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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 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 | 2 | [55, 97, 35, 12, 97, 55, 43, 9, 25, 17, 12, 35, 9, 25, 17, 9, 25, 17] | 18 | 0.04202771186828613 | 18 | 4 | 9 | [[[12, 55, "_"], [35, 97, 43], [17, 25, 9]]] | [[[12, 55, "_"], [35, 97, 43], [17, 25, 9]]] | ["[[12, 55, '_'], [35, 97, 43], [17, 25, 9]]"] |
1 | 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", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.21660590171813965 | 16 | 4 | 16 | [[["i", "c", "a", "m"], ["h", "p", "l", "o"], ["_", "r", "a", "y"], ["d", "l", "e", "r"]]] | [[["i", "c", "a", "m"], ["h", "p", "l", "o"], ["_", "r", "a", "y"], ["d", "l", "e", "r"]], ["cam", "hill", "pray", "doer"]] | ["[['i', 'c', 'a', 'm'], ['h', 'p', 'l', 'o'], ['_', 'r', 'a', 'y'], ['d', 'l', 'e', 'r']]", "['cam', 'hill', 'pray', 'doer']"] |
1 | 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 | ["W", "X", "G", "H", "A", "D", "P", "H", "A"] | 9 | 0.020942211151123047 | 9 | 10 | 13 | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 0]... | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 0]... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 0... |
1 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [14, 2, 5, 8, 65, 5, 16, 2, 5, 2, 12, 17, 16, 15, 20, 4, 19, 9, 10, 64, 2, 10, 14, 2, 17], such that the sum of the chosen coins adds up to 208. Each coin in the list is unique and can only be used once. Also coins carry a... | coin_exchange | subset_sum | 15 | [64, 16, 4, 5, 5, 19, 65, 16, 12, 2] | 44 | 0.03430962562561035 | 10 | 25 | 25 | [[14, 2, 5, 8, 65, 5, 16, 2, 5, 2, 12, 17, 16, 15, 20, 4, 19, 9, 10, 64, 2, 10, 14, 2, 17]] | [[14, 2, 5, 8, 65, 5, 16, 2, 5, 2, 12, 17, 16, 15, 20, 4, 19, 9, 10, 64, 2, 10, 14, 2, 17], {"20": 13, "4": 2, "17": 16, "19": 8, "64": 4, "5": 3, "14": 10, "10": 9, "65": 11, "16": 2, "12": 7, "8": 5, "2": 2, "15": 14, "9": 8}, 208] | ["[14, 2, 5, 8, 65, 5, 16, 2, 5, 2, 12, 17, 16, 15, 20, 4, 19, 9, 10, 64, 2, 10, 14, 2, 17]", "{20: 13, 4: 2, 17: 16, 19: 8, 64: 4, 5: 3, 14: 10, 10: 9, 65: 11, 16: 2, 12: 7, 8: 5, 2: 2, 15: 14, 9: 8}", "208"] |
1 | 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, 1], [2, 0], [2, 0], [1, 0], [1, 0], [2, 1], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 17 | 0.9051551818847656 | 17 | 6 | 12 | [[["Green", "Red", "Green", "Red"], ["Blue", "Blue", "Red", "Green"], ["Red", "Blue", "Green", "Blue"]], 6] | [[["Green", "Red", "Green", "Red"], ["Blue", "Blue", "Red", "Green"], ["Red", "Blue", "Green", "Blue"]], 6] | ["[['Green', 'Red', 'Green', 'Red'], ['Blue', 'Blue', 'Red', 'Green'], ['Red', 'Blue', 'Green', 'Blue']]", "6"] |
1 | We have a 3x3 numerical grid, with numbers ranging from 13 to 46 (13 included in the range but 46 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, 31], [1, 0, 14], [1, 2, 32], [2, 0, 13]] | 267 | 0.23554539680480957 | 4 | 33 | 9 | ["[['16', '', '41'], ['', '30', ''], ['', '29', '30']]", 13, 46] | ["[['16', '', '41'], ['', '30', ''], ['', '29', '30']]", 13, 46] | ["[['16', '', '41'], ['', '30', ''], ['', '29', '30']]", "13", "46"] |
1 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 29 to 48. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 107, and sum of row 1 must be 103. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 1, 31], [1, 0, 29], [1, 1, 44], [1, 2, 30], [2, 0, 34], [2, 1, 32], [2, 2, 33]] | 314 | 0.3927474021911621 | 7 | 19 | 9 | ["[['35', '', '46'], ['', '', ''], ['', '', '']]", 3, 29, 48] | ["[['35', '', '46'], ['', '', ''], ['', '', '']]", 29, 48, [1, 2], [1, 2], [107], [103], 124] | ["[['35', '', '46'], ['', '', ''], ['', '', '']]", "29", "48", "[None, 107, None]", "[None, 103, None]", "124"] |
1 | 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], [5, 0], [3, 1], [3, 2], [5, 2], [4, 5], [4, 2], [1, 3], [4, 5]] | 32 | 0.06039690971374512 | 10 | 30 | 12 | [[[], [], [], ["Blue", "Yellow", "Blue", "Blue"], ["Red", "Green", "Yellow", "Green"], ["Red", "Red", "Yellow", "Green"]], 4, {"0": 5, "1": 5, "2": 3, "3": 1, "4": 5, "5": 1}] | [[[], [], [], ["Blue", "Yellow", "Blue", "Blue"], ["Red", "Green", "Yellow", "Green"], ["Red", "Red", "Yellow", "Green"]], 4, {"0": 5, "1": 5, "2": 3, "3": 1, "4": 5, "5": 1}, 3] | ["[[], [], [], ['Blue', 'Yellow', 'Blue', 'Blue'], ['Red', 'Green', 'Yellow', 'Green'], ['Red', 'Red', 'Yellow', 'Green']]", "{0: 5, 1: 5, 2: 3, 3: 1, 4: 5, 5: 1}", "4", "3"] |
1 | 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, 7) to his destination workshop at index (2, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[5, 7], [4, 7], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [2, 1]] | 64 | 0.030263185501098633 | 10 | 4 | 4 | [[["13", "x", "x", "3", "10", "20", "3", "x", "5"], ["x", "x", "x", "x", "20", "16", "x", "x", "17"], ["3", "14", "18", "8", "1", "20", "14", "x", "7"], ["13", "3", "6", "10", "7", "4", "6", "6", "1"], ["10", "12", "2", "x", "11", "x", "10", "8", "11"], ["x", "x", "x", "11", "6", "18", "13", "20", "17"], ["x", "x", "16... | [[["13", "x", "x", "3", "10", "20", "3", "x", "5"], ["x", "x", "x", "x", "20", "16", "x", "x", "17"], ["3", "14", "18", "8", "1", "20", "14", "x", "7"], ["13", "3", "6", "10", "7", "4", "6", "6", "1"], ["10", "12", "2", "x", "11", "x", "10", "8", "11"], ["x", "x", "x", "11", "6", "18", "13", "20", "17"], ["x", "x", "16... | ["[['13', 'x', 'x', '3', '10', '20', '3', 'x', '5'], ['x', 'x', 'x', 'x', '20', '16', 'x', 'x', '17'], ['3', '14', '18', '8', '1', '20', '14', 'x', '7'], ['13', '3', '6', '10', '7', '4', '6', '6', '1'], ['10', '12', '2', 'x', '11', 'x', '10', '8', '11'], ['x', 'x', 'x', '11', '6', '18', '13', '20', '17'], ['x', 'x', '1... |
1 | 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, 0], [7, 1], [6, 1], [5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [3, 5], [3, 6], [2, 7]] | 11 | 0.03385114669799805 | 11 | 8 | 2 | ["[[0, 1, 0, 1, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 1, 1, 1, 1, 0, 1, 0]]", 3] | ["[[0, 1, 0, 1, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 1, 1, 1, 1, 0, 1, 0]]", [8, 0], [2, 7], 3] | ["[[0, 1, 0, 1, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 1, 1, 1, 1, 0, 1, 0]]", "(8, 0)", "(2, 7)", "3"] |
1 | Given 5 labeled water jugs with capacities 41, 26, 44, 75, 40, 136 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 274, 297, 343 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 | [["+", 40, 3], ["+", 75, 3], ["+", 136, 3], ["-", 44, 3], ["+", 136, 3], ["+", 26, 2], ["+", 40, 2], ["+", 136, 2], ["-", 41, 2], ["+", 136, 2], ["+", 40, 1], ["+", 40, 1], ["+", 44, 1], ["+", 75, 1], ["+", 75, 1]] | 15 | 0.05471658706665039 | 15 | 36 | 3 | [[41, 26, 44, 75, 40, 136], [274, 297, 343]] | [[41, 26, 44, 75, 40, 136], [274, 297, 343]] | ["[41, 26, 44, 75, 40, 136]", "[274, 297, 343]"] |
2 | 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 | 2 | [53, 100, 63, 40, 30, 19, 69, 53, 40, 30, 19, 40, 53, 99, 100, 63, 30, 19] | 18 | 0.03798794746398926 | 18 | 4 | 9 | [[[99, 69, 19], [53, "_", 30], [100, 63, 40]]] | [[[99, 69, 19], [53, "_", 30], [100, 63, 40]]] | ["[[99, 69, 19], [53, '_', 30], [100, 63, 40]]"] |
2 | 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-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.23615717887878418 | 16 | 4 | 16 | [[["o", "a", "u", "o"], ["p", "r", "l", "e"], ["f", "a", "_", "f"], ["m", "k", "d", "d"]]] | [[["o", "a", "u", "o"], ["p", "r", "l", "e"], ["f", "a", "_", "f"], ["m", "k", "d", "d"]], ["ako", "pole", "raff", "mudd"]] | ["[['o', 'a', 'u', 'o'], ['p', 'r', 'l', 'e'], ['f', 'a', '_', 'f'], ['m', 'k', 'd', 'd']]", "['ako', 'pole', 'raff', 'mudd']"] |
2 | 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 | ["D", "Z", "I", "Q", "K", "R", "S", "Q", "K"] | 9 | 0.027526378631591797 | 9 | 10 | 13 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0]... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0]... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0... |
2 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [13, 10, 12, 10, 16, 7, 9, 14, 13, 18, 36, 11, 7, 14, 7, 8, 19, 7, 39, 13, 3, 18, 20, 4, 3, 18, 15, 2, 19, 16], such that the sum of the chosen coins adds up to 203. Each coin in the list is unique and can only be used onc... | coin_exchange | subset_sum | 16 | [7, 7, 7, 13, 13, 39, 36, 10, 15, 10, 11, 13, 2, 7, 4, 9] | 78 | 0.03766942024230957 | 16 | 30 | 30 | [[13, 10, 12, 10, 16, 7, 9, 14, 13, 18, 36, 11, 7, 14, 7, 8, 19, 7, 39, 13, 3, 18, 20, 4, 3, 18, 15, 2, 19, 16]] | [[13, 10, 12, 10, 16, 7, 9, 14, 13, 18, 36, 11, 7, 14, 7, 8, 19, 7, 39, 13, 3, 18, 20, 4, 3, 18, 15, 2, 19, 16], {"15": 5, "36": 15, "39": 9, "9": 8, "13": 3, "2": 2, "18": 10, "12": 12, "3": 3, "8": 8, "11": 6, "10": 4, "4": 4, "14": 10, "7": 3, "16": 16, "20": 18, "19": 17}, 203] | ["[13, 10, 12, 10, 16, 7, 9, 14, 13, 18, 36, 11, 7, 14, 7, 8, 19, 7, 39, 13, 3, 18, 20, 4, 3, 18, 15, 2, 19, 16]", "{15: 5, 36: 15, 39: 9, 9: 8, 13: 3, 2: 2, 18: 10, 12: 12, 3: 3, 8: 8, 11: 6, 10: 4, 4: 4, 14: 10, 7: 3, 16: 16, 20: 18, 19: 17}", "203"] |
2 | 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, 2], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [1, 0]] | 10 | 0.05974388122558594 | 10 | 6 | 12 | [[["Red", "Blue", "Blue", "Blue"], ["Green", "Green", "Red", "Green"], ["Green", "Blue", "Red", "Red"]], 6] | [[["Red", "Blue", "Blue", "Blue"], ["Green", "Green", "Red", "Green"], ["Green", "Blue", "Red", "Red"]], 6] | ["[['Red', 'Blue', 'Blue', 'Blue'], ['Green', 'Green', 'Red', 'Green'], ['Green', 'Blue', 'Red', 'Red']]", "6"] |
2 | We have a 3x3 numerical grid, with numbers ranging from 8 to 41 (8 included in the range but 41 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 an... | consecutive_grid | underdetermined_system | 7 | [[1, 0, 11], [2, 0, 30], [2, 1, 28], [2, 2, 8]] | 185 | 0.6896023750305176 | 4 | 33 | 9 | ["[['10', '15', '39'], ['', '27', '29'], ['', '', '']]", 8, 41] | ["[['10', '15', '39'], ['', '27', '29'], ['', '', '']]", 8, 41] | ["[['10', '15', '39'], ['', '27', '29'], ['', '', '']]", "8", "41"] |
2 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 20 to 39. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 82, and sum of row 1 must be 87. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 6 | [[0, 0, 20], [0, 1, 22], [0, 2, 25], [1, 1, 36], [1, 2, 21], [2, 0, 33], [2, 1, 24], [2, 2, 23]] | 234 | 3.1459109783172607 | 8 | 19 | 9 | ["[['', '', ''], ['30', '', ''], ['', '', '']]", 3, 20, 39] | ["[['', '', ''], ['30', '', ''], ['', '', '']]", 20, 39, [1, 2], [1, 2], [82], [87], 94] | ["[['', '', ''], ['30', '', ''], ['', '', '']]", "20", "39", "[None, 82, None]", "[None, 87, None]", "94"] |
2 | 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, 2], [0, 2], [1, 5], [1, 5], [0, 1], [0, 2], [3, 4], [3, 5], [3, 1], [0, 3], [4, 3]] | 26 | 0.10936236381530762 | 11 | 30 | 12 | [[["Red", "Green", "Red", "Blue"], ["Red", "Yellow", "Yellow", "Green"], [], ["Blue", "Yellow", "Green", "Blue"], [], []], 4, {"0": 5, "1": 3, "2": 3, "3": 1, "4": 3, "5": 2}] | [[["Red", "Green", "Red", "Blue"], ["Red", "Yellow", "Yellow", "Green"], [], ["Blue", "Yellow", "Green", "Blue"], [], []], 4, {"0": 5, "1": 3, "2": 3, "3": 1, "4": 3, "5": 2}, 3] | ["[['Red', 'Green', 'Red', 'Blue'], ['Red', 'Yellow', 'Yellow', 'Green'], [], ['Blue', 'Yellow', 'Green', 'Blue'], [], []]", "{0: 5, 1: 3, 2: 3, 3: 1, 4: 3, 5: 2}", "4", "3"] |
2 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 2) to his destination workshop at index (5, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[2, 2], [2, 3], [2, 4], [2, 5], [1, 5], [1, 6], [2, 6], [2, 7], [2, 8], [3, 8], [4, 8], [5, 8]] | 88 | 0.027752399444580078 | 12 | 4 | 4 | [[["x", "13", "9", "x", "x", "16", "6", "18", "7"], ["x", "3", "11", "x", "x", "5", "7", "x", "19"], ["8", "x", "2", "5", "6", "12", "9", "10", "7"], ["12", "1", "6", "20", "19", "18", "12", "x", "14"], ["16", "5", "10", "3", "x", "x", "x", "1", "9"], ["x", "3", "x", "x", "x", "x", "x", "x", "4"], ["7", "10", "x", "1",... | [[["x", "13", "9", "x", "x", "16", "6", "18", "7"], ["x", "3", "11", "x", "x", "5", "7", "x", "19"], ["8", "x", "2", "5", "6", "12", "9", "10", "7"], ["12", "1", "6", "20", "19", "18", "12", "x", "14"], ["16", "5", "10", "3", "x", "x", "x", "1", "9"], ["x", "3", "x", "x", "x", "x", "x", "x", "4"], ["7", "10", "x", "1",... | ["[['x', '13', '9', 'x', 'x', '16', '6', '18', '7'], ['x', '3', '11', 'x', 'x', '5', '7', 'x', '19'], ['8', 'x', '2', '5', '6', '12', '9', '10', '7'], ['12', '1', '6', '20', '19', '18', '12', 'x', '14'], ['16', '5', '10', '3', 'x', 'x', 'x', '1', '9'], ['x', '3', 'x', 'x', 'x', 'x', 'x', 'x', '4'], ['7', '10', 'x', '1'... |
2 | 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, 4], [0, 5], [1, 5], [2, 5], [2, 6], [3, 6], [4, 5], [5, 4], [5, 3], [5, 2], [6, 2], [7, 1], [8, 1], [8, 0]] | 14 | 0.03374505043029785 | 14 | 8 | 2 | ["[[1, 1, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0]]", 3] | ["[[1, 1, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0]]", [0, 4], [8, 0], 3] | ["[[1, 1, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0]]", "(0, 4)", "(8, 0)", "3"] |
2 | Given 5 labeled water jugs with capacities 31, 102, 53, 33, 32, 24 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 188, 198, 289 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 | [["+", 32, 3], ["+", 102, 3], ["+", 102, 3], ["+", 53, 3], ["+", 31, 2], ["+", 32, 2], ["+", 33, 2], ["+", 102, 2], ["+", 33, 1], ["+", 53, 1], ["+", 102, 1]] | 11 | 0.04619026184082031 | 11 | 36 | 3 | [[31, 102, 53, 33, 32, 24], [188, 198, 289]] | [[31, 102, 53, 33, 32, 24], [188, 198, 289]] | ["[31, 102, 53, 33, 32, 24]", "[188, 198, 289]"] |
3 | 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 | 2 | [50, 82, 74, 50, 61, 11] | 6 | 0.028201580047607422 | 6 | 4 | 9 | [[[87, 50, 82], [68, "_", 74], [23, 61, 11]]] | [[[87, 50, 82], [68, "_", 74], [23, 61, 11]]] | ["[[87, 50, 82], [68, '_', 74], [23, 61, 11]]"] |
3 | 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", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 18 | 0.22588300704956055 | 18 | 4 | 16 | [[["v", "t", "u", "i"], ["o", "w", "e", "i"], ["y", "d", "_", "c"], ["d", "i", "e", "m"]]] | [[["v", "t", "u", "i"], ["o", "w", "e", "i"], ["y", "d", "_", "c"], ["d", "i", "e", "m"]], ["twi", "ovey", "udic", "diem"]] | ["[['v', 't', 'u', 'i'], ['o', 'w', 'e', 'i'], ['y', 'd', '_', 'c'], ['d', 'i', 'e', 'm']]", "['twi', 'ovey', 'udic', 'diem']"] |
3 | 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 | ["M", "G", "R", "Y", "R", "O", "A", "X", "A"] | 9 | 0.0287935733795166 | 9 | 10 | 13 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0]... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0]... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0... |
3 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [13, 19, 9, 4, 18, 17, 2, 14, 17, 17, 8, 6, 4, 10, 19, 37, 20, 19, 14, 7, 6, 11, 21, 9, 3, 10, 21, 20, 2, 17, 2], such that the sum of the chosen coins adds up to 215. Each coin in the list is unique and can only be used o... | coin_exchange | subset_sum | 17 | [14, 21, 20, 4, 37, 4, 21, 20, 18, 8, 17, 14, 17] | 55 | 0.0338587760925293 | 13 | 31 | 31 | [[13, 19, 9, 4, 18, 17, 2, 14, 17, 17, 8, 6, 4, 10, 19, 37, 20, 19, 14, 7, 6, 11, 21, 9, 3, 10, 21, 20, 2, 17, 2]] | [[13, 19, 9, 4, 18, 17, 2, 14, 17, 17, 8, 6, 4, 10, 19, 37, 20, 19, 14, 7, 6, 11, 21, 9, 3, 10, 21, 20, 2, 17, 2], {"14": 2, "18": 9, "11": 10, "9": 6, "10": 9, "13": 10, "37": 9, "6": 5, "2": 2, "4": 1, "8": 3, "19": 10, "17": 7, "7": 6, "3": 3, "21": 3, "20": 4}, 215] | ["[13, 19, 9, 4, 18, 17, 2, 14, 17, 17, 8, 6, 4, 10, 19, 37, 20, 19, 14, 7, 6, 11, 21, 9, 3, 10, 21, 20, 2, 17, 2]", "{14: 2, 18: 9, 11: 10, 9: 6, 10: 9, 13: 10, 37: 9, 6: 5, 2: 2, 4: 1, 8: 3, 19: 10, 17: 7, 7: 6, 3: 3, 21: 3, 20: 4}", "215"] |
3 | 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], [2, 0], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1]] | 19 | 2.109553337097168 | 19 | 6 | 12 | [[["Red", "Blue", "Blue", "Red"], ["Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Green"]], 6] | [[["Red", "Blue", "Blue", "Red"], ["Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Green"]], 6] | ["[['Red', 'Blue', 'Blue', 'Red'], ['Red', 'Blue', 'Blue', 'Green'], ['Green', 'Green', 'Red', 'Green']]", "6"] |
3 | We have a 3x3 numerical grid, with numbers ranging from 20 to 53 (20 included in the range but 53 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, 23], [1, 1, 28], [1, 2, 49], [2, 0, 29]] | 344 | 0.18951058387756348 | 4 | 33 | 9 | ["[['22', '', '48'], ['27', '', ''], ['', '42', '52']]", 20, 53] | ["[['22', '', '48'], ['27', '', ''], ['', '42', '52']]", 20, 53] | ["[['22', '', '48'], ['27', '', ''], ['', '42', '52']]", "20", "53"] |
3 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 20 to 39. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 99, and sum of row 1 must be 86. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 6 | [[0, 1, 26], [0, 2, 20], [1, 0, 23], [1, 1, 35], [1, 2, 28], [2, 0, 21], [2, 1, 38], [2, 2, 22]] | 238 | 6.525880575180054 | 8 | 19 | 9 | ["[['25', '', ''], ['', '', ''], ['', '', '']]", 3, 20, 39] | ["[['25', '', ''], ['', '', ''], ['', '', '']]", 20, 39, [1, 2], [1, 2], [99], [86], 76] | ["[['25', '', ''], ['', '', ''], ['', '', '']]", "20", "39", "[None, 99, None]", "[None, 86, None]", "76"] |
3 | 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, 4], [2, 5], [2, 4], [2, 1], [3, 0], [3, 5], [3, 0], [2, 4], [3, 5]] | 21 | 0.11831974983215332 | 10 | 30 | 12 | [[[], ["Yellow", "Green", "Red", "Red"], ["Blue", "Green", "Red", "Green"], ["Yellow", "Blue", "Yellow", "Blue"], [], []], 4, {"0": 3, "1": 6, "2": 5, "3": 6, "4": 1, "5": 1}] | [[[], ["Yellow", "Green", "Red", "Red"], ["Blue", "Green", "Red", "Green"], ["Yellow", "Blue", "Yellow", "Blue"], [], []], 4, {"0": 3, "1": 6, "2": 5, "3": 6, "4": 1, "5": 1}, 3] | ["[[], ['Yellow', 'Green', 'Red', 'Red'], ['Blue', 'Green', 'Red', 'Green'], ['Yellow', 'Blue', 'Yellow', 'Blue'], [], []]", "{0: 3, 1: 6, 2: 5, 3: 6, 4: 1, 5: 1}", "4", "3"] |
3 | 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, 7) to his destination workshop at index (1, 2), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[7, 7], [6, 7], [6, 6], [6, 5], [5, 5], [4, 5], [3, 5], [2, 5], [2, 4], [1, 4], [1, 3], [1, 2]] | 71 | 0.02632451057434082 | 12 | 4 | 4 | [[["10", "14", "4", "16", "x", "17", "5", "x", "x"], ["5", "20", "16", "3", "1", "8", "x", "16", "19"], ["1", "x", "5", "13", "3", "15", "19", "15", "x"], ["x", "16", "13", "20", "x", "8", "x", "x", "x"], ["x", "16", "x", "17", "11", "1", "x", "15", "x"], ["10", "x", "14", "11", "5", "7", "12", "x", "5"], ["7", "x", "1... | [[["10", "14", "4", "16", "x", "17", "5", "x", "x"], ["5", "20", "16", "3", "1", "8", "x", "16", "19"], ["1", "x", "5", "13", "3", "15", "19", "15", "x"], ["x", "16", "13", "20", "x", "8", "x", "x", "x"], ["x", "16", "x", "17", "11", "1", "x", "15", "x"], ["10", "x", "14", "11", "5", "7", "12", "x", "5"], ["7", "x", "1... | ["[['10', '14', '4', '16', 'x', '17', '5', 'x', 'x'], ['5', '20', '16', '3', '1', '8', 'x', '16', '19'], ['1', 'x', '5', '13', '3', '15', '19', '15', 'x'], ['x', '16', '13', '20', 'x', '8', 'x', 'x', 'x'], ['x', '16', 'x', '17', '11', '1', 'x', '15', 'x'], ['10', 'x', '14', '11', '5', '7', '12', 'x', '5'], ['7', 'x', '... |
3 | 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, 6], [7, 5], [6, 5], [5, 5], [4, 6], [3, 5], [3, 4], [2, 4], [2, 3], [2, 2], [1, 2], [1, 1], [1, 0], [0, 0]] | 14 | 0.03221940994262695 | 14 | 8 | 2 | ["[[0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0]]", 3] | ["[[0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0]]", [8, 6], [0, 0], 3] | ["[[0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0]]", "(8, 6)", "(0, 0)", "3"] |
3 | Given 5 labeled water jugs with capacities 43, 149, 131, 132, 70, 104 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 284, 297, 436 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 | [["+", 131, 3], ["+", 131, 3], ["+", 70, 3], ["+", 104, 3], ["+", 131, 2], ["+", 132, 2], ["-", 70, 2], ["+", 104, 2], ["+", 104, 1], ["+", 104, 1], ["-", 132, 1], ["+", 104, 1], ["+", 104, 1]] | 13 | 0.038121938705444336 | 13 | 36 | 3 | [[43, 149, 131, 132, 70, 104], [284, 297, 436]] | [[43, 149, 131, 132, 70, 104], [284, 297, 436]] | ["[43, 149, 131, 132, 70, 104]", "[284, 297, 436]"] |
4 | 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 | 2 | [24, 42, 89, 70, 83, 71, 42, 24, 25, 66, 70, 89, 66, 70, 89, 83, 71, 42] | 18 | 0.03897857666015625 | 18 | 4 | 9 | [[[66, 89, 70], [25, 42, 83], ["_", 24, 71]]] | [[[66, 89, 70], [25, 42, 83], ["_", 24, 71]]] | ["[[66, 89, 70], [25, 42, 83], ['_', 24, 71]]"] |
4 | 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", "down-right", "down-left", "up-left", "up-left"] | 6 | 0.2581043243408203 | 6 | 4 | 16 | [[["_", "m", "u", "p"], ["c", "e", "r", "a"], ["d", "r", "e", "b"], ["v", "e", "l", "o"]]] | [[["_", "m", "u", "p"], ["c", "e", "r", "a"], ["d", "r", "e", "b"], ["v", "e", "l", "o"]], ["map", "cere", "drub", "velo"]] | ["[['_', 'm', 'u', 'p'], ['c', 'e', 'r', 'a'], ['d', 'r', 'e', 'b'], ['v', 'e', 'l', 'o']]", "['map', 'cere', 'drub', 'velo']"] |
4 | 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 | ["L", "Z", "N", "K", "N", "I", "D", "R", "D"] | 9 | 0.026905059814453125 | 9 | 10 | 13 | [[[0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0]... | [[[0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0]... | ["[[0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0... |
4 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [14, 19, 3, 8, 5, 107, 4, 10, 9, 2, 11, 7, 11, 11, 4, 10, 17, 14, 18, 10, 21, 13, 2, 13, 19, 5, 8, 4, 7, 6, 10], such that the sum of the chosen coins adds up to 215. Each coin in the list is unique and can only be used on... | coin_exchange | subset_sum | 18 | [18, 6, 9, 8, 2, 5, 5, 17, 14, 8, 107, 14, 2] | 60 | 0.03795170783996582 | 13 | 31 | 31 | [[14, 19, 3, 8, 5, 107, 4, 10, 9, 2, 11, 7, 11, 11, 4, 10, 17, 14, 18, 10, 21, 13, 2, 13, 19, 5, 8, 4, 7, 6, 10]] | [[14, 19, 3, 8, 5, 107, 4, 10, 9, 2, 11, 7, 11, 11, 4, 10, 17, 14, 18, 10, 21, 13, 2, 13, 19, 5, 8, 4, 7, 6, 10], {"17": 9, "107": 7, "13": 11, "10": 7, "19": 12, "9": 2, "4": 4, "14": 8, "21": 14, "6": 2, "5": 3, "2": 2, "3": 3, "7": 6, "18": 6, "8": 4, "11": 11}, 215] | ["[14, 19, 3, 8, 5, 107, 4, 10, 9, 2, 11, 7, 11, 11, 4, 10, 17, 14, 18, 10, 21, 13, 2, 13, 19, 5, 8, 4, 7, 6, 10]", "{17: 9, 107: 7, 13: 11, 10: 7, 19: 12, 9: 2, 4: 4, 14: 8, 21: 14, 6: 2, 5: 3, 2: 2, 3: 3, 7: 6, 18: 6, 8: 4, 11: 11}", "215"] |
4 | 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], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [2, 0], [2, 1], [2, 0], [1, 2], [1, 2]] | 14 | 0.22463750839233398 | 14 | 6 | 12 | [[["Red", "Red", "Blue", "Blue"], ["Red", "Blue", "Red", "Green"], ["Green", "Blue", "Green", "Green"]], 6] | [[["Red", "Red", "Blue", "Blue"], ["Red", "Blue", "Red", "Green"], ["Green", "Blue", "Green", "Green"]], 6] | ["[['Red', 'Red', 'Blue', 'Blue'], ['Red', 'Blue', 'Red', 'Green'], ['Green', 'Blue', 'Green', 'Green']]", "6"] |
4 | We have a 3x3 numerical grid, with numbers ranging from 20 to 53 (20 included in the range but 53 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, 20], [1, 1, 33], [1, 2, 34], [2, 0, 47], [2, 2, 21]] | 255 | 0.18683171272277832 | 5 | 33 | 9 | ["[['', '32', '37'], ['29', '', ''], ['', '46', '']]", 20, 53] | ["[['', '32', '37'], ['29', '', ''], ['', '46', '']]", 20, 53] | ["[['', '32', '37'], ['29', '', ''], ['', '46', '']]", "20", "53"] |
4 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 20 to 39. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 72, and sum of row 1 must be 95. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 6 | [[0, 1, 22], [0, 2, 20], [1, 0, 30], [1, 1, 27], [1, 2, 38], [2, 0, 24], [2, 1, 23], [2, 2, 25]] | 230 | 0.5546069145202637 | 8 | 19 | 9 | ["[['21', '', ''], ['', '', ''], ['', '', '']]", 3, 20, 39] | ["[['21', '', ''], ['', '', ''], ['', '', '']]", 20, 39, [1, 2], [1, 2], [72], [95], 71] | ["[['21', '', ''], ['', '', ''], ['', '', '']]", "20", "39", "[None, 72, None]", "[None, 95, None]", "71"] |
4 | 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, 3], [0, 1], [4, 1], [4, 3], [0, 5], [4, 0], [2, 4], [2, 1], [2, 0], [5, 4], [2, 3]] | 45 | 0.024616003036499023 | 11 | 30 | 12 | [[["Red", "Green", "Yellow", "Blue"], [], ["Yellow", "Green", "Blue", "Red"], [], ["Green", "Red", "Blue", "Yellow"], []], 4, {"0": 2, "1": 6, "2": 5, "3": 2, "4": 5, "5": 7}] | [[["Red", "Green", "Yellow", "Blue"], [], ["Yellow", "Green", "Blue", "Red"], [], ["Green", "Red", "Blue", "Yellow"], []], 4, {"0": 2, "1": 6, "2": 5, "3": 2, "4": 5, "5": 7}, 3] | ["[['Red', 'Green', 'Yellow', 'Blue'], [], ['Yellow', 'Green', 'Blue', 'Red'], [], ['Green', 'Red', 'Blue', 'Yellow'], []]", "{0: 2, 1: 6, 2: 5, 3: 2, 4: 5, 5: 7}", "4", "3"] |
4 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 0) to his destination workshop at index (5, 6), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[2, 0], [2, 1], [2, 2], [2, 3], [3, 3], [3, 4], [3, 5], [4, 5], [5, 5], [5, 6]] | 88 | 0.02671647071838379 | 10 | 4 | 4 | [[["18", "9", "2", "x", "9", "14", "x", "1", "x"], ["3", "14", "18", "7", "x", "3", "x", "2", "19"], ["6", "18", "20", "3", "13", "x", "6", "10", "x"], ["20", "x", "12", "4", "14", "6", "x", "x", "x"], ["7", "18", "8", "5", "19", "3", "x", "x", "7"], ["15", "9", "14", "16", "5", "14", "6", "x", "x"], ["x", "5", "13", "... | [[["18", "9", "2", "x", "9", "14", "x", "1", "x"], ["3", "14", "18", "7", "x", "3", "x", "2", "19"], ["6", "18", "20", "3", "13", "x", "6", "10", "x"], ["20", "x", "12", "4", "14", "6", "x", "x", "x"], ["7", "18", "8", "5", "19", "3", "x", "x", "7"], ["15", "9", "14", "16", "5", "14", "6", "x", "x"], ["x", "5", "13", "... | ["[['18', '9', '2', 'x', '9', '14', 'x', '1', 'x'], ['3', '14', '18', '7', 'x', '3', 'x', '2', '19'], ['6', '18', '20', '3', '13', 'x', '6', '10', 'x'], ['20', 'x', '12', '4', '14', '6', 'x', 'x', 'x'], ['7', '18', '8', '5', '19', '3', 'x', 'x', '7'], ['15', '9', '14', '16', '5', '14', '6', 'x', 'x'], ['x', '5', '13', ... |
4 | 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, 1], [7, 1], [6, 2], [5, 3], [5, 4], [4, 5], [3, 5], [3, 6], [3, 7], [3, 8], [2, 8], [1, 8], [1, 7], [1, 6], [0, 6], [0, 5]] | 16 | 0.026789426803588867 | 16 | 8 | 2 | ["[[0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 1]]", 3] | ["[[0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 1]]", [8, 1], [0, 5], 3] | ["[[0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 1]]", "(8, 1)", "(0, 5)", "3"] |
4 | Given 5 labeled water jugs with capacities 36, 88, 132, 70, 87, 111 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 225, 237, 243 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 | [["+", 111, 3], ["+", 132, 3], ["+", 87, 2], ["+", 132, 2], ["-", 70, 2], ["+", 88, 2], ["+", 70, 1], ["+", 132, 1], ["-", 88, 1], ["+", 111, 1]] | 10 | 0.033365726470947266 | 10 | 36 | 3 | [[36, 88, 132, 70, 87, 111], [225, 237, 243]] | [[36, 88, 132, 70, 87, 111], [225, 237, 243]] | ["[36, 88, 132, 70, 87, 111]", "[225, 237, 243]"] |
5 | 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 | 2 | [95, 58, 38, 78, 98, 95, 7, 70, 58, 7, 70, 58] | 12 | 0.029888629913330078 | 12 | 4 | 9 | [[[78, 98, 89], [38, "_", 7], [58, 95, 70]]] | [[[78, 98, 89], [38, "_", 7], [58, 95, 70]]] | ["[[78, 98, 89], [38, '_', 7], [58, 95, 70]]"] |
5 | 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-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 12 | 0.1913444995880127 | 12 | 4 | 16 | [[["a", "s", "t", "x"], ["t", "r", "s", "a"], ["s", "u", "_", "p"], ["c", "a", "d", "e"]]] | [[["a", "s", "t", "x"], ["t", "r", "s", "a"], ["s", "u", "_", "p"], ["c", "a", "d", "e"]], ["sax", "tass", "turp", "cade"]] | ["[['a', 's', 't', 'x'], ['t', 'r', 's', 'a'], ['s', 'u', '_', 'p'], ['c', 'a', 'd', 'e']]", "['sax', 'tass', 'turp', 'cade']"] |
5 | 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", "O", "X", "K", "E", "K", "Z", "S", "Z"] | 9 | 0.03679943084716797 | 9 | 10 | 13 | [[[0, 0, 1, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1], [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, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1], [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, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0... |
5 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [20, 10, 16, 21, 15, 21, 13, 6, 19, 9, 7, 5, 2, 6, 9, 22, 4, 13, 3, 16, 22, 18, 6, 5, 14, 7, 7, 2, 17, 9, 8, 83, 14], such that the sum of the chosen coins adds up to 239. Each coin in the list is unique and can only be us... | coin_exchange | subset_sum | 19 | [18, 21, 16, 2, 15, 2, 9, 9, 21, 83, 16, 6, 4, 17] | 48 | 0.03824257850646973 | 14 | 33 | 33 | [[20, 10, 16, 21, 15, 21, 13, 6, 19, 9, 7, 5, 2, 6, 9, 22, 4, 13, 3, 16, 22, 18, 6, 5, 14, 7, 7, 2, 17, 9, 8, 83, 14]] | [[20, 10, 16, 21, 15, 21, 13, 6, 19, 9, 7, 5, 2, 6, 9, 22, 4, 13, 3, 16, 22, 18, 6, 5, 14, 7, 7, 2, 17, 9, 8, 83, 14], {"22": 18, "21": 1, "14": 12, "10": 8, "8": 6, "17": 9, "6": 4, "7": 6, "9": 3, "20": 13, "19": 12, "5": 3, "13": 8, "4": 3, "83": 14, "3": 2, "18": 1, "2": 1, "16": 2, "15": 3}, 239] | ["[20, 10, 16, 21, 15, 21, 13, 6, 19, 9, 7, 5, 2, 6, 9, 22, 4, 13, 3, 16, 22, 18, 6, 5, 14, 7, 7, 2, 17, 9, 8, 83, 14]", "{22: 18, 21: 1, 14: 12, 10: 8, 8: 6, 17: 9, 6: 4, 7: 6, 9: 3, 20: 13, 19: 12, 5: 3, 13: 8, 4: 3, 83: 14, 3: 2, 18: 1, 2: 1, 16: 2, 15: 3}", "239"] |
5 | 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, 2], [1, 0], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 2]] | 12 | 0.08999156951904297 | 12 | 6 | 12 | [[["Green", "Blue", "Blue", "Blue"], ["Red", "Green", "Red", "Red"], ["Green", "Red", "Green", "Blue"]], 6] | [[["Green", "Blue", "Blue", "Blue"], ["Red", "Green", "Red", "Red"], ["Green", "Red", "Green", "Blue"]], 6] | ["[['Green', 'Blue', 'Blue', 'Blue'], ['Red', 'Green', 'Red', 'Red'], ['Green', 'Red', 'Green', 'Blue']]", "6"] |
5 | We have a 3x3 numerical grid, with numbers ranging from 44 to 77 (44 included in the range but 77 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, 67], [1, 0, 47], [2, 0, 46], [2, 1, 45], [2, 2, 44]] | 557 | 0.45664143562316895 | 5 | 33 | 9 | ["[['66', '', '74'], ['', '60', '62'], ['', '', '']]", 44, 77] | ["[['66', '', '74'], ['', '60', '62'], ['', '', '']]", 44, 77] | ["[['66', '', '74'], ['', '60', '62'], ['', '', '']]", "44", "77"] |
5 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 20 to 39. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 82, and sum of row 1 must be 82. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 7 | [[0, 0, 20], [0, 1, 23], [0, 2, 27], [1, 0, 24], [1, 1, 33], [1, 2, 25], [2, 1, 26], [2, 2, 21]] | 221 | 0.6350831985473633 | 8 | 19 | 9 | ["[['', '', ''], ['', '', ''], ['22', '', '']]", 3, 20, 39] | ["[['', '', ''], ['', '', ''], ['22', '', '']]", 20, 39, [1, 2], [1, 2], [82], [82], 82] | ["[['', '', ''], ['', '', ''], ['22', '', '']]", "20", "39", "[None, 82, None]", "[None, 82, None]", "82"] |
5 | 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, 3], [0, 1], [0, 5], [0, 5], [4, 0], [4, 1], [4, 0], [2, 3], [2, 3], [2, 5], [2, 1]] | 26 | 0.1328294277191162 | 11 | 30 | 12 | [[["Red", "Green", "Green", "Yellow"], [], ["Blue", "Blue", "Green", "Red"], [], ["Blue", "Yellow", "Red", "Yellow"], []], 4, {"0": 4, "1": 1, "2": 7, "3": 3, "4": 2, "5": 2}] | [[["Red", "Green", "Green", "Yellow"], [], ["Blue", "Blue", "Green", "Red"], [], ["Blue", "Yellow", "Red", "Yellow"], []], 4, {"0": 4, "1": 1, "2": 7, "3": 3, "4": 2, "5": 2}, 3] | ["[['Red', 'Green', 'Green', 'Yellow'], [], ['Blue', 'Blue', 'Green', 'Red'], [], ['Blue', 'Yellow', 'Red', 'Yellow'], []]", "{0: 4, 1: 1, 2: 7, 3: 3, 4: 2, 5: 2}", "4", "3"] |
5 | 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, 0) to his destination workshop at index (3, 7), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[5, 0], [4, 0], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7]] | 95 | 0.022897005081176758 | 10 | 4 | 4 | [[["8", "x", "4", "7", "10", "x", "12", "5", "x"], ["x", "x", "4", "11", "16", "4", "12", "15", "x"], ["3", "x", "16", "16", "4", "x", "x", "x", "x"], ["11", "6", "3", "12", "8", "2", "19", "14", "x"], ["20", "18", "19", "x", "4", "18", "x", "15", "13"], ["8", "15", "x", "16", "11", "x", "10", "14", "1"], ["x", "x", "x... | [[["8", "x", "4", "7", "10", "x", "12", "5", "x"], ["x", "x", "4", "11", "16", "4", "12", "15", "x"], ["3", "x", "16", "16", "4", "x", "x", "x", "x"], ["11", "6", "3", "12", "8", "2", "19", "14", "x"], ["20", "18", "19", "x", "4", "18", "x", "15", "13"], ["8", "15", "x", "16", "11", "x", "10", "14", "1"], ["x", "x", "x... | ["[['8', 'x', '4', '7', '10', 'x', '12', '5', 'x'], ['x', 'x', '4', '11', '16', '4', '12', '15', 'x'], ['3', 'x', '16', '16', '4', 'x', 'x', 'x', 'x'], ['11', '6', '3', '12', '8', '2', '19', '14', 'x'], ['20', '18', '19', 'x', '4', '18', 'x', '15', '13'], ['8', '15', 'x', '16', '11', 'x', '10', '14', '1'], ['x', 'x', '... |
5 | 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, 0], [0, 1], [0, 2], [0, 3], [1, 3], [1, 4], [2, 5], [3, 5], [4, 6], [5, 7]] | 10 | 0.031831979751586914 | 10 | 8 | 2 | ["[[0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1]]", 3] | ["[[0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1]]", [0, 0], [5, 7], 3] | ["[[0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1]]", "(0, 0)", "(5, 7)", "3"] |
5 | Given 5 labeled water jugs with capacities 145, 101, 17, 75, 102, 129 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 260, 287, 413 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 | [["+", 17, 3], ["+", 101, 3], ["+", 145, 3], ["+", 75, 3], ["+", 75, 3], ["+", 101, 2], ["+", 101, 2], ["-", 17, 2], ["+", 102, 2], ["+", 101, 1], ["-", 17, 1], ["+", 75, 1], ["+", 101, 1]] | 13 | 0.04054903984069824 | 13 | 36 | 3 | [[145, 101, 17, 75, 102, 129], [260, 287, 413]] | [[145, 101, 17, 75, 102, 129], [260, 287, 413]] | ["[145, 101, 17, 75, 102, 129]", "[260, 287, 413]"] |
6 | 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 | 2 | [38, 41, 82, 90, 41, 82, 55, 28, 36, 46, 90, 41, 82, 55, 41, 82, 55, 38] | 18 | 0.046418190002441406 | 18 | 4 | 9 | [[[46, 82, 90], [36, 41, 38], [28, 55, "_"]]] | [[[46, 82, 90], [36, 41, 38], [28, 55, "_"]]] | ["[[46, 82, 90], [36, 41, 38], [28, 55, '_']]"] |
6 | 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", "up-left", "up-left"] | 10 | 0.16235899925231934 | 10 | 4 | 16 | [[["l", "c", "_", "o"], ["s", "c", "o", "h"], ["d", "y", "a", "e"], ["h", "s", "l", "t"]]] | [[["l", "c", "_", "o"], ["s", "c", "o", "h"], ["d", "y", "a", "e"], ["h", "s", "l", "t"]], ["cho", "slod", "syce", "halt"]] | ["[['l', 'c', '_', 'o'], ['s', 'c', 'o', 'h'], ['d', 'y', 'a', 'e'], ['h', 's', 'l', 't']]", "['cho', 'slod', 'syce', 'halt']"] |
6 | 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", "I", "F", "J", "F", "K", "D", "O", "D"] | 9 | 0.028170108795166016 | 9 | 10 | 13 | [[[0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0]... | [[[0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0]... | ["[[0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0... |
6 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [20, 25, 10, 4, 13, 3, 10, 17, 5, 25, 17, 2, 19, 24, 25, 10, 19, 8, 2, 20, 15, 84, 23, 87, 19, 8, 12, 17, 23, 6], such that the sum of the chosen coins adds up to 250. Each coin in the list is unique and can only be used o... | coin_exchange | subset_sum | 20 | [3, 5, 87, 84, 24, 20, 25, 2] | 43 | 0.036344051361083984 | 8 | 30 | 30 | [[20, 25, 10, 4, 13, 3, 10, 17, 5, 25, 17, 2, 19, 24, 25, 10, 19, 8, 2, 20, 15, 84, 23, 87, 19, 8, 12, 17, 23, 6]] | [[20, 25, 10, 4, 13, 3, 10, 17, 5, 25, 17, 2, 19, 24, 25, 10, 19, 8, 2, 20, 15, 84, 23, 87, 19, 8, 12, 17, 23, 6], {"12": 12, "19": 8, "84": 20, "24": 1, "5": 1, "3": 1, "4": 2, "87": 7, "10": 5, "25": 7, "6": 5, "20": 5, "15": 7, "23": 17, "13": 4, "17": 16, "2": 1, "8": 5}, 250] | ["[20, 25, 10, 4, 13, 3, 10, 17, 5, 25, 17, 2, 19, 24, 25, 10, 19, 8, 2, 20, 15, 84, 23, 87, 19, 8, 12, 17, 23, 6]", "{12: 12, 19: 8, 84: 20, 24: 1, 5: 1, 3: 1, 4: 2, 87: 7, 10: 5, 25: 7, 6: 5, 20: 5, 15: 7, 23: 17, 13: 4, 17: 16, 2: 1, 8: 5}", "250"] |
6 | 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, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0]] | 22 | 7.465789318084717 | 22 | 6 | 12 | [[["Blue", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Red"], ["Green", "Green", "Blue", "Red"]], 6] | [[["Blue", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Red"], ["Green", "Green", "Blue", "Red"]], 6] | ["[['Blue', 'Green', 'Blue', 'Red'], ['Red', 'Blue', 'Green', 'Red'], ['Green', 'Green', 'Blue', 'Red']]", "6"] |
6 | We have a 3x3 numerical grid, with numbers ranging from 41 to 74 (41 included in the range but 74 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, 49], [1, 0, 42], [1, 1, 45], [2, 0, 43], [2, 1, 44]] | 470 | 0.18347549438476562 | 5 | 33 | 9 | ["[['41', '48', ''], ['', '', '63'], ['', '', '67']]", 41, 74] | ["[['41', '48', ''], ['', '', '63'], ['', '', '67']]", 41, 74] | ["[['41', '48', ''], ['', '', '63'], ['', '', '67']]", "41", "74"] |
6 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 19 to 43. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 82, and sum of row 1 must be 82. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 7 | [[0, 0, 19], [0, 2, 25], [1, 0, 21], [1, 1, 39], [1, 2, 22], [2, 0, 32], [2, 1, 23]] | 234 | 7.9251344203948975 | 7 | 19 | 9 | ["[['', '20', ''], ['', '', ''], ['', '', '33']]", 3, 19, 43] | ["[['', '20', ''], ['', '', ''], ['', '', '33']]", 19, 43, [1, 2], [1, 2], [82], [82], 96] | ["[['', '20', ''], ['', '', ''], ['', '', '33']]", "19", "43", "[None, 82, None]", "[None, 82, None]", "96"] |
6 | 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, 5], [2, 5], [2, 4], [3, 4], [3, 2], [0, 1], [0, 1], [3, 5], [3, 1], [0, 4]] | 26 | 0.06659841537475586 | 10 | 30 | 12 | [[["Yellow", "Blue", "Blue", "Green"], [], ["Yellow", "Green", "Red", "Red"], ["Green", "Red", "Yellow", "Blue"], [], []], 4, {"0": 7, "1": 3, "2": 5, "3": 5, "4": 1, "5": 3}] | [[["Yellow", "Blue", "Blue", "Green"], [], ["Yellow", "Green", "Red", "Red"], ["Green", "Red", "Yellow", "Blue"], [], []], 4, {"0": 7, "1": 3, "2": 5, "3": 5, "4": 1, "5": 3}, 3] | ["[['Yellow', 'Blue', 'Blue', 'Green'], [], ['Yellow', 'Green', 'Red', 'Red'], ['Green', 'Red', 'Yellow', 'Blue'], [], []]", "{0: 7, 1: 3, 2: 5, 3: 5, 4: 1, 5: 3}", "4", "3"] |
6 | 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, 5) to his destination workshop at index (1, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [4, 1], [3, 1], [2, 1], [1, 1], [1, 0]] | 82 | 0.027018070220947266 | 10 | 4 | 4 | [[["6", "16", "x", "x", "15", "x", "14", "11", "x"], ["5", "2", "1", "x", "3", "x", "4", "13", "x"], ["x", "7", "x", "x", "13", "x", "10", "14", "5"], ["6", "16", "x", "13", "6", "x", "16", "x", "x"], ["x", "1", "17", "x", "6", "3", "x", "x", "3"], ["11", "10", "7", "19", "15", "8", "12", "6", "x"], ["18", "x", "x", "9... | [[["6", "16", "x", "x", "15", "x", "14", "11", "x"], ["5", "2", "1", "x", "3", "x", "4", "13", "x"], ["x", "7", "x", "x", "13", "x", "10", "14", "5"], ["6", "16", "x", "13", "6", "x", "16", "x", "x"], ["x", "1", "17", "x", "6", "3", "x", "x", "3"], ["11", "10", "7", "19", "15", "8", "12", "6", "x"], ["18", "x", "x", "9... | ["[['6', '16', 'x', 'x', '15', 'x', '14', '11', 'x'], ['5', '2', '1', 'x', '3', 'x', '4', '13', 'x'], ['x', '7', 'x', 'x', '13', 'x', '10', '14', '5'], ['6', '16', 'x', '13', '6', 'x', '16', 'x', 'x'], ['x', '1', '17', 'x', '6', '3', 'x', 'x', '3'], ['11', '10', '7', '19', '15', '8', '12', '6', 'x'], ['18', 'x', 'x', '... |
6 | 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, 6], [1, 6], [2, 5], [3, 5], [4, 4], [5, 3], [6, 3], [7, 3], [7, 2], [8, 2]] | 10 | 0.02278614044189453 | 10 | 8 | 2 | ["[[1, 0, 1, 0, 0, 1, 0, 1, 0], [1, 1, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 1, 1, 1]]", 3] | ["[[1, 0, 1, 0, 0, 1, 0, 1, 0], [1, 1, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 1, 1, 1]]", [0, 6], [8, 2], 3] | ["[[1, 0, 1, 0, 0, 1, 0, 1, 0], [1, 1, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 1, 1, 1]]", "(0, 6)", "(8, 2)", "3"] |
6 | Given 5 labeled water jugs with capacities 76, 135, 134, 19, 10, 30 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 390, 420, 439 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 | [["+", 76, 3], ["+", 76, 3], ["+", 134, 3], ["+", 19, 3], ["+", 134, 3], ["+", 134, 2], ["+", 134, 2], ["+", 76, 2], ["+", 76, 2], ["+", 76, 1], ["+", 76, 1], ["+", 134, 1], ["-", 30, 1], ["+", 134, 1]] | 14 | 0.05055570602416992 | 14 | 36 | 3 | [[76, 135, 134, 19, 10, 30], [390, 420, 439]] | [[76, 135, 134, 19, 10, 30], [390, 420, 439]] | ["[76, 135, 134, 19, 10, 30]", "[390, 420, 439]"] |
7 | 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 | [31, 37, 13, 31, 16, 36, 86, 89, 37, 16, 36, 86, 89, 37, 16, 13] | 16 | 0.03079676628112793 | 16 | 4 | 9 | [[[36, 16, 48], [86, "_", 13], [89, 31, 37]]] | [[[36, 16, 48], [86, "_", 13], [89, 31, 37]]] | ["[[36, 16, 48], [86, '_', 13], [89, 31, 37]]"] |
7 | 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", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left"] | 14 | 0.1806955337524414 | 14 | 4 | 16 | [[["u", "c", "r", "y"], ["d", "n", "n", "r"], ["_", "u", "m", "p"], ["k", "e", "e", "e"]]] | [[["u", "c", "r", "y"], ["d", "n", "n", "r"], ["_", "u", "m", "p"], ["k", "e", "e", "e"]], ["cry", "dune", "rump", "knee"]] | ["[['u', 'c', 'r', 'y'], ['d', 'n', 'n', 'r'], ['_', 'u', 'm', 'p'], ['k', 'e', 'e', 'e']]", "['cry', 'dune', 'rump', 'knee']"] |
7 | 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 | ["Z", "A", "P", "H", "J", "R", "B", "F", "M", "H", "N", "B"] | 12 | 0.02784132957458496 | 12 | 10 | 13 | [[[0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0]... | [[[0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0]... | ["[[0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0... |
7 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [41, 4, 22, 8, 5, 5, 20, 4, 3, 19, 4, 13, 3, 18, 20, 9, 15, 3, 3, 14, 3, 14, 9, 4, 15, 19, 6, 15, 22, 19, 3, 3, 20, 9, 20, 11, 22, 15, 20], such that the sum of the chosen coins adds up to 220. Each coin in the list is uni... | coin_exchange | subset_sum | 21 | [14, 8, 6, 11, 41, 22, 20, 14, 4, 5, 5, 9, 9, 9, 13, 15, 15] | 115 | 0.03900480270385742 | 17 | 39 | 39 | [[41, 4, 22, 8, 5, 5, 20, 4, 3, 19, 4, 13, 3, 18, 20, 9, 15, 3, 3, 14, 3, 14, 9, 4, 15, 19, 6, 15, 22, 19, 3, 3, 20, 9, 20, 11, 22, 15, 20]] | [[41, 4, 22, 8, 5, 5, 20, 4, 3, 19, 4, 13, 3, 18, 20, 9, 15, 3, 3, 14, 3, 14, 9, 4, 15, 19, 6, 15, 22, 19, 3, 3, 20, 9, 20, 11, 22, 15, 20], {"20": 11, "15": 13, "9": 7, "8": 3, "3": 1, "6": 3, "5": 2, "13": 11, "4": 4, "22": 11, "19": 19, "11": 1, "14": 2, "41": 16, "18": 18}, 220] | ["[41, 4, 22, 8, 5, 5, 20, 4, 3, 19, 4, 13, 3, 18, 20, 9, 15, 3, 3, 14, 3, 14, 9, 4, 15, 19, 6, 15, 22, 19, 3, 3, 20, 9, 20, 11, 22, 15, 20]", "{20: 11, 15: 13, 9: 7, 8: 3, 3: 1, 6: 3, 5: 2, 13: 11, 4: 4, 22: 11, 19: 19, 11: 1, 14: 2, 41: 16, 18: 18}", "220"] |
7 | 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, 2], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [0, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]] | 20 | 2.5152063369750977 | 20 | 6 | 12 | [[["Red", "Red", "Blue", "Green"], ["Blue", "Red", "Blue", "Green"], ["Blue", "Green", "Red", "Green"]], 6] | [[["Red", "Red", "Blue", "Green"], ["Blue", "Red", "Blue", "Green"], ["Blue", "Green", "Red", "Green"]], 6] | ["[['Red', 'Red', 'Blue', 'Green'], ['Blue', 'Red', 'Blue', 'Green'], ['Blue', 'Green', 'Red', 'Green']]", "6"] |
7 | We have a 3x3 numerical grid, with numbers ranging from 25 to 58 (25 included in the range but 58 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, 25], [0, 1, 26], [1, 0, 47], [1, 2, 43], [2, 0, 48], [2, 1, 49]] | 359 | 0.5126192569732666 | 6 | 33 | 9 | ["[['', '', '42'], ['', '46', ''], ['', '', '55']]", 25, 58] | ["[['', '', '42'], ['', '46', ''], ['', '', '55']]", 25, 58] | ["[['', '', '42'], ['', '46', ''], ['', '', '55']]", "25", "58"] |
7 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 19 to 43. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 111, and sum of row 1 must be 94. Also, the sum of the numbers in the diagonal from the top right to th... | magic_square | underdetermined_system | 7 | [[0, 1, 33], [1, 0, 23], [1, 1, 36], [1, 2, 35], [2, 0, 20], [2, 1, 42], [2, 2, 19]] | 271 | 1.7812092304229736 | 7 | 19 | 9 | ["[['37', '', '26'], ['', '', ''], ['', '', '']]", 3, 19, 43] | ["[['37', '', '26'], ['', '', ''], ['', '', '']]", 19, 43, [1, 2], [1, 2], [111], [94], 82] | ["[['37', '', '26'], ['', '', ''], ['', '', '']]", "19", "43", "[None, 111, None]", "[None, 94, None]", "82"] |
7 | 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, 1], [5, 1], [5, 1], [3, 0], [3, 2], [4, 3], [0, 5], [2, 4]] | 37 | 0.026184558868408203 | 8 | 30 | 12 | [[[], [], [], ["Yellow", "Green", "Blue", "Blue"], ["Red", "Blue", "Green", "Green"], ["Red", "Red", "Yellow", "Yellow"]], 4, {"0": 5, "1": 3, "2": 5, "3": 6, "4": 5, "5": 7}] | [[[], [], [], ["Yellow", "Green", "Blue", "Blue"], ["Red", "Blue", "Green", "Green"], ["Red", "Red", "Yellow", "Yellow"]], 4, {"0": 5, "1": 3, "2": 5, "3": 6, "4": 5, "5": 7}, 3] | ["[[], [], [], ['Yellow', 'Green', 'Blue', 'Blue'], ['Red', 'Blue', 'Green', 'Green'], ['Red', 'Red', 'Yellow', 'Yellow']]", "{0: 5, 1: 3, 2: 5, 3: 6, 4: 5, 5: 7}", "4", "3"] |
7 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (6, 1) to his destination workshop at index (2, 6), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[6, 1], [6, 2], [5, 2], [4, 2], [4, 3], [3, 3], [2, 3], [2, 4], [2, 5], [2, 6]] | 74 | 0.021251201629638672 | 10 | 4 | 4 | [[["x", "7", "7", "12", "7", "x", "13", "1", "18"], ["9", "18", "x", "4", "19", "8", "x", "15", "10"], ["9", "x", "10", "5", "5", "9", "8", "x", "x"], ["14", "4", "19", "9", "14", "x", "x", "7", "9"], ["9", "4", "11", "15", "7", "x", "17", "3", "x"], ["11", "x", "2", "18", "15", "15", "x", "x", "x"], ["x", "5", "10", "... | [[["x", "7", "7", "12", "7", "x", "13", "1", "18"], ["9", "18", "x", "4", "19", "8", "x", "15", "10"], ["9", "x", "10", "5", "5", "9", "8", "x", "x"], ["14", "4", "19", "9", "14", "x", "x", "7", "9"], ["9", "4", "11", "15", "7", "x", "17", "3", "x"], ["11", "x", "2", "18", "15", "15", "x", "x", "x"], ["x", "5", "10", "... | ["[['x', '7', '7', '12', '7', 'x', '13', '1', '18'], ['9', '18', 'x', '4', '19', '8', 'x', '15', '10'], ['9', 'x', '10', '5', '5', '9', '8', 'x', 'x'], ['14', '4', '19', '9', '14', 'x', 'x', '7', '9'], ['9', '4', '11', '15', '7', 'x', '17', '3', 'x'], ['11', 'x', '2', '18', '15', '15', 'x', 'x', 'x'], ['x', '5', '10', ... |
7 | 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, 2], [8, 3], [8, 4], [8, 5], [8, 6], [7, 7], [6, 8], [5, 8], [4, 8], [3, 8], [2, 8], [1, 7], [0, 7]] | 13 | 0.030285120010375977 | 13 | 8 | 2 | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]", 3] | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]", [8, 2], [0, 7], 3] | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]", "(8, 2)", "(0, 7)", "3"] |
7 | Given 5 labeled water jugs with capacities 22, 48, 29, 111, 92, 28 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 164, 233, 289 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 | [["+", 48, 3], ["+", 111, 3], ["+", 111, 3], ["-", 29, 3], ["+", 48, 3], ["+", 29, 2], ["+", 92, 2], ["+", 92, 2], ["-", 28, 2], ["+", 48, 2], ["+", 22, 1], ["+", 22, 1], ["+", 28, 1], ["+", 92, 1]] | 14 | 0.03762245178222656 | 14 | 36 | 3 | [[22, 48, 29, 111, 92, 28], [164, 233, 289]] | [[22, 48, 29, 111, 92, 28], [164, 233, 289]] | ["[22, 48, 29, 111, 92, 28]", "[164, 233, 289]"] |
8 | 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 | [74, 72, 56, 96, 33, 56, 49, 77, 96, 49, 72, 59, 56, 33, 49, 72, 59, 56] | 18 | 0.03490924835205078 | 18 | 4 | 9 | [[[77, 49, "_"], [56, 72, 74], [96, 33, 59]]] | [[[77, 49, "_"], [56, 72, 74], [96, 33, 59]]] | ["[[77, 49, '_'], [56, 72, 74], [96, 33, 59]]"] |
8 | 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", "down-right", "down-left", "up-left", "up-right", "up-left"] | 8 | 0.16104960441589355 | 8 | 4 | 16 | [[["h", "k", "t", "n"], ["k", "e", "a", "k"], ["e", "i", "_", "l"], ["w", "l", "n", "t"]]] | [[["h", "k", "t", "n"], ["k", "e", "a", "k"], ["e", "i", "_", "l"], ["w", "l", "n", "t"]], ["ken", "khat", "kill", "went"]] | ["[['h', 'k', 't', 'n'], ['k', 'e', 'a', 'k'], ['e', 'i', '_', 'l'], ['w', 'l', 'n', 't']]", "['ken', 'khat', 'kill', 'went']"] |
8 | 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 | ["U", "L", "O", "A", "X", "Y", "A", "X"] | 8 | 0.029206514358520508 | 8 | 10 | 13 | [[[0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]... | [[[0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]... | ["[[0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0... |
8 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [4, 17, 8, 15, 6, 14, 2, 4, 16, 10, 6, 5, 14, 8, 18, 2, 17, 9, 17, 59, 3, 10, 21, 4, 9, 14, 14, 20, 14, 8, 14, 18, 5, 16, 14, 17, 5, 3], such that the sum of the chosen coins adds up to 214. Each coin in the list is unique... | coin_exchange | subset_sum | 22 | [17, 17, 17, 14, 8, 59, 14, 8, 17, 14, 8, 21] | 39 | 0.037581682205200195 | 12 | 38 | 38 | [[4, 17, 8, 15, 6, 14, 2, 4, 16, 10, 6, 5, 14, 8, 18, 2, 17, 9, 17, 59, 3, 10, 21, 4, 9, 14, 14, 20, 14, 8, 14, 18, 5, 16, 14, 17, 5, 3]] | [[4, 17, 8, 15, 6, 14, 2, 4, 16, 10, 6, 5, 14, 8, 18, 2, 17, 9, 17, 59, 3, 10, 21, 4, 9, 14, 14, 20, 14, 8, 14, 18, 5, 16, 14, 17, 5, 3], {"15": 6, "5": 5, "17": 1, "14": 4, "2": 2, "8": 2, "10": 9, "59": 9, "16": 8, "4": 3, "18": 10, "20": 11, "21": 8, "6": 6, "9": 9, "3": 3}, 214] | ["[4, 17, 8, 15, 6, 14, 2, 4, 16, 10, 6, 5, 14, 8, 18, 2, 17, 9, 17, 59, 3, 10, 21, 4, 9, 14, 14, 20, 14, 8, 14, 18, 5, 16, 14, 17, 5, 3]", "{15: 6, 5: 5, 17: 1, 14: 4, 2: 2, 8: 2, 10: 9, 59: 9, 16: 8, 4: 3, 18: 10, 20: 11, 21: 8, 6: 6, 9: 9, 3: 3}", "214"] |
8 | 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, 2], [1, 0], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [0, 1]] | 15 | 0.3737452030181885 | 15 | 6 | 12 | [[["Green", "Blue", "Red", "Red"], ["Red", "Green", "Green", "Blue"], ["Red", "Green", "Blue", "Blue"]], 6] | [[["Green", "Blue", "Red", "Red"], ["Red", "Green", "Green", "Blue"], ["Red", "Green", "Blue", "Blue"]], 6] | ["[['Green', 'Blue', 'Red', 'Red'], ['Red', 'Green', 'Green', 'Blue'], ['Red', 'Green', 'Blue', 'Blue']]", "6"] |
8 | We have a 3x3 numerical grid, with numbers ranging from 19 to 52 (19 included in the range but 52 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, 19], [0, 1, 37], [0, 2, 45], [1, 0, 21], [2, 0, 35], [2, 2, 20]] | 285 | 6.972386598587036 | 6 | 33 | 9 | ["[['', '', ''], ['', '36', '44'], ['', '34', '']]", 19, 52] | ["[['', '', ''], ['', '36', '44'], ['', '34', '']]", 19, 52] | ["[['', '', ''], ['', '36', '44'], ['', '34', '']]", "19", "52"] |
8 | 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 130, 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 | 7 | [[0, 1, 38], [0, 2, 35], [1, 0, 39], [1, 1, 51], [1, 2, 54], [2, 0, 37], [2, 1, 41], [2, 2, 36]] | 383 | 2.281245708465576 | 8 | 19 | 9 | ["[['52', '', ''], ['', '', ''], ['', '', '']]", 3, 35, 59] | ["[['52', '', ''], ['', '', ''], ['', '', '']]", 35, 59, [1, 2], [1, 2], [130], [144], 123] | ["[['52', '', ''], ['', '', ''], ['', '', '']]", "35", "59", "[None, 130, None]", "[None, 144, None]", "123"] |
8 | 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, 2], [0, 4], [0, 4], [5, 0], [5, 2], [5, 0], [2, 5], [2, 5], [1, 2], [1, 2], [1, 4], [1, 2]] | 23 | 0.13733744621276855 | 12 | 30 | 12 | [[["Blue", "Green", "Green", "Red"], ["Yellow", "Yellow", "Green", "Yellow"], [], [], [], ["Red", "Blue", "Red", "Blue"]], 4, {"0": 3, "1": 6, "2": 1, "3": 7, "4": 2, "5": 3}] | [[["Blue", "Green", "Green", "Red"], ["Yellow", "Yellow", "Green", "Yellow"], [], [], [], ["Red", "Blue", "Red", "Blue"]], 4, {"0": 3, "1": 6, "2": 1, "3": 7, "4": 2, "5": 3}, 3] | ["[['Blue', 'Green', 'Green', 'Red'], ['Yellow', 'Yellow', 'Green', 'Yellow'], [], [], [], ['Red', 'Blue', 'Red', 'Blue']]", "{0: 3, 1: 6, 2: 1, 3: 7, 4: 2, 5: 3}", "4", "3"] |
8 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 8) to his destination workshop at index (6, 3), indexing from 0. Ben's car can move... | traffic | pathfinding | 1 | [[2, 8], [2, 7], [3, 7], [4, 7], [4, 6], [4, 5], [4, 4], [5, 4], [5, 3], [6, 3]] | 85 | 0.026849031448364258 | 10 | 4 | 4 | [[["x", "x", "x", "x", "13", "x", "x", "3", "8"], ["x", "18", "19", "19", "2", "9", "x", "x", "x"], ["15", "x", "6", "x", "x", "x", "13", "13", "4"], ["7", "x", "4", "10", "x", "11", "10", "17", "x"], ["2", "7", "x", "x", "8", "16", "4", "1", "4"], ["x", "x", "x", "5", "16", "15", "x", "17", "10"], ["x", "x", "x", "5",... | [[["x", "x", "x", "x", "13", "x", "x", "3", "8"], ["x", "18", "19", "19", "2", "9", "x", "x", "x"], ["15", "x", "6", "x", "x", "x", "13", "13", "4"], ["7", "x", "4", "10", "x", "11", "10", "17", "x"], ["2", "7", "x", "x", "8", "16", "4", "1", "4"], ["x", "x", "x", "5", "16", "15", "x", "17", "10"], ["x", "x", "x", "5",... | ["[['x', 'x', 'x', 'x', '13', 'x', 'x', '3', '8'], ['x', '18', '19', '19', '2', '9', 'x', 'x', 'x'], ['15', 'x', '6', 'x', 'x', 'x', '13', '13', '4'], ['7', 'x', '4', '10', 'x', '11', '10', '17', 'x'], ['2', '7', 'x', 'x', '8', '16', '4', '1', '4'], ['x', 'x', 'x', '5', '16', '15', 'x', '17', '10'], ['x', 'x', 'x', '5'... |
8 | 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, 8], [1, 7], [2, 7], [3, 7], [4, 7], [5, 6], [5, 5], [6, 5], [7, 4], [7, 3], [8, 3]] | 11 | 0.03156876564025879 | 11 | 8 | 2 | ["[[0, 1, 1, 1, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1], [0, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1]]", 3] | ["[[0, 1, 1, 1, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1], [0, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1]]", [0, 8], [8, 3], 3] | ["[[0, 1, 1, 1, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1], [0, 0, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1]]", "(0, 8)", "(8, 3)", "3"] |
8 | Given 5 labeled water jugs with capacities 59, 68, 104, 106, 69, 42 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 196, 210, 238 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 | [["+", 106, 3], ["+", 106, 3], ["-", 42, 3], ["+", 68, 3], ["+", 104, 2], ["+", 106, 2], ["+", 59, 1], ["+", 68, 1], ["+", 69, 1]] | 9 | 0.032889366149902344 | 9 | 36 | 3 | [[59, 68, 104, 106, 69, 42], [196, 210, 238]] | [[59, 68, 104, 106, 69, 42], [196, 210, 238]] | ["[59, 68, 104, 106, 69, 42]", "[196, 210, 238]"] |
9 | 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 | [19, 31, 68, 6, 12, 23, 30, 68, 23, 30, 68, 43, 31, 19] | 14 | 0.02962183952331543 | 14 | 4 | 9 | [[[23, 30, 43], [12, 31, 19], [6, 68, "_"]]] | [[[23, 30, 43], [12, 31, 19], [6, 68, "_"]]] | ["[[23, 30, 43], [12, 31, 19], [6, 68, '_']]"] |
9 | 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-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.14909648895263672 | 16 | 4 | 16 | [[["_", "s", "a", "n"], ["q", "u", "o", "u"], ["c", "h", "u", "t"], ["l", "t", "r", "e"]]] | [[["_", "s", "a", "n"], ["q", "u", "o", "u"], ["c", "h", "u", "t"], ["l", "t", "r", "e"]], ["sun", "quot", "chat", "lure"]] | ["[['_', 's', 'a', 'n'], ['q', 'u', 'o', 'u'], ['c', 'h', 'u', 't'], ['l', 't', 'r', 'e']]", "['sun', 'quot', 'chat', 'lure']"] |
9 | 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 | ["C", "Y", "F", "T", "W", "R", "W", "F"] | 8 | 0.022681236267089844 | 8 | 10 | 13 | [[[0, 1, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 0]... | [[[0, 1, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 0]... | ["[[0, 1, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 0... |
9 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [3, 6, 9, 10, 13, 15, 18, 5, 21, 19, 12, 15, 5, 9, 4, 16, 8, 4, 7, 7, 7, 2, 16, 14, 18, 3, 89, 21, 12, 10, 7, 14, 4, 11, 6, 20], such that the sum of the chosen coins adds up to 229. Each coin in the list is unique and can... | coin_exchange | subset_sum | 23 | [3, 89, 20, 14, 21, 14, 8, 13, 21, 16, 10] | 37 | 0.03856658935546875 | 11 | 36 | 36 | [[3, 6, 9, 10, 13, 15, 18, 5, 21, 19, 12, 15, 5, 9, 4, 16, 8, 4, 7, 7, 7, 2, 16, 14, 18, 3, 89, 21, 12, 10, 7, 14, 4, 11, 6, 20]] | [[3, 6, 9, 10, 13, 15, 18, 5, 21, 19, 12, 15, 5, 9, 4, 16, 8, 4, 7, 7, 7, 2, 16, 14, 18, 3, 89, 21, 12, 10, 7, 14, 4, 11, 6, 20], {"14": 1, "89": 13, "2": 2, "5": 2, "4": 4, "6": 6, "8": 2, "16": 5, "21": 4, "20": 2, "18": 9, "11": 10, "10": 3, "12": 12, "15": 5, "13": 1, "3": 1, "19": 19, "7": 7, "9": 3}, 229] | ["[3, 6, 9, 10, 13, 15, 18, 5, 21, 19, 12, 15, 5, 9, 4, 16, 8, 4, 7, 7, 7, 2, 16, 14, 18, 3, 89, 21, 12, 10, 7, 14, 4, 11, 6, 20]", "{14: 1, 89: 13, 2: 2, 5: 2, 4: 4, 6: 6, 8: 2, 16: 5, 21: 4, 20: 2, 18: 9, 11: 10, 10: 3, 12: 12, 15: 5, 13: 1, 3: 1, 19: 19, 7: 7, 9: 3}", "229"] |
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Dataset Card for SearchBench
Dataset Summary
SearchBench is a benchmark designed to evaluate Language Models' (LLMs) ability to solve state-based problems that require combinatorial search and backtracking. SearchBench problems require a systematic exploration of action paths and backtracking to feasible states, which poses a significant challenge for LLMs to solve end-to-end, due to their autoregressive next-token prediction architecture.
The dataset is composed of five problem categories: puzzles, subset sum, sorting, pathfinding, and under-determined systems. These categories are further divided into 11 distinct problem types. Each problem type is adapted from NP-hard puzzles and combinatorial problems, with modifications made to the rules and constraints of each problem. The dataset contains approximately 100 instances of each problem type with varying levels of difficulty.
Automated pipelines are implemented for each problem type to generate an unlimited number of solvable instances and to assess the feasibility, correctness, and optimality of the solutions generated by the LLMs.
This benchmark provides insights into LLMs' capacity to implement new algorithms to solve complex problems. It also investigates the non-linear reasoning capability of LLMs to solve search problems end-to-end using only text.
Languages
The text in the dataset is in English. The associated BCP-47 code is en.
Dataset Structure
Data Instances
Each instance contains a natural language description of a problem and the optimal solution for the problem calculated using an A* algorithm with provable admissible and consistent heuristic implementation.
{
“problem_statement”: “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 in the list, with the blank tile ('_') placed in the top left corner of the board in the end. We can rearrange the tiles by swapping the blank space with any of its 4 diagonal neighboring tiles. Given the list of words and initial state of the board below, where the black space is represented as '_', what is the shortest list of swap actions (reported in python syntax) that can sort the board into the given list of target words? The list must only include the 4 diagonal swap directions: up-right, down-right, up-left, or down-left, representing the direction in ehich the blank space was swpped in. Target words: cam, hill, pray, doer The initial board: [['i', 'c', 'a', 'm'], ['h', 'p', 'l', 'o'], ['_', 'r', 'a', 'y'], ['d', 'l', 'e', 'r']]”,
“opt_solution”: "['up-right', 'down-right', 'down-left', 'up-left', 'up-right', 'down-right', 'up-right', 'up-left', 'down-left', 'down-left', 'down-right', 'up-right', 'up-right', 'up-left', 'down-left', 'up-left']",
}
Data Fields
Each instance in the dataset comes with several additional fields. These fields offer insights about the problem and allow for automatic evaluation of the solutions generated by the LLMs across multiple dimensions. For a more detailed description of the fields for each instance, please refer to the supplementary material of the paper.
- diff_sorted_id: A unique identifier for each problem, sorted by difficulty level within a specific problem type.
- problem_statement: The description of the problem to be solved, given to language models.
- problem_type: The type of problem, out of 11 possible types.
- problem_category: The category of the problem, out of five possible categories.
- relative_diff_score: A score indicating the problem's difficulty relative to other problems of the same type.
- opt_solution: A list of actions leading to the goal state with the minimum cost.
- opt_solution_cost: The cost of the optimal solution for the problem.
- opt_solution_compute_t: The time taken by the A* implementation to solve the problem.
- solution_depth: The number of actions required to reach the goal state with minimum cost.
- max_successor_states: The maximum number of successor states that can be reached from any state in the problem.
- num_vars_per_state: An upper limit on the number of variables in each state of the problem.
- is_feasible_args: Variables that must be passed to the 'is_feasible' function to check if a solution adheres to the problem's rules and constraints.
- is_correct_args: Variables that must be passed to the 'is_correct' function to evaluate the correctness of a solution.
- A*_args: Variables that must be passed to the A* implementation to obtain the optimal solution for the problem.
Additional Information
Licensing Information
The SearchBench dataset is licensed under the CC BY-SA.
Citation Information
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