: 11, 11: 8, 15: 11, 4: 3, 9: 2, 23: 14, 7: 5, 20: 12, 6: 2, 8: 3, 17: 6, 13: 3, 3: 3, 2: 1, 10: 5}", "236"] |
10 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 1], [0, 2], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 18 | 1.260277509689331 | 18 | 6 | 12 | [[["Blue", "Green", "Green", "Red"], ["Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Red"]], 6] | [[["Blue", "Green", "Green", "Red"], ["Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Red"]], 6] | ["[['Blue', 'Green', 'Green', 'Red'], ['Red', 'Red', 'Green', 'Blue'], ['Green', 'Blue', 'Blue', 'Red']]", "6"] |
10 | We have a 3x3 numerical grid, with numbers ranging from 41 to 79 (41 included in the range but 79 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 0, 41], [0, 2, 60], [1, 1, 51], [2, 0, 48]] | 500 | 0.1792917251586914 | 4 | 38 | 9 | ["[['', '59', ''], ['47', '', '62'], ['', '50', '63']]", 41, 79] | ["[['', '59', ''], ['47', '', '62'], ['', '50', '63']]", 41, 79] | ["[['', '59', ''], ['47', '', '62'], ['', '50', '63']]", "41", "79"] |
10 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 35 to 59. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 154, and sum of row 1 must be 151. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 35], [0, 1, 40], [0, 2, 36], [1, 0, 38], [1, 1, 58], [1, 2, 55], [2, 0, 39], [2, 1, 56]] | 414 | 232.39282536506653 | 8 | 24 | 9 | ["[['', '', ''], ['', '', ''], ['', '', '57']]", 3, 35, 59] | ["[['', '', ''], ['', '', ''], ['', '', '57']]", 35, 59, [1, 2], [1, 2], [154], [151], 133] | ["[['', '', ''], ['', '', ''], ['', '', '57']]", "35", "59", "[None, 154, None]", "[None, 151, None]", "133"] |
10 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[3, 0], [3, 1], [2, 5], [4, 5], [3, 0], [4, 3], [4, 5], [1, 3], [4, 0]] | 33 | 0.05746722221374512 | 9 | 30 | 12 | [[[], [], ["Green", "Blue", "Blue", "Blue"], ["Yellow", "Red", "Yellow", "Red"], ["Green", "Red", "Green", "Yellow"], []], 4, {"0": 1, "1": 7, "2": 2, "3": 4, "4": 6, "5": 5}] | [[[], [], ["Green", "Blue", "Blue", "Blue"], ["Yellow", "Red", "Yellow", "Red"], ["Green", "Red", "Green", "Yellow"], []], 4, {"0": 1, "1": 7, "2": 2, "3": 4, "4": 6, "5": 5}, 3] | ["[[], [], ['Green', 'Blue', 'Blue', 'Blue'], ['Yellow', 'Red', 'Yellow', 'Red'], ['Green', 'Red', 'Green', 'Yellow'], []]", "{0: 1, 1: 7, 2: 2, 3: 4, 4: 6, 5: 5}", "4", "3"] |
10 | 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, 6), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, 4], [5, 4], [6, 4], [6, 5], [7, 5], [6, 5], [6, 6]] | 93 | 0.021834135055541992 | 12 | 4 | 4 | [[["x", "x", "6", "x", "7", "x", "9", "4", "11"], ["x", "3", "x", "6", "5", "3", "15", "x", "3"], ["x", "x", "x", "4", "x", "9", "1", "8", "x"], ["15", "18", "1", "6", "5", "10", "6", "14", "8"], ["18", "10", "7", "18", "2", "x", "x", "x", "7"], ["11", "9", "16", "x", "11", "x", "11", "x", "17"], ["7", "x", "18", "x", ... | [[["x", "x", "6", "x", "7", "x", "9", "4", "11"], ["x", "3", "x", "6", "5", "3", "15", "x", "3"], ["x", "x", "x", "4", "x", "9", "1", "8", "x"], ["15", "18", "1", "6", "5", "10", "6", "14", "8"], ["18", "10", "7", "18", "2", "x", "x", "x", "7"], ["11", "9", "16", "x", "11", "x", "11", "x", "17"], ["7", "x", "18", "x", ... | ["[['x', 'x', '6', 'x', '7', 'x', '9', '4', '11'], ['x', '3', 'x', '6', '5', '3', '15', 'x', '3'], ['x', 'x', 'x', '4', 'x', '9', '1', '8', 'x'], ['15', '18', '1', '6', '5', '10', '6', '14', '8'], ['18', '10', '7', '18', '2', 'x', 'x', 'x', '7'], ['11', '9', '16', 'x', '11', 'x', '11', 'x', '17'], ['7', 'x', '18', 'x',... |
10 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[8, 8], [7, 7], [7, 6], [7, 5], [8, 4], [7, 3], [6, 3], [5, 3], [4, 3], [3, 3], [3, 2], [2, 2], [2, 1]] | 13 | 0.029077768325805664 | 13 | 8 | 2 | ["[[0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 0]]", 3] | ["[[0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 0]]", [8, 8], [2, 1], 3] | ["[[0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 0]]", "(8, 8)", "(2, 1)", "3"] |
10 | Given 5 labeled water jugs with capacities 14, 119, 62, 18, 133, 13 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 218, 272, 314 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water... | water_jug | subset_sum | 4 | [["+", 119, 3], ["+", 119, 3], ["+", 62, 3], ["+", 14, 3], ["+", 133, 2], ["+", 133, 2], ["-", 13, 2], ["+", 14, 2], ["-", 13, 2], ["+", 18, 2], ["+", 14, 1], ["+", 133, 1], ["-", 62, 1], ["+", 133, 1]] | 14 | 0.029827594757080078 | 14 | 36 | 3 | [[14, 119, 62, 18, 133, 13], [218, 272, 314]] | [[14, 119, 62, 18, 133, 13], [218, 272, 314]] | ["[14, 119, 62, 18, 133, 13]", "[218, 272, 314]"] |
11 | 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 | 3 | [54, 50, 95, 53, 85, 54, 53, 95, 50, 53, 95, 85, 54, 55, 76, 95, 85, 50, 53, 59, 95, 85, 55, 54] | 24 | 0.10947823524475098 | 24 | 4 | 9 | [[[59, 76, 55], [54, "_", 85], [50, 95, 53]]] | [[[59, 76, 55], [54, "_", 85], [50, 95, 53]]] | ["[[59, 76, 55], [54, '_', 85], [50, 95, 53]]"] |
11 | 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 | 1 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left"] | 16 | 0.2195606231689453 | 16 | 4 | 16 | [[["o", "b", "e", "d"], ["c", "o", "d", "u"], ["w", "a", "_", "p"], ["y", "u", "l", "p"]]] | [[["o", "b", "e", "d"], ["c", "o", "d", "u"], ["w", "a", "_", "p"], ["y", "u", "l", "p"]], ["bud", "codo", "waup", "yelp"]] | ["[['o', 'b', 'e', 'd'], ['c', 'o', 'd', 'u'], ['w', 'a', '_', 'p'], ['y', 'u', 'l', 'p']]", "['bud', 'codo', 'waup', 'yelp']"] |
11 | 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 | 10 | ["Q", "Z", "Y", "T", "A", "M", "E", "S", "E", "B", "T"] | 11 | 0.028751611709594727 | 11 | 10 | 13 | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0]... | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0]... | ["[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0... |
11 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [21, 20, 21, 11, 23, 16, 16, 16, 3, 20, 2, 19, 16, 21, 18, 7, 20, 3, 16, 18, 7, 22, 3, 22, 7, 21, 12, 22, 5, 6, 17, 16, 8, 8, 14, 4, 18, 9, 4, 20, 2], such that the sum of the chosen coins adds up to 228. Each coin in the ... | coin_exchange | subset_sum | 25 | [18, 6, 9, 19, 18, 14, 12, 2, 7, 7, 17, 23, 22, 18, 16, 2, 7, 11] | 66 | 0.04258108139038086 | 18 | 41 | 41 | [[21, 20, 21, 11, 23, 16, 16, 16, 3, 20, 2, 19, 16, 21, 18, 7, 20, 3, 16, 18, 7, 22, 3, 22, 7, 21, 12, 22, 5, 6, 17, 16, 8, 8, 14, 4, 18, 9, 4, 20, 2]] | [[21, 20, 21, 11, 23, 16, 16, 16, 3, 20, 2, 19, 16, 21, 18, 7, 20, 3, 16, 18, 7, 22, 3, 22, 7, 21, 12, 22, 5, 6, 17, 16, 8, 8, 14, 4, 18, 9, 4, 20, 2], {"6": 1, "7": 3, "9": 1, "18": 1, "2": 1, "11": 7, "5": 3, "12": 2, "3": 3, "22": 6, "14": 3, "20": 15, "4": 3, "17": 4, "16": 8, "23": 18, "21": 16, "19": 2, "8": 6}, ... | ["[21, 20, 21, 11, 23, 16, 16, 16, 3, 20, 2, 19, 16, 21, 18, 7, 20, 3, 16, 18, 7, 22, 3, 22, 7, 21, 12, 22, 5, 6, 17, 16, 8, 8, 14, 4, 18, 9, 4, 20, 2]", "{6: 1, 7: 3, 9: 1, 18: 1, 2: 1, 11: 7, 5: 3, 12: 2, 3: 3, 22: 6, 14: 3, 20: 15, 4: 3, 17: 4, 16: 8, 23: 18, 21: 16, 19: 2, 8: 6}", "228"] |
11 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 16 | 0.6104025840759277 | 16 | 6 | 12 | [[["Green", "Red", "Red", "Green"], ["Blue", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Red"]], 6] | [[["Green", "Red", "Red", "Green"], ["Blue", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Red"]], 6] | ["[['Green', 'Red', 'Red', 'Green'], ['Blue', 'Red', 'Green', 'Blue'], ['Green', 'Blue', 'Blue', 'Red']]", "6"] |
11 | We have a 3x3 numerical grid, with numbers ranging from 33 to 71 (33 included in the range but 71 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 0, 51], [0, 1, 53], [1, 1, 52], [2, 2, 57]] | 487 | 0.27827906608581543 | 4 | 38 | 9 | ["[['', '', '55'], ['50', '', '56'], ['40', '43', '']]", 33, 71] | ["[['', '', '55'], ['50', '', '56'], ['40', '43', '']]", 33, 71] | ["[['', '', '55'], ['50', '', '56'], ['40', '43', '']]", "33", "71"] |
11 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 35 to 59. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 127, and sum of row 1 must be 144. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 35], [0, 1, 36], [1, 0, 40], [1, 1, 54], [1, 2, 50], [2, 0, 39], [2, 1, 37], [2, 2, 38]] | 377 | 1.0946576595306396 | 8 | 24 | 9 | ["[['', '', '48'], ['', '', ''], ['', '', '']]", 3, 35, 59] | ["[['', '', '48'], ['', '', ''], ['', '', '']]", 35, 59, [1, 2], [1, 2], [127], [144], 141] | ["[['', '', '48'], ['', '', ''], ['', '', '']]", "35", "59", "[None, 127, None]", "[None, 144, None]", "141"] |
11 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[1, 0], [1, 0], [1, 2], [3, 2], [3, 1], [5, 2], [5, 1], [5, 0], [3, 5], [3, 5]] | 30 | 0.07445669174194336 | 10 | 30 | 12 | [[[], ["Blue", "Blue", "Green", "Red"], [], ["Green", "Red", "Yellow", "Yellow"], [], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 3, "1": 5, "2": 1, "3": 6, "4": 7, "5": 4}] | [[[], ["Blue", "Blue", "Green", "Red"], [], ["Green", "Red", "Yellow", "Yellow"], [], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 3, "1": 5, "2": 1, "3": 6, "4": 7, "5": 4}, 3] | ["[[], ['Blue', 'Blue', 'Green', 'Red'], [], ['Green', 'Red', 'Yellow', 'Yellow'], [], ['Green', 'Red', 'Blue', 'Yellow']]", "{0: 3, 1: 5, 2: 1, 3: 6, 4: 7, 5: 4}", "4", "3"] |
11 | 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 (4, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [2, 6], [2, 7], [2, 8], [3, 8], [4, 8], [5, 8], [4, 8]] | 163 | 0.0204925537109375 | 14 | 4 | 4 | [[["x", "15", "x", "18", "8", "6", "11", "x", "7"], ["9", "10", "18", "9", "2", "16", "9", "8", "x"], ["14", "x", "x", "10", "18", "x", "13", "12", "14"], ["11", "18", "4", "11", "14", "2", "20", "x", "15"], ["12", "x", "x", "8", "10", "x", "x", "10", "11"], ["5", "19", "20", "15", "11", "x", "14", "x", "18"], ["x", "5... | [[["x", "15", "x", "18", "8", "6", "11", "x", "7"], ["9", "10", "18", "9", "2", "16", "9", "8", "x"], ["14", "x", "x", "10", "18", "x", "13", "12", "14"], ["11", "18", "4", "11", "14", "2", "20", "x", "15"], ["12", "x", "x", "8", "10", "x", "x", "10", "11"], ["5", "19", "20", "15", "11", "x", "14", "x", "18"], ["x", "5... | ["[['x', '15', 'x', '18', '8', '6', '11', 'x', '7'], ['9', '10', '18', '9', '2', '16', '9', '8', 'x'], ['14', 'x', 'x', '10', '18', 'x', '13', '12', '14'], ['11', '18', '4', '11', '14', '2', '20', 'x', '15'], ['12', 'x', 'x', '8', '10', 'x', 'x', '10', '11'], ['5', '19', '20', '15', '11', 'x', '14', 'x', '18'], ['x', '... |
11 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[8, 7], [7, 7], [6, 7], [5, 6], [5, 5], [4, 4], [3, 4], [2, 4], [1, 3], [0, 3]] | 10 | 0.03075408935546875 | 10 | 8 | 2 | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 0, 0]]", 3] | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 0, 0]]", [8, 7], [0, 3], 3] | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 1, 0, 0]]", "(8, 7)", "(0, 3)", "3"] |
11 | Given 5 labeled water jugs with capacities 140, 58, 129, 130, 125 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 391, 401, 431 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water i... | water_jug | subset_sum | 4 | [["+", 140, 3], ["+", 140, 3], ["+", 140, 3], ["-", 129, 3], ["+", 140, 3], ["+", 125, 2], ["+", 125, 2], ["+", 140, 2], ["-", 129, 2], ["+", 140, 2], ["+", 125, 1], ["+", 125, 1], ["+", 130, 1], ["-", 129, 1], ["+", 140, 1]] | 15 | 0.04181361198425293 | 15 | 30 | 3 | [[140, 58, 129, 130, 125], [391, 401, 431]] | [[140, 58, 129, 130, 125], [391, 401, 431]] | ["[140, 58, 129, 130, 125]", "[391, 401, 431]"] |
12 | 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 | 3 | [35, 51, 73, 22, 54, 35, 51, 66, 76, 90, 35, 54, 22, 51, 66, 76, 90, 66, 54, 22] | 20 | 0.061293601989746094 | 20 | 4 | 9 | [[[66, 35, 51], [76, "_", 73], [90, 54, 22]]] | [[[66, 35, 51], [76, "_", 73], [90, 54, 22]]] | ["[[66, 35, 51], [76, '_', 73], [90, 54, 22]]"] |
12 | 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 | 1 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 10 | 0.185685396194458 | 10 | 4 | 16 | [[["k", "h", "a", "t"], ["s", "a", "a", "a"], ["i", "l", "_", "t"], ["m", "g", "n", "d"]]] | [[["k", "h", "a", "t"], ["s", "a", "a", "a"], ["i", "l", "_", "t"], ["m", "g", "n", "d"]], ["hat", "skag", "alit", "mand"]] | ["[['k', 'h', 'a', 't'], ['s', 'a', 'a', 'a'], ['i', 'l', '_', 't'], ['m', 'g', 'n', 'd']]", "['hat', 'skag', 'alit', 'mand']"] |
12 | 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 | 10 | ["B", "I", "L", "V", "N", "L", "V"] | 7 | 0.027237892150878906 | 7 | 10 | 13 | [[[0, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]... | [[[0, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]... | ["[[0, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0... |
12 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [9, 2, 23, 20, 13, 4, 15, 16, 12, 21, 13, 9, 2, 14, 13, 14, 4, 19, 12, 6, 21, 23, 4, 18, 2, 23, 23, 6, 18, 23, 3, 16, 7, 2, 22, 16, 8, 10, 23, 17, 3, 18, 8], such that the sum of the chosen coins adds up to 230. Each coin ... | coin_exchange | subset_sum | 26 | [20, 18, 4, 9, 4, 15, 12, 6, 19, 18, 12, 6, 4, 9, 17, 23, 18, 16] | 69 | 0.04821968078613281 | 18 | 43 | 43 | [[9, 2, 23, 20, 13, 4, 15, 16, 12, 21, 13, 9, 2, 14, 13, 14, 4, 19, 12, 6, 21, 23, 4, 18, 2, 23, 23, 6, 18, 23, 3, 16, 7, 2, 22, 16, 8, 10, 23, 17, 3, 18, 8]] | [[9, 2, 23, 20, 13, 4, 15, 16, 12, 21, 13, 9, 2, 14, 13, 14, 4, 19, 12, 6, 21, 23, 4, 18, 2, 23, 23, 6, 18, 23, 3, 16, 7, 2, 22, 16, 8, 10, 23, 17, 3, 18, 8], {"9": 1, "17": 6, "2": 2, "22": 9, "13": 13, "16": 8, "12": 4, "4": 1, "21": 14, "14": 10, "19": 9, "10": 7, "7": 6, "8": 7, "6": 2, "23": 16, "18": 3, "20": 2, ... | ["[9, 2, 23, 20, 13, 4, 15, 16, 12, 21, 13, 9, 2, 14, 13, 14, 4, 19, 12, 6, 21, 23, 4, 18, 2, 23, 23, 6, 18, 23, 3, 16, 7, 2, 22, 16, 8, 10, 23, 17, 3, 18, 8]", "{9: 1, 17: 6, 2: 2, 22: 9, 13: 13, 16: 8, 12: 4, 4: 1, 21: 14, 14: 10, 19: 9, 10: 7, 7: 6, 8: 7, 6: 2, 23: 16, 18: 3, 20: 2, 3: 1, 15: 2}", "230"] |
12 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 2], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 2], [1, 0]] | 16 | 0.49949169158935547 | 16 | 6 | 12 | [[["Blue", "Blue", "Red", "Blue"], ["Red", "Green", "Green", "Green"], ["Red", "Red", "Blue", "Green"]], 6] | [[["Blue", "Blue", "Red", "Blue"], ["Red", "Green", "Green", "Green"], ["Red", "Red", "Blue", "Green"]], 6] | ["[['Blue', 'Blue', 'Red', 'Blue'], ['Red', 'Green', 'Green', 'Green'], ['Red', 'Red', 'Blue', 'Green']]", "6"] |
12 | We have a 3x3 numerical grid, with numbers ranging from 35 to 73 (35 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 or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 1, 36], [0, 2, 35], [1, 0, 38], [2, 0, 37]] | 475 | 0.1643369197845459 | 4 | 38 | 9 | ["[['57', '', ''], ['', '50', '63'], ['', '69', '71']]", 35, 73] | ["[['57', '', ''], ['', '50', '63'], ['', '69', '71']]", 35, 73] | ["[['57', '', ''], ['', '50', '63'], ['', '69', '71']]", "35", "73"] |
12 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 28 to 57. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 126, and sum of row 1 must be 124. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 29], [0, 2, 31], [1, 1, 52], [1, 2, 33], [2, 0, 53], [2, 1, 28], [2, 2, 30]] | 341 | 1.8470244407653809 | 7 | 24 | 9 | ["[['', '46', ''], ['39', '', ''], ['', '', '']]", 3, 28, 57] | ["[['', '46', ''], ['39', '', ''], ['', '', '']]", 28, 57, [1, 2], [1, 2], [126], [124], 136] | ["[['', '46', ''], ['39', '', ''], ['', '', '']]", "28", "57", "[None, 126, None]", "[None, 124, None]", "136"] |
12 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[1, 3], [1, 3], [4, 2], [4, 3], [1, 2], [4, 2], [0, 4], [0, 1], [0, 1], [0, 4]] | 36 | 0.08908510208129883 | 10 | 30 | 12 | [[["Green", "Yellow", "Yellow", "Green"], ["Red", "Red", "Blue", "Yellow"], [], [], ["Blue", "Red", "Blue", "Green"], []], 4, {"0": 2, "1": 2, "2": 3, "3": 7, "4": 1, "5": 7}] | [[["Green", "Yellow", "Yellow", "Green"], ["Red", "Red", "Blue", "Yellow"], [], [], ["Blue", "Red", "Blue", "Green"], []], 4, {"0": 2, "1": 2, "2": 3, "3": 7, "4": 1, "5": 7}, 3] | ["[['Green', 'Yellow', 'Yellow', 'Green'], ['Red', 'Red', 'Blue', 'Yellow'], [], [], ['Blue', 'Red', 'Blue', 'Green'], []]", "{0: 2, 1: 2, 2: 3, 3: 7, 4: 1, 5: 7}", "4", "3"] |
12 | 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, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 1], [3, 2], [4, 2], [4, 3], [4, 4], [3, 4], [3, 5], [2, 5], [2, 6], [2, 7], [2, 8], [3, 8], [4, 8], [5, 8]] | 132 | 0.020636796951293945 | 14 | 4 | 4 | [[["19", "x", "17", "14", "3", "x", "10", "5", "2"], ["x", "x", "1", "x", "x", "x", "19", "7", "1"], ["16", "12", "x", "3", "19", "2", "14", "1", "14"], ["x", "1", "16", "x", "12", "3", "13", "x", "3"], ["x", "x", "7", "19", "10", "x", "5", "x", "19"], ["5", "x", "x", "6", "14", "x", "x", "10", "12"], ["x", "x", "x", "... | [[["19", "x", "17", "14", "3", "x", "10", "5", "2"], ["x", "x", "1", "x", "x", "x", "19", "7", "1"], ["16", "12", "x", "3", "19", "2", "14", "1", "14"], ["x", "1", "16", "x", "12", "3", "13", "x", "3"], ["x", "x", "7", "19", "10", "x", "5", "x", "19"], ["5", "x", "x", "6", "14", "x", "x", "10", "12"], ["x", "x", "x", "... | ["[['19', 'x', '17', '14', '3', 'x', '10', '5', '2'], ['x', 'x', '1', 'x', 'x', 'x', '19', '7', '1'], ['16', '12', 'x', '3', '19', '2', '14', '1', '14'], ['x', '1', '16', 'x', '12', '3', '13', 'x', '3'], ['x', 'x', '7', '19', '10', 'x', '5', 'x', '19'], ['5', 'x', 'x', '6', '14', 'x', 'x', '10', '12'], ['x', 'x', 'x', ... |
12 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[3, 7], [4, 6], [5, 5], [5, 4], [6, 3], [6, 2], [6, 1], [7, 1], [7, 0], [8, 0]] | 10 | 0.029245376586914062 | 10 | 8 | 2 | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1]]", 3] | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1]]", [3, 7], [8, 0], 3] | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1]]", "(3, 7)", "(8, 0)", "3"] |
12 | Given 5 labeled water jugs with capacities 46, 99, 145, 131, 78, 100 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 247, 340, 368 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wate... | water_jug | subset_sum | 4 | [["+", 78, 3], ["+", 145, 3], ["+", 145, 3], ["+", 78, 2], ["+", 131, 2], ["+", 131, 2], ["+", 131, 1], ["-", 46, 1], ["+", 131, 1], ["-", 100, 1], ["+", 131, 1]] | 11 | 0.027457475662231445 | 11 | 36 | 3 | [[46, 99, 145, 131, 78, 100], [247, 340, 368]] | [[46, 99, 145, 131, 78, 100], [247, 340, 368]] | ["[46, 99, 145, 131, 78, 100]", "[247, 340, 368]"] |
13 | 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 | 4 | [29, 97, 36, 41, 97, 36, 51, 29, 36, 51, 43, 61, 29, 43, 41, 82, 61, 41, 43, 29] | 20 | 0.04056262969970703 | 20 | 4 | 9 | [[[41, 36, 82], [29, 97, 43], ["_", 51, 61]]] | [[[41, 36, 82], [29, 97, 43], ["_", 51, 61]]] | ["[[41, 36, 82], [29, 97, 43], ['_', 51, 61]]"] |
13 | 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 | 1 | ["down-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.17847561836242676 | 16 | 4 | 16 | [[["b", "l", "_", "g"], ["a", "n", "a", "s"], ["m", "u", "a", "a"], ["s", "h", "a", "m"]]] | [[["b", "l", "_", "g"], ["a", "n", "a", "s"], ["m", "u", "a", "a"], ["s", "h", "a", "m"]], ["lag", "abas", "numa", "sham"]] | ["[['b', 'l', '_', 'g'], ['a', 'n', 'a', 's'], ['m', 'u', 'a', 'a'], ['s', 'h', 'a', 'm']]", "['lag', 'abas', 'numa', 'sham']"] |
13 | 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 | 10 | ["H", "V", "E", "T", "X", "Y", "X", "L", "E"] | 9 | 0.02870488166809082 | 9 | 10 | 13 | [[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 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, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0]... | [[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 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, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0]... | ["[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 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, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0... |
13 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [20, 19, 2, 12, 23, 18, 15, 13, 10, 6, 9, 4, 9, 16, 5, 8, 19, 6, 7, 2, 6, 15, 10, 9, 4, 6, 19, 10, 10, 16, 21, 17, 21, 16, 13, 6, 16, 8, 7, 11, 13, 7, 21, 15, 15, 6, 11, 19, 7], such that the sum of the chosen coins adds u... | coin_exchange | subset_sum | 27 | [16, 2, 9, 19, 19, 19, 16, 19, 16, 12, 2, 9, 9, 11, 11, 10, 17] | 59 | 0.04360342025756836 | 17 | 49 | 49 | [[20, 19, 2, 12, 23, 18, 15, 13, 10, 6, 9, 4, 9, 16, 5, 8, 19, 6, 7, 2, 6, 15, 10, 9, 4, 6, 19, 10, 10, 16, 21, 17, 21, 16, 13, 6, 16, 8, 7, 11, 13, 7, 21, 15, 15, 6, 11, 19, 7]] | [[20, 19, 2, 12, 23, 18, 15, 13, 10, 6, 9, 4, 9, 16, 5, 8, 19, 6, 7, 2, 6, 15, 10, 9, 4, 6, 19, 10, 10, 16, 21, 17, 21, 16, 13, 6, 16, 8, 7, 11, 13, 7, 21, 15, 15, 6, 11, 19, 7], {"6": 6, "8": 6, "16": 4, "15": 11, "12": 3, "10": 5, "20": 14, "9": 3, "17": 8, "7": 5, "5": 5, "2": 1, "11": 4, "23": 18, "19": 3, "13": 13... | ["[20, 19, 2, 12, 23, 18, 15, 13, 10, 6, 9, 4, 9, 16, 5, 8, 19, 6, 7, 2, 6, 15, 10, 9, 4, 6, 19, 10, 10, 16, 21, 17, 21, 16, 13, 6, 16, 8, 7, 11, 13, 7, 21, 15, 15, 6, 11, 19, 7]", "{6: 6, 8: 6, 16: 4, 15: 11, 12: 3, 10: 5, 20: 14, 9: 3, 17: 8, 7: 5, 5: 5, 2: 1, 11: 4, 23: 18, 19: 3, 13: 13, 18: 6, 4: 3, 21: 20}", "216... |
13 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[1, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2]] | 18 | 1.4882152080535889 | 18 | 6 | 12 | [[["Green", "Blue", "Blue", "Green"], ["Red", "Green", "Red", "Blue"], ["Red", "Green", "Blue", "Red"]], 6] | [[["Green", "Blue", "Blue", "Green"], ["Red", "Green", "Red", "Blue"], ["Red", "Green", "Blue", "Red"]], 6] | ["[['Green', 'Blue', 'Blue', 'Green'], ['Red', 'Green', 'Red', 'Blue'], ['Red', 'Green', 'Blue', 'Red']]", "6"] |
13 | We have a 3x3 numerical grid, with numbers ranging from 21 to 59 (21 included in the range but 59 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 2, 46], [1, 0, 47], [1, 1, 44], [1, 2, 35], [2, 0, 48]] | 342 | 0.32321739196777344 | 5 | 38 | 9 | ["[['29', '45', ''], ['', '', ''], ['', '43', '34']]", 21, 59] | ["[['29', '45', ''], ['', '', ''], ['', '43', '34']]", 21, 59] | ["[['29', '45', ''], ['', '', ''], ['', '43', '34']]", "21", "59"] |
13 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 28 to 57. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 129, and sum of row 1 must be 133. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 1, 29], [0, 2, 30], [1, 1, 56], [1, 2, 43], [2, 0, 50], [2, 1, 44], [2, 2, 28]] | 355 | 2.4692792892456055 | 7 | 24 | 9 | ["[['41', '', ''], ['34', '', ''], ['', '', '']]", 3, 28, 57] | ["[['41', '', ''], ['34', '', ''], ['', '', '']]", 28, 57, [1, 2], [1, 2], [129], [133], 136] | ["[['41', '', ''], ['34', '', ''], ['', '', '']]", "28", "57", "[None, 129, None]", "[None, 133, None]", "136"] |
13 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[2, 1], [2, 4], [0, 2], [0, 4], [5, 4], [5, 1], [5, 0], [5, 1]] | 24 | 0.023777484893798828 | 8 | 30 | 12 | [[["Green", "Red", "Blue", "Blue"], [], ["Yellow", "Red", "Green", "Green"], [], [], ["Red", "Yellow", "Blue", "Yellow"]], 4, {"0": 4, "1": 2, "2": 2, "3": 7, "4": 4, "5": 5}] | [[["Green", "Red", "Blue", "Blue"], [], ["Yellow", "Red", "Green", "Green"], [], [], ["Red", "Yellow", "Blue", "Yellow"]], 4, {"0": 4, "1": 2, "2": 2, "3": 7, "4": 4, "5": 5}, 3] | ["[['Green', 'Red', 'Blue', 'Blue'], [], ['Yellow', 'Red', 'Green', 'Green'], [], [], ['Red', 'Yellow', 'Blue', 'Yellow']]", "{0: 4, 1: 2, 2: 2, 3: 7, 4: 4, 5: 5}", "4", "3"] |
13 | 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, 7) to his destination workshop at index (5, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 7], [2, 7], [2, 8], [1, 8], [0, 8], [0, 7], [0, 6], [1, 6], [1, 5], [2, 5], [2, 4], [3, 4], [4, 4], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]] | 161 | 0.020489215850830078 | 18 | 4 | 4 | [[["x", "x", "x", "x", "9", "x", "20", "3", "9"], ["17", "11", "17", "x", "9", "2", "7", "x", "15"], ["x", "4", "2", "19", "12", "6", "x", "4", "17"], ["15", "x", "x", "15", "11", "19", "x", "9", "5"], ["3", "9", "19", "15", "2", "x", "x", "18", "x"], ["19", "5", "9", "11", "9", "x", "x", "3", "x"], ["x", "x", "2", "8"... | [[["x", "x", "x", "x", "9", "x", "20", "3", "9"], ["17", "11", "17", "x", "9", "2", "7", "x", "15"], ["x", "4", "2", "19", "12", "6", "x", "4", "17"], ["15", "x", "x", "15", "11", "19", "x", "9", "5"], ["3", "9", "19", "15", "2", "x", "x", "18", "x"], ["19", "5", "9", "11", "9", "x", "x", "3", "x"], ["x", "x", "2", "8"... | ["[['x', 'x', 'x', 'x', '9', 'x', '20', '3', '9'], ['17', '11', '17', 'x', '9', '2', '7', 'x', '15'], ['x', '4', '2', '19', '12', '6', 'x', '4', '17'], ['15', 'x', 'x', '15', '11', '19', 'x', '9', '5'], ['3', '9', '19', '15', '2', 'x', 'x', '18', 'x'], ['19', '5', '9', '11', '9', 'x', 'x', '3', 'x'], ['x', 'x', '2', '8... |
13 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[1, 0], [1, 1], [1, 2], [2, 3], [2, 4], [2, 5], [3, 5], [4, 6], [5, 7], [5, 8]] | 10 | 0.029414653778076172 | 10 | 8 | 2 | ["[[0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0]]", 3] | ["[[0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0]]", [1, 0], [5, 8], 3] | ["[[0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0]]", "(1, 0)", "(5, 8)", "3"] |
13 | Given 5 labeled water jugs with capacities 57, 84, 47, 76, 85, 69 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 203, 217, 334 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water i... | water_jug | subset_sum | 4 | [["+", 47, 3], ["+", 76, 3], ["+", 85, 3], ["+", 57, 3], ["+", 69, 3], ["+", 85, 2], ["+", 85, 2], ["+", 47, 2], ["+", 47, 1], ["+", 57, 1], ["+", 84, 1], ["-", 69, 1], ["+", 84, 1]] | 13 | 0.028015613555908203 | 13 | 36 | 3 | [[57, 84, 47, 76, 85, 69], [203, 217, 334]] | [[57, 84, 47, 76, 85, 69], [203, 217, 334]] | ["[57, 84, 47, 76, 85, 69]", "[203, 217, 334]"] |
14 | 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 | 4 | [21, 45, 39, 21, 45, 19, 51, 28, 89, 43, 21, 39, 19, 45, 28, 51, 45, 28, 39, 19] | 20 | 0.045632362365722656 | 20 | 4 | 9 | [[[28, 51, 19], [89, "_", 21], [43, 39, 45]]] | [[[28, 51, 19], [89, "_", 21], [43, 39, 45]]] | ["[[28, 51, 19], [89, '_', 21], [43, 39, 45]]"] |
14 | 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 | 1 | ["down-right", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 12 | 0.1393892765045166 | 12 | 4 | 16 | [[["_", "a", "t", "n"], ["b", "i", "r", "n"], ["k", "r", "e", "y"], ["b", "a", "l", "i"]]] | [[["_", "a", "t", "n"], ["b", "i", "r", "n"], ["k", "r", "e", "y"], ["b", "a", "l", "i"]], ["ann", "birk", "trey", "bali"]] | ["[['_', 'a', 't', 'n'], ['b', 'i', 'r', 'n'], ['k', 'r', 'e', 'y'], ['b', 'a', 'l', 'i']]", "['ann', 'birk', 'trey', 'bali']"] |
14 | 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 | 10 | ["N", "U", "F", "H", "M", "Z", "H", "M"] | 8 | 0.027659177780151367 | 8 | 10 | 13 | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 0, 0, 0, 0]... | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 0, 0, 0, 0]... | ["[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 0, 0, 0, 0... |
14 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [9, 18, 7, 20, 4, 12, 5, 5, 18, 5, 2, 11, 5, 16, 19, 8, 10, 9, 12, 14, 17, 6, 14, 16, 20, 10, 10, 13, 4, 13, 7, 14, 14, 10, 2, 7, 14, 11, 16, 10, 10, 5, 14, 20, 4, 17], such that the sum of the chosen coins adds up to 206.... | coin_exchange | subset_sum | 28 | [12, 2, 9, 9, 4, 7, 13, 13, 12, 4, 7, 4, 7, 19, 18, 10, 11, 10, 2, 5, 11, 17] | 102 | 0.040293216705322266 | 22 | 46 | 46 | [[9, 18, 7, 20, 4, 12, 5, 5, 18, 5, 2, 11, 5, 16, 19, 8, 10, 9, 12, 14, 17, 6, 14, 16, 20, 10, 10, 13, 4, 13, 7, 14, 14, 10, 2, 7, 14, 11, 16, 10, 10, 5, 14, 20, 4, 17]] | [[9, 18, 7, 20, 4, 12, 5, 5, 18, 5, 2, 11, 5, 16, 19, 8, 10, 9, 12, 14, 17, 6, 14, 16, 20, 10, 10, 13, 4, 13, 7, 14, 14, 10, 2, 7, 14, 11, 16, 10, 10, 5, 14, 20, 4, 17], {"17": 16, "8": 8, "6": 6, "16": 12, "5": 4, "14": 12, "18": 9, "12": 1, "19": 12, "4": 2, "7": 3, "10": 7, "11": 7, "13": 6, "2": 1, "9": 1, "20": 10... | ["[9, 18, 7, 20, 4, 12, 5, 5, 18, 5, 2, 11, 5, 16, 19, 8, 10, 9, 12, 14, 17, 6, 14, 16, 20, 10, 10, 13, 4, 13, 7, 14, 14, 10, 2, 7, 14, 11, 16, 10, 10, 5, 14, 20, 4, 17]", "{17: 16, 8: 8, 6: 6, 16: 12, 5: 4, 14: 12, 18: 9, 12: 1, 19: 12, 4: 2, 7: 3, 10: 7, 11: 7, 13: 6, 2: 1, 9: 1, 20: 10}", "206"] |
14 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 2], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [0, 1], [0, 2], [1, 2], [1, 2], [1, 0], [2, 1], [2, 1]] | 18 | 1.1862623691558838 | 18 | 6 | 12 | [[["Green", "Blue", "Green", "Blue"], ["Red", "Green", "Red", "Red"], ["Green", "Blue", "Red", "Blue"]], 6] | [[["Green", "Blue", "Green", "Blue"], ["Red", "Green", "Red", "Red"], ["Green", "Blue", "Red", "Blue"]], 6] | ["[['Green', 'Blue', 'Green', 'Blue'], ['Red', 'Green', 'Red', 'Red'], ['Green', 'Blue', 'Red', 'Blue']]", "6"] |
14 | We have a 3x3 numerical grid, with numbers ranging from 11 to 49 (11 included in the range but 49 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 1, 22], [1, 0, 13], [1, 1, 15], [1, 2, 23], [2, 1, 14]] | 268 | 0.8595123291015625 | 5 | 38 | 9 | ["[['41', '', '21'], ['', '', ''], ['12', '', '42']]", 11, 49] | ["[['41', '', '21'], ['', '', ''], ['12', '', '42']]", 11, 49] | ["[['41', '', '21'], ['', '', ''], ['12', '', '42']]", "11", "49"] |
14 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 28 to 57. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 143, and sum of row 1 must be 134. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 28], [0, 2, 30], [1, 1, 56], [1, 2, 40], [2, 0, 45], [2, 1, 55], [2, 2, 29]] | 353 | 3.0488429069519043 | 7 | 24 | 9 | ["[['', '32', ''], ['38', '', ''], ['', '', '']]", 3, 28, 57] | ["[['', '32', ''], ['38', '', ''], ['', '', '']]", 28, 57, [1, 2], [1, 2], [143], [134], 131] | ["[['', '32', ''], ['38', '', ''], ['', '', '']]", "28", "57", "[None, 143, None]", "[None, 134, None]", "131"] |
14 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 1], [4, 1], [4, 1], [2, 3], [2, 3], [2, 3], [4, 5], [0, 4], [0, 5], [0, 4], [2, 5]] | 42 | 0.16206979751586914 | 11 | 30 | 12 | [[["Green", "Yellow", "Red", "Yellow"], [], ["Blue", "Blue", "Blue", "Red"], [], ["Green", "Green", "Red", "Yellow"], []], 4, {"0": 3, "1": 6, "2": 5, "3": 5, "4": 3, "5": 1}] | [[["Green", "Yellow", "Red", "Yellow"], [], ["Blue", "Blue", "Blue", "Red"], [], ["Green", "Green", "Red", "Yellow"], []], 4, {"0": 3, "1": 6, "2": 5, "3": 5, "4": 3, "5": 1}, 3] | ["[['Green', 'Yellow', 'Red', 'Yellow'], [], ['Blue', 'Blue', 'Blue', 'Red'], [], ['Green', 'Green', 'Red', 'Yellow'], []]", "{0: 3, 1: 6, 2: 5, 3: 5, 4: 3, 5: 1}", "4", "3"] |
14 | 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 (7, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 1], [3, 0], [4, 0], [5, 0], [6, 0], [6, 1], [6, 2], [7, 2], [7, 3], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [7, 8]] | 119 | 0.02022695541381836 | 16 | 4 | 4 | [[["x", "3", "13", "18", "x", "x", "3", "x", "x"], ["x", "3", "x", "x", "18", "1", "13", "x", "x"], ["x", "x", "x", "6", "x", "13", "x", "11", "1"], ["4", "3", "x", "x", "x", "x", "6", "6", "11"], ["14", "16", "x", "x", "x", "x", "x", "18", "11"], ["14", "x", "11", "x", "x", "4", "x", "1", "x"], ["18", "7", "1", "x", "... | [[["x", "3", "13", "18", "x", "x", "3", "x", "x"], ["x", "3", "x", "x", "18", "1", "13", "x", "x"], ["x", "x", "x", "6", "x", "13", "x", "11", "1"], ["4", "3", "x", "x", "x", "x", "6", "6", "11"], ["14", "16", "x", "x", "x", "x", "x", "18", "11"], ["14", "x", "11", "x", "x", "4", "x", "1", "x"], ["18", "7", "1", "x", "... | ["[['x', '3', '13', '18', 'x', 'x', '3', 'x', 'x'], ['x', '3', 'x', 'x', '18', '1', '13', 'x', 'x'], ['x', 'x', 'x', '6', 'x', '13', 'x', '11', '1'], ['4', '3', 'x', 'x', 'x', 'x', '6', '6', '11'], ['14', '16', 'x', 'x', 'x', 'x', 'x', '18', '11'], ['14', 'x', '11', 'x', 'x', '4', 'x', '1', 'x'], ['18', '7', '1', 'x', ... |
14 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[0, 7], [1, 7], [2, 7], [2, 6], [2, 5], [1, 4], [2, 3], [3, 2], [4, 2], [5, 2], [5, 1], [5, 0], [6, 0], [7, 0]] | 14 | 0.03127884864807129 | 14 | 8 | 2 | ["[[1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0]]", 3] | ["[[1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0]]", [0, 7], [7, 0], 3] | ["[[1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0]]", "(0, 7)", "(7, 0)", "3"] |
14 | Given 5 labeled water jugs with capacities 144, 37, 73, 79, 75, 74 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 236, 333, 386 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water ... | water_jug | subset_sum | 4 | [["+", 74, 3], ["+", 75, 3], ["+", 79, 3], ["+", 79, 3], ["+", 79, 3], ["+", 73, 2], ["+", 79, 2], ["+", 144, 2], ["+", 37, 2], ["+", 73, 1], ["+", 79, 1], ["+", 79, 1], ["-", 74, 1], ["+", 79, 1]] | 14 | 0.03917884826660156 | 14 | 36 | 3 | [[144, 37, 73, 79, 75, 74], [236, 333, 386]] | [[144, 37, 73, 79, 75, 74], [236, 333, 386]] | ["[144, 37, 73, 79, 75, 74]", "[236, 333, 386]"] |
15 | 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 | 4 | [73, 67, 82, 73, 67, 24, 47, 82, 62, 80, 82, 47, 24, 62, 73, 67, 62, 24, 47, 73, 67, 62] | 22 | 0.08130145072937012 | 22 | 4 | 9 | [[[80, 62, 76], [47, 67, 82], [24, 73, "_"]]] | [[[80, 62, 76], [47, 67, 82], [24, 73, "_"]]] | ["[[80, 62, 76], [47, 67, 82], [24, 73, '_']]"] |
15 | 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 | 1 | ["down-right", "down-left", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-left"] | 14 | 0.1922132968902588 | 14 | 4 | 16 | [[["a", "r", "_", "c"], ["h", "a", "v", "e"], ["a", "g", "s", "d"], ["b", "i", "t", "z"]]] | [[["a", "r", "_", "c"], ["h", "a", "v", "e"], ["a", "g", "s", "d"], ["b", "i", "t", "z"]], ["ric", "have", "sgad", "batz"]] | ["[['a', 'r', '_', 'c'], ['h', 'a', 'v', 'e'], ['a', 'g', 's', 'd'], ['b', 'i', 't', 'z']]", "['ric', 'have', 'sgad', 'batz']"] |
15 | 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 | 10 | ["E", "R", "T", "X", "W", "J", "A", "X", "W"] | 9 | 0.02704644203186035 | 9 | 10 | 13 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 1], [1, 1, 1, 0, 0, 1, 0, 1, 0, 0]... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 1], [1, 1, 1, 0, 0, 1, 0, 1, 0, 0]... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 1], [1, 1, 1, 0, 0, 1, 0, 1, 0, 0... |
15 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [1, 2, 17, 12, 7, 17, 2, 20, 4, 4, 17, 19, 15, 16, 18, 21, 18, 10, 3, 9, 12, 13, 8, 16, 9, 14, 13, 5, 13, 6, 20, 6, 13, 12, 8, 14, 15, 7, 10, 3, 16, 16, 9, 3, 2, 6, 9, 14, 16, 20, 11, 4, 17], such that the sum of the chose... | coin_exchange | subset_sum | 29 | [3, 3, 11, 19, 12, 2, 9, 9, 9, 9, 13, 12, 13, 13, 13, 21, 12, 15, 15] | 74 | 0.046939849853515625 | 19 | 53 | 53 | [[1, 2, 17, 12, 7, 17, 2, 20, 4, 4, 17, 19, 15, 16, 18, 21, 18, 10, 3, 9, 12, 13, 8, 16, 9, 14, 13, 5, 13, 6, 20, 6, 13, 12, 8, 14, 15, 7, 10, 3, 16, 16, 9, 3, 2, 6, 9, 14, 16, 20, 11, 4, 17]] | [[1, 2, 17, 12, 7, 17, 2, 20, 4, 4, 17, 19, 15, 16, 18, 21, 18, 10, 3, 9, 12, 13, 8, 16, 9, 14, 13, 5, 13, 6, 20, 6, 13, 12, 8, 14, 15, 7, 10, 3, 16, 16, 9, 3, 2, 6, 9, 14, 16, 20, 11, 4, 17], {"8": 5, "5": 2, "19": 2, "4": 4, "9": 2, "3": 1, "2": 2, "12": 1, "13": 6, "6": 5, "11": 1, "17": 14, "7": 4, "16": 13, "21": ... | ["[1, 2, 17, 12, 7, 17, 2, 20, 4, 4, 17, 19, 15, 16, 18, 21, 18, 10, 3, 9, 12, 13, 8, 16, 9, 14, 13, 5, 13, 6, 20, 6, 13, 12, 8, 14, 15, 7, 10, 3, 16, 16, 9, 3, 2, 6, 9, 14, 16, 20, 11, 4, 17]", "{8: 5, 5: 2, 19: 2, 4: 4, 9: 2, 3: 1, 2: 2, 12: 1, 13: 6, 6: 5, 11: 1, 17: 14, 7: 4, 16: 13, 21: 10, 14: 13, 1: 1, 18: 12, 1... |
15 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [0, 2]] | 14 | 0.14858675003051758 | 14 | 6 | 12 | [[["Blue", "Red", "Red", "Blue"], ["Green", "Green", "Red", "Red"], ["Green", "Green", "Blue", "Blue"]], 6] | [[["Blue", "Red", "Red", "Blue"], ["Green", "Green", "Red", "Red"], ["Green", "Green", "Blue", "Blue"]], 6] | ["[['Blue', 'Red', 'Red', 'Blue'], ['Green', 'Green', 'Red', 'Red'], ['Green', 'Green', 'Blue', 'Blue']]", "6"] |
15 | We have a 3x3 numerical grid, with numbers ranging from 18 to 56 (18 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 or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 0, 18], [0, 1, 19], [1, 1, 25], [1, 2, 24], [2, 0, 32]] | 252 | 0.17498183250427246 | 5 | 38 | 9 | ["[['', '', '23'], ['31', '', ''], ['', '42', '51']]", 18, 56] | ["[['', '', '23'], ['31', '', ''], ['', '42', '51']]", 18, 56] | ["[['', '', '23'], ['31', '', ''], ['', '42', '51']]", "18", "56"] |
15 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 48 to 77. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 190, and sum of row 1 must be 167. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 49], [0, 1, 51], [0, 2, 52], [1, 0, 48], [1, 1, 64], [2, 0, 56], [2, 1, 75], [2, 2, 50]] | 500 | 37.735610485076904 | 8 | 24 | 9 | ["[['', '', ''], ['', '', '55'], ['', '', '']]", 3, 48, 77] | ["[['', '', ''], ['', '', '55'], ['', '', '']]", 48, 77, [1, 2], [1, 2], [190], [167], 172] | ["[['', '', ''], ['', '', '55'], ['', '', '']]", "48", "77", "[None, 190, None]", "[None, 167, None]", "172"] |
15 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[4, 0], [5, 0], [3, 1], [5, 2], [5, 1], [3, 2], [3, 2], [4, 5], [4, 0], [1, 3], [1, 3], [4, 5]] | 45 | 0.027285099029541016 | 12 | 30 | 12 | [[[], [], [], ["Red", "Green", "Green", "Red"], ["Yellow", "Blue", "Yellow", "Blue"], ["Yellow", "Green", "Red", "Blue"]], 4, {"0": 4, "1": 5, "2": 5, "3": 2, "4": 5, "5": 2}] | [[[], [], [], ["Red", "Green", "Green", "Red"], ["Yellow", "Blue", "Yellow", "Blue"], ["Yellow", "Green", "Red", "Blue"]], 4, {"0": 4, "1": 5, "2": 5, "3": 2, "4": 5, "5": 2}, 3] | ["[[], [], [], ['Red', 'Green', 'Green', 'Red'], ['Yellow', 'Blue', 'Yellow', 'Blue'], ['Yellow', 'Green', 'Red', 'Blue']]", "{0: 4, 1: 5, 2: 5, 3: 2, 4: 5, 5: 2}", "4", "3"] |
15 | 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, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[3, 1], [2, 1], [3, 1], [4, 1], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8]] | 109 | 0.020708322525024414 | 12 | 4 | 4 | [[["4", "13", "x", "9", "x", "x", "x", "x", "x"], ["1", "11", "x", "16", "5", "7", "12", "16", "x"], ["12", "11", "x", "14", "x", "x", "12", "x", "3"], ["9", "11", "x", "9", "10", "x", "8", "x", "x"], ["20", "2", "x", "1", "16", "12", "18", "17", "10"], ["10", "13", "4", "15", "13", "2", "20", "3", "15"], ["x", "6", "1... | [[["4", "13", "x", "9", "x", "x", "x", "x", "x"], ["1", "11", "x", "16", "5", "7", "12", "16", "x"], ["12", "11", "x", "14", "x", "x", "12", "x", "3"], ["9", "11", "x", "9", "10", "x", "8", "x", "x"], ["20", "2", "x", "1", "16", "12", "18", "17", "10"], ["10", "13", "4", "15", "13", "2", "20", "3", "15"], ["x", "6", "1... | ["[['4', '13', 'x', '9', 'x', 'x', 'x', 'x', 'x'], ['1', '11', 'x', '16', '5', '7', '12', '16', 'x'], ['12', '11', 'x', '14', 'x', 'x', '12', 'x', '3'], ['9', '11', 'x', '9', '10', 'x', '8', 'x', 'x'], ['20', '2', 'x', '1', '16', '12', '18', '17', '10'], ['10', '13', '4', '15', '13', '2', '20', '3', '15'], ['x', '6', '... |
15 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 9x9. 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 n... | trampoline_matrix | pathfinding | 9 | [[0, 7], [0, 6], [1, 6], [2, 6], [2, 5], [3, 5], [3, 4], [4, 3], [5, 3], [6, 2], [7, 1]] | 11 | 0.029547452926635742 | 11 | 8 | 2 | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0]]", 3] | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0]]", [0, 7], [7, 1], 3] | ["[[1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0]]", "(0, 7)", "(7, 1)", "3"] |
15 | Given 5 labeled water jugs with capacities 19, 50, 12, 63, 143, 13 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 160, 170, 330 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water ... | water_jug | subset_sum | 4 | [["+", 63, 3], ["+", 143, 3], ["-", 19, 3], ["+", 143, 3], ["+", 63, 2], ["+", 63, 2], ["-", 19, 2], ["+", 63, 2], ["+", 143, 1], ["-", 63, 1], ["-", 63, 1], ["+", 143, 1]] | 12 | 0.03795623779296875 | 12 | 36 | 3 | [[19, 50, 12, 63, 143, 13], [160, 170, 330]] | [[19, 50, 12, 63, 143, 13], [160, 170, 330]] | ["[19, 50, 12, 63, 143, 13]", "[160, 170, 330]"] |
16 | 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 | 4 | [53, 59, 93, 77, 81, 85, 98, 74, 85, 98, 77, 93, 59, 77, 93, 81, 98, 93, 77, 53] | 20 | 0.028780221939086914 | 20 | 4 | 9 | [[[77, 81, 74], [93, 85, 98], [59, 53, "_"]]] | [[[77, 81, 74], [93, 85, 98], [59, 53, "_"]]] | ["[[77, 81, 74], [93, 85, 98], [59, 53, '_']]"] |
16 | 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 | 1 | ["up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 8 | 0.13991522789001465 | 8 | 4 | 16 | [[["o", "g", "h", "a"], ["y", "c", "d", "l"], ["o", "a", "_", "l"], ["a", "w", "l", "e"]]] | [[["o", "g", "h", "a"], ["y", "c", "d", "l"], ["o", "a", "_", "l"], ["a", "w", "l", "e"]], ["goa", "yodh", "wall", "acle"]] | ["[['o', 'g', 'h', 'a'], ['y', 'c', 'd', 'l'], ['o', 'a', '_', 'l'], ['a', 'w', 'l', 'e']]", "['goa', 'yodh', 'wall', 'acle']"] |
16 | 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 | 10 | ["S", "A", "J", "P", "I", "C", "G", "V", "P", "Y", "G"] | 11 | 0.030188560485839844 | 11 | 10 | 13 | [[[0, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0]... | [[[0, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0]... | ["[[0, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0... |
16 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [11, 13, 22, 11, 16, 20, 10, 10, 17, 21, 6, 6, 15, 15, 21, 6, 4, 16, 9, 11, 3, 13, 2, 9, 11, 1, 7, 2, 2, 12, 5, 2, 11, 16, 20, 9, 2, 4, 10, 17, 11, 22, 11, 2, 18, 23, 15, 22, 11, 15, 20, 9], such that the sum of the chosen... | coin_exchange | subset_sum | 30 | [9, 9, 9, 21, 2, 13, 13, 15, 15, 15, 15, 21, 16, 12, 6, 9, 6, 17] | 43 | 0.04377126693725586 | 18 | 52 | 52 | [[11, 13, 22, 11, 16, 20, 10, 10, 17, 21, 6, 6, 15, 15, 21, 6, 4, 16, 9, 11, 3, 13, 2, 9, 11, 1, 7, 2, 2, 12, 5, 2, 11, 16, 20, 9, 2, 4, 10, 17, 11, 22, 11, 2, 18, 23, 15, 22, 11, 15, 20, 9]] | [[11, 13, 22, 11, 16, 20, 10, 10, 17, 21, 6, 6, 15, 15, 21, 6, 4, 16, 9, 11, 3, 13, 2, 9, 11, 1, 7, 2, 2, 12, 5, 2, 11, 16, 20, 9, 2, 4, 10, 17, 11, 22, 11, 2, 18, 23, 15, 22, 11, 15, 20, 9], {"6": 2, "11": 9, "3": 3, "15": 2, "9": 1, "18": 13, "22": 13, "16": 5, "21": 2, "5": 2, "12": 4, "7": 5, "4": 3, "13": 2, "1": ... | ["[11, 13, 22, 11, 16, 20, 10, 10, 17, 21, 6, 6, 15, 15, 21, 6, 4, 16, 9, 11, 3, 13, 2, 9, 11, 1, 7, 2, 2, 12, 5, 2, 11, 16, 20, 9, 2, 4, 10, 17, 11, 22, 11, 2, 18, 23, 15, 22, 11, 15, 20, 9]", "{6: 2, 11: 9, 3: 3, 15: 2, 9: 1, 18: 13, 22: 13, 16: 5, 21: 2, 5: 2, 12: 4, 7: 5, 4: 3, 13: 2, 1: 1, 20: 14, 2: 1, 10: 4, 23:... |
16 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 0], [2, 1], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0]] | 23 | 8.691032648086548 | 23 | 6 | 12 | [[["Red", "Green", "Green", "Blue"], ["Red", "Green", "Red", "Blue"], ["Blue", "Red", "Green", "Blue"]], 6] | [[["Red", "Green", "Green", "Blue"], ["Red", "Green", "Red", "Blue"], ["Blue", "Red", "Green", "Blue"]], 6] | ["[['Red', 'Green', 'Green', 'Blue'], ['Red', 'Green', 'Red', 'Blue'], ['Blue', 'Red', 'Green', 'Blue']]", "6"] |
16 | We have a 3x3 numerical grid, with numbers ranging from 28 to 66 (28 included in the range but 66 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 1, 29], [0, 2, 28], [1, 0, 38], [1, 1, 31], [1, 2, 30], [2, 1, 45]] | 342 | 0.1785869598388672 | 6 | 38 | 9 | ["[['37', '', ''], ['', '', ''], ['44', '', '61']]", 28, 66] | ["[['37', '', ''], ['', '', ''], ['44', '', '61']]", 28, 66] | ["[['37', '', ''], ['', '', ''], ['44', '', '61']]", "28", "66"] |
16 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 48 to 77. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 200, and sum of row 1 must be 191. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 48], [0, 1, 51], [0, 2, 53], [1, 0, 49], [1, 1, 76], [2, 0, 72], [2, 1, 73], [2, 2, 50]] | 538 | 89.56194949150085 | 8 | 24 | 9 | ["[['', '', ''], ['', '', '66'], ['', '', '']]", 3, 48, 77] | ["[['', '', ''], ['', '', '66'], ['', '', '']]", 48, 77, [1, 2], [1, 2], [200], [191], 201] | ["[['', '', ''], ['', '', '66'], ['', '', '']]", "48", "77", "[None, 200, None]", "[None, 191, None]", "201"] |
16 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[2, 3], [5, 3], [5, 3], [5, 4], [2, 1], [2, 1], [5, 1], [2, 4], [0, 2], [0, 2], [0, 4], [0, 2]] | 39 | 0.09036970138549805 | 12 | 30 | 12 | [[["Green", "Green", "Blue", "Green"], [], ["Yellow", "Red", "Red", "Blue"], [], [], ["Yellow", "Yellow", "Blue", "Red"]], 4, {"0": 6, "1": 5, "2": 2, "3": 3, "4": 3, "5": 6}] | [[["Green", "Green", "Blue", "Green"], [], ["Yellow", "Red", "Red", "Blue"], [], [], ["Yellow", "Yellow", "Blue", "Red"]], 4, {"0": 6, "1": 5, "2": 2, "3": 3, "4": 3, "5": 6}, 3] | ["[['Green', 'Green', 'Blue', 'Green'], [], ['Yellow', 'Red', 'Red', 'Blue'], [], [], ['Yellow', 'Yellow', 'Blue', 'Red']]", "{0: 6, 1: 5, 2: 2, 3: 3, 4: 3, 5: 6}", "4", "3"] |
16 | 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, 1) to his destination workshop at index (3, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 1], [6, 1], [5, 1], [5, 2], [4, 2], [4, 3], [3, 3], [2, 3], [1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 8], [1, 9], [2, 9], [3, 9]] | 187 | 0.020601749420166016 | 19 | 4 | 4 | [[["x", "x", "x", "16", "1", "13", "17", "7", "14", "x"], ["x", "10", "x", "12", "x", "13", "x", "8", "19", "4"], ["9", "13", "x", "13", "x", "x", "15", "x", "x", "16"], ["3", "8", "x", "16", "12", "x", "x", "x", "x", "13"], ["13", "x", "1", "15", "18", "8", "x", "10", "x", "x"], ["8", "1", "2", "14", "x", "8", "x", "4... | [[["x", "x", "x", "16", "1", "13", "17", "7", "14", "x"], ["x", "10", "x", "12", "x", "13", "x", "8", "19", "4"], ["9", "13", "x", "13", "x", "x", "15", "x", "x", "16"], ["3", "8", "x", "16", "12", "x", "x", "x", "x", "13"], ["13", "x", "1", "15", "18", "8", "x", "10", "x", "x"], ["8", "1", "2", "14", "x", "8", "x", "4... | ["[['x', 'x', 'x', '16', '1', '13', '17', '7', '14', 'x'], ['x', '10', 'x', '12', 'x', '13', 'x', '8', '19', '4'], ['9', '13', 'x', '13', 'x', 'x', '15', 'x', 'x', '16'], ['3', '8', 'x', '16', '12', 'x', 'x', 'x', 'x', '13'], ['13', 'x', '1', '15', '18', '8', 'x', '10', 'x', 'x'], ['8', '1', '2', '14', 'x', '8', 'x', '... |
16 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. 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 | 10 | [[0, 1], [0, 2], [0, 3], [1, 3], [1, 4], [2, 5], [2, 6], [3, 6], [3, 7], [4, 7], [5, 8], [6, 9]] | 12 | 0.03220367431640625 | 12 | 8 | 2 | ["[[1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1... | ["[[1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1... | ["[[1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1... |
16 | Given 5 labeled water jugs with capacities 102, 130, 82, 131, 133, 116 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 265, 368, 378 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wa... | water_jug | subset_sum | 4 | [["+", 116, 3], ["+", 131, 3], ["+", 131, 3], ["+", 102, 2], ["+", 133, 2], ["+", 133, 2], ["+", 130, 1], ["+", 133, 1], ["-", 131, 1], ["+", 133, 1]] | 10 | 0.033504486083984375 | 10 | 36 | 3 | [[102, 130, 82, 131, 133, 116], [265, 368, 378]] | [[102, 130, 82, 131, 133, 116], [265, 368, 378]] | ["[102, 130, 82, 131, 133, 116]", "[265, 368, 378]"] |
17 | 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 | 4 | [53, 49, 22, 99, 18, 27, 99, 18, 49, 22, 18, 49, 9, 53, 22, 9, 27, 79, 53, 22] | 20 | 0.027205705642700195 | 20 | 4 | 9 | [[[27, 18, 79], [22, 99, 9], [49, 53, "_"]]] | [[[27, 18, 79], [22, 99, 9], [49, 53, "_"]]] | ["[[27, 18, 79], [22, 99, 9], [49, 53, '_']]"] |
17 | 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 | 1 | ["down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 16 | 0.18766021728515625 | 16 | 4 | 16 | [[["e", "h", "r", "y"], ["w", "f", "r", "r"], ["_", "u", "d", "d"], ["f", "a", "i", "b"]]] | [[["e", "h", "r", "y"], ["w", "f", "r", "r"], ["_", "u", "d", "d"], ["f", "a", "i", "b"]], ["hay", "werf", "rudd", "frib"]] | ["[['e', 'h', 'r', 'y'], ['w', 'f', 'r', 'r'], ['_', 'u', 'd', 'd'], ['f', 'a', 'i', 'b']]", "['hay', 'werf', 'rudd', 'frib']"] |
17 | 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 | 10 | ["V", "H", "T", "Y", "I", "E", "Y", "I"] | 8 | 0.026442289352416992 | 8 | 10 | 13 | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0]... | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0]... | ["[[0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0... |
17 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [4, 2, 18, 5, 18, 13, 22, 15, 5, 14, 15, 21, 23, 13, 19, 22, 6, 12, 19, 8, 15, 8, 12, 15, 11, 17, 7, 19, 23, 9, 3, 4, 12, 10, 11, 2, 22, 19, 19, 11, 18, 6, 10, 23, 20, 1, 6, 23, 8, 6], such that the sum of the chosen coins... | coin_exchange | subset_sum | 31 | [20, 18, 6, 4, 13, 6, 4, 13, 6, 19, 18, 19, 18, 8, 15, 14, 15, 17] | 61 | 0.06324076652526855 | 18 | 50 | 50 | [[4, 2, 18, 5, 18, 13, 22, 15, 5, 14, 15, 21, 23, 13, 19, 22, 6, 12, 19, 8, 15, 8, 12, 15, 11, 17, 7, 19, 23, 9, 3, 4, 12, 10, 11, 2, 22, 19, 19, 11, 18, 6, 10, 23, 20, 1, 6, 23, 8, 6]] | [[4, 2, 18, 5, 18, 13, 22, 15, 5, 14, 15, 21, 23, 13, 19, 22, 6, 12, 19, 8, 15, 8, 12, 15, 11, 17, 7, 19, 23, 9, 3, 4, 12, 10, 11, 2, 22, 19, 19, 11, 18, 6, 10, 23, 20, 1, 6, 23, 8, 6], {"21": 18, "1": 1, "13": 3, "20": 2, "19": 7, "5": 4, "18": 4, "4": 1, "15": 5, "12": 7, "17": 5, "22": 10, "8": 3, "7": 5, "23": 11, ... | ["[4, 2, 18, 5, 18, 13, 22, 15, 5, 14, 15, 21, 23, 13, 19, 22, 6, 12, 19, 8, 15, 8, 12, 15, 11, 17, 7, 19, 23, 9, 3, 4, 12, 10, 11, 2, 22, 19, 19, 11, 18, 6, 10, 23, 20, 1, 6, 23, 8, 6]", "{21: 18, 1: 1, 13: 3, 20: 2, 19: 7, 5: 4, 18: 4, 4: 1, 15: 5, 12: 7, 17: 5, 22: 10, 8: 3, 7: 5, 23: 11, 9: 7, 10: 8, 3: 2, 14: 4, 6... |
17 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[0, 2], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [0, 1], [0, 2], [0, 1], [2, 0]] | 17 | 0.8329384326934814 | 17 | 6 | 12 | [[["Blue", "Red", "Blue", "Red"], ["Green", "Red", "Green", "Green"], ["Blue", "Green", "Blue", "Red"]], 6] | [[["Blue", "Red", "Blue", "Red"], ["Green", "Red", "Green", "Green"], ["Blue", "Green", "Blue", "Red"]], 6] | ["[['Blue', 'Red', 'Blue', 'Red'], ['Green', 'Red', 'Green', 'Green'], ['Blue', 'Green', 'Blue', 'Red']]", "6"] |
17 | We have a 3x3 numerical grid, with numbers ranging from 38 to 76 (38 included in the range but 76 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 0, 43], [1, 0, 45], [1, 1, 44], [1, 2, 39], [2, 0, 64], [2, 2, 40]] | 367 | 0.9439022541046143 | 6 | 38 | 9 | ["[['', '42', '38'], ['', '', ''], ['', '63', '']]", 38, 76] | ["[['', '42', '38'], ['', '', ''], ['', '63', '']]", 38, 76] | ["[['', '42', '38'], ['', '', ''], ['', '63', '']]", "38", "76"] |
17 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 48 to 77. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 166, and sum of row 1 must be 192. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 49], [0, 2, 51], [1, 0, 53], [1, 1, 66], [1, 2, 73], [2, 0, 67], [2, 1, 48], [2, 2, 50]] | 509 | 26.031718254089355 | 8 | 29 | 9 | ["[['', '52', ''], ['', '', ''], ['', '', '']]", 3, 48, 77] | ["[['', '52', ''], ['', '', ''], ['', '', '']]", 48, 77, [1, 2], [1, 2], [166], [192], 184] | ["[['', '52', ''], ['', '', ''], ['', '', '']]", "48", "77", "[None, 166, None]", "[None, 192, None]", "184"] |
17 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 1], [0, 3], [0, 5], [2, 3], [4, 1], [4, 1], [2, 0], [2, 0], [4, 2], [5, 2], [3, 4], [3, 4]] | 39 | 0.03980541229248047 | 12 | 30 | 12 | [[["Blue", "Red", "Green", "Yellow"], [], ["Red", "Yellow", "Yellow", "Green"], [], ["Blue", "Blue", "Green", "Red"], []], 4, {"0": 2, "1": 3, "2": 3, "3": 6, "4": 1, "5": 6}] | [[["Blue", "Red", "Green", "Yellow"], [], ["Red", "Yellow", "Yellow", "Green"], [], ["Blue", "Blue", "Green", "Red"], []], 4, {"0": 2, "1": 3, "2": 3, "3": 6, "4": 1, "5": 6}, 3] | ["[['Blue', 'Red', 'Green', 'Yellow'], [], ['Red', 'Yellow', 'Yellow', 'Green'], [], ['Blue', 'Blue', 'Green', 'Red'], []]", "{0: 2, 1: 3, 2: 3, 3: 6, 4: 1, 5: 6}", "4", "3"] |
17 | 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 (7, 9) to his destination workshop at index (3, 2), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[7, 9], [8, 9], [9, 9], [9, 8], [9, 7], [9, 6], [9, 5], [8, 5], [8, 4], [8, 3], [7, 3], [7, 2], [6, 2], [5, 2], [4, 2], [3, 2]] | 129 | 0.028354406356811523 | 16 | 4 | 4 | [[["16", "2", "16", "x", "4", "x", "x", "1", "16", "x"], ["x", "x", "19", "x", "3", "x", "5", "x", "x", "x"], ["x", "x", "x", "3", "x", "x", "2", "x", "10", "x"], ["11", "5", "20", "x", "1", "3", "1", "x", "9", "x"], ["x", "x", "8", "19", "x", "16", "9", "x", "16", "15"], ["x", "3", "5", "10", "x", "x", "x", "4", "1", ... | [[["16", "2", "16", "x", "4", "x", "x", "1", "16", "x"], ["x", "x", "19", "x", "3", "x", "5", "x", "x", "x"], ["x", "x", "x", "3", "x", "x", "2", "x", "10", "x"], ["11", "5", "20", "x", "1", "3", "1", "x", "9", "x"], ["x", "x", "8", "19", "x", "16", "9", "x", "16", "15"], ["x", "3", "5", "10", "x", "x", "x", "4", "1", ... | ["[['16', '2', '16', 'x', '4', 'x', 'x', '1', '16', 'x'], ['x', 'x', '19', 'x', '3', 'x', '5', 'x', 'x', 'x'], ['x', 'x', 'x', '3', 'x', 'x', '2', 'x', '10', 'x'], ['11', '5', '20', 'x', '1', '3', '1', 'x', '9', 'x'], ['x', 'x', '8', '19', 'x', '16', '9', 'x', '16', '15'], ['x', '3', '5', '10', 'x', 'x', 'x', '4', '1',... |
17 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. 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 | 10 | [[0, 4], [1, 4], [2, 5], [2, 6], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 8], [9, 8]] | 11 | 0.0298614501953125 | 11 | 8 | 2 | ["[[0, 1, 1, 1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0... | ["[[0, 1, 1, 1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0... | ["[[0, 1, 1, 1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0... |
17 | Given 5 labeled water jugs with capacities 143, 117, 116, 103, 84, 87 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 398, 440, 440 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wat... | water_jug | subset_sum | 4 | [["+", 103, 3], ["+", 117, 3], ["+", 117, 3], ["+", 103, 3], ["+", 103, 2], ["+", 117, 2], ["+", 117, 2], ["+", 103, 2], ["+", 84, 1], ["+", 87, 1], ["+", 143, 1], ["+", 84, 1]] | 12 | 0.03967571258544922 | 12 | 36 | 3 | [[143, 117, 116, 103, 84, 87], [398, 440, 440]] | [[143, 117, 116, 103, 84, 87], [398, 440, 440]] | ["[143, 117, 116, 103, 84, 87]", "[398, 440, 440]"] |
18 | 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 | 4 | [83, 96, 52, 88, 98, 52, 96, 85, 88, 96, 85, 83, 80, 50, 52, 85, 83, 80] | 18 | 0.027386188507080078 | 18 | 4 | 9 | [[[88, 52, 85], [98, 96, 83], [50, 80, "_"]]] | [[[88, 52, 85], [98, 96, 83], [50, 80, "_"]]] | ["[[88, 52, 85], [98, 96, 83], [50, 80, '_']]"] |
18 | 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 | 1 | ["down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 12 | 0.20071721076965332 | 12 | 4 | 16 | [[["o", "m", "y", "i"], ["g", "d", "o", "e"], ["_", "o", "b", "d"], ["p", "o", "c", "k"]]] | [[["o", "m", "y", "i"], ["g", "d", "o", "e"], ["_", "o", "b", "d"], ["p", "o", "c", "k"]], ["moi", "good", "boyd", "peck"]] | ["[['o', 'm', 'y', 'i'], ['g', 'd', 'o', 'e'], ['_', 'o', 'b', 'd'], ['p', 'o', 'c', 'k']]", "['moi', 'good', 'boyd', 'peck']"] |
18 | 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 | 11 | ["Q", "F", "D", "Y", "N", "C", "K", "H", "Y", "R", "J", "K"] | 12 | 0.049555063247680664 | 12 | 11 | 14 | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0,... | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0,... | ["[[0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0... |
18 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [10, 5, 6, 2, 16, 19, 18, 5, 11, 12, 11, 7, 13, 19, 11, 12, 8, 17, 5, 18, 3, 12, 10, 14, 20, 18, 10, 11, 20, 13, 8, 8, 2, 7, 17, 10, 7, 21, 9, 20, 17, 1, 8, 19, 17, 16, 17, 10, 20, 8, 16, 14, 9], such that the sum of the c... | coin_exchange | subset_sum | 32 | [18, 10, 13, 10, 13, 10, 6, 7, 7, 7, 19, 18, 16, 10, 19, 18, 10] | 63 | 0.049751996994018555 | 17 | 53 | 53 | [[10, 5, 6, 2, 16, 19, 18, 5, 11, 12, 11, 7, 13, 19, 11, 12, 8, 17, 5, 18, 3, 12, 10, 14, 20, 18, 10, 11, 20, 13, 8, 8, 2, 7, 17, 10, 7, 21, 9, 20, 17, 1, 8, 19, 17, 16, 17, 10, 20, 8, 16, 14, 9]] | [[10, 5, 6, 2, 16, 19, 18, 5, 11, 12, 11, 7, 13, 19, 11, 12, 8, 17, 5, 18, 3, 12, 10, 14, 20, 18, 10, 11, 20, 13, 8, 8, 2, 7, 17, 10, 7, 21, 9, 20, 17, 1, 8, 19, 17, 16, 17, 10, 20, 8, 16, 14, 9], {"7": 2, "3": 2, "18": 1, "13": 3, "2": 2, "19": 17, "16": 6, "10": 1, "9": 9, "12": 7, "8": 7, "6": 3, "21": 18, "11": 10,... | ["[10, 5, 6, 2, 16, 19, 18, 5, 11, 12, 11, 7, 13, 19, 11, 12, 8, 17, 5, 18, 3, 12, 10, 14, 20, 18, 10, 11, 20, 13, 8, 8, 2, 7, 17, 10, 7, 21, 9, 20, 17, 1, 8, 19, 17, 16, 17, 10, 20, 8, 16, 14, 9]", "{7: 2, 3: 2, 18: 1, 13: 3, 2: 2, 19: 17, 16: 6, 10: 1, 9: 9, 12: 7, 8: 7, 6: 3, 21: 18, 11: 10, 14: 13, 1: 1, 5: 5, 20: ... |
18 | The game of 'Sort It' begins with 3 tubes, each filled with 4 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 | 7 | [[2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2]] | 16 | 0.4702601432800293 | 16 | 6 | 12 | [[["Green", "Green", "Red", "Blue"], ["Red", "Red", "Blue", "Green"], ["Red", "Green", "Blue", "Blue"]], 6] | [[["Green", "Green", "Red", "Blue"], ["Red", "Red", "Blue", "Green"], ["Red", "Green", "Blue", "Blue"]], 6] | ["[['Green', 'Green', 'Red', 'Blue'], ['Red', 'Red', 'Blue', 'Green'], ['Red', 'Green', 'Blue', 'Blue']]", "6"] |
18 | We have a 3x3 numerical grid, with numbers ranging from 16 to 54 (16 included in the range but 54 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 2, 18], [1, 0, 22], [1, 1, 21], [1, 2, 19], [2, 0, 45], [2, 2, 20]] | 165 | 1.0585572719573975 | 6 | 38 | 9 | ["[['16', '17', ''], ['', '', ''], ['', '44', '']]", 16, 54] | ["[['16', '17', ''], ['', '', ''], ['', '44', '']]", 16, 54] | ["[['16', '17', ''], ['', '', ''], ['', '44', '']]", "16", "54"] |
18 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 48 to 77. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 191, and sum of row 1 must be 194. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 49], [0, 1, 48], [0, 2, 51], [1, 0, 52], [1, 1, 73], [1, 2, 69], [2, 0, 62], [2, 2, 50]] | 524 | 7.050852060317993 | 8 | 29 | 9 | ["[['', '', ''], ['', '', ''], ['', '70', '']]", 3, 48, 77] | ["[['', '', ''], ['', '', ''], ['', '70', '']]", 48, 77, [1, 2], [1, 2], [191], [194], 186] | ["[['', '', ''], ['', '', ''], ['', '70', '']]", "48", "77", "[None, 191, None]", "[None, 194, None]", "186"] |
18 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 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 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[2, 1], [3, 0], [5, 0], [3, 4], [3, 4], [2, 3], [2, 4], [5, 1], [5, 0], [1, 5], [1, 5], [3, 2], [3, 2]] | 73 | 0.037363290786743164 | 13 | 30 | 12 | [[[], [], ["Blue", "Green", "Yellow", "Green"], ["Red", "Yellow", "Yellow", "Green"], [], ["Red", "Blue", "Red", "Blue"]], 4, {"0": 7, "1": 6, "2": 2, "3": 7, "4": 7, "5": 4}] | [[[], [], ["Blue", "Green", "Yellow", "Green"], ["Red", "Yellow", "Yellow", "Green"], [], ["Red", "Blue", "Red", "Blue"]], 4, {"0": 7, "1": 6, "2": 2, "3": 7, "4": 7, "5": 4}, 3] | ["[[], [], ['Blue', 'Green', 'Yellow', 'Green'], ['Red', 'Yellow', 'Yellow', 'Green'], [], ['Red', 'Blue', 'Red', 'Blue']]", "{0: 7, 1: 6, 2: 2, 3: 7, 4: 7, 5: 4}", "4", "3"] |
18 | 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 (1, 8) to his destination workshop at index (4, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[1, 8], [2, 8], [2, 7], [2, 6], [3, 6], [3, 5], [4, 5], [5, 5], [4, 5], [4, 4], [4, 3], [4, 2], [4, 1]] | 126 | 0.026239633560180664 | 13 | 4 | 4 | [[["13", "x", "x", "x", "x", "x", "8", "x", "x", "6"], ["x", "x", "x", "8", "10", "x", "17", "x", "15", "14"], ["x", "6", "x", "x", "x", "16", "12", "7", "8", "11"], ["x", "15", "x", "1", "11", "19", "9", "17", "x", "x"], ["18", "20", "16", "19", "12", "1", "x", "x", "x", "5"], ["11", "x", "18", "14", "x", "2", "x", "9... | [[["13", "x", "x", "x", "x", "x", "8", "x", "x", "6"], ["x", "x", "x", "8", "10", "x", "17", "x", "15", "14"], ["x", "6", "x", "x", "x", "16", "12", "7", "8", "11"], ["x", "15", "x", "1", "11", "19", "9", "17", "x", "x"], ["18", "20", "16", "19", "12", "1", "x", "x", "x", "5"], ["11", "x", "18", "14", "x", "2", "x", "9... | ["[['13', 'x', 'x', 'x', 'x', 'x', '8', 'x', 'x', '6'], ['x', 'x', 'x', '8', '10', 'x', '17', 'x', '15', '14'], ['x', '6', 'x', 'x', 'x', '16', '12', '7', '8', '11'], ['x', '15', 'x', '1', '11', '19', '9', '17', 'x', 'x'], ['18', '20', '16', '19', '12', '1', 'x', 'x', 'x', '5'], ['11', 'x', '18', '14', 'x', '2', 'x', '... |
18 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. 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 | 10 | [[8, 2], [7, 3], [6, 4], [5, 4], [4, 5], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [2, 9], [1, 9], [1, 8]] | 13 | 0.031194448471069336 | 13 | 8 | 2 | ["[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1... | ["[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1... | ["[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1... |
18 | Given 5 labeled water jugs with capacities 71, 124, 95, 42, 56, 41 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 291, 292, 326 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of water ... | water_jug | subset_sum | 4 | [["+", 95, 3], ["+", 95, 3], ["+", 95, 3], ["+", 41, 3], ["+", 56, 2], ["+", 71, 2], ["+", 124, 2], ["+", 41, 2], ["+", 42, 1], ["+", 95, 1], ["+", 124, 1], ["-", 41, 1], ["+", 71, 1]] | 13 | 0.03421187400817871 | 13 | 36 | 3 | [[71, 124, 95, 42, 56, 41], [291, 292, 326]] | [[71, 124, 95, 42, 56, 41], [291, 292, 326]] | ["[71, 124, 95, 42, 56, 41]", "[291, 292, 326]"] |
19 | 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 | [16, 89, 69, 35, 64, 32, 23, 14, 35, 69, 89, 35, 32, 23] | 14 | 0.030463218688964844 | 14 | 4 | 9 | [[[89, 69, 35], [16, 14, 64], ["_", 23, 32]]] | [[[89, 69, 35], [16, 14, 64], ["_", 23, 32]]] | ["[[89, 69, 35], [16, 14, 64], ['_', 23, 32]]"] |
19 | 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 | 2 | ["up-left", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left"] | 12 | 0.19801783561706543 | 12 | 4 | 20 | [[["l", "a", "e", "o", "n"], ["p", "z", "i", "n", "r"], ["l", "a", "g", "o", "_"], ["i", "e", "e", "u", "m"]]] | [[["l", "a", "e", "o", "n"], ["p", "z", "i", "n", "r"], ["l", "a", "g", "o", "_"], ["i", "e", "e", "u", "m"]], ["aeon", "plier", "gazon", "ileum"]] | ["[['l', 'a', 'e', 'o', 'n'], ['p', 'z', 'i', 'n', 'r'], ['l', 'a', 'g', 'o', '_'], ['i', 'e', 'e', 'u', 'm']]", "['aeon', 'plier', 'gazon', 'ileum']"] |
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