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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
37 | 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], [0, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 0], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2]] | 16 | 1.3703632354736328 | 16 | 6 | 12 | [[["Red", "Red", "Blue", "Red"], ["Red", "Blue", "Green", "Blue"], ["Green", "Green", "Blue", "Green"]], 7] | [[["Red", "Red", "Blue", "Red"], ["Red", "Blue", "Green", "Blue"], ["Green", "Green", "Blue", "Green"]], 7] | ["[['Red', 'Red', 'Blue', 'Red'], ['Red', 'Blue', 'Green', 'Blue'], ['Green', 'Green', 'Blue', 'Green']]", "7"] |
37 | We have a 3x3 numerical grid, with numbers ranging from 48 to 101 (48 included in the range but 101 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 wit... | consecutive_grid | underdetermined_system | 8 | [[0, 1, 58], [1, 0, 49], [1, 2, 87], [2, 0, 48]] | 686 | 0.38043832778930664 | 4 | 53 | 9 | ["[['57', '', '86'], ['', '75', ''], ['', '76', '90']]", 48, 101] | ["[['57', '', '86'], ['', '75', ''], ['', '76', '90']]", 48, 101] | ["[['57', '', '86'], ['', '75', ''], ['', '76', '90']]", "48", "101"] |
37 | 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 150, and sum of row 1 must be 209. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 1, 40], [0, 2, 42], [1, 0, 60], [1, 1, 61], [1, 2, 88], [2, 0, 66], [2, 2, 41]] | 495 | 6.065331697463989 | 7 | 39 | 9 | ["[['48', '', ''], ['', '', ''], ['', '49', '']]", 3, 40, 89] | ["[['48', '', ''], ['', '', ''], ['', '49', '']]", 40, 89, [1, 2], [1, 2], [150], [209], 169] | ["[['48', '', ''], ['', '', ''], ['', '49', '']]", "40", "89", "[None, 150, None]", "[None, 209, None]", "169"] |
37 | 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, 0], [2, 5], [2, 3], [7, 6], [2, 5], [4, 0], [4, 0], [4, 5], [7, 4], [7, 5], [7, 2], [1, 7], [1, 2], [1, 7], [1, 4], [6, 7], [1, 0], [3, 2]] | 70 | 8.884233713150024 | 18 | 56 | 20 | [[[], ["Blue", "Black", "Blue", "Yellow", "Red"], ["Red", "Green", "Black", "Green", "Black"], [], ["Red", "Red", "Green", "Yellow", "Yellow"], [], [], ["Blue", "Yellow", "Green", "Black", "Blue"]], 5, {"0": 3, "1": 2, "2": 1, "3": 7, "4": 5, "5": 5, "6": 6, "7": 4}] | [[[], ["Blue", "Black", "Blue", "Yellow", "Red"], ["Red", "Green", "Black", "Green", "Black"], [], ["Red", "Red", "Green", "Yellow", "Yellow"], [], [], ["Blue", "Yellow", "Green", "Black", "Blue"]], 5, {"0": 3, "1": 2, "2": 1, "3": 7, "4": 5, "5": 5, "6": 6, "7": 4}, 4] | ["[[], ['Blue', 'Black', 'Blue', 'Yellow', 'Red'], ['Red', 'Green', 'Black', 'Green', 'Black'], [], ['Red', 'Red', 'Green', 'Yellow', 'Yellow'], [], [], ['Blue', 'Yellow', 'Green', 'Black', 'Blue']]", "{0: 3, 1: 2, 2: 1, 3: 7, 4: 5, 5: 5, 6: 6, 7: 4}", "5", "4"] |
37 | 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, 5) to his destination workshop at index (1, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[7, 5], [6, 5], [5, 5], [4, 5], [4, 4], [3, 4], [3, 3], [2, 3], [2, 2], [1, 2], [1, 1], [1, 0]] | 84 | 0.0287020206451416 | 12 | 4 | 4 | [[["15", "x", "12", "x", "9", "19", "x", "x", "13", "x", "16"], ["14", "6", "3", "18", "x", "8", "18", "x", "x", "x", "x"], ["16", "10", "9", "4", "9", "5", "15", "4", "x", "x", "2"], ["5", "9", "x", "8", "1", "15", "7", "15", "x", "x", "x"], ["6", "x", "3", "x", "4", "6", "6", "19", "x", "16", "13"], ["17", "x", "11",... | [[["15", "x", "12", "x", "9", "19", "x", "x", "13", "x", "16"], ["14", "6", "3", "18", "x", "8", "18", "x", "x", "x", "x"], ["16", "10", "9", "4", "9", "5", "15", "4", "x", "x", "2"], ["5", "9", "x", "8", "1", "15", "7", "15", "x", "x", "x"], ["6", "x", "3", "x", "4", "6", "6", "19", "x", "16", "13"], ["17", "x", "11",... | ["[['15', 'x', '12', 'x', '9', '19', 'x', 'x', '13', 'x', '16'], ['14', '6', '3', '18', 'x', '8', '18', 'x', 'x', 'x', 'x'], ['16', '10', '9', '4', '9', '5', '15', '4', 'x', 'x', '2'], ['5', '9', 'x', '8', '1', '15', '7', '15', 'x', 'x', 'x'], ['6', 'x', '3', 'x', '4', '6', '6', '19', 'x', '16', '13'], ['17', 'x', '11'... |
37 | 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, 8], [3, 7], [3, 6], [3, 5], [3, 4], [4, 4], [5, 3], [5, 2], [5, 1], [5, 0], [6, 0]] | 13 | 0.02647542953491211 | 13 | 8 | 2 | ["[[1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [0... | ["[[1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [0... | ["[[1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [0... |
37 | Given 9 labeled water jugs with capacities 19, 122, 104, 145, 38, 141, 126, 82, 37, 33 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 256, 399, 410 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed ... | water_jug | subset_sum | 6 | [["+", 145, 3], ["+", 145, 3], ["+", 38, 3], ["+", 82, 3], ["+", 122, 2], ["+", 122, 2], ["+", 33, 2], ["+", 122, 2], ["+", 82, 1], ["+", 141, 1], ["+", 33, 1]] | 11 | 0.04917335510253906 | 11 | 60 | 3 | [[19, 122, 104, 145, 38, 141, 126, 82, 37, 33], [256, 399, 410]] | [[19, 122, 104, 145, 38, 141, 126, 82, 37, 33], [256, 399, 410]] | ["[19, 122, 104, 145, 38, 141, 126, 82, 37, 33]", "[256, 399, 410]"] |
38 | 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 | [79, 26, 17, 73, 74, 59, 75, 79, 64, 29, 47, 17, 59, 74, 73, 39, 17, 47, 26, 59, 47, 17] | 22 | 0.22814416885375977 | 22 | 4 | 12 | [[[75, 59, 74, 73], ["_", 79, 26, 17], [64, 29, 47, 39]]] | [[[75, 59, 74, 73], ["_", 79, 26, 17], [64, 29, 47, 39]]] | ["[[75, 59, 74, 73], ['_', 79, 26, 17], [64, 29, 47, 39]]"] |
38 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 20 | 0.39636731147766113 | 20 | 4 | 24 | [[["s", "n", "_", "e", "y", "e"], ["a", "e", "t", "i", "l", "e"], ["o", "e", "c", "i", "v", "t"], ["m", "l", "w", "s", "e", "r"]]] | [[["s", "n", "_", "e", "y", "e"], ["a", "e", "t", "i", "l", "e"], ["o", "e", "c", "i", "v", "t"], ["m", "l", "w", "s", "e", "r"]], ["nieve", "astely", "oecist", "mewler"]] | ["[['s', 'n', '_', 'e', 'y', 'e'], ['a', 'e', 't', 'i', 'l', 'e'], ['o', 'e', 'c', 'i', 'v', 't'], ['m', 'l', 'w', 's', 'e', 'r']]", "['nieve', 'astely', 'oecist', 'mewler']"] |
38 | 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 | ["Q", "D", "S", "F", "V", "Y", "F", "V"] | 8 | 0.028425216674804688 | 8 | 12 | 15 | [[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0... | [[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0... | ["[[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, ... |
38 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [30, 24, 27, 14, 29, 17, 4, 21, 20, 14, 19, 23, 18, 4, 12, 9, 24, 26, 21, 17, 3, 13, 25, 20, 16, 12, 2, 9, 17, 5, 6, 24, 13, 11, 6, 15, 13, 5, 13, 25, 10, 15, 10, 3, 2, 18, 7, 23, 5, 18, 21, 6], such that the sum of the ch... | coin_exchange | subset_sum | 31 | [9, 9, 21, 21, 10, 27, 29, 18, 10, 15, 25, 20, 18, 21, 25, 20, 2] | 58 | 0.056997060775756836 | 17 | 52 | 52 | [[30, 24, 27, 14, 29, 17, 4, 21, 20, 14, 19, 23, 18, 4, 12, 9, 24, 26, 21, 17, 3, 13, 25, 20, 16, 12, 2, 9, 17, 5, 6, 24, 13, 11, 6, 15, 13, 5, 13, 25, 10, 15, 10, 3, 2, 18, 7, 23, 5, 18, 21, 6]] | [[30, 24, 27, 14, 29, 17, 4, 21, 20, 14, 19, 23, 18, 4, 12, 9, 24, 26, 21, 17, 3, 13, 25, 20, 16, 12, 2, 9, 17, 5, 6, 24, 13, 11, 6, 15, 13, 5, 13, 25, 10, 15, 10, 3, 2, 18, 7, 23, 5, 18, 21, 6], {"14": 11, "3": 1, "18": 5, "21": 1, "27": 2, "19": 14, "6": 6, "25": 8, "5": 3, "29": 4, "7": 6, "24": 10, "10": 2, "13": 9... | ["[30, 24, 27, 14, 29, 17, 4, 21, 20, 14, 19, 23, 18, 4, 12, 9, 24, 26, 21, 17, 3, 13, 25, 20, 16, 12, 2, 9, 17, 5, 6, 24, 13, 11, 6, 15, 13, 5, 13, 25, 10, 15, 10, 3, 2, 18, 7, 23, 5, 18, 21, 6]", "{14: 11, 3: 1, 18: 5, 21: 1, 27: 2, 19: 14, 6: 6, 25: 8, 5: 3, 29: 4, 7: 6, 24: 10, 10: 2, 13: 9, 9: 1, 11: 8, 16: 10, 2:... |
38 | 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], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1]] | 19 | 5.927346706390381 | 19 | 6 | 12 | [[["Blue", "Green", "Blue", "Red"], ["Red", "Green", "Blue", "Red"], ["Green", "Red", "Green", "Blue"]], 7] | [[["Blue", "Green", "Blue", "Red"], ["Red", "Green", "Blue", "Red"], ["Green", "Red", "Green", "Blue"]], 7] | ["[['Blue', 'Green', 'Blue', 'Red'], ['Red', 'Green', 'Blue', 'Red'], ['Green', 'Red', 'Green', 'Blue']]", "7"] |
38 | We have a 3x3 numerical grid, with numbers ranging from 45 to 98 (45 included in the range but 98 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, 45], [1, 0, 46], [1, 1, 90], [2, 2, 97]] | 749 | 0.5823245048522949 | 4 | 53 | 9 | ["[['', '89', '95'], ['', '', '96'], ['74', '93', '']]", 45, 98] | ["[['', '89', '95'], ['', '', '96'], ['74', '93', '']]", 45, 98] | ["[['', '89', '95'], ['', '', '96'], ['74', '93', '']]", "45", "98"] |
38 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 40 to 66. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 227, 215, None for columns 1 to 2 respectively, and the sums of rows must be None, 207, 218, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 41], [0, 2, 46], [1, 0, 48], [1, 1, 55], [2, 0, 58], [2, 2, 63], [3, 0, 59], [3, 1, 64]] | 840 | 3.1795032024383545 | 8 | 39 | 9 | ["[['', '56', '', '40'], ['', '', '44', '60'], ['', '52', '', '45'], ['', '', '62', '47']]", 4, 40, 66] | ["[['', '56', '', '40'], ['', '', '44', '60'], ['', '52', '', '45'], ['', '', '62', '47']]", 40, 66, [1, 3], [1, 3], [227, 215], [207, 218], 195] | ["[['', '56', '', '40'], ['', '', '44', '60'], ['', '52', '', '45'], ['', '', '62', '47']]", "40", "66", "[None, 227, 215, None]", "[None, 207, 218, None]", "195"] |
38 | 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, 7], [6, 4], [6, 7], [3, 2], [3, 4], [3, 4], [1, 7], [1, 7], [1, 3], [1, 5], [6, 5], [6, 3], [0, 5], [0, 1], [0, 5], [0, 4], [2, 1], [6, 1]] | 90 | 0.06386184692382812 | 18 | 56 | 20 | [[["Blue", "Black", "Yellow", "Black", "Red"], ["Blue", "Blue", "Green", "Black", "Yellow"], [], ["Yellow", "Red", "Red", "Green", "Green"], [], [], ["Red", "Blue", "Black", "Green", "Yellow"], []], 5, {"0": 7, "1": 5, "2": 7, "3": 2, "4": 6, "5": 7, "6": 5, "7": 3}] | [[["Blue", "Black", "Yellow", "Black", "Red"], ["Blue", "Blue", "Green", "Black", "Yellow"], [], ["Yellow", "Red", "Red", "Green", "Green"], [], [], ["Red", "Blue", "Black", "Green", "Yellow"], []], 5, {"0": 7, "1": 5, "2": 7, "3": 2, "4": 6, "5": 7, "6": 5, "7": 3}, 4] | ["[['Blue', 'Black', 'Yellow', 'Black', 'Red'], ['Blue', 'Blue', 'Green', 'Black', 'Yellow'], [], ['Yellow', 'Red', 'Red', 'Green', 'Green'], [], [], ['Red', 'Blue', 'Black', 'Green', 'Yellow'], []]", "{0: 7, 1: 5, 2: 7, 3: 2, 4: 6, 5: 7, 6: 5, 7: 3}", "5", "4"] |
38 | 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, 6) to his destination workshop at index (8, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 3 | [[3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [8, 1], [8, 0]] | 131 | 0.035286903381347656 | 12 | 4 | 4 | [[["x", "x", "x", "3", "x", "x", "16", "x", "2", "16", "3"], ["8", "x", "8", "5", "x", "x", "10", "x", "19", "4", "x"], ["x", "x", "18", "1", "16", "x", "9", "15", "x", "x", "11"], ["x", "x", "17", "16", "4", "19", "2", "x", "1", "11", "x"], ["9", "x", "5", "16", "18", "x", "x", "7", "x", "18", "6"], ["x", "15", "7", "... | [[["x", "x", "x", "3", "x", "x", "16", "x", "2", "16", "3"], ["8", "x", "8", "5", "x", "x", "10", "x", "19", "4", "x"], ["x", "x", "18", "1", "16", "x", "9", "15", "x", "x", "11"], ["x", "x", "17", "16", "4", "19", "2", "x", "1", "11", "x"], ["9", "x", "5", "16", "18", "x", "x", "7", "x", "18", "6"], ["x", "15", "7", "... | ["[['x', 'x', 'x', '3', 'x', 'x', '16', 'x', '2', '16', '3'], ['8', 'x', '8', '5', 'x', 'x', '10', 'x', '19', '4', 'x'], ['x', 'x', '18', '1', '16', 'x', '9', '15', 'x', 'x', '11'], ['x', 'x', '17', '16', '4', '19', '2', 'x', '1', '11', 'x'], ['9', 'x', '5', '16', '18', 'x', 'x', '7', 'x', '18', '6'], ['x', '15', '7', ... |
38 | 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 | [[8, 8], [7, 7], [7, 6], [6, 5], [5, 4], [4, 4], [3, 4], [3, 3], [2, 3], [2, 2], [1, 2], [0, 2], [0, 1], [0, 0]] | 14 | 0.025176048278808594 | 14 | 8 | 2 | ["[[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0... | ["[[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0... | ["[[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0... |
38 | Given 9 labeled water jugs with capacities 117, 128, 36, 129, 103, 53, 21, 119, 105, 26 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 394, 425, 426 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed... | water_jug | subset_sum | 6 | [["+", 53, 3], ["+", 117, 3], ["+", 128, 3], ["+", 128, 3], ["+", 26, 2], ["+", 128, 2], ["+", 128, 2], ["+", 26, 2], ["+", 117, 2], ["+", 117, 1], ["+", 128, 1], ["+", 21, 1], ["+", 128, 1]] | 13 | 0.05204272270202637 | 13 | 60 | 3 | [[117, 128, 36, 129, 103, 53, 21, 119, 105, 26], [394, 425, 426]] | [[117, 128, 36, 129, 103, 53, 21, 119, 105, 26], [394, 425, 426]] | ["[117, 128, 36, 129, 103, 53, 21, 119, 105, 26]", "[394, 425, 426]"] |
39 | 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 | [15, 88, 48, 55, 57, 39, 59, 57, 88, 15, 39, 100, 30, 59, 100, 30, 82, 39, 30, 82, 59, 100, 57, 88, 82, 57, 88, 82, 55, 48] | 30 | 0.43415212631225586 | 30 | 4 | 12 | [[[30, 39, 59, 78], [100, 57, 55, 48], [82, "_", 15, 88]]] | [[[30, 39, 59, 78], [100, 57, 55, 48], [82, "_", 15, 88]]] | ["[[30, 39, 59, 78], [100, 57, 55, 48], [82, '_', 15, 88]]"] |
39 | 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-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left"] | 14 | 0.235795259475708 | 14 | 4 | 24 | [[["n", "j", "_", "b", "e", "y"], ["e", "i", "t", "u", "n", "o"], ["x", "e", "n", "i", "b", "m"], ["e", "n", "w", "o", "m", "b"]]] | [[["n", "j", "_", "b", "e", "y"], ["e", "i", "t", "u", "n", "o"], ["x", "e", "n", "i", "b", "m"], ["e", "n", "w", "o", "m", "b"]], ["jibby", "entone", "xenium", "enwomb"]] | ["[['n', 'j', '_', 'b', 'e', 'y'], ['e', 'i', 't', 'u', 'n', 'o'], ['x', 'e', 'n', 'i', 'b', 'm'], ['e', 'n', 'w', 'o', 'm', 'b']]", "['jibby', 'entone', 'xenium', 'enwomb']"] |
39 | 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 | ["O", "Z", "N", "E", "T", "Y", "W", "T", "J", "N"] | 10 | 0.033557891845703125 | 10 | 12 | 15 | [[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1... | [[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1... | ["[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, ... |
39 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [26, 24, 8, 2, 11, 10, 11, 14, 20, 9, 13, 10, 25, 21, 7, 20, 15, 27, 18, 12, 23, 4, 2, 4, 22, 23, 15, 16, 24, 14, 22, 13, 15, 21, 5, 14, 2, 21, 14, 10, 2, 2, 24, 26, 17, 2, 20, 22, 3, 27, 8, 20, 2, 25, 7], such that the su... | coin_exchange | subset_sum | 32 | [22, 18, 16, 12, 13, 13, 21, 21, 20, 21, 20, 27, 22, 20, 2, 5] | 54 | 0.061914682388305664 | 16 | 55 | 55 | [[26, 24, 8, 2, 11, 10, 11, 14, 20, 9, 13, 10, 25, 21, 7, 20, 15, 27, 18, 12, 23, 4, 2, 4, 22, 23, 15, 16, 24, 14, 22, 13, 15, 21, 5, 14, 2, 21, 14, 10, 2, 2, 24, 26, 17, 2, 20, 22, 3, 27, 8, 20, 2, 25, 7]] | [[26, 24, 8, 2, 11, 10, 11, 14, 20, 9, 13, 10, 25, 21, 7, 20, 15, 27, 18, 12, 23, 4, 2, 4, 22, 23, 15, 16, 24, 14, 22, 13, 15, 21, 5, 14, 2, 21, 14, 10, 2, 2, 24, 26, 17, 2, 20, 22, 3, 27, 8, 20, 2, 25, 7], {"24": 18, "14": 4, "15": 10, "23": 15, "26": 12, "22": 4, "17": 8, "5": 2, "18": 2, "16": 3, "11": 3, "2": 1, "2... | ["[26, 24, 8, 2, 11, 10, 11, 14, 20, 9, 13, 10, 25, 21, 7, 20, 15, 27, 18, 12, 23, 4, 2, 4, 22, 23, 15, 16, 24, 14, 22, 13, 15, 21, 5, 14, 2, 21, 14, 10, 2, 2, 24, 26, 17, 2, 20, 22, 3, 27, 8, 20, 2, 25, 7]", "{24: 18, 14: 4, 15: 10, 23: 15, 26: 12, 22: 4, 17: 8, 5: 2, 18: 2, 16: 3, 11: 3, 2: 1, 27: 9, 3: 3, 10: 5, 20:... |
39 | 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, 1], [2, 1], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 2], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1]] | 19 | 6.7476325035095215 | 19 | 6 | 12 | [[["Red", "Green", "Blue", "Red"], ["Blue", "Red", "Blue", "Green"], ["Green", "Red", "Blue", "Green"]], 7] | [[["Red", "Green", "Blue", "Red"], ["Blue", "Red", "Blue", "Green"], ["Green", "Red", "Blue", "Green"]], 7] | ["[['Red', 'Green', 'Blue', 'Red'], ['Blue', 'Red', 'Blue', 'Green'], ['Green', 'Red', 'Blue', 'Green']]", "7"] |
39 | We have a 3x3 numerical grid, with numbers ranging from 18 to 71 (18 included in the range but 71 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 0, 18], [0, 2, 61], [1, 0, 19], [1, 1, 40]] | 351 | 0.6906087398529053 | 4 | 53 | 9 | ["[['', '60', ''], ['', '', '53'], ['52', '39', '20']]", 18, 71] | ["[['', '60', ''], ['', '', '53'], ['52', '39', '20']]", 18, 71] | ["[['', '60', ''], ['', '', '53'], ['52', '39', '20']]", "18", "71"] |
39 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 24 to 50. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 174, 158, None for columns 1 to 2 respectively, and the sums of rows must be None, 158, 131, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 24], [0, 2, 36], [0, 3, 29], [1, 1, 44], [2, 0, 25], [2, 3, 27], [3, 0, 40], [3, 2, 48], [3, 3, 26]] | 576 | 7.876656532287598 | 9 | 39 | 9 | ["[['', '35', '', ''], ['43', '', '41', '30'], ['', '46', '33', ''], ['', '49', '', '']]", 4, 24, 50] | ["[['', '35', '', ''], ['43', '', '41', '30'], ['', '46', '33', ''], ['', '49', '', '']]", 24, 50, [1, 3], [1, 3], [174, 158], [158, 131], 156] | ["[['', '35', '', ''], ['43', '', '41', '30'], ['', '46', '33', ''], ['', '49', '', '']]", "24", "50", "[None, 174, 158, None]", "[None, 158, 131, None]", "156"] |
39 | 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, 1], [6, 2], [6, 1], [6, 1], [5, 6], [5, 7], [4, 6], [5, 2], [5, 3], [7, 5], [0, 3], [0, 5], [4, 2], [4, 3], [4, 2], [4, 5], [0, 3]] | 78 | 4.903253078460693 | 18 | 56 | 20 | [[["Green", "Green", "Black", "Blue", "Black"], [], [], [], ["Yellow", "Red", "Black", "Red", "Blue"], ["Yellow", "Blue", "Red", "Black", "Blue"], ["Red", "Green", "Green", "Yellow", "Yellow"], []], 5, {"0": 8, "1": 8, "2": 1, "3": 2, "4": 9, "5": 4, "6": 7, "7": 8}] | [[["Green", "Green", "Black", "Blue", "Black"], [], [], [], ["Yellow", "Red", "Black", "Red", "Blue"], ["Yellow", "Blue", "Red", "Black", "Blue"], ["Red", "Green", "Green", "Yellow", "Yellow"], []], 5, {"0": 8, "1": 8, "2": 1, "3": 2, "4": 9, "5": 4, "6": 7, "7": 8}, 4] | ["[['Green', 'Green', 'Black', 'Blue', 'Black'], [], [], [], ['Yellow', 'Red', 'Black', 'Red', 'Blue'], ['Yellow', 'Blue', 'Red', 'Black', 'Blue'], ['Red', 'Green', 'Green', 'Yellow', 'Yellow'], []]", "{0: 8, 1: 8, 2: 1, 3: 2, 4: 9, 5: 4, 6: 7, 7: 8}", "5", "4"] |
39 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 1) to his destination workshop at index (5, 10), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[3, 1], [3, 2], [2, 2], [2, 3], [2, 4], [3, 4], [3, 5], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 9], [5, 10]] | 79 | 0.028283357620239258 | 14 | 4 | 4 | [[["15", "8", "18", "3", "19", "x", "17", "x", "x", "x", "x"], ["19", "16", "x", "18", "20", "2", "5", "7", "11", "12", "3"], ["18", "x", "18", "1", "2", "x", "x", "x", "12", "16", "4"], ["9", "20", "4", "19", "5", "15", "x", "x", "x", "6", "4"], ["x", "18", "8", "1", "x", "7", "1", "7", "10", "1", "4"], ["x", "18", "x... | [[["15", "8", "18", "3", "19", "x", "17", "x", "x", "x", "x"], ["19", "16", "x", "18", "20", "2", "5", "7", "11", "12", "3"], ["18", "x", "18", "1", "2", "x", "x", "x", "12", "16", "4"], ["9", "20", "4", "19", "5", "15", "x", "x", "x", "6", "4"], ["x", "18", "8", "1", "x", "7", "1", "7", "10", "1", "4"], ["x", "18", "x... | ["[['15', '8', '18', '3', '19', 'x', '17', 'x', 'x', 'x', 'x'], ['19', '16', 'x', '18', '20', '2', '5', '7', '11', '12', '3'], ['18', 'x', '18', '1', '2', 'x', 'x', 'x', '12', '16', '4'], ['9', '20', '4', '19', '5', '15', 'x', 'x', 'x', '6', '4'], ['x', '18', '8', '1', 'x', '7', '1', '7', '10', '1', '4'], ['x', '18', '... |
39 | 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 | [[9, 9], [8, 8], [7, 9], [6, 9], [6, 8], [5, 8], [4, 8], [3, 7], [3, 6], [3, 5], [3, 4], [2, 4], [1, 4], [0, 4], [0, 3]] | 15 | 0.025874614715576172 | 15 | 8 | 2 | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0], [1... | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0], [1... | ["[[0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0], [1... |
39 | Given 9 labeled water jugs with capacities 76, 63, 111, 59, 11, 108, 16, 66, 75, 67 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 191, 269, 328 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the... | water_jug | subset_sum | 6 | [["+", 66, 3], ["+", 75, 3], ["+", 76, 3], ["+", 111, 3], ["+", 59, 2], ["+", 75, 2], ["+", 76, 2], ["+", 59, 2], ["+", 75, 1], ["+", 108, 1], ["-", 67, 1], ["+", 75, 1]] | 12 | 0.045966386795043945 | 12 | 60 | 3 | [[76, 63, 111, 59, 11, 108, 16, 66, 75, 67], [191, 269, 328]] | [[76, 63, 111, 59, 11, 108, 16, 66, 75, 67], [191, 269, 328]] | ["[76, 63, 111, 59, 11, 108, 16, 66, 75, 67]", "[191, 269, 328]"] |
40 | 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 | [26, 82, 3, 7, 34, 94, 93, 11, 28, 93, 94, 34, 11, 26, 82, 15, 50, 82, 26, 28, 93, 94, 34, 11, 7, 3] | 26 | 0.45993494987487793 | 26 | 4 | 12 | [[[28, 11, 50, 15], [94, 93, "_", 26], [34, 7, 3, 82]]] | [[[28, 11, 50, 15], [94, 93, "_", 26], [34, 7, 3, 82]]] | ["[[28, 11, 50, 15], [94, 93, '_', 26], [34, 7, 3, 82]]"] |
40 | 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-right", "up-left"] | 6 | 0.2233717441558838 | 6 | 4 | 24 | [[["a", "n", "_", "l", "l", "e"], ["y", "p", "p", "o", "a", "n"], ["r", "i", "m", "a", "y", "a"], ["c", "t", "a", "w", "l", "y"]]] | [[["a", "n", "_", "l", "l", "e"], ["y", "p", "p", "o", "a", "n"], ["r", "i", "m", "a", "y", "a"], ["c", "t", "a", "w", "l", "y"]], ["nolle", "yapman", "pitaya", "crawly"]] | ["[['a', 'n', '_', 'l', 'l', 'e'], ['y', 'p', 'p', 'o', 'a', 'n'], ['r', 'i', 'm', 'a', 'y', 'a'], ['c', 't', 'a', 'w', 'l', 'y']]", "['nolle', 'yapman', 'pitaya', 'crawly']"] |
40 | 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 | ["F", "Q", "R", "Z", "R", "G", "L", "A", "D", "A"] | 10 | 0.030649185180664062 | 10 | 12 | 15 | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, 0... | [[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, 0... | ["[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, ... |
40 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [25, 22, 26, 12, 18, 12, 5, 6, 6, 21, 28, 26, 6, 26, 9, 11, 27, 24, 16, 1, 12, 5, 10, 23, 11, 10, 28, 2, 3, 7, 23, 28, 27, 12, 3, 3, 27, 21, 13, 8, 18, 25, 6, 7, 9, 25, 18, 18, 23, 12, 11, 15, 2, 16], such that the sum of ... | coin_exchange | subset_sum | 33 | [18, 23, 18, 23, 18, 23, 18, 8, 11, 15, 2, 11, 11, 27, 12, 2, 3, 3, 9, 9, 13, 12] | 73 | 0.06098175048828125 | 22 | 54 | 54 | [[25, 22, 26, 12, 18, 12, 5, 6, 6, 21, 28, 26, 6, 26, 9, 11, 27, 24, 16, 1, 12, 5, 10, 23, 11, 10, 28, 2, 3, 7, 23, 28, 27, 12, 3, 3, 27, 21, 13, 8, 18, 25, 6, 7, 9, 25, 18, 18, 23, 12, 11, 15, 2, 16]] | [[25, 22, 26, 12, 18, 12, 5, 6, 6, 21, 28, 26, 6, 26, 9, 11, 27, 24, 16, 1, 12, 5, 10, 23, 11, 10, 28, 2, 3, 7, 23, 28, 27, 12, 3, 3, 27, 21, 13, 8, 18, 25, 6, 7, 9, 25, 18, 18, 23, 12, 11, 15, 2, 16], {"10": 6, "24": 14, "5": 3, "3": 1, "16": 6, "27": 10, "13": 1, "12": 4, "21": 17, "8": 2, "28": 10, "6": 3, "1": 1, "... | ["[25, 22, 26, 12, 18, 12, 5, 6, 6, 21, 28, 26, 6, 26, 9, 11, 27, 24, 16, 1, 12, 5, 10, 23, 11, 10, 28, 2, 3, 7, 23, 28, 27, 12, 3, 3, 27, 21, 13, 8, 18, 25, 6, 7, 9, 25, 18, 18, 23, 12, 11, 15, 2, 16]", "{10: 6, 24: 14, 5: 3, 3: 1, 16: 6, 27: 10, 13: 1, 12: 4, 21: 17, 8: 2, 28: 10, 6: 3, 1: 1, 18: 2, 25: 14, 11: 3, 23... |
40 | 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], [1, 2], [1, 2], [0, 1], [0, 1], [2, 1], [0, 1], [2, 0], [2, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2]] | 15 | 0.6760032176971436 | 15 | 6 | 12 | [[["Blue", "Green", "Green", "Blue"], ["Red", "Blue", "Green", "Green"], ["Red", "Red", "Red", "Blue"]], 7] | [[["Blue", "Green", "Green", "Blue"], ["Red", "Blue", "Green", "Green"], ["Red", "Red", "Red", "Blue"]], 7] | ["[['Blue', 'Green', 'Green', 'Blue'], ['Red', 'Blue', 'Green', 'Green'], ['Red', 'Red', 'Red', 'Blue']]", "7"] |
40 | We have a 3x3 numerical grid, with numbers ranging from 34 to 87 (34 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 | 9 | [[0, 0, 34], [0, 1, 35], [0, 2, 36], [1, 1, 38], [1, 2, 37]] | 350 | 0.1763606071472168 | 5 | 53 | 9 | ["[['', '', ''], ['65', '', ''], ['79', '73', '50']]", 34, 87] | ["[['', '', ''], ['65', '', ''], ['79', '73', '50']]", 34, 87] | ["[['', '', ''], ['65', '', ''], ['79', '73', '50']]", "34", "87"] |
40 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 24 to 50. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 149, 178, None for columns 1 to 2 respectively, and the sums of rows must be None, 135, 130, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 1, 30], [0, 2, 42], [0, 3, 33], [1, 0, 26], [1, 1, 34], [1, 2, 47], [1, 3, 28], [2, 0, 24], [3, 2, 49]] | 560 | 11.717026948928833 | 9 | 39 | 9 | ["[['38', '', '', ''], ['', '', '', ''], ['', '39', '40', '27'], ['32', '46', '', '25']]", 4, 24, 50] | ["[['38', '', '', ''], ['', '', '', ''], ['', '39', '40', '27'], ['32', '46', '', '25']]", 24, 50, [1, 3], [1, 3], [149, 178], [135, 130], 151] | ["[['38', '', '', ''], ['', '', '', ''], ['', '39', '40', '27'], ['32', '46', '', '25']]", "24", "50", "[None, 149, 178, None]", "[None, 135, 130, None]", "151"] |
40 | 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, 0], [2, 5], [4, 0], [4, 6], [4, 6], [4, 1], [3, 4], [2, 4], [2, 1], [2, 4], [3, 1], [7, 1], [7, 0], [7, 6], [7, 0], [3, 2], [3, 6], [3, 2], [5, 2], [7, 2]] | 78 | 9.45132565498352 | 20 | 56 | 20 | [[[], [], ["Green", "Yellow", "Black", "Red", "Black"], ["Black", "Red", "Yellow", "Blue", "Yellow"], ["Green", "Blue", "Blue", "Red", "Black"], [], [], ["Red", "Green", "Blue", "Green", "Yellow"]], 5, {"0": 5, "1": 5, "2": 1, "3": 7, "4": 7, "5": 9, "6": 1, "7": 6}] | [[[], [], ["Green", "Yellow", "Black", "Red", "Black"], ["Black", "Red", "Yellow", "Blue", "Yellow"], ["Green", "Blue", "Blue", "Red", "Black"], [], [], ["Red", "Green", "Blue", "Green", "Yellow"]], 5, {"0": 5, "1": 5, "2": 1, "3": 7, "4": 7, "5": 9, "6": 1, "7": 6}, 4] | ["[[], [], ['Green', 'Yellow', 'Black', 'Red', 'Black'], ['Black', 'Red', 'Yellow', 'Blue', 'Yellow'], ['Green', 'Blue', 'Blue', 'Red', 'Black'], [], [], ['Red', 'Green', 'Blue', 'Green', 'Yellow']]", "{0: 5, 1: 5, 2: 1, 3: 7, 4: 7, 5: 9, 6: 1, 7: 6}", "5", "4"] |
40 | 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, 10) to his destination workshop at index (5, 1), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[3, 10], [3, 9], [2, 9], [2, 8], [2, 7], [1, 7], [0, 7], [0, 6], [0, 5], [0, 4], [0, 3], [1, 3], [1, 2], [2, 2], [2, 1], [2, 0], [3, 0], [4, 0], [4, 1], [5, 1]] | 164 | 0.028056621551513672 | 20 | 4 | 4 | [[["x", "10", "x", "8", "13", "8", "4", "3", "15", "x", "17"], ["9", "x", "6", "4", "17", "x", "16", "3", "19", "x", "x"], ["8", "3", "18", "x", "x", "3", "x", "7", "12", "16", "17"], ["8", "x", "x", "13", "x", "7", "x", "8", "x", "12", "9"], ["2", "9", "x", "x", "9", "4", "18", "x", "x", "11", "x"], ["14", "20", "x", ... | [[["x", "10", "x", "8", "13", "8", "4", "3", "15", "x", "17"], ["9", "x", "6", "4", "17", "x", "16", "3", "19", "x", "x"], ["8", "3", "18", "x", "x", "3", "x", "7", "12", "16", "17"], ["8", "x", "x", "13", "x", "7", "x", "8", "x", "12", "9"], ["2", "9", "x", "x", "9", "4", "18", "x", "x", "11", "x"], ["14", "20", "x", ... | ["[['x', '10', 'x', '8', '13', '8', '4', '3', '15', 'x', '17'], ['9', 'x', '6', '4', '17', 'x', '16', '3', '19', 'x', 'x'], ['8', '3', '18', 'x', 'x', '3', 'x', '7', '12', '16', '17'], ['8', 'x', 'x', '13', 'x', '7', 'x', '8', 'x', '12', '9'], ['2', '9', 'x', 'x', '9', '4', '18', 'x', 'x', '11', 'x'], ['14', '20', 'x',... |
40 | 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 | [[9, 9], [8, 8], [7, 7], [7, 6], [6, 5], [6, 4], [6, 3], [5, 3], [5, 2], [4, 2], [4, 1], [4, 0], [3, 0], [2, 0]] | 14 | 0.03258109092712402 | 14 | 8 | 2 | ["[[1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1... | ["[[1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1... | ["[[1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1... |
40 | Given 9 labeled water jugs with capacities 62, 144, 80, 72, 100, 127, 18, 82, 42, 99 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 258, 310, 514 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed th... | water_jug | subset_sum | 6 | [["+", 82, 3], ["+", 144, 3], ["+", 144, 3], ["+", 144, 3], ["+", 62, 2], ["+", 144, 2], ["+", 42, 2], ["+", 62, 2], ["+", 42, 1], ["+", 72, 1], ["+", 144, 1]] | 11 | 0.03391599655151367 | 11 | 60 | 3 | [[62, 144, 80, 72, 100, 127, 18, 82, 42, 99], [258, 310, 514]] | [[62, 144, 80, 72, 100, 127, 18, 82, 42, 99], [258, 310, 514]] | ["[62, 144, 80, 72, 100, 127, 18, 82, 42, 99]", "[258, 310, 514]"] |
41 | 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 | [54, 33, 61, 18, 29, 54, 33, 61, 54, 33, 61, 10, 77, 54, 10, 77, 81, 89, 54, 44, 18, 10, 33, 29] | 24 | 0.06885409355163574 | 24 | 4 | 12 | [[[81, 10, 54, "_"], [89, 77, 33, 29], [26, 44, 61, 18]]] | [[[81, 10, 54, "_"], [89, 77, 33, 29], [26, 44, 61, 18]]] | ["[[81, 10, 54, '_'], [89, 77, 33, 29], [26, 44, 61, 18]]"] |
41 | 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-right", "down-left", "up-left", "down-left", "up-left", "up-right", "up-right", "down-right", "up-right", "down-right", "down-left", "up-left", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 20 | 0.3230454921722412 | 20 | 4 | 24 | [[["o", "a", "_", "i", "t", "s"], ["d", "r", "o", "o", "o", "a"], ["c", "e", "m", "i", "l", "e"], ["c", "c", "m", "t", "i", "e"]]] | [[["o", "a", "_", "i", "t", "s"], ["d", "r", "o", "o", "o", "a"], ["c", "e", "m", "i", "l", "e"], ["c", "c", "m", "t", "i", "e"]], ["alias", "doocot", "cerite", "commie"]] | ["[['o', 'a', '_', 'i', 't', 's'], ['d', 'r', 'o', 'o', 'o', 'a'], ['c', 'e', 'm', 'i', 'l', 'e'], ['c', 'c', 'm', 't', 'i', 'e']]", "['alias', 'doocot', 'cerite', 'commie']"] |
41 | 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 | ["E", "G", "Q", "Y", "A", "C", "Z", "Y", "A"] | 9 | 0.02761673927307129 | 9 | 12 | 15 | [[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0... | [[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0... | ["[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, ... |
41 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [20, 27, 20, 26, 2, 19, 25, 5, 14, 28, 7, 4, 20, 25, 9, 7, 3, 9, 27, 23, 2, 17, 25, 19, 10, 2, 8, 15, 3, 6, 24, 6, 22, 3, 10, 3, 2, 24, 7, 16, 2, 24, 21, 5, 23, 25, 10, 5, 20, 14, 24, 12, 11, 11, 13], such that the sum of ... | coin_exchange | subset_sum | 34 | [7, 7, 21, 25, 24, 25, 24, 25, 24, 27, 26, 24, 25] | 66 | 0.05327725410461426 | 13 | 55 | 55 | [[20, 27, 20, 26, 2, 19, 25, 5, 14, 28, 7, 4, 20, 25, 9, 7, 3, 9, 27, 23, 2, 17, 25, 19, 10, 2, 8, 15, 3, 6, 24, 6, 22, 3, 10, 3, 2, 24, 7, 16, 2, 24, 21, 5, 23, 25, 10, 5, 20, 14, 24, 12, 11, 11, 13]] | [[20, 27, 20, 26, 2, 19, 25, 5, 14, 28, 7, 4, 20, 25, 9, 7, 3, 9, 27, 23, 2, 17, 25, 19, 10, 2, 8, 15, 3, 6, 24, 6, 22, 3, 10, 3, 2, 24, 7, 16, 2, 24, 21, 5, 23, 25, 10, 5, 20, 14, 24, 12, 11, 11, 13], {"14": 7, "15": 15, "2": 2, "22": 7, "7": 1, "25": 7, "10": 4, "11": 11, "16": 11, "27": 8, "3": 2, "13": 5, "19": 10,... | ["[20, 27, 20, 26, 2, 19, 25, 5, 14, 28, 7, 4, 20, 25, 9, 7, 3, 9, 27, 23, 2, 17, 25, 19, 10, 2, 8, 15, 3, 6, 24, 6, 22, 3, 10, 3, 2, 24, 7, 16, 2, 24, 21, 5, 23, 25, 10, 5, 20, 14, 24, 12, 11, 11, 13]", "{14: 7, 15: 15, 2: 2, 22: 7, 7: 1, 25: 7, 10: 4, 11: 11, 16: 11, 27: 8, 3: 2, 13: 5, 19: 10, 8: 5, 23: 18, 5: 4, 12... |
41 | 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, 1], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 17 | 2.059692859649658 | 17 | 6 | 12 | [[["Green", "Blue", "Red", "Blue"], ["Red", "Green", "Blue", "Green"], ["Red", "Blue", "Green", "Red"]], 7] | [[["Green", "Blue", "Red", "Blue"], ["Red", "Green", "Blue", "Green"], ["Red", "Blue", "Green", "Red"]], 7] | ["[['Green', 'Blue', 'Red', 'Blue'], ['Red', 'Green', 'Blue', 'Green'], ['Red', 'Blue', 'Green', 'Red']]", "7"] |
41 | We have a 3x3 numerical grid, with numbers ranging from 29 to 82 (29 included in the range but 82 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 0, 40], [0, 1, 30], [0, 2, 29], [1, 1, 41], [2, 1, 42]] | 369 | 0.19344615936279297 | 5 | 53 | 9 | ["[['', '', ''], ['39', '', '50'], ['32', '', '55']]", 29, 82] | ["[['', '', ''], ['39', '', '50'], ['32', '', '55']]", 29, 82] | ["[['', '', ''], ['39', '', '50'], ['32', '', '55']]", "29", "82"] |
41 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 24 to 50. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 135, 160, None for columns 1 to 2 respectively, and the sums of rows must be None, 125, 164, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 25], [0, 1, 26], [0, 3, 36], [1, 0, 24], [1, 2, 27], [2, 1, 49], [2, 2, 46], [3, 2, 47], [3, 3, 28]] | 554 | 4.838366508483887 | 9 | 44 | 9 | ["[['', '', '40', ''], ['', '31', '', '43'], ['37', '', '', '32'], ['34', '29', '', '']]", 4, 24, 50] | ["[['', '', '40', ''], ['', '31', '', '43'], ['37', '', '', '32'], ['34', '29', '', '']]", 24, 50, [1, 3], [1, 3], [135, 160], [125, 164], 146] | ["[['', '', '40', ''], ['', '31', '', '43'], ['37', '', '', '32'], ['34', '29', '', '']]", "24", "50", "[None, 135, 160, None]", "[None, 125, 164, None]", "146"] |
41 | 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 | [[6, 2], [6, 4], [6, 5], [6, 7], [0, 6], [1, 5], [1, 6], [0, 2], [0, 7], [0, 6], [1, 4], [1, 4], [3, 2], [3, 7], [3, 4], [1, 5], [3, 5], [3, 7], [0, 2]] | 66 | 34.940831422805786 | 19 | 56 | 20 | [[["Green", "Blue", "Yellow", "Green", "Blue"], ["Black", "Green", "Red", "Red", "Black"], [], ["Blue", "Yellow", "Red", "Black", "Yellow"], [], [], ["Blue", "Red", "Black", "Yellow", "Green"], []], 5, {"0": 2, "1": 1, "2": 2, "3": 8, "4": 4, "5": 3, "6": 6, "7": 3}] | [[["Green", "Blue", "Yellow", "Green", "Blue"], ["Black", "Green", "Red", "Red", "Black"], [], ["Blue", "Yellow", "Red", "Black", "Yellow"], [], [], ["Blue", "Red", "Black", "Yellow", "Green"], []], 5, {"0": 2, "1": 1, "2": 2, "3": 8, "4": 4, "5": 3, "6": 6, "7": 3}, 4] | ["[['Green', 'Blue', 'Yellow', 'Green', 'Blue'], ['Black', 'Green', 'Red', 'Red', 'Black'], [], ['Blue', 'Yellow', 'Red', 'Black', 'Yellow'], [], [], ['Blue', 'Red', 'Black', 'Yellow', 'Green'], []]", "{0: 2, 1: 1, 2: 2, 3: 8, 4: 4, 5: 3, 6: 6, 7: 3}", "5", "4"] |
41 | 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, 10) to his destination workshop at index (3, 0), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[5, 10], [4, 10], [4, 9], [3, 9], [2, 9], [2, 8], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [2, 2], [3, 2], [3, 1], [3, 0]] | 142 | 0.02771902084350586 | 17 | 4 | 4 | [[["19", "7", "11", "x", "3", "18", "8", "x", "x", "x", "x"], ["12", "18", "6", "1", "13", "12", "14", "11", "13", "5", "19"], ["11", "10", "10", "18", "15", "x", "12", "x", "4", "17", "10"], ["4", "3", "3", "7", "x", "19", "x", "x", "x", "12", "9"], ["x", "x", "6", "19", "x", "4", "14", "x", "9", "4", "15"], ["4", "7"... | [[["19", "7", "11", "x", "3", "18", "8", "x", "x", "x", "x"], ["12", "18", "6", "1", "13", "12", "14", "11", "13", "5", "19"], ["11", "10", "10", "18", "15", "x", "12", "x", "4", "17", "10"], ["4", "3", "3", "7", "x", "19", "x", "x", "x", "12", "9"], ["x", "x", "6", "19", "x", "4", "14", "x", "9", "4", "15"], ["4", "7"... | ["[['19', '7', '11', 'x', '3', '18', '8', 'x', 'x', 'x', 'x'], ['12', '18', '6', '1', '13', '12', '14', '11', '13', '5', '19'], ['11', '10', '10', '18', '15', 'x', '12', 'x', '4', '17', '10'], ['4', '3', '3', '7', 'x', '19', 'x', 'x', 'x', '12', '9'], ['x', 'x', '6', '19', 'x', '4', '14', 'x', '9', '4', '15'], ['4', '7... |
41 | 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, 0], [9, 1], [8, 1], [7, 2], [6, 3], [5, 3], [5, 4], [5, 5], [4, 5], [4, 6], [3, 6], [3, 7], [2, 7]] | 13 | 0.023111343383789062 | 13 | 8 | 2 | ["[[1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1... | ["[[1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1... | ["[[1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1... |
41 | Given 9 labeled water jugs with capacities 80, 69, 12, 52, 107, 53, 82, 95, 108 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 170, 385, 499 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo... | water_jug | subset_sum | 6 | [["+", 69, 3], ["+", 107, 3], ["+", 107, 3], ["+", 108, 3], ["+", 108, 3], ["+", 52, 2], ["+", 107, 2], ["+", 107, 2], ["+", 107, 2], ["+", 12, 2], ["+", 52, 1], ["+", 107, 1], ["-", 69, 1], ["+", 80, 1]] | 14 | 0.027560949325561523 | 14 | 54 | 3 | [[80, 69, 12, 52, 107, 53, 82, 95, 108], [170, 385, 499]] | [[80, 69, 12, 52, 107, 53, 82, 95, 108], [170, 385, 499]] | ["[80, 69, 12, 52, 107, 53, 82, 95, 108]", "[170, 385, 499]"] |
42 | 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 | [2, 37, 21, 70, 9, 2, 37, 22, 54, 37, 22, 21, 70, 4, 33, 9, 4, 22, 21, 54, 37, 11] | 22 | 0.05596041679382324 | 22 | 4 | 12 | [[[74, 37, 2, 22], [4, 21, "_", 54], [33, 70, 9, 11]]] | [[[74, 37, 2, 22], [4, 21, "_", 54], [33, 70, 9, 11]]] | ["[[74, 37, 2, 22], [4, 21, '_', 54], [33, 70, 9, 11]]"] |
42 | 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-right", "up-right", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left"] | 22 | 0.27234864234924316 | 22 | 4 | 24 | [[["_", "j", "a", "r", "e", "b"], ["z", "o", "y", "s", "i", "i"], ["r", "e", "r", "s", "t", "y"], ["g", "e", "i", "q", "u", "a"]]] | [[["_", "j", "a", "r", "e", "b"], ["z", "o", "y", "s", "i", "i"], ["r", "e", "r", "s", "t", "y"], ["g", "e", "i", "q", "u", "a"]], ["jerib", "zoysia", "reesty", "griqua"]] | ["[['_', 'j', 'a', 'r', 'e', 'b'], ['z', 'o', 'y', 's', 'i', 'i'], ['r', 'e', 'r', 's', 't', 'y'], ['g', 'e', 'i', 'q', 'u', 'a']]", "['jerib', 'zoysia', 'reesty', 'griqua']"] |
42 | 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 | ["F", "A", "H", "C", "T", "N", "S", "P", "N", "M", "H"] | 11 | 0.03896760940551758 | 11 | 12 | 15 | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0... | [[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0... | ["[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, ... |
42 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [24, 10, 24, 3, 21, 7, 21, 26, 8, 14, 24, 5, 13, 10, 25, 6, 9, 4, 18, 4, 15, 4, 10, 23, 6, 13, 26, 20, 8, 10, 29, 27, 27, 20, 2, 15, 9, 9, 25, 8, 2, 27, 5, 22, 19, 26, 2, 29, 12, 9, 6, 12, 2, 15, 5, 16, 3, 29, 19], such th... | coin_exchange | subset_sum | 35 | [27, 27, 26, 2, 13, 29, 26, 27, 29, 29, 26, 2, 23, 14] | 41 | 0.06342601776123047 | 14 | 59 | 59 | [[24, 10, 24, 3, 21, 7, 21, 26, 8, 14, 24, 5, 13, 10, 25, 6, 9, 4, 18, 4, 15, 4, 10, 23, 6, 13, 26, 20, 8, 10, 29, 27, 27, 20, 2, 15, 9, 9, 25, 8, 2, 27, 5, 22, 19, 26, 2, 29, 12, 9, 6, 12, 2, 15, 5, 16, 3, 29, 19]] | [[24, 10, 24, 3, 21, 7, 21, 26, 8, 14, 24, 5, 13, 10, 25, 6, 9, 4, 18, 4, 15, 4, 10, 23, 6, 13, 26, 20, 8, 10, 29, 27, 27, 20, 2, 15, 9, 9, 25, 8, 2, 27, 5, 22, 19, 26, 2, 29, 12, 9, 6, 12, 2, 15, 5, 16, 3, 29, 19], {"5": 2, "9": 8, "12": 5, "14": 4, "22": 8, "26": 3, "8": 7, "27": 2, "20": 13, "3": 3, "13": 3, "2": 1,... | ["[24, 10, 24, 3, 21, 7, 21, 26, 8, 14, 24, 5, 13, 10, 25, 6, 9, 4, 18, 4, 15, 4, 10, 23, 6, 13, 26, 20, 8, 10, 29, 27, 27, 20, 2, 15, 9, 9, 25, 8, 2, 27, 5, 22, 19, 26, 2, 29, 12, 9, 6, 12, 2, 15, 5, 16, 3, 29, 19]", "{5: 2, 9: 8, 12: 5, 14: 4, 22: 8, 26: 3, 8: 7, 27: 2, 20: 13, 3: 3, 13: 3, 2: 1, 19: 19, 29: 4, 10: 3... |
42 | 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], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1]] | 19 | 6.271071672439575 | 19 | 6 | 12 | [[["Blue", "Green", "Blue", "Red"], ["Red", "Green", "Blue", "Red"], ["Green", "Red", "Green", "Blue"]], 7] | [[["Blue", "Green", "Blue", "Red"], ["Red", "Green", "Blue", "Red"], ["Green", "Red", "Green", "Blue"]], 7] | ["[['Blue', 'Green', 'Blue', 'Red'], ['Red', 'Green', 'Blue', 'Red'], ['Green', 'Red', 'Green', 'Blue']]", "7"] |
42 | We have a 3x3 numerical grid, with numbers ranging from 45 to 98 (45 included in the range but 98 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, 1, 49], [1, 2, 47], [2, 0, 52], [2, 1, 48], [2, 2, 45]] | 538 | 0.20381546020507812 | 5 | 53 | 9 | ["[['46', '80', '90'], ['51', '', ''], ['', '', '']]", 45, 98] | ["[['46', '80', '90'], ['51', '', ''], ['', '', '']]", 45, 98] | ["[['46', '80', '90'], ['51', '', ''], ['', '', '']]", "45", "98"] |
42 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 24 to 50. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 141, 134, None for columns 1 to 2 respectively, and the sums of rows must be None, 133, 150, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 26], [0, 2, 27], [0, 3, 33], [1, 0, 28], [1, 2, 37], [1, 3, 30], [2, 0, 29], [2, 3, 39], [3, 3, 31]] | 540 | 0.6481747627258301 | 9 | 44 | 9 | ["[['', '42', '', ''], ['', '38', '', ''], ['', '36', '46', ''], ['49', '25', '24', '']]", 4, 24, 50] | ["[['', '42', '', ''], ['', '38', '', ''], ['', '36', '46', ''], ['49', '25', '24', '']]", 24, 50, [1, 3], [1, 3], [141, 134], [133, 150], 155] | ["[['', '42', '', ''], ['', '38', '', ''], ['', '36', '46', ''], ['49', '25', '24', '']]", "24", "50", "[None, 141, 134, None]", "[None, 133, 150, None]", "155"] |
42 | 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, 7], [6, 4], [6, 7], [3, 2], [3, 4], [3, 4], [1, 7], [1, 7], [1, 3], [1, 5], [6, 5], [6, 3], [0, 5], [0, 1], [0, 5], [0, 4], [2, 1], [6, 1]] | 90 | 0.08126401901245117 | 18 | 56 | 20 | [[["Blue", "Black", "Yellow", "Black", "Red"], ["Blue", "Blue", "Green", "Black", "Yellow"], [], ["Yellow", "Red", "Red", "Green", "Green"], [], [], ["Red", "Blue", "Black", "Green", "Yellow"], []], 5, {"0": 7, "1": 5, "2": 7, "3": 2, "4": 6, "5": 7, "6": 5, "7": 3}] | [[["Blue", "Black", "Yellow", "Black", "Red"], ["Blue", "Blue", "Green", "Black", "Yellow"], [], ["Yellow", "Red", "Red", "Green", "Green"], [], [], ["Red", "Blue", "Black", "Green", "Yellow"], []], 5, {"0": 7, "1": 5, "2": 7, "3": 2, "4": 6, "5": 7, "6": 5, "7": 3}, 4] | ["[['Blue', 'Black', 'Yellow', 'Black', 'Red'], ['Blue', 'Blue', 'Green', 'Black', 'Yellow'], [], ['Yellow', 'Red', 'Red', 'Green', 'Green'], [], [], ['Red', 'Blue', 'Black', 'Green', 'Yellow'], []]", "{0: 7, 1: 5, 2: 7, 3: 2, 4: 6, 5: 7, 6: 5, 7: 3}", "5", "4"] |
42 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (6, 10) to his destination workshop at index (3, 2), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[6, 10], [7, 10], [7, 9], [7, 8], [7, 7], [7, 6], [6, 6], [5, 6], [4, 6], [3, 6], [3, 5], [3, 4], [3, 3], [3, 2]] | 146 | 0.027129411697387695 | 14 | 4 | 4 | [[["14", "x", "11", "x", "x", "8", "15", "17", "18", "x", "11"], ["13", "9", "2", "7", "9", "12", "7", "x", "x", "x", "12"], ["x", "2", "8", "13", "5", "x", "x", "7", "18", "x", "x"], ["19", "6", "1", "6", "19", "13", "14", "x", "x", "17", "x"], ["x", "9", "6", "x", "x", "14", "10", "x", "x", "5", "x"], ["12", "x", "x"... | [[["14", "x", "11", "x", "x", "8", "15", "17", "18", "x", "11"], ["13", "9", "2", "7", "9", "12", "7", "x", "x", "x", "12"], ["x", "2", "8", "13", "5", "x", "x", "7", "18", "x", "x"], ["19", "6", "1", "6", "19", "13", "14", "x", "x", "17", "x"], ["x", "9", "6", "x", "x", "14", "10", "x", "x", "5", "x"], ["12", "x", "x"... | ["[['14', 'x', '11', 'x', 'x', '8', '15', '17', '18', 'x', '11'], ['13', '9', '2', '7', '9', '12', '7', 'x', 'x', 'x', '12'], ['x', '2', '8', '13', '5', 'x', 'x', '7', '18', 'x', 'x'], ['19', '6', '1', '6', '19', '13', '14', 'x', 'x', '17', 'x'], ['x', '9', '6', 'x', 'x', '14', '10', 'x', 'x', '5', 'x'], ['12', 'x', 'x... |
42 | 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, 9], [10, 8], [9, 7], [8, 6], [8, 5], [7, 4], [7, 3], [7, 2], [6, 2], [5, 2], [4, 2], [4, 1], [3, 1]] | 13 | 0.029900312423706055 | 13 | 8 | 2 | ["[[0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1... | ["[[0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1... | ["[[0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1... |
42 | Given 9 labeled water jugs with capacities 36, 72, 16, 80, 45, 67, 38, 32, 149, 37 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 201, 202, 233 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the ... | water_jug | subset_sum | 6 | [["+", 32, 3], ["+", 36, 3], ["+", 149, 3], ["+", 16, 3], ["+", 37, 2], ["+", 149, 2], ["+", 16, 2], ["+", 36, 1], ["+", 149, 1], ["+", 16, 1]] | 10 | 0.032448768615722656 | 10 | 60 | 3 | [[36, 72, 16, 80, 45, 67, 38, 32, 149, 37], [201, 202, 233]] | [[36, 72, 16, 80, 45, 67, 38, 32, 149, 37], [201, 202, 233]] | ["[36, 72, 16, 80, 45, 67, 38, 32, 149, 37]", "[201, 202, 233]"] |
43 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [99, 49, 68, 42, 49, 68, 67, 23, 88, 56, 52, 99, 68, 67, 23, 88, 33, 26, 42, 49, 67, 68, 88, 52, 56, 33, 26, 23, 49, 42] | 30 | 0.6710901260375977 | 30 | 4 | 12 | [[[52, "_", 99, 42], [56, 67, 49, 68], [88, 23, 33, 26]]] | [[[52, "_", 99, 42], [56, 67, 49, 68], [88, 23, 33, 26]]] | ["[[52, '_', 99, 42], [56, 67, 49, 68], [88, 23, 33, 26]]"] |
43 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-right", "up-right", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-left", "up-left", "up-right", "up-left"] | 22 | 0.4346792697906494 | 22 | 4 | 24 | [[["a", "d", "a", "o", "n", "e"], ["p", "m", "l", "n", "a", "i"], ["_", "n", "c", "o", "d", "a"], ["s", "a", "l", "t", "l", "y"]]] | [[["a", "d", "a", "o", "n", "e"], ["p", "m", "l", "n", "a", "i"], ["_", "n", "c", "o", "d", "a"], ["s", "a", "l", "t", "l", "y"]], ["dione", "palmad", "ancona", "saltly"]] | ["[['a', 'd', 'a', 'o', 'n', 'e'], ['p', 'm', 'l', 'n', 'a', 'i'], ['_', 'n', 'c', 'o', 'd', 'a'], ['s', 'a', 'l', 't', 'l', 'y']]", "['dione', 'palmad', 'ancona', 'saltly']"] |
43 | 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 | ["Y", "J", "I", "M", "P", "L", "M", "T", "G", "E", "B", "E"] | 12 | 0.034844398498535156 | 12 | 12 | 15 | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0... | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, ... |
43 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [69, 32, 32, 6, 19, 13, 21, 68, 32, 16, 21, 29, 20, 13, 21, 24, 26, 5, 23, 18, 16, 24, 2, 17, 15, 30, 26], such that the sum of the chosen coins adds up to 322. Each coin in the list is unique and can only be used once. Al... | coin_exchange | subset_sum | 15 | [68, 30, 16, 17, 29, 26, 6, 13, 69, 32, 16] | 61 | 0.04106879234313965 | 11 | 27 | 27 | [[69, 32, 32, 6, 19, 13, 21, 68, 32, 16, 21, 29, 20, 13, 21, 24, 26, 5, 23, 18, 16, 24, 2, 17, 15, 30, 26]] | [[69, 32, 32, 6, 19, 13, 21, 68, 32, 16, 21, 29, 20, 13, 21, 24, 26, 5, 23, 18, 16, 24, 2, 17, 15, 30, 26], {"30": 3, "20": 11, "24": 15, "26": 6, "68": 2, "29": 5, "13": 2, "2": 1, "17": 2, "32": 11, "18": 4, "15": 9, "5": 3, "21": 11, "69": 19, "6": 3, "16": 4, "23": 17, "19": 15}, 322] | ["[69, 32, 32, 6, 19, 13, 21, 68, 32, 16, 21, 29, 20, 13, 21, 24, 26, 5, 23, 18, 16, 24, 2, 17, 15, 30, 26]", "{30: 3, 20: 11, 24: 15, 26: 6, 68: 2, 29: 5, 13: 2, 2: 1, 17: 2, 32: 11, 18: 4, 15: 9, 5: 3, 21: 11, 69: 19, 6: 3, 16: 4, 23: 17, 19: 15}", "322"] |
43 | 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], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 17 | 2.007240056991577 | 17 | 6 | 12 | [[["Green", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Blue"], ["Green", "Blue", "Red", "Red"]], 7] | [[["Green", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Blue"], ["Green", "Blue", "Red", "Red"]], 7] | ["[['Green', 'Green', 'Blue', 'Red'], ['Red', 'Blue', 'Green', 'Blue'], ['Green', 'Blue', 'Red', 'Red']]", "7"] |
43 | We have a 3x3 numerical grid, with numbers ranging from 7 to 60 (7 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 an... | consecutive_grid | underdetermined_system | 10 | [[0, 1, 8], [0, 2, 7], [1, 0, 10], [1, 1, 11], [2, 0, 9], [2, 2, 28]] | 142 | 20.925482749938965 | 6 | 53 | 9 | ["[['13', '', ''], ['', '', '27'], ['', '26', '']]", 7, 60] | ["[['13', '', ''], ['', '', '27'], ['', '26', '']]", 7, 60] | ["[['13', '', ''], ['', '', '27'], ['', '26', '']]", "7", "60"] |
43 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 61. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 212, 185, None for columns 1 to 2 respectively, and the sums of rows must be None, 180, 202, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 35], [0, 3, 40], [1, 0, 38], [1, 1, 57], [2, 1, 60], [2, 2, 52], [2, 3, 36], [3, 0, 45], [3, 1, 44], [3, 2, 46]] | 735 | 81.89644312858582 | 10 | 44 | 9 | ["[['', '51', '39', ''], ['', '', '48', '37'], ['54', '', '', ''], ['', '', '', '53']]", 4, 35, 61] | ["[['', '51', '39', ''], ['', '', '48', '37'], ['54', '', '', ''], ['', '', '', '53']]", 35, 61, [1, 3], [1, 3], [212, 185], [180, 202], 193] | ["[['', '51', '39', ''], ['', '', '48', '37'], ['54', '', '', ''], ['', '', '', '53']]", "35", "61", "[None, 212, 185, None]", "[None, 180, 202, None]", "193"] |
43 | 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, 5], [4, 7], [4, 3], [1, 6], [1, 5], [4, 7], [2, 4], [1, 6], [2, 1], [2, 5], [2, 5], [3, 4], [0, 1], [0, 1], [0, 6], [0, 7], [0, 6], [2, 7]] | 55 | 19.498444318771362 | 18 | 56 | 20 | [[["Green", "Green", "Red", "Blue", "Red"], ["Black", "Red", "Black", "Red", "Green"], ["Yellow", "Green", "Black", "Black", "Blue"], [], ["Blue", "Yellow", "Blue", "Yellow", "Yellow"], [], [], []], 5, {"0": 5, "1": 2, "2": 8, "3": 7, "4": 5, "5": 6, "6": 1, "7": 1}] | [[["Green", "Green", "Red", "Blue", "Red"], ["Black", "Red", "Black", "Red", "Green"], ["Yellow", "Green", "Black", "Black", "Blue"], [], ["Blue", "Yellow", "Blue", "Yellow", "Yellow"], [], [], []], 5, {"0": 5, "1": 2, "2": 8, "3": 7, "4": 5, "5": 6, "6": 1, "7": 1}, 4] | ["[['Green', 'Green', 'Red', 'Blue', 'Red'], ['Black', 'Red', 'Black', 'Red', 'Green'], ['Yellow', 'Green', 'Black', 'Black', 'Blue'], [], ['Blue', 'Yellow', 'Blue', 'Yellow', 'Yellow'], [], [], []]", "{0: 5, 1: 2, 2: 8, 3: 7, 4: 5, 5: 6, 6: 1, 7: 1}", "5", "4"] |
43 | 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, 10) to his destination workshop at index (6, 2), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[3, 10], [3, 9], [2, 9], [2, 8], [2, 7], [3, 7], [4, 7], [4, 6], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [6, 2]] | 115 | 0.026669740676879883 | 14 | 4 | 4 | [[["x", "10", "2", "x", "x", "x", "3", "x", "4", "x", "14"], ["x", "x", "17", "16", "8", "x", "x", "x", "x", "1", "x"], ["18", "18", "16", "16", "15", "x", "x", "17", "12", "16", "15"], ["x", "4", "x", "x", "18", "9", "x", "15", "x", "1", "9"], ["3", "2", "7", "x", "x", "17", "2", "14", "x", "4", "2"], ["16", "17", "6"... | [[["x", "10", "2", "x", "x", "x", "3", "x", "4", "x", "14"], ["x", "x", "17", "16", "8", "x", "x", "x", "x", "1", "x"], ["18", "18", "16", "16", "15", "x", "x", "17", "12", "16", "15"], ["x", "4", "x", "x", "18", "9", "x", "15", "x", "1", "9"], ["3", "2", "7", "x", "x", "17", "2", "14", "x", "4", "2"], ["16", "17", "6"... | ["[['x', '10', '2', 'x', 'x', 'x', '3', 'x', '4', 'x', '14'], ['x', 'x', '17', '16', '8', 'x', 'x', 'x', 'x', '1', 'x'], ['18', '18', '16', '16', '15', 'x', 'x', '17', '12', '16', '15'], ['x', '4', 'x', 'x', '18', '9', 'x', '15', 'x', '1', '9'], ['3', '2', '7', 'x', 'x', '17', '2', '14', 'x', '4', '2'], ['16', '17', '6... |
43 | 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, 9], [7, 8], [6, 7], [5, 7], [5, 6], [5, 5], [4, 5], [3, 5], [3, 4], [3, 3], [3, 2], [2, 2], [2, 1]] | 15 | 0.028983116149902344 | 15 | 8 | 2 | ["[[1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1... | ["[[1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1... | ["[[1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0], [1... |
43 | Given 9 labeled water jugs with capacities 104, 14, 83, 46, 128, 34, 137, 15, 19, 126 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 342, 373, 447 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed t... | water_jug | subset_sum | 6 | [["+", 34, 3], ["+", 126, 3], ["+", 137, 3], ["+", 46, 3], ["+", 104, 3], ["+", 104, 2], ["+", 126, 2], ["+", 15, 2], ["+", 128, 2], ["+", 104, 1], ["+", 126, 1], ["-", 14, 1], ["+", 126, 1]] | 13 | 0.06156110763549805 | 13 | 60 | 3 | [[104, 14, 83, 46, 128, 34, 137, 15, 19, 126], [342, 373, 447]] | [[104, 14, 83, 46, 128, 34, 137, 15, 19, 126], [342, 373, 447]] | ["[104, 14, 83, 46, 128, 34, 137, 15, 19, 126]", "[342, 373, 447]"] |
44 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [22, 23, 54, 10, 58, 22, 23, 54, 22, 23, 81, 85, 100, 21, 27, 12, 10, 22, 23, 81, 85, 100, 54, 27, 12, 10] | 26 | 0.062206268310546875 | 26 | 4 | 12 | [[[81, "_", 58, 10], [85, 22, 23, 54], [100, 21, 27, 12]]] | [[[81, "_", 58, 10], [85, 22, 23, 54], [100, 21, 27, 12]]] | ["[[81, '_', 58, 10], [85, 22, 23, 54], [100, 21, 27, 12]]"] |
44 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.3068218231201172 | 16 | 4 | 24 | [[["h", "b", "n", "s", "i", "t"], ["t", "e", "r", "k", "v", "e"], ["i", "i", "_", "c", "o", "b"], ["h", "u", "m", "a", "t", "e"]]] | [[["h", "b", "n", "s", "i", "t"], ["t", "e", "r", "k", "v", "e"], ["i", "i", "_", "c", "o", "b"], ["h", "u", "m", "a", "t", "e"]], ["besit", "thrive", "kincob", "humate"]] | ["[['h', 'b', 'n', 's', 'i', 't'], ['t', 'e', 'r', 'k', 'v', 'e'], ['i', 'i', '_', 'c', 'o', 'b'], ['h', 'u', 'm', 'a', 't', 'e']]", "['besit', 'thrive', 'kincob', 'humate']"] |
44 | 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 | ["E", "C", "L", "T", "D", "H", "T", "D"] | 8 | 0.028389930725097656 | 8 | 12 | 15 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, ... |
44 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [2, 27, 9, 80, 20, 81, 13, 24, 16, 6, 26, 12, 3, 26, 20, 8, 16, 8, 20, 22, 9, 34, 23, 8, 12, 34, 4, 6, 22, 19], such that the sum of the chosen coins adds up to 346. Each coin in the list is unique and can only be used onc... | coin_exchange | subset_sum | 16 | [8, 4, 27, 8, 23, 6, 81, 80, 34, 26, 20, 8, 6, 2, 13] | 71 | 0.03767251968383789 | 15 | 30 | 30 | [[2, 27, 9, 80, 20, 81, 13, 24, 16, 6, 26, 12, 3, 26, 20, 8, 16, 8, 20, 22, 9, 34, 23, 8, 12, 34, 4, 6, 22, 19]] | [[2, 27, 9, 80, 20, 81, 13, 24, 16, 6, 26, 12, 3, 26, 20, 8, 16, 8, 20, 22, 9, 34, 23, 8, 12, 34, 4, 6, 22, 19], {"12": 9, "16": 12, "13": 5, "34": 8, "9": 9, "23": 4, "81": 2, "80": 20, "8": 1, "19": 19, "2": 2, "22": 13, "20": 7, "26": 11, "4": 1, "6": 2, "27": 4, "3": 1, "24": 12}, 346] | ["[2, 27, 9, 80, 20, 81, 13, 24, 16, 6, 26, 12, 3, 26, 20, 8, 16, 8, 20, 22, 9, 34, 23, 8, 12, 34, 4, 6, 22, 19]", "{12: 9, 16: 12, 13: 5, 34: 8, 9: 9, 23: 4, 81: 2, 80: 20, 8: 1, 19: 19, 2: 2, 22: 13, 20: 7, 26: 11, 4: 1, 6: 2, 27: 4, 3: 1, 24: 12}", "346"] |
44 | 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, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1]] | 11 | 0.07266616821289062 | 11 | 6 | 12 | [[["Red", "Red", "Blue", "Blue"], ["Red", "Green", "Green", "Green"], ["Red", "Blue", "Blue", "Green"]], 7] | [[["Red", "Red", "Blue", "Blue"], ["Red", "Green", "Green", "Green"], ["Red", "Blue", "Blue", "Green"]], 7] | ["[['Red', 'Red', 'Blue', 'Blue'], ['Red', 'Green', 'Green', 'Green'], ['Red', 'Blue', 'Blue', 'Green']]", "7"] |
44 | We have a 3x3 numerical grid, with numbers ranging from 31 to 84 (31 included in the range but 84 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, 31], [0, 2, 71], [1, 1, 43], [2, 0, 44], [2, 1, 33], [2, 2, 32]] | 439 | 185.86225056648254 | 6 | 53 | 9 | ["[['', '58', ''], ['42', '', '70'], ['', '', '']]", 31, 84] | ["[['', '58', ''], ['42', '', '70'], ['', '', '']]", 31, 84] | ["[['', '58', ''], ['42', '', '70'], ['', '', '']]", "31", "84"] |
44 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 61. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 188, 188, None for columns 1 to 2 respectively, and the sums of rows must be None, 177, 160, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 36], [0, 1, 60], [0, 3, 38], [1, 0, 40], [1, 1, 42], [1, 2, 52], [2, 0, 35], [2, 1, 37], [2, 2, 41], [3, 2, 56]] | 714 | 512.5996880531311 | 10 | 44 | 9 | ["[['', '', '39', ''], ['', '', '', '43'], ['', '', '', '47'], ['46', '49', '', '53']]", 4, 35, 61] | ["[['', '', '39', ''], ['', '', '', '43'], ['', '', '', '47'], ['46', '49', '', '53']]", 35, 61, [1, 3], [1, 3], [188, 188], [177, 160], 173] | ["[['', '', '39', ''], ['', '', '', '43'], ['', '', '', '47'], ['46', '49', '', '53']]", "35", "61", "[None, 188, 188, None]", "[None, 177, 160, None]", "173"] |
44 | 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 | [[6, 0], [7, 5], [6, 5], [6, 1], [6, 5], [4, 3], [4, 1], [4, 3], [4, 6], [4, 5], [7, 1], [7, 6], [7, 3], [2, 7], [2, 7], [2, 1], [2, 6], [0, 7], [2, 3]] | 53 | 14.416839361190796 | 19 | 56 | 20 | [[[], [], ["Blue", "Blue", "Green", "Black", "Red"], [], ["Red", "Green", "Red", "Black", "Yellow"], [], ["Blue", "Yellow", "Green", "Yellow", "Black"], ["Yellow", "Green", "Black", "Red", "Blue"]], 5, {"0": 6, "1": 2, "2": 7, "3": 1, "4": 1, "5": 5, "6": 3, "7": 2}] | [[[], [], ["Blue", "Blue", "Green", "Black", "Red"], [], ["Red", "Green", "Red", "Black", "Yellow"], [], ["Blue", "Yellow", "Green", "Yellow", "Black"], ["Yellow", "Green", "Black", "Red", "Blue"]], 5, {"0": 6, "1": 2, "2": 7, "3": 1, "4": 1, "5": 5, "6": 3, "7": 2}, 4] | ["[[], [], ['Blue', 'Blue', 'Green', 'Black', 'Red'], [], ['Red', 'Green', 'Red', 'Black', 'Yellow'], [], ['Blue', 'Yellow', 'Green', 'Yellow', 'Black'], ['Yellow', 'Green', 'Black', 'Red', 'Blue']]", "{0: 6, 1: 2, 2: 7, 3: 1, 4: 1, 5: 5, 6: 3, 7: 2}", "5", "4"] |
44 | 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 (8, 10) to his destination workshop at index (3, 4), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[8, 10], [7, 10], [7, 9], [6, 9], [5, 9], [4, 9], [3, 9], [3, 8], [2, 8], [2, 7], [2, 6], [2, 5], [3, 5], [3, 4]] | 85 | 0.02710127830505371 | 14 | 4 | 4 | [[["x", "16", "5", "13", "x", "x", "2", "x", "6", "x", "x"], ["x", "x", "17", "x", "15", "x", "10", "x", "5", "17", "x"], ["x", "x", "x", "x", "15", "3", "10", "2", "4", "13", "14"], ["x", "x", "x", "x", "17", "2", "4", "x", "1", "4", "5"], ["2", "x", "x", "2", "6", "17", "x", "x", "x", "4", "19"], ["19", "5", "x", "x"... | [[["x", "16", "5", "13", "x", "x", "2", "x", "6", "x", "x"], ["x", "x", "17", "x", "15", "x", "10", "x", "5", "17", "x"], ["x", "x", "x", "x", "15", "3", "10", "2", "4", "13", "14"], ["x", "x", "x", "x", "17", "2", "4", "x", "1", "4", "5"], ["2", "x", "x", "2", "6", "17", "x", "x", "x", "4", "19"], ["19", "5", "x", "x"... | ["[['x', '16', '5', '13', 'x', 'x', '2', 'x', '6', 'x', 'x'], ['x', 'x', '17', 'x', '15', 'x', '10', 'x', '5', '17', 'x'], ['x', 'x', 'x', 'x', '15', '3', '10', '2', '4', '13', '14'], ['x', 'x', 'x', 'x', '17', '2', '4', 'x', '1', '4', '5'], ['2', 'x', 'x', '2', '6', '17', 'x', 'x', 'x', '4', '19'], ['19', '5', 'x', 'x... |
44 | 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 | [[2, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 3], [7, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9], [9, 9], [10, 9]] | 14 | 0.028450727462768555 | 14 | 8 | 2 | ["[[1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0... | ["[[1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0... | ["[[1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0], [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0... |
44 | Given 9 labeled water jugs with capacities 67, 55, 84, 148, 107, 114, 17, 143, 40, 39 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 192, 247, 479 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed t... | water_jug | subset_sum | 6 | [["+", 143, 3], ["+", 148, 3], ["+", 40, 3], ["+", 148, 3], ["+", 143, 2], ["-", 39, 2], ["+", 143, 2], ["+", 39, 1], ["+", 39, 1], ["+", 114, 1]] | 10 | 0.030488252639770508 | 10 | 60 | 3 | [[67, 55, 84, 148, 107, 114, 17, 143, 40, 39], [192, 247, 479]] | [[67, 55, 84, 148, 107, 114, 17, 143, 40, 39], [192, 247, 479]] | ["[67, 55, 84, 148, 107, 114, 17, 143, 40, 39]", "[192, 247, 479]"] |
45 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [31, 19, 64, 65, 19, 31, 88, 96, 35, 67, 69, 88, 96, 19, 31, 96, 88, 55, 11, 64, 96, 11, 55, 88, 11, 55, 64, 96, 65, 31, 19, 11, 55, 64, 88, 69, 67, 35] | 38 | 18.521990299224854 | 38 | 4 | 12 | [[[11, 55, 69, 67], [19, 31, "_", 35], [64, 65, 88, 96]]] | [[[11, 55, 69, 67], [19, 31, "_", 35], [64, 65, 88, 96]]] | ["[[11, 55, 69, 67], [19, 31, '_', 35], [64, 65, 88, 96]]"] |
45 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-left"] | 16 | 0.26326990127563477 | 16 | 4 | 24 | [[["w", "k", "u", "a", "d", "i"], ["s", "a", "a", "r", "m", "y"], ["h", "g", "_", "i", "s", "h"], ["w", "h", "e", "a", "t", "y"]]] | [[["w", "k", "u", "a", "d", "i"], ["s", "a", "a", "r", "m", "y"], ["h", "g", "_", "i", "s", "h"], ["w", "h", "e", "a", "t", "y"]], ["khadi", "swarmy", "aguish", "wheaty"]] | ["[['w', 'k', 'u', 'a', 'd', 'i'], ['s', 'a', 'a', 'r', 'm', 'y'], ['h', 'g', '_', 'i', 's', 'h'], ['w', 'h', 'e', 'a', 't', 'y']]", "['khadi', 'swarmy', 'aguish', 'wheaty']"] |
45 | 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 | ["C", "B", "I", "Q", "M", "H", "Q", "M"] | 8 | 0.029607534408569336 | 8 | 12 | 15 | [[[0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1... | [[[0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1... | ["[[0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, ... |
45 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [21, 10, 19, 6, 20, 7, 23, 18, 4, 15, 4, 13, 2, 5, 32, 28, 113, 3, 9, 9, 11, 21, 112, 6, 6, 11, 29], such that the sum of the chosen coins adds up to 337. Each coin in the list is unique and can only be used once. Also coi... | coin_exchange | subset_sum | 17 | [23, 6, 19, 6, 11, 11, 113, 112, 32, 4] | 58 | 0.0367283821105957 | 10 | 27 | 27 | [[21, 10, 19, 6, 20, 7, 23, 18, 4, 15, 4, 13, 2, 5, 32, 28, 113, 3, 9, 9, 11, 21, 112, 6, 6, 11, 29]] | [[21, 10, 19, 6, 20, 7, 23, 18, 4, 15, 4, 13, 2, 5, 32, 28, 113, 3, 9, 9, 11, 21, 112, 6, 6, 11, 29], {"10": 7, "5": 3, "11": 3, "23": 2, "21": 13, "19": 3, "18": 18, "29": 20, "3": 2, "9": 7, "20": 18, "6": 2, "112": 20, "2": 1, "4": 4, "7": 4, "32": 1, "15": 8, "13": 10, "28": 17, "113": 18}, 337] | ["[21, 10, 19, 6, 20, 7, 23, 18, 4, 15, 4, 13, 2, 5, 32, 28, 113, 3, 9, 9, 11, 21, 112, 6, 6, 11, 29]", "{10: 7, 5: 3, 11: 3, 23: 2, 21: 13, 19: 3, 18: 18, 29: 20, 3: 2, 9: 7, 20: 18, 6: 2, 112: 20, 2: 1, 4: 4, 7: 4, 32: 1, 15: 8, 13: 10, 28: 17, 113: 18}", "337"] |
45 | 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], [2, 0], [2, 0], [2, 1], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 2]] | 12 | 0.17496824264526367 | 12 | 6 | 12 | [[["Red", "Green", "Green", "Green"], ["Blue", "Red", "Blue", "Blue"], ["Green", "Red", "Red", "Blue"]], 7] | [[["Red", "Green", "Green", "Green"], ["Blue", "Red", "Blue", "Blue"], ["Green", "Red", "Red", "Blue"]], 7] | ["[['Red', 'Green', 'Green', 'Green'], ['Blue', 'Red', 'Blue', 'Blue'], ['Green', 'Red', 'Red', 'Blue']]", "7"] |
45 | We have a 3x3 numerical grid, with numbers ranging from 22 to 75 (22 included in the range but 75 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, 22], [0, 2, 53], [1, 2, 52], [2, 0, 49], [2, 1, 24], [2, 2, 23]] | 349 | 2.575047731399536 | 6 | 53 | 9 | ["[['', '51', ''], ['48', '50', ''], ['', '', '']]", 22, 75] | ["[['', '51', ''], ['48', '50', ''], ['', '', '']]", 22, 75] | ["[['', '51', ''], ['48', '50', ''], ['', '', '']]", "22", "75"] |
45 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 61. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 177, 196, None for columns 1 to 2 respectively, and the sums of rows must be None, 183, 190, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 36], [0, 2, 42], [0, 3, 47], [1, 1, 37], [1, 2, 53], [1, 3, 35], [2, 0, 38], [2, 2, 44], [3, 2, 57], [3, 3, 40]] | 725 | 2.623443365097046 | 10 | 44 | 9 | ["[['', '50', '', ''], ['58', '', '', ''], ['', '49', '', '59'], ['39', '41', '', '']]", 4, 35, 61] | ["[['', '50', '', ''], ['58', '', '', ''], ['', '49', '', '59'], ['39', '41', '', '']]", 35, 61, [1, 3], [1, 3], [177, 196], [183, 190], 188] | ["[['', '50', '', ''], ['58', '', '', ''], ['', '49', '', '59'], ['39', '41', '', '']]", "35", "61", "[None, 177, 196, None]", "[None, 183, 190, None]", "188"] |
45 | 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, 3], [0, 4], [1, 2], [1, 5], [1, 5], [7, 2], [7, 5], [1, 2], [7, 1], [0, 1], [0, 7], [0, 1], [6, 0], [6, 2], [6, 5], [6, 0], [6, 1], [3, 0], [4, 7]] | 77 | 4.278231382369995 | 19 | 56 | 20 | [[["Red", "Yellow", "Red", "Yellow", "Black"], ["Black", "Blue", "Green", "Green", "Blue"], [], [], [], [], ["Black", "Blue", "Green", "Black", "Yellow"], ["Blue", "Green", "Yellow", "Red", "Red"]], 5, {"0": 2, "1": 3, "2": 5, "3": 9, "4": 8, "5": 5, "6": 8, "7": 1}] | [[["Red", "Yellow", "Red", "Yellow", "Black"], ["Black", "Blue", "Green", "Green", "Blue"], [], [], [], [], ["Black", "Blue", "Green", "Black", "Yellow"], ["Blue", "Green", "Yellow", "Red", "Red"]], 5, {"0": 2, "1": 3, "2": 5, "3": 9, "4": 8, "5": 5, "6": 8, "7": 1}, 4] | ["[['Red', 'Yellow', 'Red', 'Yellow', 'Black'], ['Black', 'Blue', 'Green', 'Green', 'Blue'], [], [], [], [], ['Black', 'Blue', 'Green', 'Black', 'Yellow'], ['Blue', 'Green', 'Yellow', 'Red', 'Red']]", "{0: 2, 1: 3, 2: 5, 3: 9, 4: 8, 5: 5, 6: 8, 7: 1}", "5", "4"] |
45 | 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, 10) to his destination workshop at index (6, 1), indexing from 0. Ben's car can mov... | traffic | pathfinding | 3 | [[3, 10], [4, 10], [5, 10], [5, 9], [5, 8], [5, 7], [5, 6], [5, 5], [6, 5], [6, 4], [6, 3], [6, 2], [6, 1]] | 119 | 0.02744436264038086 | 13 | 4 | 4 | [[["x", "x", "17", "12", "12", "10", "9", "9", "18", "x", "1"], ["x", "8", "x", "9", "x", "x", "18", "5", "1", "12", "14"], ["2", "19", "4", "x", "x", "x", "x", "x", "x", "15", "x"], ["17", "8", "6", "x", "x", "10", "15", "x", "x", "x", "13"], ["x", "x", "x", "9", "17", "x", "x", "x", "x", "12", "17"], ["x", "20", "3",... | [[["x", "x", "17", "12", "12", "10", "9", "9", "18", "x", "1"], ["x", "8", "x", "9", "x", "x", "18", "5", "1", "12", "14"], ["2", "19", "4", "x", "x", "x", "x", "x", "x", "15", "x"], ["17", "8", "6", "x", "x", "10", "15", "x", "x", "x", "13"], ["x", "x", "x", "9", "17", "x", "x", "x", "x", "12", "17"], ["x", "20", "3",... | ["[['x', 'x', '17', '12', '12', '10', '9', '9', '18', 'x', '1'], ['x', '8', 'x', '9', 'x', 'x', '18', '5', '1', '12', '14'], ['2', '19', '4', 'x', 'x', 'x', 'x', 'x', 'x', '15', 'x'], ['17', '8', '6', 'x', 'x', '10', '15', 'x', 'x', 'x', '13'], ['x', 'x', 'x', '9', '17', 'x', 'x', 'x', 'x', '12', '17'], ['x', '20', '3'... |
45 | 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, 0], [1, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 8], [1, 9], [2, 9], [3, 9], [4, 9], [5, 10], [6, 10], [7, 10], [8, 9]] | 18 | 0.029386281967163086 | 18 | 8 | 2 | ["[[0, 1, 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, 0, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [1... | ["[[0, 1, 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, 0, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [1... | ["[[0, 1, 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, 0, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], [1... |
45 | Given 9 labeled water jugs with capacities 116, 16, 79, 75, 30, 87, 28, 96, 15, 134 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 155, 208, 295 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the... | water_jug | subset_sum | 6 | [["+", 30, 3], ["+", 116, 3], ["+", 134, 3], ["+", 15, 3], ["+", 96, 2], ["+", 96, 2], ["+", 16, 2], ["+", 75, 1], ["-", 16, 1], ["+", 96, 1]] | 10 | 0.038698434829711914 | 10 | 60 | 3 | [[116, 16, 79, 75, 30, 87, 28, 96, 15, 134], [155, 208, 295]] | [[116, 16, 79, 75, 30, 87, 28, 96, 15, 134], [155, 208, 295]] | ["[116, 16, 79, 75, 30, 87, 28, 96, 15, 134]", "[155, 208, 295]"] |
46 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [85, 45, 77, 85, 61, 100, 91, 10, 85, 57, 95, 39, 10, 85, 57, 61, 100, 91, 85, 57, 61, 95, 83, 77, 45, 100, 95, 83, 77, 45, 83, 77, 39, 10] | 34 | 2.4867141246795654 | 34 | 4 | 12 | [[[85, "_", 61, 100], [45, 77, 10, 91], [83, 57, 95, 39]]] | [[[85, "_", 61, 100], [45, 77, 10, 91], [83, 57, 95, 39]]] | ["[[85, '_', 61, 100], [45, 77, 10, 91], [83, 57, 95, 39]]"] |
46 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "up-left", "up-right", "up-right", "down-right", "up-right", "down-right", "down-left", "up-left", "down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 18 | 0.27361011505126953 | 18 | 4 | 24 | [[["e", "a", "y", "u", "i", "e"], ["m", "k", "s", "o", "d", "l"], ["c", "a", "_", "l", "e", "d"], ["g", "l", "r", "o", "u", "s"]]] | [[["e", "a", "y", "u", "i", "e"], ["m", "k", "s", "o", "d", "l"], ["c", "a", "_", "l", "e", "d"], ["g", "l", "r", "o", "u", "s"]], ["akule", "mesode", "callid", "gyrous"]] | ["[['e', 'a', 'y', 'u', 'i', 'e'], ['m', 'k', 's', 'o', 'd', 'l'], ['c', 'a', '_', 'l', 'e', 'd'], ['g', 'l', 'r', 'o', 'u', 's']]", "['akule', 'mesode', 'callid', 'gyrous']"] |
46 | 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 | ["O", "Y", "W", "K", "M", "A", "C", "K", "M"] | 9 | 0.027652263641357422 | 9 | 12 | 15 | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0... | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, ... |
46 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [11, 6, 147, 6, 19, 29, 28, 32, 18, 20, 12, 22, 4, 20, 27, 3, 3, 18, 19, 9, 2, 28, 31, 20, 2, 27, 22, 30, 3], such that the sum of the chosen coins adds up to 324. Each coin in the list is unique and can only be used once.... | coin_exchange | subset_sum | 18 | [32, 28, 12, 19, 19, 147, 28, 20, 6, 9, 4] | 49 | 0.04179191589355469 | 11 | 29 | 29 | [[11, 6, 147, 6, 19, 29, 28, 32, 18, 20, 12, 22, 4, 20, 27, 3, 3, 18, 19, 9, 2, 28, 31, 20, 2, 27, 22, 30, 3]] | [[11, 6, 147, 6, 19, 29, 28, 32, 18, 20, 12, 22, 4, 20, 27, 3, 3, 18, 19, 9, 2, 28, 31, 20, 2, 27, 22, 30, 3], {"27": 18, "6": 2, "22": 12, "18": 11, "4": 3, "12": 4, "28": 6, "147": 10, "32": 6, "19": 3, "29": 12, "31": 19, "20": 4, "2": 2, "30": 17, "3": 2, "11": 10, "9": 2}, 324] | ["[11, 6, 147, 6, 19, 29, 28, 32, 18, 20, 12, 22, 4, 20, 27, 3, 3, 18, 19, 9, 2, 28, 31, 20, 2, 27, 22, 30, 3]", "{27: 18, 6: 2, 22: 12, 18: 11, 4: 3, 12: 4, 28: 6, 147: 10, 32: 6, 19: 3, 29: 12, 31: 19, 20: 4, 2: 2, 30: 17, 3: 2, 11: 10, 9: 2}", "324"] |
46 | 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, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 2], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0]] | 16 | 1.27297043800354 | 16 | 6 | 12 | [[["Red", "Blue", "Red", "Red"], ["Blue", "Green", "Green", "Blue"], ["Green", "Blue", "Green", "Red"]], 7] | [[["Red", "Blue", "Red", "Red"], ["Blue", "Green", "Green", "Blue"], ["Green", "Blue", "Green", "Red"]], 7] | ["[['Red', 'Blue', 'Red', 'Red'], ['Blue', 'Green', 'Green', 'Blue'], ['Green', 'Blue', 'Green', 'Red']]", "7"] |
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