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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
28 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [26, 19, 7, 24, 27, 15, 9, 9, 9, 26, 15, 23, 6, 6, 24, 8, 21, 6, 6, 7, 25, 22, 8, 2, 7, 5, 8, 18, 14, 15, 24, 10, 4, 23, 21, 8, 18, 12, 16], such that the sum of the chosen coins adds up to 267. Each coin in the list is un... | coin_exchange | subset_sum | 21 | [9, 9, 9, 23, 12, 23, 6, 25, 6, 27, 26, 16, 6, 15, 15, 6, 4, 5, 15, 10] | 109 | 0.044671058654785156 | 20 | 39 | 39 | [[26, 19, 7, 24, 27, 15, 9, 9, 9, 26, 15, 23, 6, 6, 24, 8, 21, 6, 6, 7, 25, 22, 8, 2, 7, 5, 8, 18, 14, 15, 24, 10, 4, 23, 21, 8, 18, 12, 16]] | [[26, 19, 7, 24, 27, 15, 9, 9, 9, 26, 15, 23, 6, 6, 24, 8, 21, 6, 6, 7, 25, 22, 8, 2, 7, 5, 8, 18, 14, 15, 24, 10, 4, 23, 21, 8, 18, 12, 16], {"24": 14, "27": 10, "22": 14, "16": 7, "14": 12, "6": 3, "8": 7, "23": 6, "18": 18, "5": 3, "25": 8, "7": 6, "12": 3, "15": 8, "9": 2, "19": 15, "2": 1, "4": 1, "26": 15, "10": ... | ["[26, 19, 7, 24, 27, 15, 9, 9, 9, 26, 15, 23, 6, 6, 24, 8, 21, 6, 6, 7, 25, 22, 8, 2, 7, 5, 8, 18, 14, 15, 24, 10, 4, 23, 21, 8, 18, 12, 16]", "{24: 14, 27: 10, 22: 14, 16: 7, 14: 12, 6: 3, 8: 7, 23: 6, 18: 18, 5: 3, 25: 8, 7: 6, 12: 3, 15: 8, 9: 2, 19: 15, 2: 1, 4: 1, 26: 15, 10: 8, 21: 19}", "267"] |
28 | 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 | 8 | [[0, 1], [0, 2], [0, 2], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [0, 1]] | 14 | 0.5192186832427979 | 14 | 6 | 12 | [[["Red", "Green", "Green", "Blue"], ["Blue", "Red", "Red", "Red"], ["Blue", "Green", "Green", "Blue"]], 7] | [[["Red", "Green", "Green", "Blue"], ["Blue", "Red", "Red", "Red"], ["Blue", "Green", "Green", "Blue"]], 7] | ["[['Red', 'Green', 'Green', 'Blue'], ['Blue', 'Red', 'Red', 'Red'], ['Blue', 'Green', 'Green', 'Blue']]", "7"] |
28 | We have a 3x3 numerical grid, with numbers ranging from 12 to 60 (12 included in the range but 60 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 1, 13], [0, 2, 53], [1, 1, 19], [2, 1, 23]] | 276 | 0.17951035499572754 | 4 | 48 | 9 | ["[['12', '', ''], ['18', '', '52'], ['22', '', '31']]", 12, 60] | ["[['12', '', ''], ['18', '', '52'], ['22', '', '31']]", 12, 60] | ["[['12', '', ''], ['18', '', '52'], ['22', '', '31']]", "12", "60"] |
28 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 26 to 65. 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 124. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 1, 27], [0, 2, 26], [1, 0, 31], [1, 1, 52], [1, 2, 41], [2, 0, 30], [2, 1, 28], [2, 2, 29]] | 315 | 4.654482126235962 | 8 | 34 | 9 | ["[['51', '', ''], ['', '', ''], ['', '', '']]", 3, 26, 65] | ["[['51', '', ''], ['', '', ''], ['', '', '']]", 26, 65, [1, 2], [1, 2], [107], [124], 108] | ["[['51', '', ''], ['', '', ''], ['', '', '']]", "26", "65", "[None, 107, None]", "[None, 124, None]", "108"] |
28 | 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, 4], [0, 1], [5, 0], [2, 1], [2, 4], [2, 3], [5, 3], [5, 4], [2, 1], [3, 5], [3, 5]] | 52 | 0.031346797943115234 | 11 | 30 | 12 | [[["Green", "Yellow", "Red", "Red"], [], ["Yellow", "Green", "Blue", "Yellow"], [], [], ["Red", "Blue", "Green", "Blue"]], 4, {"0": 3, "1": 7, "2": 7, "3": 7, "4": 2, "5": 4}] | [[["Green", "Yellow", "Red", "Red"], [], ["Yellow", "Green", "Blue", "Yellow"], [], [], ["Red", "Blue", "Green", "Blue"]], 4, {"0": 3, "1": 7, "2": 7, "3": 7, "4": 2, "5": 4}, 3] | ["[['Green', 'Yellow', 'Red', 'Red'], [], ['Yellow', 'Green', 'Blue', 'Yellow'], [], [], ['Red', 'Blue', 'Green', 'Blue']]", "{0: 3, 1: 7, 2: 7, 3: 7, 4: 2, 5: 4}", "4", "3"] |
28 | 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, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 0], [5, 1], [5, 2], [4, 2], [4, 3], [4, 4], [3, 4], [2, 4], [2, 5], [2, 6], [3, 6], [3, 7], [3, 8]] | 129 | 0.028196334838867188 | 13 | 4 | 4 | [[["15", "x", "8", "x", "6", "9", "x", "x", "x", "x"], ["14", "x", "8", "x", "14", "x", "5", "11", "x", "9"], ["x", "17", "8", "x", "17", "15", "12", "x", "x", "13"], ["x", "13", "x", "x", "2", "x", "17", "17", "1", "x"], ["6", "x", "1", "5", "17", "x", "2", "18", "11", "7"], ["12", "8", "17", "10", "x", "x", "x", "15"... | [[["15", "x", "8", "x", "6", "9", "x", "x", "x", "x"], ["14", "x", "8", "x", "14", "x", "5", "11", "x", "9"], ["x", "17", "8", "x", "17", "15", "12", "x", "x", "13"], ["x", "13", "x", "x", "2", "x", "17", "17", "1", "x"], ["6", "x", "1", "5", "17", "x", "2", "18", "11", "7"], ["12", "8", "17", "10", "x", "x", "x", "15"... | ["[['15', 'x', '8', 'x', '6', '9', 'x', 'x', 'x', 'x'], ['14', 'x', '8', 'x', '14', 'x', '5', '11', 'x', '9'], ['x', '17', '8', 'x', '17', '15', '12', 'x', 'x', '13'], ['x', '13', 'x', 'x', '2', 'x', '17', '17', '1', 'x'], ['6', 'x', '1', '5', '17', 'x', '2', '18', '11', '7'], ['12', '8', '17', '10', 'x', 'x', 'x', '15... |
28 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[8, 0], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [3, 2], [3, 3], [2, 4], [1, 5], [0, 6]] | 12 | 0.031847238540649414 | 12 | 8 | 2 | ["[[1, 0, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 1... | ["[[1, 0, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 1... | ["[[1, 0, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 1... |
28 | Given 7 labeled water jugs with capacities 149, 128, 67, 43, 55, 38, 129 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 385, 387, 491 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ... | water_jug | subset_sum | 5 | [["+", 128, 3], ["+", 129, 3], ["+", 67, 3], ["+", 129, 3], ["+", 38, 3], ["+", 129, 2], ["+", 129, 2], ["+", 129, 2], ["+", 128, 1], ["+", 128, 1], ["+", 129, 1]] | 11 | 0.039963722229003906 | 11 | 42 | 3 | [[149, 128, 67, 43, 55, 38, 129], [385, 387, 491]] | [[149, 128, 67, 43, 55, 38, 129], [385, 387, 491]] | ["[149, 128, 67, 43, 55, 38, 129]", "[385, 387, 491]"] |
29 | 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 | 6 | [12, 30, 21, 80, 16, 12, 30, 21, 80, 30, 28, 37, 12, 28, 21, 67, 37, 21, 28, 12] | 20 | 0.03293919563293457 | 20 | 4 | 9 | [[[30, 12, 67], [21, "_", 28], [80, 16, 37]]] | [[[30, 12, 67], [21, "_", 28], [80, 16, 37]]] | ["[[30, 12, 67], [21, '_', 28], [80, 16, 37]]"] |
29 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left"] | 22 | 0.3418314456939697 | 22 | 4 | 20 | [[["d", "t", "s", "l", "a"], ["u", "a", "a", "e", "i"], ["_", "l", "g", "i", "a"], ["w", "r", "n", "c", "h"]]] | [[["d", "t", "s", "l", "a"], ["u", "a", "a", "e", "i"], ["_", "l", "g", "i", "a"], ["w", "r", "n", "c", "h"]], ["tala", "udasi", "glair", "wench"]] | ["[['d', 't', 's', 'l', 'a'], ['u', 'a', 'a', 'e', 'i'], ['_', 'l', 'g', 'i', 'a'], ['w', 'r', 'n', 'c', 'h']]", "['tala', 'udasi', 'glair', 'wench']"] |
29 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["G", "B", "J", "S", "N", "D", "E", "R", "E", "S"] | 10 | 0.029485225677490234 | 10 | 11 | 14 | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0,... | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0,... | ["[[0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0... |
29 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [5, 21, 4, 18, 17, 13, 27, 10, 27, 21, 25, 22, 27, 29, 28, 15, 16, 12, 7, 19, 8, 19, 9, 21, 29, 15, 15, 23, 8, 13, 20, 9, 13, 16, 3, 14, 11, 15, 2, 23, 18, 4], such that the sum of the chosen coins adds up to 295. Each coi... | coin_exchange | subset_sum | 22 | [28, 14, 15, 19, 10, 15, 15, 15, 27, 16, 19, 27, 27, 4, 11, 17, 16] | 28 | 0.045546770095825195 | 17 | 42 | 42 | [[5, 21, 4, 18, 17, 13, 27, 10, 27, 21, 25, 22, 27, 29, 28, 15, 16, 12, 7, 19, 8, 19, 9, 21, 29, 15, 15, 23, 8, 13, 20, 9, 13, 16, 3, 14, 11, 15, 2, 23, 18, 4]] | [[5, 21, 4, 18, 17, 13, 27, 10, 27, 21, 25, 22, 27, 29, 28, 15, 16, 12, 7, 19, 8, 19, 9, 21, 29, 15, 15, 23, 8, 13, 20, 9, 13, 16, 3, 14, 11, 15, 2, 23, 18, 4], {"14": 2, "12": 11, "20": 5, "4": 2, "23": 12, "28": 1, "25": 8, "27": 3, "19": 1, "21": 6, "16": 2, "29": 7, "13": 5, "17": 2, "22": 15, "10": 1, "15": 1, "3"... | ["[5, 21, 4, 18, 17, 13, 27, 10, 27, 21, 25, 22, 27, 29, 28, 15, 16, 12, 7, 19, 8, 19, 9, 21, 29, 15, 15, 23, 8, 13, 20, 9, 13, 16, 3, 14, 11, 15, 2, 23, 18, 4]", "{14: 2, 12: 11, 20: 5, 4: 2, 23: 12, 28: 1, 25: 8, 27: 3, 19: 1, 21: 6, 16: 2, 29: 7, 13: 5, 17: 2, 22: 15, 10: 1, 15: 1, 3: 2, 8: 5, 5: 4, 9: 1, 7: 2, 2: 2... |
29 | 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 | 8 | [[1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [0, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0]] | 17 | 1.9683549404144287 | 17 | 6 | 12 | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | ["[['Red', 'Blue', 'Blue', 'Red'], ['Blue', 'Green', 'Blue', 'Green'], ['Green', 'Red', 'Green', 'Red']]", "7"] |
29 | We have a 3x3 numerical grid, with numbers ranging from 40 to 88 (40 included in the range but 88 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, 40], [0, 1, 49], [1, 0, 42], [2, 2, 41]] | 444 | 0.1726534366607666 | 4 | 48 | 9 | ["[['', '', '65'], ['', '47', '56'], ['48', '44', '']]", 40, 88] | ["[['', '', '65'], ['', '47', '56'], ['48', '44', '']]", 40, 88] | ["[['', '', '65'], ['', '47', '56'], ['48', '44', '']]", "40", "88"] |
29 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 34 to 78. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 180, and sum of row 1 must be 156. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 35], [0, 2, 34], [1, 1, 57], [1, 2, 50], [2, 0, 36], [2, 1, 46], [2, 2, 37]] | 421 | 1.5807371139526367 | 7 | 34 | 9 | ["[['', '77', ''], ['49', '', ''], ['', '', '']]", 3, 34, 78] | ["[['', '77', ''], ['49', '', ''], ['', '', '']]", 34, 78, [1, 2], [1, 2], [180], [156], 127] | ["[['', '77', ''], ['49', '', ''], ['', '', '']]", "34", "78", "[None, 180, None]", "[None, 156, None]", "127"] |
29 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 1], [0, 2], [0, 2], [5, 1], [5, 0], [3, 5], [3, 2], [3, 0], [3, 1]] | 40 | 0.0707550048828125 | 9 | 30 | 12 | [[["Yellow", "Green", "Green", "Blue"], [], [], ["Red", "Green", "Blue", "Yellow"], [], ["Yellow", "Blue", "Red", "Red"]], 4, {"0": 1, "1": 5, "2": 6, "3": 7, "4": 7, "5": 5}] | [[["Yellow", "Green", "Green", "Blue"], [], [], ["Red", "Green", "Blue", "Yellow"], [], ["Yellow", "Blue", "Red", "Red"]], 4, {"0": 1, "1": 5, "2": 6, "3": 7, "4": 7, "5": 5}, 3] | ["[['Yellow', 'Green', 'Green', 'Blue'], [], [], ['Red', 'Green', 'Blue', 'Yellow'], [], ['Yellow', 'Blue', 'Red', 'Red']]", "{0: 1, 1: 5, 2: 6, 3: 7, 4: 7, 5: 5}", "4", "3"] |
29 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 9) to his destination workshop at index (6, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[3, 9], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1]] | 75 | 0.03969311714172363 | 12 | 4 | 4 | [[["x", "x", "x", "4", "6", "x", "9", "15", "11", "2"], ["19", "x", "14", "3", "10", "18", "x", "x", "x", "1"], ["x", "9", "x", "11", "7", "14", "x", "x", "16", "18"], ["x", "5", "4", "5", "2", "4", "7", "5", "19", "14"], ["x", "3", "20", "x", "5", "16", "x", "x", "1", "9"], ["x", "3", "15", "9", "4", "x", "x", "x", "x... | [[["x", "x", "x", "4", "6", "x", "9", "15", "11", "2"], ["19", "x", "14", "3", "10", "18", "x", "x", "x", "1"], ["x", "9", "x", "11", "7", "14", "x", "x", "16", "18"], ["x", "5", "4", "5", "2", "4", "7", "5", "19", "14"], ["x", "3", "20", "x", "5", "16", "x", "x", "1", "9"], ["x", "3", "15", "9", "4", "x", "x", "x", "x... | ["[['x', 'x', 'x', '4', '6', 'x', '9', '15', '11', '2'], ['19', 'x', '14', '3', '10', '18', 'x', 'x', 'x', '1'], ['x', '9', 'x', '11', '7', '14', 'x', 'x', '16', '18'], ['x', '5', '4', '5', '2', '4', '7', '5', '19', '14'], ['x', '3', '20', 'x', '5', '16', 'x', 'x', '1', '9'], ['x', '3', '15', '9', '4', 'x', 'x', 'x', '... |
29 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[9, 0], [8, 1], [7, 2], [6, 2], [5, 2], [4, 2], [3, 2], [3, 3], [3, 4], [2, 5], [1, 5]] | 11 | 0.029387712478637695 | 11 | 8 | 2 | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1... | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1... | ["[[1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1... |
29 | Given 7 labeled water jugs with capacities 150, 84, 29, 140, 98, 83, 32 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 243, 250, 446 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of w... | water_jug | subset_sum | 5 | [["+", 140, 3], ["+", 140, 3], ["+", 83, 3], ["+", 83, 3], ["+", 83, 2], ["+", 83, 2], ["+", 84, 2], ["+", 83, 1], ["+", 150, 1], ["-", 140, 1], ["+", 150, 1]] | 11 | 0.039078712463378906 | 11 | 42 | 3 | [[150, 84, 29, 140, 98, 83, 32], [243, 250, 446]] | [[150, 84, 29, 140, 98, 83, 32], [243, 250, 446]] | ["[150, 84, 29, 140, 98, 83, 32]", "[243, 250, 446]"] |
30 | 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 | 6 | [95, 49, 15, 74, 68, 15, 74, 39, 49, 74, 15, 68, 39, 15, 68, 78, 69, 95, 74, 68, 78, 69, 95, 78, 68, 49] | 26 | 0.1302354335784912 | 26 | 4 | 9 | [[[78, 69, "_"], [68, 49, 95], [74, 15, 39]]] | [[[78, 69, "_"], [68, 49, 95], [74, 15, 39]]] | ["[[78, 69, '_'], [68, 49, 95], [74, 15, 39]]"] |
30 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 16 | 0.23216724395751953 | 16 | 4 | 20 | [[["a", "l", "_", "t", "e"], ["s", "h", "r", "b", "s"], ["e", "r", "u", "a", "n"], ["w", "y", "i", "n", "g"]]] | [[["a", "l", "_", "t", "e"], ["s", "h", "r", "b", "s"], ["e", "r", "u", "a", "n"], ["w", "y", "i", "n", "g"]], ["lete", "sarus", "bryan", "whing"]] | ["[['a', 'l', '_', 't', 'e'], ['s', 'h', 'r', 'b', 's'], ['e', 'r', 'u', 'a', 'n'], ['w', 'y', 'i', 'n', 'g']]", "['lete', 'sarus', 'bryan', 'whing']"] |
30 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["G", "U", "P", "H", "V", "P", "H"] | 7 | 0.02849578857421875 | 7 | 11 | 14 | [[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0,... | [[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0,... | ["[[0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0... |
30 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [46, 10, 4, 8, 2, 22, 26, 49, 4, 19, 2, 9, 23, 28, 6, 21, 9, 14, 15, 21, 22, 3, 14, 2, 28, 13, 20, 2, 28, 7, 16, 27, 22, 18, 28, 10, 14, 14, 4, 20, 18], such that the sum of the chosen coins adds up to 294. Each coin in th... | coin_exchange | subset_sum | 23 | [14, 10, 8, 9, 49, 46, 18, 14, 23, 18, 14, 10, 27, 16, 14, 4] | 106 | 0.04515695571899414 | 16 | 41 | 41 | [[46, 10, 4, 8, 2, 22, 26, 49, 4, 19, 2, 9, 23, 28, 6, 21, 9, 14, 15, 21, 22, 3, 14, 2, 28, 13, 20, 2, 28, 7, 16, 27, 22, 18, 28, 10, 14, 14, 4, 20, 18]] | [[46, 10, 4, 8, 2, 22, 26, 49, 4, 19, 2, 9, 23, 28, 6, 21, 9, 14, 15, 21, 22, 3, 14, 2, 28, 13, 20, 2, 28, 7, 16, 27, 22, 18, 28, 10, 14, 14, 4, 20, 18], {"21": 14, "19": 16, "4": 3, "23": 10, "10": 3, "18": 7, "9": 3, "27": 13, "20": 12, "13": 9, "26": 17, "3": 3, "6": 6, "49": 16, "2": 2, "15": 7, "28": 13, "46": 10,... | ["[46, 10, 4, 8, 2, 22, 26, 49, 4, 19, 2, 9, 23, 28, 6, 21, 9, 14, 15, 21, 22, 3, 14, 2, 28, 13, 20, 2, 28, 7, 16, 27, 22, 18, 28, 10, 14, 14, 4, 20, 18]", "{21: 14, 19: 16, 4: 3, 23: 10, 10: 3, 18: 7, 9: 3, 27: 13, 20: 12, 13: 9, 26: 17, 3: 3, 6: 6, 49: 16, 2: 2, 15: 7, 28: 13, 46: 10, 8: 3, 7: 6, 22: 20, 14: 5, 16: 8... |
30 | 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 | 8 | [[0, 1], [0, 1], [2, 0], [2, 0], [1, 0], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 13 | 0.31441617012023926 | 13 | 6 | 12 | [[["Red", "Blue", "Green", "Green"], ["Blue", "Red", "Green", "Blue"], ["Green", "Blue", "Red", "Red"]], 7] | [[["Red", "Blue", "Green", "Green"], ["Blue", "Red", "Green", "Blue"], ["Green", "Blue", "Red", "Red"]], 7] | ["[['Red', 'Blue', 'Green', 'Green'], ['Blue', 'Red', 'Green', 'Blue'], ['Green', 'Blue', 'Red', 'Red']]", "7"] |
30 | We have a 3x3 numerical grid, with numbers ranging from 39 to 87 (39 included in the range but 87 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, 58], [0, 2, 40], [1, 1, 43], [2, 1, 41]] | 514 | 0.1707303524017334 | 4 | 48 | 9 | ["[['', '57', ''], ['42', '', '72'], ['39', '', '73']]", 39, 87] | ["[['', '57', ''], ['42', '', '72'], ['39', '', '73']]", 39, 87] | ["[['', '57', ''], ['42', '', '72'], ['39', '', '73']]", "39", "87"] |
30 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 34 to 78. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 172, and sum of row 1 must be 212. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 34], [0, 1, 37], [1, 0, 69], [1, 1, 68], [1, 2, 75], [2, 1, 67], [2, 2, 35]] | 482 | 8.460258960723877 | 7 | 34 | 9 | ["[['', '', '59'], ['', '', ''], ['38', '', '']]", 3, 34, 78] | ["[['', '', '59'], ['', '', ''], ['38', '', '']]", 34, 78, [1, 2], [1, 2], [172], [212], 165] | ["[['', '', '59'], ['', '', ''], ['38', '', '']]", "34", "78", "[None, 172, None]", "[None, 212, None]", "165"] |
30 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[3, 0], [3, 0], [3, 0], [4, 2], [4, 2], [4, 2], [1, 4], [1, 3], [1, 4], [1, 3]] | 24 | 0.20731306076049805 | 10 | 30 | 12 | [[[], ["Blue", "Red", "Blue", "Red"], [], ["Green", "Green", "Green", "Red"], ["Yellow", "Yellow", "Yellow", "Blue"], []], 4, {"0": 3, "1": 6, "2": 3, "3": 2, "4": 1, "5": 1}] | [[[], ["Blue", "Red", "Blue", "Red"], [], ["Green", "Green", "Green", "Red"], ["Yellow", "Yellow", "Yellow", "Blue"], []], 4, {"0": 3, "1": 6, "2": 3, "3": 2, "4": 1, "5": 1}, 3] | ["[[], ['Blue', 'Red', 'Blue', 'Red'], [], ['Green', 'Green', 'Green', 'Red'], ['Yellow', 'Yellow', 'Yellow', 'Blue'], []]", "{0: 3, 1: 6, 2: 3, 3: 2, 4: 1, 5: 1}", "4", "3"] |
30 | 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 (4, 9) to his destination workshop at index (6, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[4, 9], [4, 8], [4, 7], [3, 7], [3, 6], [3, 5], [4, 5], [4, 4], [5, 4], [6, 4], [6, 3], [6, 2], [6, 1]] | 138 | 0.0320286750793457 | 13 | 4 | 4 | [[["8", "x", "x", "9", "15", "13", "11", "2", "x", "x"], ["13", "x", "x", "x", "5", "x", "x", "7", "x", "x"], ["12", "3", "x", "x", "x", "x", "x", "10", "x", "x"], ["12", "x", "x", "9", "15", "9", "11", "5", "17", "x"], ["3", "5", "12", "x", "11", "5", "x", "15", "1", "18"], ["14", "3", "x", "x", "18", "14", "19", "19"... | [[["8", "x", "x", "9", "15", "13", "11", "2", "x", "x"], ["13", "x", "x", "x", "5", "x", "x", "7", "x", "x"], ["12", "3", "x", "x", "x", "x", "x", "10", "x", "x"], ["12", "x", "x", "9", "15", "9", "11", "5", "17", "x"], ["3", "5", "12", "x", "11", "5", "x", "15", "1", "18"], ["14", "3", "x", "x", "18", "14", "19", "19"... | ["[['8', 'x', 'x', '9', '15', '13', '11', '2', 'x', 'x'], ['13', 'x', 'x', 'x', '5', 'x', 'x', '7', 'x', 'x'], ['12', '3', 'x', 'x', 'x', 'x', 'x', '10', 'x', 'x'], ['12', 'x', 'x', '9', '15', '9', '11', '5', '17', 'x'], ['3', '5', '12', 'x', '11', '5', 'x', '15', '1', '18'], ['14', '3', 'x', 'x', '18', '14', '19', '19... |
30 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[0, 9], [1, 8], [1, 7], [2, 7], [2, 6], [3, 6], [4, 6], [4, 5], [5, 5], [6, 4], [7, 3]] | 11 | 0.02998661994934082 | 11 | 8 | 2 | ["[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0... | ["[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0... | ["[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1], [1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0... |
30 | Given 7 labeled water jugs with capacities 111, 84, 17, 22, 63, 75, 148, 64 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 253, 280, 448 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount ... | water_jug | subset_sum | 5 | [["+", 63, 3], ["+", 111, 3], ["+", 148, 3], ["-", 22, 3], ["+", 148, 3], ["+", 22, 2], ["+", 84, 2], ["+", 111, 2], ["+", 63, 2], ["+", 75, 1], ["+", 84, 1], ["-", 17, 1], ["+", 111, 1]] | 13 | 0.0519099235534668 | 13 | 48 | 3 | [[111, 84, 17, 22, 63, 75, 148, 64], [253, 280, 448]] | [[111, 84, 17, 22, 63, 75, 148, 64], [253, 280, 448]] | ["[111, 84, 17, 22, 63, 75, 148, 64]", "[253, 280, 448]"] |
31 | 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 | [21, 17, 14, 90, 51, 14, 17, 21, 90, 53, 75, 90, 53, 51, 43, 27] | 16 | 0.03641033172607422 | 16 | 4 | 12 | [[[75, 53, 73, 62], ["_", 14, 90, 43], [21, 17, 51, 27]]] | [[[75, 53, 73, 62], ["_", 14, 90, 43], [21, 17, 51, 27]]] | ["[[75, 53, 73, 62], ['_', 14, 90, 43], [21, 17, 51, 27]]"] |
31 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left... | 26 | 0.4536299705505371 | 26 | 4 | 20 | [[["t", "d", "u", "k", "e"], ["a", "a", "o", "l", "l"], ["a", "m", "_", "z", "i"], ["n", "e", "u", "y", "n"]]] | [[["t", "d", "u", "k", "e"], ["a", "a", "o", "l", "l"], ["a", "m", "_", "z", "i"], ["n", "e", "u", "y", "n"]], ["dyke", "atoll", "amuze", "niuan"]] | ["[['t', 'd', 'u', 'k', 'e'], ['a', 'a', 'o', 'l', 'l'], ['a', 'm', '_', 'z', 'i'], ['n', 'e', 'u', 'y', 'n']]", "['dyke', 'atoll', 'amuze', 'niuan']"] |
31 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["J", "B", "E", "A", "U", "N", "U", "S", "E"] | 9 | 0.02808380126953125 | 9 | 11 | 14 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0,... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0,... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0... |
31 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 23, 57, 18, 6, 5, 21, 15, 14, 23, 5, 16, 9, 8, 19, 8, 19, 6, 8, 3, 12, 2, 14, 3, 3, 4, 26, 6, 6, 25, 9, 13, 20, 24, 6, 26, 14, 25, 5, 26], such that the sum of the chosen coins adds up to 260. Each coin in the list is... | coin_exchange | subset_sum | 24 | [24, 14, 57, 14, 12, 6, 9, 9, 6, 23, 18, 14, 12, 23, 6, 13] | 56 | 0.04410982131958008 | 16 | 40 | 40 | [[12, 23, 57, 18, 6, 5, 21, 15, 14, 23, 5, 16, 9, 8, 19, 8, 19, 6, 8, 3, 12, 2, 14, 3, 3, 4, 26, 6, 6, 25, 9, 13, 20, 24, 6, 26, 14, 25, 5, 26]] | [[12, 23, 57, 18, 6, 5, 21, 15, 14, 23, 5, 16, 9, 8, 19, 8, 19, 6, 8, 3, 12, 2, 14, 3, 3, 4, 26, 6, 6, 25, 9, 13, 20, 24, 6, 26, 14, 25, 5, 26], {"6": 2, "12": 3, "9": 2, "2": 1, "14": 1, "16": 12, "21": 10, "4": 1, "8": 5, "26": 7, "23": 7, "57": 11, "15": 15, "19": 13, "25": 15, "13": 4, "5": 3, "24": 4, "3": 3, "18"... | ["[12, 23, 57, 18, 6, 5, 21, 15, 14, 23, 5, 16, 9, 8, 19, 8, 19, 6, 8, 3, 12, 2, 14, 3, 3, 4, 26, 6, 6, 25, 9, 13, 20, 24, 6, 26, 14, 25, 5, 26]", "{6: 2, 12: 3, 9: 2, 2: 1, 14: 1, 16: 12, 21: 10, 4: 1, 8: 5, 26: 7, 23: 7, 57: 11, 15: 15, 19: 13, 25: 15, 13: 4, 5: 3, 24: 4, 3: 3, 18: 4, 20: 10}", "260"] |
31 | 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 | 8 | [[2, 1], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 2], [1, 0], [1, 2], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1]] | 17 | 1.8599176406860352 | 17 | 6 | 12 | [[["Red", "Red", "Red", "Green"], ["Blue", "Green", "Green", "Blue"], ["Blue", "Red", "Green", "Blue"]], 7] | [[["Red", "Red", "Red", "Green"], ["Blue", "Green", "Green", "Blue"], ["Blue", "Red", "Green", "Blue"]], 7] | ["[['Red', 'Red', 'Red', 'Green'], ['Blue', 'Green', 'Green', 'Blue'], ['Blue', 'Red', 'Green', 'Blue']]", "7"] |
31 | We have a 3x3 numerical grid, with numbers ranging from 5 to 53 (5 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 an... | consecutive_grid | underdetermined_system | 9 | [[0, 2, 46], [1, 0, 9], [1, 1, 11], [2, 0, 8], [2, 2, 5]] | 203 | 9.56848430633545 | 5 | 48 | 9 | ["[['10', '25', ''], ['', '', '45'], ['', '7', '']]", 5, 53] | ["[['10', '25', ''], ['', '', '45'], ['', '7', '']]", 5, 53] | ["[['10', '25', ''], ['', '', '45'], ['', '7', '']]", "5", "53"] |
31 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 34 to 78. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 177, and sum of row 1 must be 180. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 34], [0, 1, 36], [0, 2, 38], [1, 0, 60], [2, 0, 72], [2, 1, 68], [2, 2, 35]] | 463 | 20.116249084472656 | 7 | 34 | 9 | ["[['', '', ''], ['', '73', '47'], ['', '', '']]", 3, 34, 78] | ["[['', '', ''], ['', '73', '47'], ['', '', '']]", 34, 78, [1, 2], [1, 2], [177], [180], 183] | ["[['', '', ''], ['', '73', '47'], ['', '', '']]", "34", "78", "[None, 177, None]", "[None, 180, None]", "183"] |
31 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[4, 5], [3, 1], [3, 5], [3, 1], [3, 6], [2, 3], [2, 3], [2, 5], [2, 1], [7, 1], [7, 2], [7, 5], [4, 6], [7, 2], [7, 6], [4, 3], [4, 2], [4, 6]] | 38 | 7.533451795578003 | 18 | 56 | 20 | [[[], [], ["Yellow", "Yellow", "Green", "Black", "Red"], ["Black", "Green", "Black", "Blue", "Yellow"], ["Green", "Blue", "Yellow", "Red", "Blue"], [], [], ["Black", "Red", "Green", "Red", "Blue"]], 5, {"0": 7, "1": 2, "2": 1, "3": 1, "4": 9, "5": 4, "6": 2, "7": 7}] | [[[], [], ["Yellow", "Yellow", "Green", "Black", "Red"], ["Black", "Green", "Black", "Blue", "Yellow"], ["Green", "Blue", "Yellow", "Red", "Blue"], [], [], ["Black", "Red", "Green", "Red", "Blue"]], 5, {"0": 7, "1": 2, "2": 1, "3": 1, "4": 9, "5": 4, "6": 2, "7": 7}, 4] | ["[[], [], ['Yellow', 'Yellow', 'Green', 'Black', 'Red'], ['Black', 'Green', 'Black', 'Blue', 'Yellow'], ['Green', 'Blue', 'Yellow', 'Red', 'Blue'], [], [], ['Black', 'Red', 'Green', 'Red', 'Blue']]", "{0: 7, 1: 2, 2: 1, 3: 1, 4: 9, 5: 4, 6: 2, 7: 7}", "5", "4"] |
31 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 7) to his destination workshop at index (7, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[3, 7], [3, 6], [3, 5], [2, 5], [3, 5], [4, 5], [5, 5], [5, 4], [6, 4], [6, 3], [6, 2], [6, 1], [6, 0], [7, 0]] | 121 | 0.03958845138549805 | 14 | 4 | 4 | [[["10", "x", "19", "11", "x", "x", "6", "12", "x", "x", "x"], ["2", "9", "10", "x", "x", "10", "17", "x", "x", "11", "5"], ["x", "15", "8", "9", "x", "7", "17", "20", "x", "x", "13"], ["1", "9", "15", "14", "9", "9", "13", "7", "12", "x", "10"], ["9", "x", "17", "x", "x", "7", "x", "x", "1", "x", "14"], ["16", "18", "... | [[["10", "x", "19", "11", "x", "x", "6", "12", "x", "x", "x"], ["2", "9", "10", "x", "x", "10", "17", "x", "x", "11", "5"], ["x", "15", "8", "9", "x", "7", "17", "20", "x", "x", "13"], ["1", "9", "15", "14", "9", "9", "13", "7", "12", "x", "10"], ["9", "x", "17", "x", "x", "7", "x", "x", "1", "x", "14"], ["16", "18", "... | ["[['10', 'x', '19', '11', 'x', 'x', '6', '12', 'x', 'x', 'x'], ['2', '9', '10', 'x', 'x', '10', '17', 'x', 'x', '11', '5'], ['x', '15', '8', '9', 'x', '7', '17', '20', 'x', 'x', '13'], ['1', '9', '15', '14', '9', '9', '13', '7', '12', 'x', '10'], ['9', 'x', '17', 'x', 'x', '7', 'x', 'x', '1', 'x', '14'], ['16', '18', ... |
31 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[1, 10], [2, 9], [3, 8], [4, 7], [4, 6], [4, 5], [4, 4], [5, 4], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3]] | 13 | 0.029936790466308594 | 13 | 8 | 2 | ["[[1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0... | ["[[1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0... | ["[[1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0... |
31 | Given 7 labeled water jugs with capacities 14, 46, 13, 110, 38, 21, 45, 130 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 215, 219, 262 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount ... | water_jug | subset_sum | 5 | [["+", 21, 3], ["+", 110, 3], ["+", 110, 3], ["+", 21, 3], ["+", 130, 2], ["-", 21, 2], ["+", 110, 2], ["+", 130, 1], ["-", 45, 1], ["+", 130, 1]] | 10 | 0.0400242805480957 | 10 | 48 | 3 | [[14, 46, 13, 110, 38, 21, 45, 130], [215, 219, 262]] | [[14, 46, 13, 110, 38, 21, 45, 130], [215, 219, 262]] | ["[14, 46, 13, 110, 38, 21, 45, 130]", "[215, 219, 262]"] |
32 | 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 | [24, 44, 30, 63, 44, 30, 8, 67, 63, 44, 30, 8, 47, 15, 73, 24, 15, 56, 69, 73, 56, 47, 44, 30] | 24 | 0.1358938217163086 | 24 | 4 | 12 | [[[69, 56, 8, 67], [15, 47, 44, 30], [73, "_", 24, 63]]] | [[[69, 56, 8, 67], [15, 47, 44, 30], [73, "_", 24, 63]]] | ["[[69, 56, 8, 67], [15, 47, 44, 30], [73, '_', 24, 63]]"] |
32 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-left"] | 16 | 0.24036526679992676 | 16 | 4 | 20 | [[["o", "f", "_", "c", "k"], ["s", "n", "f", "s", "a"], ["o", "i", "i", "s", "e"], ["n", "e", "s", "a", "y"]]] | [[["o", "f", "_", "c", "k"], ["s", "n", "f", "s", "a"], ["o", "i", "i", "s", "e"], ["n", "e", "s", "a", "y"]], ["fack", "sofia", "nisse", "nosey"]] | ["[['o', 'f', '_', 'c', 'k'], ['s', 'n', 'f', 's', 'a'], ['o', 'i', 'i', 's', 'e'], ['n', 'e', 's', 'a', 'y']]", "['fack', 'sofia', 'nisse', 'nosey']"] |
32 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["J", "F", "D", "E", "O", "D", "E"] | 7 | 0.02650594711303711 | 7 | 11 | 14 | [[[0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1,... | [[[0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1,... | ["[[0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1... |
32 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [19, 2, 25, 9, 6, 24, 4, 26, 17, 11, 11, 2, 17, 2, 5, 6, 3, 3, 3, 18, 26, 18, 21, 3, 5, 8, 12, 15, 8, 18, 24, 5, 19, 7, 18, 25, 12, 13, 12, 2, 25, 16, 17, 16, 3, 3], such that the sum of the chosen coins adds up to 264. Ea... | coin_exchange | subset_sum | 25 | [24, 6, 13, 15, 2, 3, 19, 6, 19, 18, 12, 17, 25, 24, 18, 25, 18] | 138 | 0.046419620513916016 | 17 | 46 | 46 | [[19, 2, 25, 9, 6, 24, 4, 26, 17, 11, 11, 2, 17, 2, 5, 6, 3, 3, 3, 18, 26, 18, 21, 3, 5, 8, 12, 15, 8, 18, 24, 5, 19, 7, 18, 25, 12, 13, 12, 2, 25, 16, 17, 16, 3, 3]] | [[19, 2, 25, 9, 6, 24, 4, 26, 17, 11, 11, 2, 17, 2, 5, 6, 3, 3, 3, 18, 26, 18, 21, 3, 5, 8, 12, 15, 8, 18, 24, 5, 19, 7, 18, 25, 12, 13, 12, 2, 25, 16, 17, 16, 3, 3], {"26": 12, "25": 20, "17": 13, "13": 4, "16": 13, "11": 10, "24": 5, "5": 4, "8": 6, "7": 5, "4": 4, "12": 9, "18": 12, "3": 2, "21": 17, "19": 7, "2": 2... | ["[19, 2, 25, 9, 6, 24, 4, 26, 17, 11, 11, 2, 17, 2, 5, 6, 3, 3, 3, 18, 26, 18, 21, 3, 5, 8, 12, 15, 8, 18, 24, 5, 19, 7, 18, 25, 12, 13, 12, 2, 25, 16, 17, 16, 3, 3]", "{26: 12, 25: 20, 17: 13, 13: 4, 16: 13, 11: 10, 24: 5, 5: 4, 8: 6, 7: 5, 4: 4, 12: 9, 18: 12, 3: 2, 21: 17, 19: 7, 2: 2, 9: 9, 6: 2, 15: 4}", "264"] |
32 | 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 | 8 | [[0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2]] | 16 | 0.9227294921875 | 16 | 6 | 12 | [[["Green", "Red", "Blue", "Green"], ["Blue", "Blue", "Red", "Blue"], ["Red", "Red", "Green", "Green"]], 7] | [[["Green", "Red", "Blue", "Green"], ["Blue", "Blue", "Red", "Blue"], ["Red", "Red", "Green", "Green"]], 7] | ["[['Green', 'Red', 'Blue', 'Green'], ['Blue', 'Blue', 'Red', 'Blue'], ['Red', 'Red', 'Green', 'Green']]", "7"] |
32 | We have a 3x3 numerical grid, with numbers ranging from 9 to 57 (9 included in the range but 57 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 | 9 | [[0, 1, 50], [0, 2, 55], [1, 1, 48], [2, 0, 36], [2, 2, 9]] | 378 | 0.3984415531158447 | 5 | 48 | 9 | ["[['49', '', ''], ['47', '', '54'], ['', '35', '']]", 9, 57] | ["[['49', '', ''], ['47', '', '54'], ['', '35', '']]", 9, 57] | ["[['49', '', ''], ['47', '', '54'], ['', '35', '']]", "9", "57"] |
32 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 31 to 75. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 135, and sum of row 1 must be 134. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 32], [0, 1, 34], [0, 2, 31], [1, 0, 35], [1, 1, 50], [1, 2, 49], [2, 1, 51], [2, 2, 33]] | 356 | 31.9260516166687 | 8 | 34 | 9 | ["[['', '', ''], ['', '', ''], ['41', '', '']]", 3, 31, 75] | ["[['', '', ''], ['', '', ''], ['41', '', '']]", 31, 75, [1, 2], [1, 2], [135], [134], 122] | ["[['', '', ''], ['', '', ''], ['41', '', '']]", "31", "75", "[None, 135, None]", "[None, 134, None]", "122"] |
32 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[0, 1], [5, 3], [5, 2], [5, 3], [5, 2], [5, 3], [6, 5], [6, 4], [0, 5], [0, 3], [0, 5], [7, 0], [7, 0], [7, 0], [6, 2], [6, 5], [7, 2], [1, 6], [4, 6], [7, 6]] | 70 | 43.11308765411377 | 20 | 56 | 20 | [[["Black", "Yellow", "Blue", "Yellow", "Red"], [], [], [], [], ["Blue", "Green", "Blue", "Green", "Blue"], ["Yellow", "Black", "Green", "Yellow", "Black"], ["Red", "Red", "Red", "Green", "Black"]], 5, {"0": 5, "1": 8, "2": 1, "3": 6, "4": 8, "5": 2, "6": 1, "7": 8}] | [[["Black", "Yellow", "Blue", "Yellow", "Red"], [], [], [], [], ["Blue", "Green", "Blue", "Green", "Blue"], ["Yellow", "Black", "Green", "Yellow", "Black"], ["Red", "Red", "Red", "Green", "Black"]], 5, {"0": 5, "1": 8, "2": 1, "3": 6, "4": 8, "5": 2, "6": 1, "7": 8}, 4] | ["[['Black', 'Yellow', 'Blue', 'Yellow', 'Red'], [], [], [], [], ['Blue', 'Green', 'Blue', 'Green', 'Blue'], ['Yellow', 'Black', 'Green', 'Yellow', 'Black'], ['Red', 'Red', 'Red', 'Green', 'Black']]", "{0: 5, 1: 8, 2: 1, 3: 6, 4: 8, 5: 2, 6: 1, 7: 8}", "5", "4"] |
32 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 2) to his destination workshop at index (2, 10), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[5, 2], [5, 3], [5, 4], [4, 4], [4, 5], [4, 6], [4, 7], [4, 8], [3, 8], [3, 9], [2, 9], [2, 10]] | 105 | 0.029694080352783203 | 12 | 4 | 4 | [[["x", "x", "13", "x", "x", "7", "x", "13", "3", "x", "13"], ["10", "4", "x", "4", "12", "2", "x", "3", "4", "x", "15"], ["x", "3", "x", "x", "15", "9", "x", "x", "18", "17", "14"], ["5", "x", "x", "x", "3", "x", "11", "x", "17", "9", "17"], ["8", "3", "13", "x", "5", "7", "8", "17", "7", "x", "x"], ["x", "x", "13", "... | [[["x", "x", "13", "x", "x", "7", "x", "13", "3", "x", "13"], ["10", "4", "x", "4", "12", "2", "x", "3", "4", "x", "15"], ["x", "3", "x", "x", "15", "9", "x", "x", "18", "17", "14"], ["5", "x", "x", "x", "3", "x", "11", "x", "17", "9", "17"], ["8", "3", "13", "x", "5", "7", "8", "17", "7", "x", "x"], ["x", "x", "13", "... | ["[['x', 'x', '13', 'x', 'x', '7', 'x', '13', '3', 'x', '13'], ['10', '4', 'x', '4', '12', '2', 'x', '3', '4', 'x', '15'], ['x', '3', 'x', 'x', '15', '9', 'x', 'x', '18', '17', '14'], ['5', 'x', 'x', 'x', '3', 'x', '11', 'x', '17', '9', '17'], ['8', '3', '13', 'x', '5', '7', '8', '17', '7', 'x', 'x'], ['x', 'x', '13', ... |
32 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 8], [6, 7], [6, 6], [7, 5], [8, 5], [9, 5], [9, 4], [9, 3], [9, 2]] | 14 | 0.03171658515930176 | 14 | 8 | 2 | ["[[1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1], [1... | ["[[1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1], [1... | ["[[1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1], [1... |
32 | Given 7 labeled water jugs with capacities 137, 29, 70, 138, 47, 64, 87, 16 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 295, 327, 442 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount ... | water_jug | subset_sum | 5 | [["+", 137, 3], ["+", 138, 3], ["+", 29, 3], ["+", 138, 3], ["+", 87, 2], ["+", 87, 2], ["+", 16, 2], ["+", 137, 2], ["+", 87, 1], ["+", 138, 1], ["+", 70, 1]] | 11 | 0.042920589447021484 | 11 | 48 | 3 | [[137, 29, 70, 138, 47, 64, 87, 16], [295, 327, 442]] | [[137, 29, 70, 138, 47, 64, 87, 16], [295, 327, 442]] | ["[137, 29, 70, 138, 47, 64, 87, 16]", "[295, 327, 442]"] |
33 | 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 | [61, 100, 95, 41, 33, 73, 15, 61, 73, 15, 61, 67, 85, 90, 100, 95, 79, 100, 95, 73, 67, 61] | 22 | 0.05052661895751953 | 22 | 4 | 12 | [[[79, 90, 85, 67], [100, 61, "_", 15], [95, 41, 33, 73]]] | [[[79, 90, 85, 67], [100, 61, "_", 15], [95, 41, 33, 73]]] | ["[[79, 90, 85, 67], [100, 61, '_', 15], [95, 41, 33, 73]]"] |
33 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-right", "down-right", "down-left", "up-left", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 22 | 0.28627824783325195 | 22 | 4 | 20 | [[["g", "j", "u", "m", "a"], ["a", "r", "o", "e", "o"], ["h", "u", "_", "g", "d"], ["s", "c", "r", "a", "f"]]] | [[["g", "j", "u", "m", "a"], ["a", "r", "o", "e", "o"], ["h", "u", "_", "g", "d"], ["s", "c", "r", "a", "f"]], ["jama", "agoho", "rudge", "scruf"]] | ["[['g', 'j', 'u', 'm', 'a'], ['a', 'r', 'o', 'e', 'o'], ['h', 'u', '_', 'g', 'd'], ['s', 'c', 'r', 'a', 'f']]", "['jama', 'agoho', 'rudge', 'scruf']"] |
33 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["D", "P", "H", "Q", "G", "X", "Q", "G"] | 8 | 0.026433229446411133 | 8 | 11 | 14 | [[[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0], [0,... | [[[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0], [0,... | ["[[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0], [0... |
33 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [9, 11, 7, 9, 12, 19, 29, 21, 11, 10, 26, 22, 18, 29, 19, 11, 18, 23, 26, 16, 18, 4, 22, 25, 17, 18, 12, 23, 3, 17, 17, 15, 22, 25, 27, 2, 26, 22, 21, 28, 10, 23, 15], such that the sum of the chosen coins adds up to 296. ... | coin_exchange | subset_sum | 26 | [22, 12, 27, 22, 2, 11, 11, 11, 19, 25, 22, 12, 19, 21, 25, 22, 4, 9] | 75 | 0.041707515716552734 | 18 | 43 | 43 | [[9, 11, 7, 9, 12, 19, 29, 21, 11, 10, 26, 22, 18, 29, 19, 11, 18, 23, 26, 16, 18, 4, 22, 25, 17, 18, 12, 23, 3, 17, 17, 15, 22, 25, 27, 2, 26, 22, 21, 28, 10, 23, 15]] | [[9, 11, 7, 9, 12, 19, 29, 21, 11, 10, 26, 22, 18, 29, 19, 11, 18, 23, 26, 16, 18, 4, 22, 25, 17, 18, 12, 23, 3, 17, 17, 15, 22, 25, 27, 2, 26, 22, 21, 28, 10, 23, 15], {"28": 16, "10": 8, "21": 8, "18": 12, "27": 6, "7": 7, "2": 2, "19": 4, "17": 13, "26": 11, "12": 1, "9": 5, "25": 15, "29": 20, "11": 2, "15": 8, "22... | ["[9, 11, 7, 9, 12, 19, 29, 21, 11, 10, 26, 22, 18, 29, 19, 11, 18, 23, 26, 16, 18, 4, 22, 25, 17, 18, 12, 23, 3, 17, 17, 15, 22, 25, 27, 2, 26, 22, 21, 28, 10, 23, 15]", "{28: 16, 10: 8, 21: 8, 18: 12, 27: 6, 7: 7, 2: 2, 19: 4, 17: 13, 26: 11, 12: 1, 9: 5, 25: 15, 29: 20, 11: 2, 15: 8, 22: 1, 16: 13, 4: 4, 3: 3, 23: 1... |
33 | 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 | 8 | [[1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2]] | 8 | 0.04319334030151367 | 8 | 6 | 12 | [[["Green", "Green", "Green", "Green"], ["Red", "Red", "Blue", "Blue"], ["Red", "Blue", "Blue", "Red"]], 7] | [[["Green", "Green", "Green", "Green"], ["Red", "Red", "Blue", "Blue"], ["Red", "Blue", "Blue", "Red"]], 7] | ["[['Green', 'Green', 'Green', 'Green'], ['Red', 'Red', 'Blue', 'Blue'], ['Red', 'Blue', 'Blue', 'Red']]", "7"] |
33 | We have a 3x3 numerical grid, with numbers ranging from 41 to 89 (41 included in the range but 89 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 | [[1, 0, 71], [1, 2, 42], [2, 0, 70], [2, 1, 69], [2, 2, 41]] | 499 | 1.6186437606811523 | 5 | 48 | 9 | ["[['79', '63', '43'], ['', '68', ''], ['', '', '']]", 41, 89] | ["[['79', '63', '43'], ['', '68', ''], ['', '', '']]", 41, 89] | ["[['79', '63', '43'], ['', '68', ''], ['', '', '']]", "41", "89"] |
33 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 31 to 75. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 138, and sum of row 1 must be 171. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 32], [0, 1, 31], [0, 2, 34], [1, 0, 35], [1, 1, 74], [1, 2, 62], [2, 0, 37], [2, 1, 33]] | 393 | 62.23959302902222 | 8 | 39 | 9 | ["[['', '', ''], ['', '', ''], ['', '', '55']]", 3, 31, 75] | ["[['', '', ''], ['', '', ''], ['', '', '55']]", 31, 75, [1, 2], [1, 2], [138], [171], 145] | ["[['', '', ''], ['', '', ''], ['', '', '55']]", "31", "75", "[None, 138, None]", "[None, 171, None]", "145"] |
33 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[2, 1], [2, 3], [2, 6], [2, 7], [4, 7], [4, 1], [4, 7], [5, 1], [5, 7], [5, 3], [0, 5], [0, 3], [0, 2], [0, 1], [0, 5], [4, 0], [4, 3], [2, 0], [2, 0], [6, 0]] | 79 | 3.2149300575256348 | 20 | 56 | 20 | [[["Black", "Yellow", "Green", "Red", "Black"], [], ["Red", "Yellow", "Green", "Blue", "Green"], [], ["Blue", "Red", "Blue", "Green", "Yellow"], ["Red", "Blue", "Yellow", "Black", "Black"], [], []], 5, {"0": 1, "1": 6, "2": 6, "3": 2, "4": 9, "5": 2, "6": 9, "7": 6}] | [[["Black", "Yellow", "Green", "Red", "Black"], [], ["Red", "Yellow", "Green", "Blue", "Green"], [], ["Blue", "Red", "Blue", "Green", "Yellow"], ["Red", "Blue", "Yellow", "Black", "Black"], [], []], 5, {"0": 1, "1": 6, "2": 6, "3": 2, "4": 9, "5": 2, "6": 9, "7": 6}, 4] | ["[['Black', 'Yellow', 'Green', 'Red', 'Black'], [], ['Red', 'Yellow', 'Green', 'Blue', 'Green'], [], ['Blue', 'Red', 'Blue', 'Green', 'Yellow'], ['Red', 'Blue', 'Yellow', 'Black', 'Black'], [], []]", "{0: 1, 1: 6, 2: 6, 3: 2, 4: 9, 5: 2, 6: 9, 7: 6}", "5", "4"] |
33 | 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, 10) to his destination workshop at index (5, 2), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[2, 10], [1, 10], [1, 9], [0, 9], [0, 8], [0, 7], [0, 6], [0, 5], [0, 4], [1, 4], [1, 3], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2]] | 151 | 0.028232812881469727 | 16 | 4 | 4 | [[["16", "10", "x", "16", "1", "12", "6", "12", "3", "7", "x"], ["x", "16", "10", "9", "12", "19", "7", "10", "12", "13", "7"], ["5", "x", "9", "x", "5", "16", "16", "8", "x", "16", "8"], ["x", "4", "14", "x", "x", "x", "x", "x", "x", "7", "18"], ["13", "12", "16", "14", "x", "2", "4", "2", "x", "6", "3"], ["x", "11", ... | [[["16", "10", "x", "16", "1", "12", "6", "12", "3", "7", "x"], ["x", "16", "10", "9", "12", "19", "7", "10", "12", "13", "7"], ["5", "x", "9", "x", "5", "16", "16", "8", "x", "16", "8"], ["x", "4", "14", "x", "x", "x", "x", "x", "x", "7", "18"], ["13", "12", "16", "14", "x", "2", "4", "2", "x", "6", "3"], ["x", "11", ... | ["[['16', '10', 'x', '16', '1', '12', '6', '12', '3', '7', 'x'], ['x', '16', '10', '9', '12', '19', '7', '10', '12', '13', '7'], ['5', 'x', '9', 'x', '5', '16', '16', '8', 'x', '16', '8'], ['x', '4', '14', 'x', 'x', 'x', 'x', 'x', 'x', '7', '18'], ['13', '12', '16', '14', 'x', '2', '4', '2', 'x', '6', '3'], ['x', '11',... |
33 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[10, 10], [9, 9], [8, 8], [7, 8], [6, 8], [5, 7], [5, 6], [4, 6], [4, 5], [3, 5], [2, 5], [1, 5], [0, 5], [0, 4]] | 14 | 0.030236005783081055 | 14 | 8 | 2 | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0... | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0... | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1], [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0... |
33 | Given 7 labeled water jugs with capacities 146, 57, 69, 52, 132, 80, 145 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 456, 538, 549 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ... | water_jug | subset_sum | 5 | [["+", 69, 3], ["+", 145, 3], ["+", 146, 3], ["+", 132, 3], ["+", 57, 3], ["+", 57, 2], ["+", 146, 2], ["+", 146, 2], ["+", 57, 2], ["+", 132, 2], ["+", 52, 1], ["+", 69, 1], ["+", 146, 1], ["+", 57, 1], ["+", 132, 1]] | 15 | 0.0576624870300293 | 15 | 42 | 3 | [[146, 57, 69, 52, 132, 80, 145], [456, 538, 549]] | [[146, 57, 69, 52, 132, 80, 145], [456, 538, 549]] | ["[146, 57, 69, 52, 132, 80, 145]", "[456, 538, 549]"] |
34 | 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 | [99, 90, 81, 42, 61, 99, 90, 81, 42, 54, 28, 45, 16, 42, 45, 16] | 16 | 0.027817249298095703 | 16 | 4 | 12 | [[[61, "_", 99, 70], [42, 81, 90, 16], [41, 54, 28, 45]]] | [[[61, "_", 99, 70], [42, 81, 90, 16], [41, 54, 28, 45]]] | ["[[61, '_', 99, 70], [42, 81, 90, 16], [41, 54, 28, 45]]"] |
34 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 16 | 0.2467634677886963 | 16 | 4 | 20 | [[["u", "s", "o", "f", "t"], ["t", "a", "n", "n", "y"], ["a", "p", "_", "m", "o"], ["f", "u", "r", "a", "m"]]] | [[["u", "s", "o", "f", "t"], ["t", "a", "n", "n", "y"], ["a", "p", "_", "m", "o"], ["f", "u", "r", "a", "m"]], ["soft", "tunny", "apama", "forum"]] | ["[['u', 's', 'o', 'f', 't'], ['t', 'a', 'n', 'n', 'y'], ['a', 'p', '_', 'm', 'o'], ['f', 'u', 'r', 'a', 'm']]", "['soft', 'tunny', 'apama', 'forum']"] |
34 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["T", "B", "J", "N", "W", "P", "N", "W"] | 8 | 0.02652597427368164 | 8 | 11 | 14 | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0,... | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0,... | ["[[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0... |
34 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [22, 14, 13, 18, 2, 5, 14, 26, 28, 9, 20, 26, 11, 29, 2, 15, 13, 11, 28, 12, 14, 6, 3, 25, 12, 24, 4, 28, 27, 10, 20, 6, 8, 7, 37, 18, 3, 10, 27, 20, 21, 8, 11, 13, 5, 19, 4, 2], such that the sum of the chosen coins adds ... | coin_exchange | subset_sum | 27 | [3, 7, 29, 24, 8, 15, 37, 8, 9, 13, 13, 13, 27, 26, 22, 12, 6, 21] | 86 | 0.05985426902770996 | 18 | 48 | 48 | [[22, 14, 13, 18, 2, 5, 14, 26, 28, 9, 20, 26, 11, 29, 2, 15, 13, 11, 28, 12, 14, 6, 3, 25, 12, 24, 4, 28, 27, 10, 20, 6, 8, 7, 37, 18, 3, 10, 27, 20, 21, 8, 11, 13, 5, 19, 4, 2]] | [[22, 14, 13, 18, 2, 5, 14, 26, 28, 9, 20, 26, 11, 29, 2, 15, 13, 11, 28, 12, 14, 6, 3, 25, 12, 24, 4, 28, 27, 10, 20, 6, 8, 7, 37, 18, 3, 10, 27, 20, 21, 8, 11, 13, 5, 19, 4, 2], {"2": 2, "14": 13, "29": 2, "13": 3, "25": 20, "28": 18, "11": 7, "9": 1, "3": 2, "15": 3, "8": 2, "7": 1, "12": 6, "26": 9, "19": 11, "24":... | ["[22, 14, 13, 18, 2, 5, 14, 26, 28, 9, 20, 26, 11, 29, 2, 15, 13, 11, 28, 12, 14, 6, 3, 25, 12, 24, 4, 28, 27, 10, 20, 6, 8, 7, 37, 18, 3, 10, 27, 20, 21, 8, 11, 13, 5, 19, 4, 2]", "{2: 2, 14: 13, 29: 2, 13: 3, 25: 20, 28: 18, 11: 7, 9: 1, 3: 2, 15: 3, 8: 2, 7: 1, 12: 6, 26: 9, 19: 11, 24: 1, 22: 9, 27: 17, 6: 4, 18: ... |
34 | 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 | 8 | [[1, 2], [0, 1], [0, 1], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1]] | 15 | 0.8411509990692139 | 15 | 6 | 12 | [[["Red", "Green", "Blue", "Blue"], ["Blue", "Red", "Green", "Red"], ["Green", "Blue", "Red", "Green"]], 7] | [[["Red", "Green", "Blue", "Blue"], ["Blue", "Red", "Green", "Red"], ["Green", "Blue", "Red", "Green"]], 7] | ["[['Red', 'Green', 'Blue', 'Blue'], ['Blue', 'Red', 'Green', 'Red'], ['Green', 'Blue', 'Red', 'Green']]", "7"] |
34 | We have a 3x3 numerical grid, with numbers ranging from 38 to 86 (38 included in the range but 86 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 10 | [[0, 1, 40], [1, 0, 43], [1, 1, 42], [1, 2, 41], [2, 0, 53], [2, 2, 39]] | 431 | 0.6136000156402588 | 6 | 48 | 9 | ["[['38', '', '77'], ['', '', ''], ['', '52', '']]", 38, 86] | ["[['38', '', '77'], ['', '', ''], ['', '52', '']]", 38, 86] | ["[['38', '', '77'], ['', '', ''], ['', '52', '']]", "38", "86"] |
34 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 40 to 89. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 183, and sum of row 1 must be 194. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 42], [0, 1, 43], [0, 2, 41], [1, 0, 44], [1, 1, 80], [1, 2, 70], [2, 1, 60]] | 491 | 38.21377420425415 | 7 | 39 | 9 | ["[['', '', ''], ['', '', ''], ['40', '', '71']]", 3, 40, 89] | ["[['', '', ''], ['', '', ''], ['40', '', '71']]", 40, 89, [1, 2], [1, 2], [183], [194], 161] | ["[['', '', ''], ['', '', ''], ['40', '', '71']]", "40", "89", "[None, 183, None]", "[None, 194, None]", "161"] |
34 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[5, 7], [1, 0], [1, 7], [1, 7], [1, 0], [2, 4], [5, 6], [3, 0], [3, 0], [3, 6], [5, 1], [5, 1], [3, 5], [3, 7], [2, 3], [2, 5], [2, 1], [4, 5], [2, 3], [6, 3], [6, 3]] | 94 | 0.048551321029663086 | 21 | 56 | 20 | [[[], ["Yellow", "Blue", "Blue", "Yellow", "Green"], ["Black", "Red", "Black", "Green", "Red"], ["Yellow", "Yellow", "Red", "Black", "Blue"], [], ["Blue", "Red", "Green", "Green", "Black"], [], []], 5, {"0": 6, "1": 3, "2": 5, "3": 2, "4": 8, "5": 3, "6": 8, "7": 5}] | [[[], ["Yellow", "Blue", "Blue", "Yellow", "Green"], ["Black", "Red", "Black", "Green", "Red"], ["Yellow", "Yellow", "Red", "Black", "Blue"], [], ["Blue", "Red", "Green", "Green", "Black"], [], []], 5, {"0": 6, "1": 3, "2": 5, "3": 2, "4": 8, "5": 3, "6": 8, "7": 5}, 4] | ["[[], ['Yellow', 'Blue', 'Blue', 'Yellow', 'Green'], ['Black', 'Red', 'Black', 'Green', 'Red'], ['Yellow', 'Yellow', 'Red', 'Black', 'Blue'], [], ['Blue', 'Red', 'Green', 'Green', 'Black'], [], []]", "{0: 6, 1: 3, 2: 5, 3: 2, 4: 8, 5: 3, 6: 8, 7: 5}", "5", "4"] |
34 | 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, 0) to his destination workshop at index (2, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [2, 8], [2, 9]] | 168 | 0.027637958526611328 | 15 | 4 | 4 | [[["12", "11", "14", "10", "2", "11", "13", "16", "3", "x", "12"], ["10", "9", "x", "8", "x", "x", "1", "16", "11", "x", "15"], ["1", "18", "1", "x", "x", "x", "x", "x", "12", "9", "x"], ["1", "14", "15", "10", "7", "15", "17", "10", "15", "15", "6"], ["18", "11", "x", "x", "x", "15", "x", "x", "1", "1", "x"], ["14", "... | [[["12", "11", "14", "10", "2", "11", "13", "16", "3", "x", "12"], ["10", "9", "x", "8", "x", "x", "1", "16", "11", "x", "15"], ["1", "18", "1", "x", "x", "x", "x", "x", "12", "9", "x"], ["1", "14", "15", "10", "7", "15", "17", "10", "15", "15", "6"], ["18", "11", "x", "x", "x", "15", "x", "x", "1", "1", "x"], ["14", "... | ["[['12', '11', '14', '10', '2', '11', '13', '16', '3', 'x', '12'], ['10', '9', 'x', '8', 'x', 'x', '1', '16', '11', 'x', '15'], ['1', '18', '1', 'x', 'x', 'x', 'x', 'x', '12', '9', 'x'], ['1', '14', '15', '10', '7', '15', '17', '10', '15', '15', '6'], ['18', '11', 'x', 'x', 'x', '15', 'x', 'x', '1', '1', 'x'], ['14', ... |
34 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[10, 10], [10, 9], [10, 8], [10, 7], [10, 6], [10, 5], [10, 4], [9, 3], [9, 2], [8, 1], [7, 0], [6, 0], [5, 0]] | 13 | 0.03441643714904785 | 13 | 8 | 2 | ["[[0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0... | ["[[0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0... | ["[[0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1], [0... |
34 | Given 7 labeled water jugs with capacities 103, 109, 146, 101, 17, 145, 68 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 448, 466, 509 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 109, 3], ["+", 145, 3], ["+", 146, 3], ["+", 109, 3], ["+", 103, 2], ["+", 109, 2], ["+", 109, 2], ["+", 145, 2], ["+", 101, 1], ["+", 101, 1], ["+", 101, 1], ["+", 145, 1]] | 12 | 0.05138897895812988 | 12 | 42 | 3 | [[103, 109, 146, 101, 17, 145, 68], [448, 466, 509]] | [[103, 109, 146, 101, 17, 145, 68], [448, 466, 509]] | ["[103, 109, 146, 101, 17, 145, 68]", "[448, 466, 509]"] |
35 | 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 | [66, 35, 94, 18, 80, 94, 69, 53, 18, 69, 35, 66, 94, 80, 69, 35, 53, 18] | 18 | 0.03965592384338379 | 18 | 4 | 12 | [[[95, "_", 80, 18], [67, 66, 35, 94], [27, 26, 69, 53]]] | [[[95, "_", 80, 18], [67, 66, 35, 94], [27, 26, 69, 53]]] | ["[[95, '_', 80, 18], [67, 66, 35, 94], [27, 26, 69, 53]]"] |
35 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "down-right", "down-right", "up-right", "up-left", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-left"] | 24 | 0.3029823303222656 | 24 | 4 | 20 | [[["a", "s", "_", "p", "e"], ["c", "u", "d", "o", "s"], ["l", "u", "u", "a", "s"], ["r", "c", "u", "n", "e"]]] | [[["a", "s", "_", "p", "e"], ["c", "u", "d", "o", "s"], ["l", "u", "u", "a", "s"], ["r", "c", "u", "n", "e"]], ["supe", "cadus", "nucal", "rouse"]] | ["[['a', 's', '_', 'p', 'e'], ['c', 'u', 'd', 'o', 's'], ['l', 'u', 'u', 'a', 's'], ['r', 'c', 'u', 'n', 'e']]", "['supe', 'cadus', 'nucal', 'rouse']"] |
35 | 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 | 12 | ["G", "V", "N", "L", "W", "P", "E", "P", "H", "L"] | 10 | 0.03540349006652832 | 10 | 12 | 15 | [[[0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0... | [[[0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0... | ["[[0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, ... |
35 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [27, 17, 6, 5, 20, 3, 4, 29, 25, 27, 20, 18, 18, 25, 2, 13, 15, 4, 12, 4, 26, 12, 26, 24, 17, 23, 2, 6, 2, 29, 3, 20, 12, 7, 9, 12, 26, 11, 2, 5, 10, 25, 3, 13, 7, 25], such that the sum of the chosen coins adds up to 295.... | coin_exchange | subset_sum | 28 | [12, 27, 12, 2, 5, 27, 12, 2, 3, 3, 5, 2, 23, 18, 12, 6, 29, 18, 6, 4, 2, 3, 29, 4, 25, 4] | 90 | 0.049031734466552734 | 26 | 46 | 46 | [[27, 17, 6, 5, 20, 3, 4, 29, 25, 27, 20, 18, 18, 25, 2, 13, 15, 4, 12, 4, 26, 12, 26, 24, 17, 23, 2, 6, 2, 29, 3, 20, 12, 7, 9, 12, 26, 11, 2, 5, 10, 25, 3, 13, 7, 25]] | [[27, 17, 6, 5, 20, 3, 4, 29, 25, 27, 20, 18, 18, 25, 2, 13, 15, 4, 12, 4, 26, 12, 26, 24, 17, 23, 2, 6, 2, 29, 3, 20, 12, 7, 9, 12, 26, 11, 2, 5, 10, 25, 3, 13, 7, 25], {"2": 1, "13": 11, "26": 13, "5": 1, "4": 2, "9": 8, "15": 8, "18": 6, "20": 18, "3": 1, "17": 17, "6": 2, "10": 10, "12": 1, "23": 10, "7": 6, "29": ... | ["[27, 17, 6, 5, 20, 3, 4, 29, 25, 27, 20, 18, 18, 25, 2, 13, 15, 4, 12, 4, 26, 12, 26, 24, 17, 23, 2, 6, 2, 29, 3, 20, 12, 7, 9, 12, 26, 11, 2, 5, 10, 25, 3, 13, 7, 25]", "{2: 1, 13: 11, 26: 13, 5: 1, 4: 2, 9: 8, 15: 8, 18: 6, 20: 18, 3: 1, 17: 17, 6: 2, 10: 10, 12: 1, 23: 10, 7: 6, 29: 13, 25: 15, 11: 10, 27: 2, 24: ... |
35 | 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 | 8 | [[1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [0, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0]] | 17 | 1.9828546047210693 | 17 | 6 | 12 | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | ["[['Red', 'Blue', 'Blue', 'Red'], ['Blue', 'Green', 'Blue', 'Green'], ['Green', 'Red', 'Green', 'Red']]", "7"] |
35 | We have a 3x3 numerical grid, with numbers ranging from 40 to 88 (40 included in the range but 88 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 | 10 | [[0, 0, 40], [0, 1, 41], [0, 2, 42], [1, 0, 43], [2, 0, 65], [2, 1, 64]] | 454 | 0.1776282787322998 | 6 | 48 | 9 | ["[['', '', ''], ['', '61', '62'], ['', '', '63']]", 40, 88] | ["[['', '', ''], ['', '61', '62'], ['', '', '63']]", 40, 88] | ["[['', '', ''], ['', '61', '62'], ['', '', '63']]", "40", "88"] |
35 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 40 to 89. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 153, and sum of row 1 must be 186. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 40], [0, 1, 42], [0, 2, 52], [1, 2, 58], [2, 0, 88], [2, 1, 63], [2, 2, 41]] | 512 | 25.803895473480225 | 7 | 39 | 9 | ["[['', '', ''], ['80', '48', ''], ['', '', '']]", 3, 40, 89] | ["[['', '', ''], ['80', '48', ''], ['', '', '']]", 40, 89, [1, 2], [1, 2], [153], [186], 188] | ["[['', '', ''], ['80', '48', ''], ['', '', '']]", "40", "89", "[None, 153, None]", "[None, 186, None]", "188"] |
35 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[1, 0], [4, 3], [6, 0], [4, 5], [4, 0], [4, 2], [6, 4], [6, 5], [7, 4], [7, 0], [7, 4], [7, 5], [6, 2], [1, 3], [1, 2], [1, 5], [7, 2], [1, 3], [6, 3]] | 54 | 0.07124614715576172 | 19 | 56 | 20 | [[[], ["Green", "Blue", "Yellow", "Black", "Blue"], [], [], ["Blue", "Black", "Green", "Yellow", "Red"], [], ["Green", "Red", "Black", "Yellow", "Blue"], ["Red", "Green", "Red", "Black", "Yellow"]], 5, {"0": 2, "1": 4, "2": 5, "3": 2, "4": 2, "5": 3, "6": 2, "7": 5}] | [[[], ["Green", "Blue", "Yellow", "Black", "Blue"], [], [], ["Blue", "Black", "Green", "Yellow", "Red"], [], ["Green", "Red", "Black", "Yellow", "Blue"], ["Red", "Green", "Red", "Black", "Yellow"]], 5, {"0": 2, "1": 4, "2": 5, "3": 2, "4": 2, "5": 3, "6": 2, "7": 5}, 4] | ["[[], ['Green', 'Blue', 'Yellow', 'Black', 'Blue'], [], [], ['Blue', 'Black', 'Green', 'Yellow', 'Red'], [], ['Green', 'Red', 'Black', 'Yellow', 'Blue'], ['Red', 'Green', 'Red', 'Black', 'Yellow']]", "{0: 2, 1: 4, 2: 5, 3: 2, 4: 2, 5: 3, 6: 2, 7: 5}", "5", "4"] |
35 | 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, 8) to his destination workshop at index (2, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[7, 8], [7, 7], [7, 6], [8, 6], [7, 6], [6, 6], [5, 6], [5, 5], [5, 4], [5, 3], [4, 3], [3, 3], [3, 2], [3, 1], [2, 1]] | 134 | 0.027469635009765625 | 15 | 4 | 4 | [[["x", "18", "x", "5", "x", "6", "5", "x", "6", "17", "x"], ["x", "x", "1", "5", "9", "13", "x", "2", "x", "x", "2"], ["x", "17", "12", "x", "x", "x", "5", "x", "x", "17", "x"], ["9", "3", "13", "8", "x", "7", "x", "x", "4", "2", "x"], ["11", "17", "x", "10", "x", "x", "x", "x", "17", "15", "11"], ["x", "10", "10", "1... | [[["x", "18", "x", "5", "x", "6", "5", "x", "6", "17", "x"], ["x", "x", "1", "5", "9", "13", "x", "2", "x", "x", "2"], ["x", "17", "12", "x", "x", "x", "5", "x", "x", "17", "x"], ["9", "3", "13", "8", "x", "7", "x", "x", "4", "2", "x"], ["11", "17", "x", "10", "x", "x", "x", "x", "17", "15", "11"], ["x", "10", "10", "1... | ["[['x', '18', 'x', '5', 'x', '6', '5', 'x', '6', '17', 'x'], ['x', 'x', '1', '5', '9', '13', 'x', '2', 'x', 'x', '2'], ['x', '17', '12', 'x', 'x', 'x', '5', 'x', 'x', '17', 'x'], ['9', '3', '13', '8', 'x', '7', 'x', 'x', '4', '2', 'x'], ['11', '17', 'x', '10', 'x', 'x', 'x', 'x', '17', '15', '11'], ['x', '10', '10', '... |
35 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[1, 9], [1, 8], [2, 7], [2, 6], [3, 6], [4, 5], [5, 5], [5, 4], [6, 3], [6, 2], [6, 1], [7, 1], [7, 0], [8, 0]] | 14 | 0.02565455436706543 | 14 | 8 | 2 | ["[[1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1], [1... | ["[[1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1], [1... | ["[[1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1], [1... |
35 | Given 7 labeled water jugs with capacities 120, 95, 49, 150, 83, 97, 44, 43 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 225, 334, 381 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount ... | water_jug | subset_sum | 5 | [["+", 97, 3], ["+", 120, 3], ["+", 120, 3], ["+", 44, 3], ["+", 150, 2], ["+", 150, 2], ["-", 49, 2], ["+", 83, 2], ["+", 43, 1], ["+", 43, 1], ["+", 44, 1], ["+", 95, 1]] | 12 | 0.03785276412963867 | 12 | 48 | 3 | [[120, 95, 49, 150, 83, 97, 44, 43], [225, 334, 381]] | [[120, 95, 49, 150, 83, 97, 44, 43], [225, 334, 381]] | ["[120, 95, 49, 150, 83, 97, 44, 43]", "[225, 334, 381]"] |
36 | 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 | [44, 29, 68, 86, 95, 80, 6, 50, 29, 44, 80, 10, 67, 95, 86, 80, 50, 6, 10, 50, 44, 29] | 22 | 0.07417702674865723 | 22 | 4 | 12 | [[[67, 86, 68, 29], [10, 95, "_", 44], [19, 80, 6, 50]]] | [[[67, 86, 68, 29], [10, 95, "_", 44], [19, 80, 6, 50]]] | ["[[67, 86, 68, 29], [10, 95, '_', 44], [19, 80, 6, 50]]"] |
36 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-right", "up-left", "down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "down-right", "up-right", "up-left", "up-left", "down-left", "up-left... | 26 | 0.8642349243164062 | 26 | 4 | 20 | [[["h", "b", "c", "t", "h"], ["k", "n", "i", "o", "a"], ["a", "s", "_", "o", "a"], ["c", "l", "a", "s", "t"]]] | [[["h", "b", "c", "t", "h"], ["k", "n", "i", "o", "a"], ["a", "s", "_", "o", "a"], ["c", "l", "a", "s", "t"]], ["bath", "khila", "ascon", "coast"]] | ["[['h', 'b', 'c', 't', 'h'], ['k', 'n', 'i', 'o', 'a'], ['a', 's', '_', 'o', 'a'], ['c', 'l', 'a', 's', 't']]", "['bath', 'khila', 'ascon', 'coast']"] |
36 | 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 | 12 | ["G", "I", "O", "R", "C", "O", "R"] | 7 | 0.022314071655273438 | 7 | 12 | 15 | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0... | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, ... |
36 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [26, 7, 24, 27, 19, 15, 12, 13, 19, 5, 17, 26, 20, 7, 3, 21, 22, 7, 17, 13, 28, 11, 19, 18, 9, 10, 25, 2, 4, 18, 14, 17, 22, 27, 14, 7, 9, 2, 11, 8, 14, 10, 18, 1, 4, 24, 2, 24, 11, 14, 27], such that the sum of the chosen... | coin_exchange | subset_sum | 29 | [7, 7, 7, 15, 10, 27, 10, 27, 18, 27, 22, 18, 12, 25, 22, 18, 2, 7] | 61 | 0.04955577850341797 | 18 | 51 | 51 | [[26, 7, 24, 27, 19, 15, 12, 13, 19, 5, 17, 26, 20, 7, 3, 21, 22, 7, 17, 13, 28, 11, 19, 18, 9, 10, 25, 2, 4, 18, 14, 17, 22, 27, 14, 7, 9, 2, 11, 8, 14, 10, 18, 1, 4, 24, 2, 24, 11, 14, 27]] | [[26, 7, 24, 27, 19, 15, 12, 13, 19, 5, 17, 26, 20, 7, 3, 21, 22, 7, 17, 13, 28, 11, 19, 18, 9, 10, 25, 2, 4, 18, 14, 17, 22, 27, 14, 7, 9, 2, 11, 8, 14, 10, 18, 1, 4, 24, 2, 24, 11, 14, 27], {"13": 8, "27": 5, "21": 13, "25": 11, "22": 6, "20": 14, "12": 1, "14": 12, "2": 2, "8": 5, "3": 2, "18": 4, "1": 1, "9": 9, "1... | ["[26, 7, 24, 27, 19, 15, 12, 13, 19, 5, 17, 26, 20, 7, 3, 21, 22, 7, 17, 13, 28, 11, 19, 18, 9, 10, 25, 2, 4, 18, 14, 17, 22, 27, 14, 7, 9, 2, 11, 8, 14, 10, 18, 1, 4, 24, 2, 24, 11, 14, 27]", "{13: 8, 27: 5, 21: 13, 25: 11, 22: 6, 20: 14, 12: 1, 14: 12, 2: 2, 8: 5, 3: 2, 18: 4, 1: 1, 9: 9, 10: 1, 19: 10, 11: 5, 28: 1... |
36 | 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 | 8 | [[2, 0], [2, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0]] | 12 | 0.14433550834655762 | 12 | 6 | 12 | [[["Blue", "Red", "Red", "Red"], ["Green", "Blue", "Green", "Green"], ["Blue", "Blue", "Green", "Red"]], 7] | [[["Blue", "Red", "Red", "Red"], ["Green", "Blue", "Green", "Green"], ["Blue", "Blue", "Green", "Red"]], 7] | ["[['Blue', 'Red', 'Red', 'Red'], ['Green', 'Blue', 'Green', 'Green'], ['Blue', 'Blue', 'Green', 'Red']]", "7"] |
36 | We have a 3x3 numerical grid, with numbers ranging from 26 to 74 (26 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 | 10 | [[0, 1, 27], [0, 2, 26], [1, 2, 58], [2, 0, 61], [2, 1, 60], [2, 2, 59]] | 394 | 207.3310091495514 | 6 | 48 | 9 | ["[['41', '', ''], ['42', '57', ''], ['', '', '']]", 26, 74] | ["[['41', '', ''], ['42', '57', ''], ['', '', '']]", 26, 74] | ["[['41', '', ''], ['42', '57', ''], ['', '', '']]", "26", "74"] |
36 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 40 to 89. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 198, and sum of row 1 must be 152. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 41], [0, 1, 57], [0, 2, 56], [1, 0, 40], [1, 1, 70], [1, 2, 42], [2, 2, 43]] | 489 | 69.91229152679443 | 7 | 39 | 9 | ["[['', '', ''], ['', '', ''], ['69', '71', '']]", 3, 40, 89] | ["[['', '', ''], ['', '', ''], ['69', '71', '']]", 40, 89, [1, 2], [1, 2], [198], [152], 195] | ["[['', '', ''], ['', '', ''], ['69', '71', '']]", "40", "89", "[None, 198, None]", "[None, 152, None]", "195"] |
36 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 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 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[0, 1], [0, 2], [0, 2], [6, 3], [6, 2], [4, 1], [4, 7], [0, 3], [4, 0], [4, 2], [5, 0], [6, 0], [6, 7], [5, 7], [5, 3], [5, 1], [5, 7], [6, 1], [4, 3]] | 76 | 4.6590895652771 | 19 | 56 | 20 | [[["Blue", "Yellow", "Yellow", "Green", "Black"], [], [], [], ["Blue", "Red", "Black", "Yellow", "Green"], ["Black", "Red", "Green", "Blue", "Red"], ["Green", "Yellow", "Black", "Red", "Blue"], []], 5, {"0": 4, "1": 4, "2": 7, "3": 1, "4": 8, "5": 8, "6": 8, "7": 4}] | [[["Blue", "Yellow", "Yellow", "Green", "Black"], [], [], [], ["Blue", "Red", "Black", "Yellow", "Green"], ["Black", "Red", "Green", "Blue", "Red"], ["Green", "Yellow", "Black", "Red", "Blue"], []], 5, {"0": 4, "1": 4, "2": 7, "3": 1, "4": 8, "5": 8, "6": 8, "7": 4}, 4] | ["[['Blue', 'Yellow', 'Yellow', 'Green', 'Black'], [], [], [], ['Blue', 'Red', 'Black', 'Yellow', 'Green'], ['Black', 'Red', 'Green', 'Blue', 'Red'], ['Green', 'Yellow', 'Black', 'Red', 'Blue'], []]", "{0: 4, 1: 4, 2: 7, 3: 1, 4: 8, 5: 8, 6: 8, 7: 4}", "5", "4"] |
36 | 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, 0) to his destination workshop at index (3, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[7, 0], [7, 1], [6, 1], [5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3], [2, 4], [1, 4], [2, 4], [3, 4], [3, 5], [4, 5], [4, 6], [4, 7], [4, 8], [3, 8]] | 164 | 0.027472734451293945 | 19 | 4 | 4 | [[["x", "11", "5", "18", "x", "14", "7", "x", "15", "11", "14"], ["x", "x", "x", "x", "13", "13", "11", "17", "8", "13", "x"], ["x", "8", "1", "5", "17", "x", "4", "8", "20", "7", "4"], ["x", "10", "x", "x", "18", "1", "x", "x", "20", "x", "x"], ["18", "15", "x", "6", "x", "4", "3", "4", "3", "13", "x"], ["5", "1", "x"... | [[["x", "11", "5", "18", "x", "14", "7", "x", "15", "11", "14"], ["x", "x", "x", "x", "13", "13", "11", "17", "8", "13", "x"], ["x", "8", "1", "5", "17", "x", "4", "8", "20", "7", "4"], ["x", "10", "x", "x", "18", "1", "x", "x", "20", "x", "x"], ["18", "15", "x", "6", "x", "4", "3", "4", "3", "13", "x"], ["5", "1", "x"... | ["[['x', '11', '5', '18', 'x', '14', '7', 'x', '15', '11', '14'], ['x', 'x', 'x', 'x', '13', '13', '11', '17', '8', '13', 'x'], ['x', '8', '1', '5', '17', 'x', '4', '8', '20', '7', '4'], ['x', '10', 'x', 'x', '18', '1', 'x', 'x', '20', 'x', 'x'], ['18', '15', 'x', '6', 'x', '4', '3', '4', '3', '13', 'x'], ['5', '1', 'x... |
36 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 11x11. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 11 | [[0, 10], [1, 9], [2, 9], [2, 8], [2, 7], [3, 6], [4, 6], [5, 6], [6, 6], [7, 7], [8, 7], [8, 6], [8, 5], [8, 4], [8, 3], [8, 2], [9, 2]] | 17 | 0.024544954299926758 | 17 | 8 | 2 | ["[[0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0... | ["[[0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0... | ["[[0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0... |
36 | Given 7 labeled water jugs with capacities 15, 138, 24, 10, 30, 82, 11, 94 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 239, 275, 286 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 138, 3], ["+", 138, 3], ["+", 10, 3], ["+", 138, 2], ["-", 11, 2], ["+", 138, 2], ["+", 10, 2], ["+", 10, 1], ["+", 82, 1], ["+", 138, 1], ["-", 15, 1], ["+", 24, 1]] | 12 | 0.038283348083496094 | 12 | 48 | 3 | [[15, 138, 24, 10, 30, 82, 11, 94], [239, 275, 286]] | [[15, 138, 24, 10, 30, 82, 11, 94], [239, 275, 286]] | ["[15, 138, 24, 10, 30, 82, 11, 94]", "[239, 275, 286]"] |
37 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 4 | [49, 67, 19, 78, 12, 94, 66, 12, 78, 49, 67, 47, 31, 19, 12, 83, 19, 12, 49, 78, 83, 49, 47, 31] | 24 | 0.03918051719665527 | 24 | 4 | 12 | [[[12, 78, 19, "_"], [94, 66, 67, 49], [28, 83, 31, 47]]] | [[[12, 78, 19, "_"], [94, 66, 67, 49], [28, 83, 31, 47]]] | ["[[12, 78, 19, '_'], [94, 66, 67, 49], [28, 83, 31, 47]]"] |
37 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-right", "down-left", "down-left", "up-left", "up-left", "up-right", "down-right", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-left"] | 14 | 0.15983343124389648 | 14 | 4 | 24 | [[["e", "u", "n", "a", "_", "e"], ["d", "r", "a", "v", "i", "e"], ["m", "a", "n", "u", "k", "a"], ["k", "h", "a", "t", "u", "m"]]] | [[["e", "u", "n", "a", "_", "e"], ["d", "r", "a", "v", "i", "e"], ["m", "a", "n", "u", "k", "a"], ["k", "h", "a", "t", "u", "m"]], ["uvate", "dearie", "manuka", "khanum"]] | ["[['e', 'u', 'n', 'a', '_', 'e'], ['d', 'r', 'a', 'v', 'i', 'e'], ['m', 'a', 'n', 'u', 'k', 'a'], ['k', 'h', 'a', 't', 'u', 'm']]", "['uvate', 'dearie', 'manuka', 'khanum']"] |
37 | 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 | 12 | ["L", "W", "F", "M", "K", "M", "T", "Q", "H", "Q"] | 10 | 0.03090953826904297 | 10 | 12 | 15 | [[[0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0... | [[[0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0... | ["[[0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, ... |
37 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [22, 15, 4, 23, 19, 3, 5, 28, 22, 27, 13, 18, 14, 11, 22, 20, 27, 24, 21, 13, 25, 11, 6, 2, 30, 29, 4, 16, 3, 13, 3, 28, 28, 20, 15, 27, 4, 18, 20, 5, 16, 21, 25, 24, 23, 15, 22, 26], such that the sum of the chosen coins ... | coin_exchange | subset_sum | 30 | [11, 11, 13, 23, 23, 14, 15, 15, 15, 4, 13, 13, 25, 29, 28, 4, 25, 16, 6] | 56 | 0.050664663314819336 | 19 | 48 | 48 | [[22, 15, 4, 23, 19, 3, 5, 28, 22, 27, 13, 18, 14, 11, 22, 20, 27, 24, 21, 13, 25, 11, 6, 2, 30, 29, 4, 16, 3, 13, 3, 28, 28, 20, 15, 27, 4, 18, 20, 5, 16, 21, 25, 24, 23, 15, 22, 26]] | [[22, 15, 4, 23, 19, 3, 5, 28, 22, 27, 13, 18, 14, 11, 22, 20, 27, 24, 21, 13, 25, 11, 6, 2, 30, 29, 4, 16, 3, 13, 3, 28, 28, 20, 15, 27, 4, 18, 20, 5, 16, 21, 25, 24, 23, 15, 22, 26], {"15": 2, "18": 17, "22": 16, "29": 7, "28": 5, "23": 1, "20": 17, "14": 3, "13": 2, "4": 2, "5": 3, "27": 10, "16": 6, "3": 2, "6": 3,... | ["[22, 15, 4, 23, 19, 3, 5, 28, 22, 27, 13, 18, 14, 11, 22, 20, 27, 24, 21, 13, 25, 11, 6, 2, 30, 29, 4, 16, 3, 13, 3, 28, 28, 20, 15, 27, 4, 18, 20, 5, 16, 21, 25, 24, 23, 15, 22, 26]", "{15: 2, 18: 17, 22: 16, 29: 7, 28: 5, 23: 1, 20: 17, 14: 3, 13: 2, 4: 2, 5: 3, 27: 10, 16: 6, 3: 2, 6: 3, 19: 8, 2: 1, 25: 6, 24: 19... |
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