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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
46 | We have a 4x4 numerical grid, with numbers ranging from 9 to 49 (9 included in the range but 49 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid cell... | consecutive_grid | underdetermined_system | 10 | [[0, 0, 26], [0, 3, 42], [1, 0, 24], [1, 1, 27], [3, 1, 13], [3, 3, 45]] | 439 | 0.18374395370483398 | 6 | 40 | 16 | ["[['', '29', '41', ''], ['', '', '32', '43'], ['23', '25', '29', '44'], ['12', '', '20', '']]", 9, 49] | ["[['', '29', '41', ''], ['', '', '32', '43'], ['23', '25', '29', '44'], ['12', '', '20', '']]", 9, 49] | ["[['', '29', '41', ''], ['', '', '32', '43'], ['23', '25', '29', '44'], ['12', '', '20', '']]", "9", "49"] |
46 | 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, 151, 189, None for columns 1 to 2 respectively, and the sums of rows must be None, 180, 176, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 36], [0, 1, 39], [0, 2, 44], [0, 3, 43], [1, 0, 45], [1, 2, 57], [2, 1, 35], [2, 2, 42], [2, 3, 51], [3, 1, 40]] | 691 | 5.864994525909424 | 10 | 44 | 9 | ["[['', '', '', ''], ['', '37', '', '41'], ['48', '', '', ''], ['49', '', '46', '38']]", 4, 35, 61] | ["[['', '', '', ''], ['', '37', '', '41'], ['48', '', '', ''], ['49', '', '46', '38']]", 35, 61, [1, 3], [1, 3], [151, 189], [180, 176], 184] | ["[['', '', '', ''], ['', '37', '', '41'], ['48', '', '', ''], ['49', '', '46', '38']]", "35", "61", "[None, 151, 189, None]", "[None, 180, 176, None]", "184"] |
46 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[4, 2], [3, 5], [4, 5], [4, 0], [3, 4], [3, 5], [3, 4], [7, 3], [7, 0], [7, 1], [7, 5], [6, 1], [6, 0], [6, 3], [7, 3], [6, 1], [6, 0], [2, 1]] | 49 | 12.073513269424438 | 18 | 56 | 20 | [[[], [], [], ["Yellow", "Black", "Yellow", "Black", "Green"], ["Red", "Yellow", "Blue", "Black", "Black"], [], ["Red", "Blue", "Green", "Red", "Blue"], ["Green", "Blue", "Red", "Yellow", "Green"]], 5, {"0": 2, "1": 1, "2": 6, "3": 3, "4": 1, "5": 5, "6": 4, "7": 2}] | [[[], [], [], ["Yellow", "Black", "Yellow", "Black", "Green"], ["Red", "Yellow", "Blue", "Black", "Black"], [], ["Red", "Blue", "Green", "Red", "Blue"], ["Green", "Blue", "Red", "Yellow", "Green"]], 5, {"0": 2, "1": 1, "2": 6, "3": 3, "4": 1, "5": 5, "6": 4, "7": 2}, 4] | ["[[], [], [], ['Yellow', 'Black', 'Yellow', 'Black', 'Green'], ['Red', 'Yellow', 'Blue', 'Black', 'Black'], [], ['Red', 'Blue', 'Green', 'Red', 'Blue'], ['Green', 'Blue', 'Red', 'Yellow', 'Green']]", "{0: 2, 1: 1, 2: 6, 3: 3, 4: 1, 5: 5, 6: 4, 7: 2}", "5", "4"] |
46 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (1, 0) to his destination workshop at index (8, 10), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[1, 0], [1, 1], [2, 1], [3, 1], [3, 2], [4, 2], [4, 3], [4, 4], [5, 4], [5, 5], [6, 5], [6, 6], [6, 7], [6, 8], [7, 8], [8, 8], [9, 8], [9, 9], [9, 10], [8, 10]] | 157 | 0.030195236206054688 | 20 | 4 | 4 | [[["3", "14", "2", "x", "x", "x", "19", "13", "17", "12", "8", "x"], ["1", "2", "13", "1", "4", "19", "x", "x", "16", "x", "x", "12"], ["9", "8", "9", "15", "x", "12", "x", "x", "x", "x", "x", "14"], ["11", "1", "10", "18", "x", "16", "1", "x", "12", "x", "x", "x"], ["7", "16", "13", "10", "13", "x", "14", "x", "x", "9... | [[["3", "14", "2", "x", "x", "x", "19", "13", "17", "12", "8", "x"], ["1", "2", "13", "1", "4", "19", "x", "x", "16", "x", "x", "12"], ["9", "8", "9", "15", "x", "12", "x", "x", "x", "x", "x", "14"], ["11", "1", "10", "18", "x", "16", "1", "x", "12", "x", "x", "x"], ["7", "16", "13", "10", "13", "x", "14", "x", "x", "9... | ["[['3', '14', '2', 'x', 'x', 'x', '19', '13', '17', '12', '8', 'x'], ['1', '2', '13', '1', '4', '19', 'x', 'x', '16', 'x', 'x', '12'], ['9', '8', '9', '15', 'x', '12', 'x', 'x', 'x', 'x', 'x', '14'], ['11', '1', '10', '18', 'x', '16', '1', 'x', '12', 'x', 'x', 'x'], ['7', '16', '13', '10', '13', 'x', '14', 'x', 'x', '... |
46 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[1, 0], [2, 0], [2, 1], [2, 2], [2, 3], [3, 3], [4, 4], [5, 4], [6, 4], [6, 5], [6, 6], [6, 7], [5, 8], [5, 9], [6, 10], [7, 11]] | 16 | 0.028974056243896484 | 16 | 8 | 2 | ["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, ... | ["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, ... | ["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, ... |
46 | Given 9 labeled water jugs with capacities 20, 142, 147, 48, 29, 113, 17, 18, 112, 68 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 287, 423, 583 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 | [["+", 142, 3], ["+", 147, 3], ["+", 147, 3], ["+", 147, 3], ["+", 112, 2], ["+", 147, 2], ["+", 17, 2], ["+", 147, 2], ["+", 142, 1], ["+", 142, 1], ["-", 17, 1], ["+", 20, 1]] | 12 | 0.04404854774475098 | 12 | 60 | 3 | [[20, 142, 147, 48, 29, 113, 17, 18, 112, 68], [287, 423, 583]] | [[20, 142, 147, 48, 29, 113, 17, 18, 112, 68], [287, 423, 583]] | ["[20, 142, 147, 48, 29, 113, 17, 18, 112, 68]", "[287, 423, 583]"] |
47 | 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 | [13, 82, 45, 13, 67, 65, 82, 67, 13, 45, 69, 92, 89, 82, 65, 8] | 16 | 0.043500661849975586 | 16 | 4 | 12 | [[[69, 92, 89, 72], [82, 13, 65, 59], [45, "_", 67, 8]]] | [[[69, 92, 89, 72], [82, 13, 65, 59], [45, "_", 67, 8]]] | ["[[69, 92, 89, 72], [82, 13, 65, 59], [45, '_', 67, 8]]"] |
47 | 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-left", "down-left", "up-left", "up-right", "up-left"] | 10 | 0.1886446475982666 | 10 | 4 | 24 | [[["r", "p", "_", "n", "n", "o"], ["u", "o", "c", "o", "i", "n"], ["l", "n", "h", "i", "g", "e"], ["b", "d", "i", "n", "k", "s"]]] | [[["r", "p", "_", "n", "n", "o"], ["u", "o", "c", "o", "i", "n"], ["l", "n", "h", "i", "g", "e"], ["b", "d", "i", "n", "k", "s"]], ["pongo", "urchin", "ondine", "blinks"]] | ["[['r', 'p', '_', 'n', 'n', 'o'], ['u', 'o', 'c', 'o', 'i', 'n'], ['l', 'n', 'h', 'i', 'g', 'e'], ['b', 'd', 'i', 'n', 'k', 's']]", "['pongo', 'urchin', 'ondine', 'blinks']"] |
47 | 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 | ["Z", "K", "D", "O", "C", "F", "D", "S", "C"] | 9 | 0.02916431427001953 | 9 | 12 | 15 | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0... | [[[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0... | ["[[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, ... |
47 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [18, 26, 17, 17, 16, 27, 30, 3, 4, 2, 24, 26, 29, 23, 2, 31, 25, 25, 4, 24, 14, 29, 4, 34, 34, 23, 35, 23, 28, 18, 8, 10, 17, 8, 22, 32], such that the sum of the chosen coins adds up to 342. Each coin in the list is uniqu... | coin_exchange | subset_sum | 19 | [17, 29, 29, 18, 8, 17, 17, 31, 22, 18, 16, 8, 4, 35, 28, 14, 4, 27] | 98 | 0.0500178337097168 | 18 | 36 | 36 | [[18, 26, 17, 17, 16, 27, 30, 3, 4, 2, 24, 26, 29, 23, 2, 31, 25, 25, 4, 24, 14, 29, 4, 34, 34, 23, 35, 23, 28, 18, 8, 10, 17, 8, 22, 32]] | [[18, 26, 17, 17, 16, 27, 30, 3, 4, 2, 24, 26, 29, 23, 2, 31, 25, 25, 4, 24, 14, 29, 4, 34, 34, 23, 35, 23, 28, 18, 8, 10, 17, 8, 22, 32], {"27": 14, "14": 1, "18": 3, "22": 9, "10": 8, "3": 2, "32": 20, "35": 16, "8": 3, "30": 20, "25": 18, "4": 3, "28": 12, "26": 16, "29": 2, "24": 20, "16": 6, "17": 3, "31": 9, "2":... | ["[18, 26, 17, 17, 16, 27, 30, 3, 4, 2, 24, 26, 29, 23, 2, 31, 25, 25, 4, 24, 14, 29, 4, 34, 34, 23, 35, 23, 28, 18, 8, 10, 17, 8, 22, 32]", "{27: 14, 14: 1, 18: 3, 22: 9, 10: 8, 3: 2, 32: 20, 35: 16, 8: 3, 30: 20, 25: 18, 4: 3, 28: 12, 26: 16, 29: 2, 24: 20, 16: 6, 17: 3, 31: 9, 2: 2, 23: 17, 34: 17}", "342"] |
47 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 8 | [[1, 2], [0, 1], [0, 1], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1]] | 15 | 0.9043323993682861 | 15 | 6 | 12 | [[["Blue", "Red", "Green", "Green"], ["Green", "Blue", "Red", "Blue"], ["Red", "Green", "Blue", "Red"]], 7] | [[["Blue", "Red", "Green", "Green"], ["Green", "Blue", "Red", "Blue"], ["Red", "Green", "Blue", "Red"]], 7] | ["[['Blue', 'Red', 'Green', 'Green'], ['Green', 'Blue', 'Red', 'Blue'], ['Red', 'Green', 'Blue', 'Red']]", "7"] |
47 | We have a 4x4 numerical grid, with numbers ranging from 27 to 67 (27 included in the range but 67 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 10 | [[0, 2, 38], [0, 3, 39], [1, 1, 40], [1, 2, 41], [1, 3, 42], [3, 2, 55]] | 531 | 0.3982374668121338 | 6 | 40 | 16 | ["[['27', '37', '', ''], ['30', '', '', ''], ['32', '44', '53', '61'], ['33', '54', '', '64']]", 27, 67] | ["[['27', '37', '', ''], ['30', '', '', ''], ['32', '44', '53', '61'], ['33', '54', '', '64']]", 27, 67] | ["[['27', '37', '', ''], ['30', '', '', ''], ['32', '44', '53', '61'], ['33', '54', '', '64']]", "27", "67"] |
47 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 34 to 60. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 198, 175, None for columns 1 to 2 respectively, and the sums of rows must be None, 201, 190, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 35], [0, 2, 34], [0, 3, 37], [1, 1, 48], [1, 2, 56], [2, 1, 59], [2, 2, 49], [2, 3, 43], [3, 0, 41], [3, 1, 45], [3, 2, 36]] | 703 | 98.62403774261475 | 11 | 44 | 9 | ["[['', '46', '', ''], ['44', '', '', '53'], ['39', '', '', ''], ['', '', '', '38']]", 4, 34, 60] | ["[['', '46', '', ''], ['44', '', '', '53'], ['39', '', '', ''], ['', '', '', '38']]", 34, 60, [1, 3], [1, 3], [198, 175], [201, 190], 193] | ["[['', '46', '', ''], ['44', '', '', '53'], ['39', '', '', ''], ['', '', '', '38']]", "34", "60", "[None, 198, 175, None]", "[None, 201, 190, None]", "193"] |
47 | 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], [5, 1], [2, 4], [2, 1], [2, 4], [5, 6], [5, 4], [5, 6], [3, 0], [3, 0], [3, 6], [3, 0], [3, 1], [7, 3], [7, 3], [7, 4], [7, 6], [5, 1], [2, 3], [7, 3]] | 92 | 0.5225863456726074 | 20 | 56 | 20 | [[[], [], ["Red", "Yellow", "Black", "Yellow", "Green"], ["Red", "Red", "Blue", "Red", "Black"], [], ["Black", "Blue", "Yellow", "Blue", "Black"], [], ["Green", "Green", "Yellow", "Blue", "Green"]], 5, {"0": 4, "1": 6, "2": 8, "3": 2, "4": 4, "5": 7, "6": 7, "7": 5}] | [[[], [], ["Red", "Yellow", "Black", "Yellow", "Green"], ["Red", "Red", "Blue", "Red", "Black"], [], ["Black", "Blue", "Yellow", "Blue", "Black"], [], ["Green", "Green", "Yellow", "Blue", "Green"]], 5, {"0": 4, "1": 6, "2": 8, "3": 2, "4": 4, "5": 7, "6": 7, "7": 5}, 4] | ["[[], [], ['Red', 'Yellow', 'Black', 'Yellow', 'Green'], ['Red', 'Red', 'Blue', 'Red', 'Black'], [], ['Black', 'Blue', 'Yellow', 'Blue', 'Black'], [], ['Green', 'Green', 'Yellow', 'Blue', 'Green']]", "{0: 4, 1: 6, 2: 8, 3: 2, 4: 4, 5: 7, 6: 7, 7: 5}", "5", "4"] |
47 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 11) to his destination workshop at index (6, 0), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[4, 11], [4, 10], [4, 9], [5, 9], [6, 9], [6, 8], [6, 7], [6, 6], [6, 5], [6, 4], [6, 3], [6, 2], [5, 2], [5, 1], [5, 0], [6, 0]] | 103 | 0.027801036834716797 | 16 | 4 | 4 | [[["5", "x", "x", "4", "x", "12", "7", "11", "8", "3", "19", "x"], ["x", "x", "6", "15", "16", "x", "x", "4", "x", "7", "8", "19"], ["18", "x", "x", "15", "x", "x", "x", "8", "4", "16", "7", "9"], ["x", "19", "x", "x", "x", "16", "x", "x", "17", "15", "x", "9"], ["15", "8", "19", "x", "4", "4", "x", "x", "x", "3", "3",... | [[["5", "x", "x", "4", "x", "12", "7", "11", "8", "3", "19", "x"], ["x", "x", "6", "15", "16", "x", "x", "4", "x", "7", "8", "19"], ["18", "x", "x", "15", "x", "x", "x", "8", "4", "16", "7", "9"], ["x", "19", "x", "x", "x", "16", "x", "x", "17", "15", "x", "9"], ["15", "8", "19", "x", "4", "4", "x", "x", "x", "3", "3",... | ["[['5', 'x', 'x', '4', 'x', '12', '7', '11', '8', '3', '19', 'x'], ['x', 'x', '6', '15', '16', 'x', 'x', '4', 'x', '7', '8', '19'], ['18', 'x', 'x', '15', 'x', 'x', 'x', '8', '4', '16', '7', '9'], ['x', '19', 'x', 'x', 'x', '16', 'x', 'x', '17', '15', 'x', '9'], ['15', '8', '19', 'x', '4', '4', 'x', 'x', 'x', '3', '3'... |
47 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[11, 9], [10, 8], [9, 7], [8, 7], [7, 7], [6, 7], [5, 7], [4, 7], [3, 7], [2, 7], [1, 6], [0, 5], [0, 4], [0, 3]] | 14 | 0.03473663330078125 | 14 | 8 | 2 | ["[[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, ... | ["[[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, ... | ["[[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, ... |
47 | Given 9 labeled water jugs with capacities 141, 101, 126, 26, 120, 75, 110, 108, 97, 100 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 254, 456, 579 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time excee... | water_jug | subset_sum | 6 | [["+", 75, 3], ["+", 126, 3], ["+", 126, 3], ["+", 126, 3], ["+", 126, 3], ["+", 75, 2], ["+", 120, 2], ["+", 120, 2], ["+", 141, 2], ["+", 108, 1], ["+", 120, 1], ["+", 26, 1]] | 12 | 0.051166534423828125 | 12 | 60 | 3 | [[141, 101, 126, 26, 120, 75, 110, 108, 97, 100], [254, 456, 579]] | [[141, 101, 126, 26, 120, 75, 110, 108, 97, 100], [254, 456, 579]] | ["[141, 101, 126, 26, 120, 75, 110, 108, 97, 100]", "[254, 456, 579]"] |
48 | 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 | [25, 56, 76, 25, 36, 65, 91, 83, 87, 91, 25, 76, 79, 98, 91, 87, 83, 70, 65, 25, 70, 65] | 22 | 0.1393580436706543 | 22 | 4 | 12 | [[[79, 98, 87, 83], [56, 76, 65, 91], [25, "_", 36, 70]]] | [[[79, 98, 87, 83], [56, 76, 65, 91], [25, "_", 36, 70]]] | ["[[79, 98, 87, 83], [56, 76, 65, 91], [25, '_', 36, 70]]"] |
48 | 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-left", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.18565845489501953 | 16 | 4 | 24 | [[["l", "a", "d", "d", "e", "d"], ["a", "h", "t", "g", "e", "a"], ["_", "n", "d", "i", "r", "n"], ["p", "a", "t", "i", "o", "n"]]] | [[["l", "a", "d", "d", "e", "d"], ["a", "h", "t", "g", "e", "a"], ["_", "n", "d", "i", "r", "n"], ["p", "a", "t", "i", "o", "n"]], ["added", "althea", "indign", "patron"]] | ["[['l', 'a', 'd', 'd', 'e', 'd'], ['a', 'h', 't', 'g', 'e', 'a'], ['_', 'n', 'd', 'i', 'r', 'n'], ['p', 'a', 't', 'i', 'o', 'n']]", "['added', 'althea', 'indign', 'patron']"] |
48 | 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 | ["I", "Y", "B", "X", "A", "N", "X", "A"] | 8 | 0.028223037719726562 | 8 | 12 | 15 | [[[0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1... | [[[0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1... | ["[[0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, ... |
48 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [19, 21, 16, 6, 34, 23, 8, 10, 14, 10, 59, 15, 17, 32, 11, 15, 8, 29, 58, 12, 3, 5, 11, 34, 2, 12, 20, 6, 29, 23, 10, 34, 33, 18], such that the sum of the chosen coins adds up to 355. Each coin in the list is unique and c... | coin_exchange | subset_sum | 20 | [5, 15, 15, 23, 23, 33, 59, 58, 32, 14, 29, 29, 20] | 92 | 0.04211783409118652 | 13 | 34 | 34 | [[19, 21, 16, 6, 34, 23, 8, 10, 14, 10, 59, 15, 17, 32, 11, 15, 8, 29, 58, 12, 3, 5, 11, 34, 2, 12, 20, 6, 29, 23, 10, 34, 33, 18]] | [[19, 21, 16, 6, 34, 23, 8, 10, 14, 10, 59, 15, 17, 32, 11, 15, 8, 29, 58, 12, 3, 5, 11, 34, 2, 12, 20, 6, 29, 23, 10, 34, 33, 18], {"6": 5, "17": 7, "12": 10, "34": 9, "5": 1, "11": 7, "10": 8, "21": 19, "15": 3, "33": 6, "3": 2, "16": 12, "58": 19, "8": 7, "14": 5, "20": 8, "2": 2, "19": 19, "59": 14, "18": 15, "29":... | ["[19, 21, 16, 6, 34, 23, 8, 10, 14, 10, 59, 15, 17, 32, 11, 15, 8, 29, 58, 12, 3, 5, 11, 34, 2, 12, 20, 6, 29, 23, 10, 34, 33, 18]", "{6: 5, 17: 7, 12: 10, 34: 9, 5: 1, 11: 7, 10: 8, 21: 19, 15: 3, 33: 6, 3: 2, 16: 12, 58: 19, 8: 7, 14: 5, 20: 8, 2: 2, 19: 19, 59: 14, 18: 15, 29: 8, 23: 6, 32: 5}", "355"] |
48 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 8 | [[1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [0, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0]] | 17 | 2.2611169815063477 | 17 | 6 | 12 | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | [[["Red", "Blue", "Blue", "Red"], ["Blue", "Green", "Blue", "Green"], ["Green", "Red", "Green", "Red"]], 7] | ["[['Red', 'Blue', 'Blue', 'Red'], ['Blue', 'Green', 'Blue', 'Green'], ['Green', 'Red', 'Green', 'Red']]", "7"] |
48 | We have a 4x4 numerical grid, with numbers ranging from 40 to 80 (40 included in the range but 80 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 10 | [[0, 0, 48], [0, 2, 75], [1, 2, 74], [2, 1, 49], [3, 2, 50], [3, 3, 52]] | 765 | 1.6650187969207764 | 6 | 40 | 16 | ["[['', '53', '', '79'], ['46', '51', '', '78'], ['45', '', '73', '77'], ['42', '47', '', '']]", 40, 80] | ["[['', '53', '', '79'], ['46', '51', '', '78'], ['45', '', '73', '77'], ['42', '47', '', '']]", 40, 80] | ["[['', '53', '', '79'], ['46', '51', '', '78'], ['45', '', '73', '77'], ['42', '47', '', '']]", "40", "80"] |
48 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 34 to 60. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 179, 194, None for columns 1 to 2 respectively, and the sums of rows must be None, 179, 190, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 34], [0, 1, 39], [0, 2, 40], [0, 3, 43], [1, 0, 38], [1, 2, 54], [2, 0, 36], [2, 3, 42], [3, 0, 51], [3, 2, 45], [3, 3, 35]] | 693 | 68.24673676490784 | 11 | 44 | 9 | ["[['', '', '', ''], ['', '46', '', '41'], ['', '57', '55', ''], ['', '37', '', '']]", 4, 34, 60] | ["[['', '', '', ''], ['', '46', '', '41'], ['', '57', '55', ''], ['', '37', '', '']]", 34, 60, [1, 3], [1, 3], [179, 194], [179, 190], 205] | ["[['', '', '', ''], ['', '46', '', '41'], ['', '57', '55', ''], ['', '37', '', '']]", "34", "60", "[None, 179, 194, None]", "[None, 179, 190, None]", "205"] |
48 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[1, 0], [4, 3], [6, 0], [4, 5], [4, 0], [4, 2], [6, 4], [6, 5], [7, 4], [7, 0], [7, 4], [7, 5], [6, 2], [1, 3], [1, 2], [1, 5], [7, 2], [1, 3], [6, 3]] | 54 | 0.07503151893615723 | 19 | 56 | 20 | [[[], ["Green", "Blue", "Yellow", "Black", "Blue"], [], [], ["Blue", "Black", "Green", "Yellow", "Red"], [], ["Green", "Red", "Black", "Yellow", "Blue"], ["Red", "Green", "Red", "Black", "Yellow"]], 5, {"0": 2, "1": 4, "2": 5, "3": 2, "4": 2, "5": 3, "6": 2, "7": 5}] | [[[], ["Green", "Blue", "Yellow", "Black", "Blue"], [], [], ["Blue", "Black", "Green", "Yellow", "Red"], [], ["Green", "Red", "Black", "Yellow", "Blue"], ["Red", "Green", "Red", "Black", "Yellow"]], 5, {"0": 2, "1": 4, "2": 5, "3": 2, "4": 2, "5": 3, "6": 2, "7": 5}, 4] | ["[[], ['Green', 'Blue', 'Yellow', 'Black', 'Blue'], [], [], ['Blue', 'Black', 'Green', 'Yellow', 'Red'], [], ['Green', 'Red', 'Black', 'Yellow', 'Blue'], ['Red', 'Green', 'Red', 'Black', 'Yellow']]", "{0: 2, 1: 4, 2: 5, 3: 2, 4: 2, 5: 3, 6: 2, 7: 5}", "5", "4"] |
48 | 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, 3) to his destination workshop at index (8, 11), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[3, 3], [3, 4], [2, 4], [3, 4], [3, 5], [3, 6], [3, 7], [4, 7], [5, 7], [5, 8], [5, 9], [6, 9], [7, 9], [7, 10], [7, 11], [8, 11]] | 110 | 0.02734541893005371 | 16 | 4 | 4 | [[["10", "x", "x", "1", "1", "x", "x", "x", "x", "x", "x", "x"], ["11", "9", "17", "x", "14", "3", "x", "13", "x", "x", "6", "x"], ["x", "5", "x", "x", "10", "13", "13", "19", "10", "x", "1", "12"], ["6", "x", "x", "17", "5", "6", "17", "4", "5", "x", "1", "x"], ["4", "11", "1", "x", "x", "x", "14", "7", "19", "4", "x"... | [[["10", "x", "x", "1", "1", "x", "x", "x", "x", "x", "x", "x"], ["11", "9", "17", "x", "14", "3", "x", "13", "x", "x", "6", "x"], ["x", "5", "x", "x", "10", "13", "13", "19", "10", "x", "1", "12"], ["6", "x", "x", "17", "5", "6", "17", "4", "5", "x", "1", "x"], ["4", "11", "1", "x", "x", "x", "14", "7", "19", "4", "x"... | ["[['10', 'x', 'x', '1', '1', 'x', 'x', 'x', 'x', 'x', 'x', 'x'], ['11', '9', '17', 'x', '14', '3', 'x', '13', 'x', 'x', '6', 'x'], ['x', '5', 'x', 'x', '10', '13', '13', '19', '10', 'x', '1', '12'], ['6', 'x', 'x', '17', '5', '6', '17', '4', '5', 'x', '1', 'x'], ['4', '11', '1', 'x', 'x', 'x', '14', '7', '19', '4', 'x... |
48 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[0, 9], [1, 8], [2, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [5, 3], [6, 3], [6, 2], [7, 2], [7, 1], [8, 1], [9, 1], [10, 0]] | 16 | 0.024382352828979492 | 16 | 8 | 2 | ["[[1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... | ["[[1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... | ["[[1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... |
48 | Given 9 labeled water jugs with capacities 121, 87, 150, 52, 43, 139, 90, 44, 59, 146 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 249, 446, 530 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 | [["+", 43, 3], ["+", 146, 3], ["+", 150, 3], ["+", 52, 3], ["+", 139, 3], ["+", 146, 2], ["+", 150, 2], ["+", 150, 2], ["+", 59, 1], ["+", 146, 1], ["+", 44, 1]] | 11 | 0.052127838134765625 | 11 | 60 | 3 | [[121, 87, 150, 52, 43, 139, 90, 44, 59, 146], [249, 446, 530]] | [[121, 87, 150, 52, 43, 139, 90, 44, 59, 146], [249, 446, 530]] | ["[121, 87, 150, 52, 43, 139, 90, 44, 59, 146]", "[249, 446, 530]"] |
49 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [62, 53, 35, 71, 11, 35, 53, 16, 35, 53, 71, 54, 39, 62, 82, 55, 69, 35, 16, 69, 55, 82, 69, 71, 54, 39, 62, 69, 71, 54, 53, 11] | 32 | 0.6614413261413574 | 32 | 4 | 12 | [[[82, "_", 39, 54], [55, 62, 53, 35], [69, 16, 11, 71]]] | [[[82, "_", 39, 54], [55, 62, 53, 35], [69, 16, 11, 71]]] | ["[[82, '_', 39, 54], [55, 62, 53, 35], [69, 16, 11, 71]]"] |
49 | 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-left", "up-left", "up-right", "up-right", "down-right", "up-right", "down-right", "down-left", "down-left", "up-left", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"... | 26 | 1.3822917938232422 | 26 | 4 | 24 | [[["a", "l", "o", "a", "m", "h"], ["f", "e", "n", "n", "a", "t"], ["t", "r", "a", "g", "_", "c"], ["c", "i", "r", "a", "n", "e"]]] | [[["a", "l", "o", "a", "m", "h"], ["f", "e", "n", "n", "a", "t"], ["t", "r", "a", "g", "_", "c"], ["c", "i", "r", "a", "n", "e"]], ["leath", "fanman", "tragic", "carone"]] | ["[['a', 'l', 'o', 'a', 'm', 'h'], ['f', 'e', 'n', 'n', 'a', 't'], ['t', 'r', 'a', 'g', '_', 'c'], ['c', 'i', 'r', 'a', 'n', 'e']]", "['leath', 'fanman', 'tragic', 'carone']"] |
49 | 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", "K", "F", "R", "C", "D", "A", "R", "W", "Q", "D"] | 11 | 0.03518843650817871 | 11 | 12 | 15 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, ... |
49 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [18, 20, 11, 6, 81, 3, 9, 5, 14, 19, 30, 2, 19, 3, 9, 22, 21, 29, 6, 25, 10, 18, 27, 26, 25, 13, 15, 16, 3, 5, 23, 26, 25, 31, 15, 12], such that the sum of the chosen coins adds up to 324. Each coin in the list is unique ... | coin_exchange | subset_sum | 21 | [3, 5, 5, 31, 30, 18, 81, 18, 10, 2, 3, 25, 25, 25, 14, 29] | 64 | 0.04390406608581543 | 16 | 36 | 36 | [[18, 20, 11, 6, 81, 3, 9, 5, 14, 19, 30, 2, 19, 3, 9, 22, 21, 29, 6, 25, 10, 18, 27, 26, 25, 13, 15, 16, 3, 5, 23, 26, 25, 31, 15, 12]] | [[18, 20, 11, 6, 81, 3, 9, 5, 14, 19, 30, 2, 19, 3, 9, 22, 21, 29, 6, 25, 10, 18, 27, 26, 25, 13, 15, 16, 3, 5, 23, 26, 25, 31, 15, 12], {"11": 6, "6": 3, "16": 11, "23": 16, "18": 3, "31": 4, "9": 2, "3": 1, "22": 10, "10": 1, "30": 4, "81": 14, "2": 1, "14": 1, "13": 11, "15": 7, "19": 16, "25": 6, "12": 12, "29": 11... | ["[18, 20, 11, 6, 81, 3, 9, 5, 14, 19, 30, 2, 19, 3, 9, 22, 21, 29, 6, 25, 10, 18, 27, 26, 25, 13, 15, 16, 3, 5, 23, 26, 25, 31, 15, 12]", "{11: 6, 6: 3, 16: 11, 23: 16, 18: 3, 31: 4, 9: 2, 3: 1, 22: 10, 10: 1, 30: 4, 81: 14, 2: 1, 14: 1, 13: 11, 15: 7, 19: 16, 25: 6, 12: 12, 29: 11, 26: 9, 5: 1, 27: 15, 20: 7, 21: 14}... |
49 | 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, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 18 | 2.9103639125823975 | 18 | 6 | 12 | [[["Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Blue"], ["Red", "Red", "Blue", "Green"]], 7] | [[["Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Blue"], ["Red", "Red", "Blue", "Green"]], 7] | ["[['Red', 'Blue', 'Blue', 'Green'], ['Green', 'Green', 'Red', 'Blue'], ['Red', 'Red', 'Blue', 'Green']]", "7"] |
49 | We have a 4x4 numerical grid, with numbers ranging from 9 to 49 (9 included in the range but 49 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid cell... | consecutive_grid | underdetermined_system | 11 | [[1, 0, 21], [1, 1, 25], [2, 2, 26], [2, 3, 27], [3, 0, 9], [3, 2, 19], [3, 3, 20]] | 376 | 36.16464829444885 | 7 | 40 | 16 | ["[['22', '35', '40', '47'], ['', '', '37', '45'], ['18', '24', '', ''], ['', '17', '', '']]", 9, 49] | ["[['22', '35', '40', '47'], ['', '', '37', '45'], ['18', '24', '', ''], ['', '17', '', '']]", 9, 49] | ["[['22', '35', '40', '47'], ['', '', '37', '45'], ['18', '24', '', ''], ['', '17', '', '']]", "9", "49"] |
49 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 34 to 60. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 165, 155, None for columns 1 to 2 respectively, and the sums of rows must be None, 169, 190, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 1, 36], [0, 2, 34], [1, 1, 40], [1, 2, 42], [1, 3, 35], [2, 0, 44], [2, 2, 41], [2, 3, 55], [3, 0, 53], [3, 1, 39], [3, 2, 38]] | 698 | 238.42562222480774 | 11 | 49 | 9 | ["[['37', '', '', '56'], ['52', '', '', ''], ['', '50', '', ''], ['', '', '', '46']]", 4, 34, 60] | ["[['37', '', '', '56'], ['52', '', '', ''], ['', '50', '', ''], ['', '', '', '46']]", 34, 60, [1, 3], [1, 3], [165, 155], [169, 190], 201] | ["[['37', '', '', '56'], ['52', '', '', ''], ['', '50', '', ''], ['', '', '', '46']]", "34", "60", "[None, 165, 155, None]", "[None, 169, 190, None]", "201"] |
49 | 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 | [[3, 4], [3, 7], [3, 5], [3, 1], [3, 4], [0, 3], [0, 4], [0, 7], [0, 5], [6, 4], [2, 1], [2, 7], [6, 1], [6, 7], [2, 0], [2, 0], [3, 0], [6, 2], [6, 1], [5, 2], [5, 2]] | 112 | 12.685235738754272 | 21 | 56 | 20 | [[["Black", "Green", "Red", "Yellow", "Black"], [], ["Blue", "Red", "Black", "Black", "Yellow"], ["Green", "Red", "Yellow", "Blue", "Green"], [], [], ["Green", "Blue", "Red", "Yellow", "Blue"], []], 5, {"0": 4, "1": 4, "2": 1, "3": 9, "4": 7, "5": 8, "6": 9, "7": 7}] | [[["Black", "Green", "Red", "Yellow", "Black"], [], ["Blue", "Red", "Black", "Black", "Yellow"], ["Green", "Red", "Yellow", "Blue", "Green"], [], [], ["Green", "Blue", "Red", "Yellow", "Blue"], []], 5, {"0": 4, "1": 4, "2": 1, "3": 9, "4": 7, "5": 8, "6": 9, "7": 7}, 4] | ["[['Black', 'Green', 'Red', 'Yellow', 'Black'], [], ['Blue', 'Red', 'Black', 'Black', 'Yellow'], ['Green', 'Red', 'Yellow', 'Blue', 'Green'], [], [], ['Green', 'Blue', 'Red', 'Yellow', 'Blue'], []]", "{0: 4, 1: 4, 2: 1, 3: 9, 4: 7, 5: 8, 6: 9, 7: 7}", "5", "4"] |
49 | 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, 11) to his destination workshop at index (4, 0), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[3, 11], [3, 10], [3, 9], [3, 8], [2, 8], [2, 7], [2, 6], [3, 6], [4, 6], [4, 5], [4, 4], [5, 4], [5, 3], [5, 2], [6, 2], [5, 2], [5, 1], [5, 0], [4, 0]] | 125 | 0.027664661407470703 | 19 | 4 | 4 | [[["x", "x", "13", "9", "x", "15", "x", "x", "2", "13", "9", "11"], ["8", "x", "4", "5", "13", "x", "x", "7", "16", "x", "15", "13"], ["x", "x", "x", "x", "3", "x", "4", "3", "18", "x", "11", "18"], ["6", "x", "14", "5", "16", "x", "11", "x", "3", "16", "3", "3"], ["15", "12", "x", "x", "10", "3", "2", "14", "x", "18",... | [[["x", "x", "13", "9", "x", "15", "x", "x", "2", "13", "9", "11"], ["8", "x", "4", "5", "13", "x", "x", "7", "16", "x", "15", "13"], ["x", "x", "x", "x", "3", "x", "4", "3", "18", "x", "11", "18"], ["6", "x", "14", "5", "16", "x", "11", "x", "3", "16", "3", "3"], ["15", "12", "x", "x", "10", "3", "2", "14", "x", "18",... | ["[['x', 'x', '13', '9', 'x', '15', 'x', 'x', '2', '13', '9', '11'], ['8', 'x', '4', '5', '13', 'x', 'x', '7', '16', 'x', '15', '13'], ['x', 'x', 'x', 'x', '3', 'x', '4', '3', '18', 'x', '11', '18'], ['6', 'x', '14', '5', '16', 'x', '11', 'x', '3', '16', '3', '3'], ['15', '12', 'x', 'x', '10', '3', '2', '14', 'x', '18'... |
49 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[6, 11], [6, 10], [7, 9], [7, 8], [8, 7], [8, 6], [8, 5], [7, 4], [6, 3], [5, 3], [5, 2], [5, 1], [4, 1], [3, 1], [2, 1], [1, 1], [0, 1], [0, 0]] | 18 | 0.025048494338989258 | 18 | 8 | 2 | ["[[0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, ... | ["[[0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, ... | ["[[0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, ... |
49 | Given 9 labeled water jugs with capacities 22, 98, 38, 116, 140, 115, 21, 80, 92, 27 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 279, 488, 578 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 | [["+", 116, 3], ["+", 140, 3], ["+", 92, 3], ["+", 115, 3], ["+", 115, 3], ["+", 92, 2], ["+", 140, 2], ["+", 140, 2], ["+", 116, 2], ["+", 21, 1], ["+", 115, 1], ["+", 116, 1], ["+", 27, 1]] | 13 | 0.04842829704284668 | 13 | 60 | 3 | [[22, 98, 38, 116, 140, 115, 21, 80, 92, 27], [279, 488, 578]] | [[22, 98, 38, 116, 140, 115, 21, 80, 92, 27], [279, 488, 578]] | ["[22, 98, 38, 116, 140, 115, 21, 80, 92, 27]", "[279, 488, 578]"] |
50 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [85, 47, 12, 94, 25, 70, 43, 64, 86, 43, 64, 12, 52, 92, 47, 52, 92, 86, 12, 25, 94, 92, 86, 12, 25, 64, 70, 94, 92, 86, 52, 47] | 32 | 0.6588661670684814 | 32 | 4 | 12 | [[[25, 94, 12, "_"], [70, 43, 47, 85], [86, 64, 52, 92]]] | [[[25, 94, 12, "_"], [70, 43, 47, 85], [86, 64, 52, 92]]] | ["[[25, 94, 12, '_'], [70, 43, 47, 85], [86, 64, 52, 92]]"] |
50 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left"] | 22 | 0.46178436279296875 | 22 | 4 | 24 | [[["y", "h", "r", "m", "_", "s"], ["b", "o", "w", "k", "r", "u"], ["r", "e", "l", "e", "u", "s"], ["c", "c", "a", "u", "t", "y"]]] | [[["y", "h", "r", "m", "_", "s"], ["b", "o", "w", "k", "r", "u"], ["r", "e", "l", "e", "u", "s"], ["c", "c", "a", "u", "t", "y"]], ["humus", "bywork", "cereus", "clarty"]] | ["[['y', 'h', 'r', 'm', '_', 's'], ['b', 'o', 'w', 'k', 'r', 'u'], ['r', 'e', 'l', 'e', 'u', 's'], ['c', 'c', 'a', 'u', 't', 'y']]", "['humus', 'bywork', 'cereus', 'clarty']"] |
50 | 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", "V", "N", "A", "O", "J", "O", "N"] | 8 | 0.029204368591308594 | 8 | 12 | 15 | [[[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0... | [[[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0... | ["[[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, ... |
50 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [19, 14, 29, 19, 29, 9, 17, 16, 25, 7, 8, 2, 23, 11, 28, 6, 29, 16, 19, 31, 30, 15, 7, 16, 23, 23, 10, 32, 8, 14, 7, 9, 6, 23, 77, 24, 22, 24, 22], such that the sum of the chosen coins adds up to 351. Each coin in the lis... | coin_exchange | subset_sum | 22 | [24, 77, 24, 16, 14, 10, 19, 16, 19, 16, 14, 19, 2, 7, 17, 29, 28] | 56 | 0.05440521240234375 | 17 | 39 | 39 | [[19, 14, 29, 19, 29, 9, 17, 16, 25, 7, 8, 2, 23, 11, 28, 6, 29, 16, 19, 31, 30, 15, 7, 16, 23, 23, 10, 32, 8, 14, 7, 9, 6, 23, 77, 24, 22, 24, 22]] | [[19, 14, 29, 19, 29, 9, 17, 16, 25, 7, 8, 2, 23, 11, 28, 6, 29, 16, 19, 31, 30, 15, 7, 16, 23, 23, 10, 32, 8, 14, 7, 9, 6, 23, 77, 24, 22, 24, 22], {"15": 6, "29": 12, "19": 3, "30": 18, "14": 2, "77": 3, "6": 5, "17": 1, "32": 16, "9": 8, "22": 15, "31": 17, "25": 10, "24": 1, "28": 11, "2": 2, "7": 4, "8": 7, "11": ... | ["[19, 14, 29, 19, 29, 9, 17, 16, 25, 7, 8, 2, 23, 11, 28, 6, 29, 16, 19, 31, 30, 15, 7, 16, 23, 23, 10, 32, 8, 14, 7, 9, 6, 23, 77, 24, 22, 24, 22]", "{15: 6, 29: 12, 19: 3, 30: 18, 14: 2, 77: 3, 6: 5, 17: 1, 32: 16, 9: 8, 22: 15, 31: 17, 25: 10, 24: 1, 28: 11, 2: 2, 7: 4, 8: 7, 11: 7, 23: 19, 10: 2, 16: 2}", "351"] |
50 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 8 | [[0, 2], [0, 2], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 2], [1, 0]] | 15 | 0.6902930736541748 | 15 | 6 | 12 | [[["Blue", "Green", "Red", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Blue", "Green", "Green"]], 7] | [[["Blue", "Green", "Red", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Blue", "Green", "Green"]], 7] | ["[['Blue', 'Green', 'Red', 'Red'], ['Red', 'Blue', 'Green', 'Red'], ['Blue', 'Blue', 'Green', 'Green']]", "7"] |
50 | We have a 4x4 numerical grid, with numbers ranging from 36 to 76 (36 included in the range but 76 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 11 | [[0, 0, 36], [0, 1, 37], [0, 2, 38], [1, 1, 48], [2, 0, 49], [3, 1, 59], [3, 3, 75]] | 665 | 72.83584880828857 | 7 | 40 | 16 | ["[['', '', '', '60'], ['47', '', '62', '65'], ['', '58', '67', '68'], ['54', '', '74', '']]", 36, 76] | ["[['', '', '', '60'], ['47', '', '62', '65'], ['', '58', '67', '68'], ['54', '', '74', '']]", 36, 76] | ["[['', '', '', '60'], ['47', '', '62', '65'], ['', '58', '67', '68'], ['54', '', '74', '']]", "36", "76"] |
50 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 9 to 40. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 77, 110, None for columns 1 to 2 respectively, and the sums of rows must be None, 114, 84, None for rows 1 to 2 ... | magic_square | underdetermined_system | 7 | [[0, 0, 10], [0, 1, 12], [0, 2, 9], [1, 1, 34], [1, 2, 30], [1, 3, 22], [2, 0, 13], [2, 3, 27]] | 379 | 0.18021273612976074 | 8 | 49 | 9 | ["[['', '', '', '39'], ['28', '', '', ''], ['', '11', '33', ''], ['18', '20', '38', '35']]", 4, 9, 40] | ["[['', '', '', '39'], ['28', '', '', ''], ['', '11', '33', ''], ['18', '20', '38', '35']]", 9, 40, [1, 3], [1, 3], [77, 110], [114, 84], 98] | ["[['', '', '', '39'], ['28', '', '', ''], ['', '11', '33', ''], ['18', '20', '38', '35']]", "9", "40", "[None, 77, 110, None]", "[None, 114, 84, None]", "98"] |
50 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[5, 7], [5, 4], [6, 4], [6, 1], [6, 7], [5, 6], [5, 6], [3, 4], [2, 0], [2, 4], [2, 1], [2, 0], [3, 2], [5, 1], [7, 2], [7, 2], [3, 0], [3, 1], [3, 0]] | 85 | 8.27693510055542 | 19 | 56 | 20 | [[[], [], ["Blue", "Green", "Black", "Blue", "Red"], ["Green", "Red", "Blue", "Black", "Blue"], [], ["Red", "Green", "Yellow", "Yellow", "Black"], ["Green", "Black", "Red", "Yellow", "Yellow"], []], 5, {"0": 1, "1": 3, "2": 3, "3": 8, "4": 7, "5": 9, "6": 8, "7": 8}] | [[[], [], ["Blue", "Green", "Black", "Blue", "Red"], ["Green", "Red", "Blue", "Black", "Blue"], [], ["Red", "Green", "Yellow", "Yellow", "Black"], ["Green", "Black", "Red", "Yellow", "Yellow"], []], 5, {"0": 1, "1": 3, "2": 3, "3": 8, "4": 7, "5": 9, "6": 8, "7": 8}, 4] | ["[[], [], ['Blue', 'Green', 'Black', 'Blue', 'Red'], ['Green', 'Red', 'Blue', 'Black', 'Blue'], [], ['Red', 'Green', 'Yellow', 'Yellow', 'Black'], ['Green', 'Black', 'Red', 'Yellow', 'Yellow'], []]", "{0: 1, 1: 3, 2: 3, 3: 8, 4: 7, 5: 9, 6: 8, 7: 8}", "5", "4"] |
50 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 9) to his destination workshop at index (7, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[3, 9], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [3, 5], [4, 5], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [6, 1], [7, 1]] | 121 | 0.027498483657836914 | 15 | 4 | 4 | [[["12", "17", "10", "x", "x", "x", "x", "9", "15", "5", "x", "x"], ["x", "x", "x", "x", "x", "12", "20", "9", "19", "8", "12", "11"], ["9", "x", "x", "2", "x", "2", "1", "9", "8", "14", "16", "x"], ["19", "x", "1", "20", "7", "9", "18", "x", "18", "7", "x", "x"], ["5", "2", "11", "9", "x", "5", "4", "16", "x", "1", "x... | [[["12", "17", "10", "x", "x", "x", "x", "9", "15", "5", "x", "x"], ["x", "x", "x", "x", "x", "12", "20", "9", "19", "8", "12", "11"], ["9", "x", "x", "2", "x", "2", "1", "9", "8", "14", "16", "x"], ["19", "x", "1", "20", "7", "9", "18", "x", "18", "7", "x", "x"], ["5", "2", "11", "9", "x", "5", "4", "16", "x", "1", "x... | ["[['12', '17', '10', 'x', 'x', 'x', 'x', '9', '15', '5', 'x', 'x'], ['x', 'x', 'x', 'x', 'x', '12', '20', '9', '19', '8', '12', '11'], ['9', 'x', 'x', '2', 'x', '2', '1', '9', '8', '14', '16', 'x'], ['19', 'x', '1', '20', '7', '9', '18', 'x', '18', '7', 'x', 'x'], ['5', '2', '11', '9', 'x', '5', '4', '16', 'x', '1', '... |
50 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[11, 11], [10, 10], [9, 10], [8, 9], [7, 9], [6, 9], [5, 9], [4, 9], [3, 9], [2, 8], [1, 7], [1, 6], [0, 6]] | 13 | 0.02417731285095215 | 13 | 8 | 2 | ["[[1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, ... | ["[[1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, ... | ["[[1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 0, ... |
50 | Given 9 labeled water jugs with capacities 137, 147, 73, 131, 91, 94, 72, 31, 103, 78 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 263, 298, 505 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 | [["+", 94, 3], ["+", 137, 3], ["+", 137, 3], ["+", 137, 3], ["+", 73, 2], ["+", 78, 2], ["+", 147, 2], ["+", 91, 1], ["+", 94, 1], ["+", 78, 1]] | 10 | 0.048264265060424805 | 10 | 60 | 3 | [[137, 147, 73, 131, 91, 94, 72, 31, 103, 78], [263, 298, 505]] | [[137, 147, 73, 131, 91, 94, 72, 31, 103, 78], [263, 298, 505]] | ["[137, 147, 73, 131, 91, 94, 72, 31, 103, 78]", "[263, 298, 505]"] |
51 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [32, 37, 78, 100, 17, 32, 37, 78, 100, 17, 32, 37, 78, 53, 19, 15, 87, 78, 15, 19, 96, 100, 53, 15, 19, 87, 78, 19, 37, 32, 15, 37, 32, 13] | 34 | 2.2093515396118164 | 34 | 4 | 12 | [[[96, 53, 19, 15], [37, 32, "_", 87], [78, 100, 17, 13]]] | [[[96, 53, 19, 15], [37, 32, "_", 87], [78, 100, 17, 13]]] | ["[[96, 53, 19, 15], [37, 32, '_', 87], [78, 100, 17, 13]]"] |
51 | 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-left", "down-left", "down-left", "down-right", "up-right", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-left", "down-right", "up-right", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-rig... | 34 | 10.377072811126709 | 34 | 4 | 24 | [[["l", "b", "l", "u", "i", "e"], ["a", "t", "g", "n", "s", "c"], ["l", "a", "o", "u", "_", "e"], ["n", "i", "n", "p", "o", "n"]]] | [[["l", "b", "l", "u", "i", "e"], ["a", "t", "g", "n", "s", "c"], ["l", "a", "o", "u", "_", "e"], ["n", "i", "n", "p", "o", "n"]], ["biune", "algist", "palule", "noncon"]] | ["[['l', 'b', 'l', 'u', 'i', 'e'], ['a', 't', 'g', 'n', 's', 'c'], ['l', 'a', 'o', 'u', '_', 'e'], ['n', 'i', 'n', 'p', 'o', 'n']]", "['biune', 'algist', 'palule', 'noncon']"] |
51 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 12 | ["G", "P", "F", "U", "C", "F", "U"] | 7 | 0.02801227569580078 | 7 | 12 | 15 | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1... | [[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1... | ["[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, ... |
51 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [31, 83, 19, 4, 13, 27, 13, 18, 21, 24, 9, 3, 2, 30, 16, 14, 31, 29, 27, 23, 18, 8, 32, 3, 3, 25, 17, 8, 32, 5, 2, 28, 30, 26, 25, 12, 12], such that the sum of the chosen coins adds up to 335. Each coin in the list is uni... | coin_exchange | subset_sum | 23 | [32, 2, 25, 25, 83, 32, 28, 29, 31, 30, 4, 5, 9] | 64 | 0.050809383392333984 | 13 | 37 | 37 | [[31, 83, 19, 4, 13, 27, 13, 18, 21, 24, 9, 3, 2, 30, 16, 14, 31, 29, 27, 23, 18, 8, 32, 3, 3, 25, 17, 8, 32, 5, 2, 28, 30, 26, 25, 12, 12]] | [[31, 83, 19, 4, 13, 27, 13, 18, 21, 24, 9, 3, 2, 30, 16, 14, 31, 29, 27, 23, 18, 8, 32, 3, 3, 25, 17, 8, 32, 5, 2, 28, 30, 26, 25, 12, 12], {"32": 1, "19": 12, "3": 1, "27": 14, "5": 3, "9": 5, "13": 11, "14": 10, "28": 6, "31": 15, "8": 8, "18": 18, "17": 7, "2": 2, "12": 9, "24": 16, "83": 6, "23": 9, "16": 15, "29"... | ["[31, 83, 19, 4, 13, 27, 13, 18, 21, 24, 9, 3, 2, 30, 16, 14, 31, 29, 27, 23, 18, 8, 32, 3, 3, 25, 17, 8, 32, 5, 2, 28, 30, 26, 25, 12, 12]", "{32: 1, 19: 12, 3: 1, 27: 14, 5: 3, 9: 5, 13: 11, 14: 10, 28: 6, 31: 15, 8: 8, 18: 18, 17: 7, 2: 2, 12: 9, 24: 16, 83: 6, 23: 9, 16: 15, 29: 4, 25: 5, 26: 18, 4: 1, 21: 10, 30:... |
51 | The game of 'Sort It' begins with 3 tubes, each filled with 5 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 | 9 | [[1, 2], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [0, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]] | 20 | 6.3350279331207275 | 20 | 6 | 15 | [[["Green", "Green", "Red", "Blue", "Blue"], ["Blue", "Green", "Green", "Red", "Red"], ["Red", "Red", "Blue", "Green", "Blue"]], 8] | [[["Green", "Green", "Red", "Blue", "Blue"], ["Blue", "Green", "Green", "Red", "Red"], ["Red", "Red", "Blue", "Green", "Blue"]], 8] | ["[['Green', 'Green', 'Red', 'Blue', 'Blue'], ['Blue', 'Green', 'Green', 'Red', 'Red'], ['Red', 'Red', 'Blue', 'Green', 'Blue']]", "8"] |
51 | We have a 4x4 numerical grid, with numbers ranging from 20 to 60 (20 included in the range but 60 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 11 | [[0, 0, 31], [0, 2, 37], [1, 2, 38], [2, 0, 21], [2, 2, 39], [3, 0, 20], [3, 3, 58]] | 547 | 4.27742338180542 | 7 | 40 | 16 | ["[['', '36', '', '55'], ['30', '34', '', '56'], ['', '33', '', '57'], ['', '32', '46', '']]", 20, 60] | ["[['', '36', '', '55'], ['30', '34', '', '56'], ['', '33', '', '57'], ['', '32', '46', '']]", 20, 60] | ["[['', '36', '', '55'], ['30', '34', '', '56'], ['', '33', '', '57'], ['', '32', '46', '']]", "20", "60"] |
51 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 9 to 40. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 102, 100, None for columns 1 to 2 respectively, and the sums of rows must be None, 72, 97, None for rows 1 to 2 ... | magic_square | underdetermined_system | 7 | [[0, 0, 12], [0, 1, 22], [1, 1, 26], [1, 2, 10], [2, 0, 14], [2, 3, 36], [3, 1, 38], [3, 3, 13]] | 333 | 1.8332746028900146 | 8 | 49 | 9 | ["[['', '', '27', '9'], ['21', '', '', '15'], ['', '16', '31', ''], ['11', '', '32', '']]", 4, 9, 40] | ["[['', '', '27', '9'], ['21', '', '', '15'], ['', '16', '31', ''], ['11', '', '32', '']]", 9, 40, [1, 3], [1, 3], [102, 100], [72, 97], 46] | ["[['', '', '27', '9'], ['21', '', '', '15'], ['', '16', '31', ''], ['11', '', '32', '']]", "9", "40", "[None, 102, 100, None]", "[None, 72, 97, None]", "46"] |
51 | 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 | [[3, 1], [3, 0], [3, 0], [3, 1], [5, 3], [5, 3], [7, 6], [7, 3], [7, 1], [4, 2], [4, 1], [4, 0], [4, 0], [7, 2], [4, 2], [5, 7], [5, 2], [5, 7], [6, 7]] | 103 | 10.823257684707642 | 19 | 56 | 20 | [[[], [], [], ["Green", "Blue", "Blue", "Green", "Black"], ["Red", "Green", "Blue", "Blue", "Red"], ["Black", "Black", "Yellow", "Red", "Yellow"], [], ["Yellow", "Black", "Green", "Red", "Yellow"]], 5, {"0": 7, "1": 8, "2": 2, "3": 8, "4": 9, "5": 6, "6": 8, "7": 1}] | [[[], [], [], ["Green", "Blue", "Blue", "Green", "Black"], ["Red", "Green", "Blue", "Blue", "Red"], ["Black", "Black", "Yellow", "Red", "Yellow"], [], ["Yellow", "Black", "Green", "Red", "Yellow"]], 5, {"0": 7, "1": 8, "2": 2, "3": 8, "4": 9, "5": 6, "6": 8, "7": 1}, 4] | ["[[], [], [], ['Green', 'Blue', 'Blue', 'Green', 'Black'], ['Red', 'Green', 'Blue', 'Blue', 'Red'], ['Black', 'Black', 'Yellow', 'Red', 'Yellow'], [], ['Yellow', 'Black', 'Green', 'Red', 'Yellow']]", "{0: 7, 1: 8, 2: 2, 3: 8, 4: 9, 5: 6, 6: 8, 7: 1}", "5", "4"] |
51 | 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, 2) to his destination workshop at index (2, 10), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[6, 2], [5, 2], [5, 3], [4, 3], [3, 3], [3, 4], [2, 4], [1, 4], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 8], [1, 9], [2, 9], [2, 10]] | 126 | 0.02806711196899414 | 17 | 4 | 4 | [[["19", "12", "x", "x", "2", "5", "4", "13", "17", "19", "x", "2"], ["x", "18", "x", "5", "5", "x", "x", "8", "12", "18", "x", "15"], ["x", "9", "4", "10", "7", "20", "x", "16", "20", "13", "15", "x"], ["8", "x", "x", "11", "1", "19", "x", "14", "6", "x", "3", "x"], ["10", "x", "4", "8", "17", "x", "18", "x", "7", "x"... | [[["19", "12", "x", "x", "2", "5", "4", "13", "17", "19", "x", "2"], ["x", "18", "x", "5", "5", "x", "x", "8", "12", "18", "x", "15"], ["x", "9", "4", "10", "7", "20", "x", "16", "20", "13", "15", "x"], ["8", "x", "x", "11", "1", "19", "x", "14", "6", "x", "3", "x"], ["10", "x", "4", "8", "17", "x", "18", "x", "7", "x"... | ["[['19', '12', 'x', 'x', '2', '5', '4', '13', '17', '19', 'x', '2'], ['x', '18', 'x', '5', '5', 'x', 'x', '8', '12', '18', 'x', '15'], ['x', '9', '4', '10', '7', '20', 'x', '16', '20', '13', '15', 'x'], ['8', 'x', 'x', '11', '1', '19', 'x', '14', '6', 'x', '3', 'x'], ['10', 'x', '4', '8', '17', 'x', '18', 'x', '7', 'x... |
51 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[1, 11], [2, 10], [2, 9], [2, 8], [2, 7], [3, 6], [4, 6], [5, 5], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4], [10, 3], [11, 3]] | 15 | 0.0235440731048584 | 15 | 8 | 2 | ["[[1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, ... | ["[[1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, ... | ["[[1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, ... |
51 | Given 9 labeled water jugs with capacities 51, 129, 150, 138, 128, 72, 69, 111, 75 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 454, 547, 601 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 | [["+", 128, 3], ["+", 128, 3], ["+", 69, 3], ["+", 138, 3], ["+", 138, 3], ["+", 69, 2], ["+", 128, 2], ["+", 150, 2], ["+", 72, 2], ["+", 128, 2], ["+", 128, 1], ["+", 128, 1], ["+", 69, 1], ["+", 129, 1]] | 14 | 0.07053852081298828 | 14 | 54 | 3 | [[51, 129, 150, 138, 128, 72, 69, 111, 75], [454, 547, 601]] | [[51, 129, 150, 138, 128, 72, 69, 111, 75], [454, 547, 601]] | ["[51, 129, 150, 138, 128, 72, 69, 111, 75]", "[454, 547, 601]"] |
52 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [67, 2, 71, 56, 37, 41, 2, 71, 50, 35, 56, 50, 35, 39, 26, 67, 71, 35, 41, 2, 35, 26, 67, 71, 48, 35, 26, 41, 39, 56, 50, 37] | 32 | 0.40317821502685547 | 32 | 4 | 12 | [[[26, 39, 50, 35], ["_", 67, 2, 71], [48, 41, 37, 56]]] | [[[26, 39, 50, 35], ["_", 67, 2, 71], [48, 41, 37, 56]]] | ["[[26, 39, 50, 35], ['_', 67, 2, 71], [48, 41, 37, 56]]"] |
52 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 3 | ["down-right", "up-right", "up-left", "up-right", "down-right", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "up-ri... | 38 | 29.637394189834595 | 38 | 4 | 24 | [[["i", "s", "n", "i", "a", "h"], ["l", "p", "e", "a", "r", "c"], ["_", "c", "e", "e", "n", "d"], ["e", "v", "e", "r", "l", "y"]]] | [[["i", "s", "n", "i", "a", "h"], ["l", "p", "e", "a", "r", "c"], ["_", "c", "e", "e", "n", "d"], ["e", "v", "e", "r", "l", "y"]], ["saiph", "lierre", "accend", "evenly"]] | ["[['i', 's', 'n', 'i', 'a', 'h'], ['l', 'p', 'e', 'a', 'r', 'c'], ['_', 'c', 'e', 'e', 'n', 'd'], ['e', 'v', 'e', 'r', 'l', 'y']]", "['saiph', 'lierre', 'accend', 'evenly']"] |
52 | 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 | 13 | ["C", "A", "M", "J", "N", "D", "J", "R", "D"] | 9 | 0.023613929748535156 | 9 | 13 | 16 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0,... |
52 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [31, 9, 2, 24, 32, 6, 13, 29, 33, 22, 12, 28, 10, 7, 33, 15, 28, 7, 14, 26, 1, 10, 28, 30, 7, 29, 17, 2, 28, 13, 28, 17, 3, 4, 4, 4, 13, 3, 19, 2, 4, 26, 27, 27, 11, 25, 12], such that the sum of the chosen coins adds up t... | coin_exchange | subset_sum | 24 | [28, 31, 28, 6, 13, 13, 33, 30, 28, 33, 28, 12, 27, 27] | 51 | 0.062195539474487305 | 14 | 47 | 47 | [[31, 9, 2, 24, 32, 6, 13, 29, 33, 22, 12, 28, 10, 7, 33, 15, 28, 7, 14, 26, 1, 10, 28, 30, 7, 29, 17, 2, 28, 13, 28, 17, 3, 4, 4, 4, 13, 3, 19, 2, 4, 26, 27, 27, 11, 25, 12]] | [[31, 9, 2, 24, 32, 6, 13, 29, 33, 22, 12, 28, 10, 7, 33, 15, 28, 7, 14, 26, 1, 10, 28, 30, 7, 29, 17, 2, 28, 13, 28, 17, 3, 4, 4, 4, 13, 3, 19, 2, 4, 26, 27, 27, 11, 25, 12], {"2": 1, "33": 8, "9": 9, "31": 3, "19": 11, "17": 8, "28": 3, "24": 12, "6": 1, "22": 7, "26": 7, "27": 5, "29": 9, "4": 4, "10": 3, "3": 2, "1... | ["[31, 9, 2, 24, 32, 6, 13, 29, 33, 22, 12, 28, 10, 7, 33, 15, 28, 7, 14, 26, 1, 10, 28, 30, 7, 29, 17, 2, 28, 13, 28, 17, 3, 4, 4, 4, 13, 3, 19, 2, 4, 26, 27, 27, 11, 25, 12]", "{2: 1, 33: 8, 9: 9, 31: 3, 19: 11, 17: 8, 28: 3, 24: 12, 6: 1, 22: 7, 26: 7, 27: 5, 29: 9, 4: 4, 10: 3, 3: 2, 11: 3, 15: 12, 7: 2, 1: 1, 12: ... |
52 | The game of 'Sort It' begins with 3 tubes, each filled with 5 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 | 9 | [[2, 1], [0, 1], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 2]] | 25 | 80.31313681602478 | 25 | 6 | 15 | [[["Green", "Green", "Blue", "Red", "Green"], ["Red", "Red", "Blue", "Red", "Blue"], ["Green", "Blue", "Blue", "Red", "Green"]], 8] | [[["Green", "Green", "Blue", "Red", "Green"], ["Red", "Red", "Blue", "Red", "Blue"], ["Green", "Blue", "Blue", "Red", "Green"]], 8] | ["[['Green', 'Green', 'Blue', 'Red', 'Green'], ['Red', 'Red', 'Blue', 'Red', 'Blue'], ['Green', 'Blue', 'Blue', 'Red', 'Green']]", "8"] |
52 | We have a 4x4 numerical grid, with numbers ranging from 22 to 62 (22 included in the range but 62 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 2, 49], [0, 3, 50], [1, 0, 24], [1, 1, 38], [1, 2, 42], [2, 0, 23], [3, 0, 22], [3, 2, 35]] | 602 | 0.3810865879058838 | 8 | 40 | 16 | ["[['43', '48', '', ''], ['', '', '', '58'], ['', '37', '41', '60'], ['', '34', '', '61']]", 22, 62] | ["[['43', '48', '', ''], ['', '', '', '58'], ['', '37', '41', '60'], ['', '34', '', '61']]", 22, 62] | ["[['43', '48', '', ''], ['', '', '', '58'], ['', '37', '41', '60'], ['', '34', '', '61']]", "22", "62"] |
52 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 9 to 40. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 121, 107, None for columns 1 to 2 respectively, and the sums of rows must be None, 89, 103, None for rows 1 to 2... | magic_square | underdetermined_system | 7 | [[0, 2, 11], [0, 3, 9], [1, 0, 10], [1, 1, 29], [1, 2, 32], [2, 0, 24], [3, 1, 26], [3, 2, 37]] | 373 | 18.999568462371826 | 8 | 49 | 9 | ["[['14', '35', '', ''], ['', '', '', '18'], ['', '31', '27', '21'], ['30', '', '', '19']]", 4, 9, 40] | ["[['14', '35', '', ''], ['', '', '', '18'], ['', '31', '27', '21'], ['30', '', '', '19']]", 9, 40, [1, 3], [1, 3], [121, 107], [89, 103], 102] | ["[['14', '35', '', ''], ['', '', '', '18'], ['', '31', '27', '21'], ['30', '', '', '19']]", "9", "40", "[None, 121, 107, None]", "[None, 89, 103, None]", "102"] |
52 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[5, 2], [4, 1], [7, 2], [7, 2], [5, 1], [5, 0], [5, 1], [4, 5], [7, 0], [7, 2], [3, 6], [3, 5], [3, 1], [3, 6], [4, 6], [4, 5], [4, 6], [3, 0], [7, 0]] | 103 | 0.04401803016662598 | 19 | 56 | 20 | [[[], [], [], ["Blue", "Yellow", "Red", "Blue", "Black"], ["Red", "Yellow", "Blue", "Yellow", "Blue"], ["Green", "Red", "Black", "Red", "Yellow"], [], ["Green", "Green", "Black", "Green", "Black"]], 5, {"0": 6, "1": 4, "2": 3, "3": 8, "4": 7, "5": 5, "6": 9, "7": 9}] | [[[], [], [], ["Blue", "Yellow", "Red", "Blue", "Black"], ["Red", "Yellow", "Blue", "Yellow", "Blue"], ["Green", "Red", "Black", "Red", "Yellow"], [], ["Green", "Green", "Black", "Green", "Black"]], 5, {"0": 6, "1": 4, "2": 3, "3": 8, "4": 7, "5": 5, "6": 9, "7": 9}, 4] | ["[[], [], [], ['Blue', 'Yellow', 'Red', 'Blue', 'Black'], ['Red', 'Yellow', 'Blue', 'Yellow', 'Blue'], ['Green', 'Red', 'Black', 'Red', 'Yellow'], [], ['Green', 'Green', 'Black', 'Green', 'Black']]", "{0: 6, 1: 4, 2: 3, 3: 8, 4: 7, 5: 5, 6: 9, 7: 9}", "5", "4"] |
52 | 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, 1) to his destination workshop at index (5, 11), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[8, 1], [8, 2], [8, 3], [8, 4], [9, 4], [8, 4], [7, 4], [7, 5], [7, 6], [7, 7], [7, 8], [7, 9], [6, 9], [5, 9], [4, 9], [5, 9], [5, 10], [5, 11]] | 175 | 0.027495384216308594 | 18 | 4 | 4 | [[["x", "3", "11", "7", "x", "x", "1", "3", "x", "x", "x", "3"], ["x", "10", "x", "x", "3", "9", "7", "8", "x", "2", "x", "17"], ["6", "16", "x", "18", "10", "5", "x", "6", "x", "x", "7", "x"], ["x", "10", "x", "8", "13", "10", "x", "x", "x", "x", "6", "13"], ["6", "11", "3", "16", "8", "15", "x", "x", "x", "13", "12",... | [[["x", "3", "11", "7", "x", "x", "1", "3", "x", "x", "x", "3"], ["x", "10", "x", "x", "3", "9", "7", "8", "x", "2", "x", "17"], ["6", "16", "x", "18", "10", "5", "x", "6", "x", "x", "7", "x"], ["x", "10", "x", "8", "13", "10", "x", "x", "x", "x", "6", "13"], ["6", "11", "3", "16", "8", "15", "x", "x", "x", "13", "12",... | ["[['x', '3', '11', '7', 'x', 'x', '1', '3', 'x', 'x', 'x', '3'], ['x', '10', 'x', 'x', '3', '9', '7', '8', 'x', '2', 'x', '17'], ['6', '16', 'x', '18', '10', '5', 'x', '6', 'x', 'x', '7', 'x'], ['x', '10', 'x', '8', '13', '10', 'x', 'x', 'x', 'x', '6', '13'], ['6', '11', '3', '16', '8', '15', 'x', 'x', 'x', '13', '12'... |
52 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[8, 1], [7, 1], [7, 2], [7, 3], [7, 4], [6, 5], [5, 5], [4, 5], [3, 6], [3, 7], [2, 7], [1, 7], [0, 8], [0, 9], [0, 10], [1, 11]] | 16 | 0.023190736770629883 | 16 | 8 | 2 | ["[[1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... | ["[[1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... | ["[[1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [0, 0, 1, 1, ... |
52 | Given 9 labeled water jugs with capacities 45, 141, 50, 114, 104, 19, 78, 18, 23, 133 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 253, 337, 385 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 | [["+", 114, 3], ["+", 133, 3], ["+", 133, 3], ["-", 18, 3], ["+", 23, 3], ["+", 45, 2], ["+", 133, 2], ["+", 18, 2], ["+", 141, 2], ["+", 104, 1], ["+", 104, 1], ["+", 45, 1]] | 12 | 0.03950142860412598 | 12 | 60 | 3 | [[45, 141, 50, 114, 104, 19, 78, 18, 23, 133], [253, 337, 385]] | [[45, 141, 50, 114, 104, 19, 78, 18, 23, 133], [253, 337, 385]] | ["[45, 141, 50, 114, 104, 19, 78, 18, 23, 133]", "[253, 337, 385]"] |
53 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [85, 61, 84, 33, 93, 85, 61, 84, 30, 89, 84, 30, 33, 93, 85, 61, 30, 33, 89, 63, 38, 98, 93, 89, 63, 84, 73, 38, 84, 73, 33, 30] | 32 | 0.45055198669433594 | 32 | 4 | 12 | [[[38, 98, 84, 33], [63, 30, 61, 93], [73, 89, 85, "_"]]] | [[[38, 98, 84, 33], [63, 30, 61, 93], [73, 89, 85, "_"]]] | ["[[38, 98, 84, 33], [63, 30, 61, 93], [73, 89, 85, '_']]"] |
53 | 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", "down-left", "down-right", "down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left"] | 22 | 0.7115309238433838 | 22 | 4 | 24 | [[["o", "l", "s", "m", "_", "n"], ["s", "o", "m", "e", "r", "k"], ["s", "p", "i", "o", "e", "y"], ["d", "o", "g", "t", "i", "e"]]] | [[["o", "l", "s", "m", "_", "n"], ["s", "o", "m", "e", "r", "k"], ["s", "p", "i", "o", "e", "y"], ["d", "o", "g", "t", "i", "e"]], ["limen", "somers", "spooky", "dogtie"]] | ["[['o', 'l', 's', 'm', '_', 'n'], ['s', 'o', 'm', 'e', 'r', 'k'], ['s', 'p', 'i', 'o', 'e', 'y'], ['d', 'o', 'g', 't', 'i', 'e']]", "['limen', 'somers', 'spooky', 'dogtie']"] |
53 | 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 | 13 | ["A", "G", "R", "E", "D", "K", "M", "E", "D"] | 9 | 0.030630111694335938 | 9 | 13 | 16 | [[[0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, ... | [[[0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, ... | ["[[0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 1, 0,... |
53 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [23, 10, 22, 30, 5, 16, 2, 28, 25, 26, 30, 25, 35, 32, 10, 4, 24, 32, 34, 12, 11, 5, 5, 18, 16, 24, 3, 12, 11, 5, 2, 7, 19, 34, 7, 30, 17, 11, 16, 10, 31, 31, 34, 27, 3, 24], such that the sum of the chosen coins adds up t... | coin_exchange | subset_sum | 25 | [34, 30, 31, 30, 28, 22, 31, 30, 35, 34, 2, 17, 23, 12] | 71 | 0.057801008224487305 | 14 | 46 | 46 | [[23, 10, 22, 30, 5, 16, 2, 28, 25, 26, 30, 25, 35, 32, 10, 4, 24, 32, 34, 12, 11, 5, 5, 18, 16, 24, 3, 12, 11, 5, 2, 7, 19, 34, 7, 30, 17, 11, 16, 10, 31, 31, 34, 27, 3, 24]] | [[23, 10, 22, 30, 5, 16, 2, 28, 25, 26, 30, 25, 35, 32, 10, 4, 24, 32, 34, 12, 11, 5, 5, 18, 16, 24, 3, 12, 11, 5, 2, 7, 19, 34, 7, 30, 17, 11, 16, 10, 31, 31, 34, 27, 3, 24], {"24": 9, "26": 11, "17": 7, "7": 4, "12": 4, "35": 18, "5": 5, "31": 8, "2": 2, "3": 1, "27": 14, "34": 3, "30": 1, "23": 6, "4": 2, "10": 8, "... | ["[23, 10, 22, 30, 5, 16, 2, 28, 25, 26, 30, 25, 35, 32, 10, 4, 24, 32, 34, 12, 11, 5, 5, 18, 16, 24, 3, 12, 11, 5, 2, 7, 19, 34, 7, 30, 17, 11, 16, 10, 31, 31, 34, 27, 3, 24]", "{24: 9, 26: 11, 17: 7, 7: 4, 12: 4, 35: 18, 5: 5, 31: 8, 2: 2, 3: 1, 27: 14, 34: 3, 30: 1, 23: 6, 4: 2, 10: 8, 18: 18, 25: 15, 28: 4, 32: 19,... |
53 | The game of 'Sort It' begins with 3 tubes, each filled with 5 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 | 9 | [[0, 1], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2]] | 21 | 11.96505355834961 | 21 | 6 | 15 | [[["Red", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Green", "Green", "Blue"], ["Red", "Green", "Blue", "Red", "Red"]], 8] | [[["Red", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Green", "Green", "Blue"], ["Red", "Green", "Blue", "Red", "Red"]], 8] | ["[['Red', 'Blue', 'Blue', 'Red', 'Green'], ['Blue', 'Green', 'Green', 'Green', 'Blue'], ['Red', 'Green', 'Blue', 'Red', 'Red']]", "8"] |
53 | We have a 4x4 numerical grid, with numbers ranging from 44 to 84 (44 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 > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 3, 61], [1, 0, 46], [1, 2, 68], [1, 3, 69], [2, 1, 70], [3, 0, 62], [3, 1, 71], [3, 2, 81]] | 787 | 0.4855637550354004 | 8 | 40 | 16 | ["[['45', '55', '59', ''], ['', '67', '', ''], ['60', '', '79', '80'], ['', '', '', '83']]", 44, 84] | ["[['45', '55', '59', ''], ['', '67', '', ''], ['60', '', '79', '80'], ['', '', '', '83']]", 44, 84] | ["[['45', '55', '59', ''], ['', '67', '', ''], ['60', '', '79', '80'], ['', '', '', '83']]", "44", "84"] |
53 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 9 to 40. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 116, 78, None for columns 1 to 2 respectively, and the sums of rows must be None, 94, 111, None for rows 1 to 2 ... | magic_square | underdetermined_system | 8 | [[0, 0, 10], [0, 1, 27], [1, 0, 21], [1, 1, 33], [2, 1, 20], [2, 2, 32], [2, 3, 28], [3, 2, 9]] | 357 | 0.4937326908111572 | 8 | 49 | 9 | ["[['', '', '22', '23'], ['', '', '15', '25'], ['31', '', '', ''], ['12', '36', '', '13']]", 4, 9, 40] | ["[['', '', '22', '23'], ['', '', '15', '25'], ['31', '', '', ''], ['12', '36', '', '13']]", 9, 40, [1, 3], [1, 3], [116, 78], [94, 111], 70] | ["[['', '', '22', '23'], ['', '', '15', '25'], ['31', '', '', ''], ['12', '36', '', '13']]", "9", "40", "[None, 116, 78, None]", "[None, 94, 111, None]", "70"] |
53 | 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], [1, 7], [1, 0], [1, 6], [4, 0], [4, 6], [4, 6], [2, 7], [2, 1], [2, 6], [2, 4], [5, 7], [5, 1], [5, 7], [5, 4], [3, 1], [0, 2], [0, 2], [5, 2]] | 95 | 5.887192726135254 | 19 | 56 | 20 | [[[], ["Blue", "Green", "Red", "Yellow", "Blue"], ["Green", "Blue", "Yellow", "Black", "Red"], [], ["Red", "Yellow", "Yellow", "Black", "Black"], ["Green", "Blue", "Green", "Black", "Red"], [], []], 5, {"0": 7, "1": 4, "2": 1, "3": 2, "4": 6, "5": 8, "6": 7, "7": 6}] | [[[], ["Blue", "Green", "Red", "Yellow", "Blue"], ["Green", "Blue", "Yellow", "Black", "Red"], [], ["Red", "Yellow", "Yellow", "Black", "Black"], ["Green", "Blue", "Green", "Black", "Red"], [], []], 5, {"0": 7, "1": 4, "2": 1, "3": 2, "4": 6, "5": 8, "6": 7, "7": 6}, 4] | ["[[], ['Blue', 'Green', 'Red', 'Yellow', 'Blue'], ['Green', 'Blue', 'Yellow', 'Black', 'Red'], [], ['Red', 'Yellow', 'Yellow', 'Black', 'Black'], ['Green', 'Blue', 'Green', 'Black', 'Red'], [], []]", "{0: 7, 1: 4, 2: 1, 3: 2, 4: 6, 5: 8, 6: 7, 7: 6}", "5", "4"] |
53 | 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, 3) to his destination workshop at index (7, 11), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[3, 3], [3, 4], [3, 5], [4, 5], [4, 6], [4, 7], [5, 7], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [7, 11]] | 112 | 0.026072263717651367 | 13 | 4 | 4 | [[["18", "x", "x", "14", "5", "x", "x", "5", "18", "x", "3", "x"], ["x", "x", "x", "9", "2", "2", "x", "15", "14", "12", "x", "18"], ["x", "x", "3", "16", "3", "9", "x", "16", "x", "14", "x", "17"], ["x", "x", "x", "19", "7", "20", "x", "x", "11", "4", "x", "4"], ["7", "x", "8", "11", "x", "1", "15", "5", "x", "x", "11... | [[["18", "x", "x", "14", "5", "x", "x", "5", "18", "x", "3", "x"], ["x", "x", "x", "9", "2", "2", "x", "15", "14", "12", "x", "18"], ["x", "x", "3", "16", "3", "9", "x", "16", "x", "14", "x", "17"], ["x", "x", "x", "19", "7", "20", "x", "x", "11", "4", "x", "4"], ["7", "x", "8", "11", "x", "1", "15", "5", "x", "x", "11... | ["[['18', 'x', 'x', '14', '5', 'x', 'x', '5', '18', 'x', '3', 'x'], ['x', 'x', 'x', '9', '2', '2', 'x', '15', '14', '12', 'x', '18'], ['x', 'x', '3', '16', '3', '9', 'x', '16', 'x', '14', 'x', '17'], ['x', 'x', 'x', '19', '7', '20', 'x', 'x', '11', '4', 'x', '4'], ['7', 'x', '8', '11', 'x', '1', '15', '5', 'x', 'x', '1... |
53 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[2, 11], [2, 10], [2, 9], [2, 8], [2, 7], [3, 7], [4, 6], [4, 5], [5, 4], [6, 4], [7, 3], [7, 2], [8, 1]] | 13 | 0.025552034378051758 | 13 | 8 | 2 | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, ... | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, ... | ["[[1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, ... |
53 | Given 9 labeled water jugs with capacities 139, 143, 17, 138, 133, 19, 126, 102, 65 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 349, 415, 458 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 | [["+", 17, 3], ["+", 138, 3], ["+", 143, 3], ["+", 17, 3], ["+", 143, 3], ["+", 133, 2], ["+", 139, 2], ["+", 143, 2], ["+", 65, 1], ["+", 126, 1], ["+", 19, 1], ["+", 139, 1]] | 12 | 0.036029815673828125 | 12 | 54 | 3 | [[139, 143, 17, 138, 133, 19, 126, 102, 65], [349, 415, 458]] | [[139, 143, 17, 138, 133, 19, 126, 102, 65], [349, 415, 458]] | ["[139, 143, 17, 138, 133, 19, 126, 102, 65]", "[349, 415, 458]"] |
54 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 6 | [20, 56, 64, 83, 57, 6, 56, 59, 74, 56, 59, 20, 99, 84, 83, 57, 6, 59, 20, 64, 59, 6] | 22 | 0.07044315338134766 | 22 | 4 | 12 | [[[100, "_", 99, 84], [59, 20, 56, 64], [74, 6, 57, 83]]] | [[[100, "_", 99, 84], [59, 20, 56, 64], [74, 6, 57, 83]]] | ["[[100, '_', 99, 84], [59, 20, 56, 64], [74, 6, 57, 83]]"] |
54 | 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", "down-right", "up-right", "up-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left... | 26 | 1.347020149230957 | 26 | 4 | 24 | [[["r", "u", "p", "f", "y", "w"], ["b", "l", "o", "e", "l", "o"], ["n", "r", "_", "g", "h", "t"], ["u", "b", "r", "i", "o", "t"]]] | [[["r", "u", "p", "f", "y", "w"], ["b", "l", "o", "e", "l", "o"], ["n", "r", "_", "g", "h", "t"], ["u", "b", "r", "i", "o", "t"]], ["unfew", "brolly", "bright", "uproot"]] | ["[['r', 'u', 'p', 'f', 'y', 'w'], ['b', 'l', 'o', 'e', 'l', 'o'], ['n', 'r', '_', 'g', 'h', 't'], ['u', 'b', 'r', 'i', 'o', 't']]", "['unfew', 'brolly', 'bright', 'uproot']"] |
54 | 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 | 13 | ["R", "E", "K", "P", "A", "Y", "M", "T", "A", "Y"] | 10 | 0.03291726112365723 | 10 | 13 | 16 | [[[0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, ... | [[[0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, ... | ["[[0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0,... |
54 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [4, 17, 14, 12, 1, 3, 12, 10, 14, 9, 30, 20, 11, 17, 11, 16, 22, 17, 30, 5, 10, 16, 19, 27, 6, 18, 20, 19, 32, 25, 30, 15, 30, 21, 19, 25, 31, 33, 19, 10, 8, 16, 8], such that the sum of the chosen coins adds up to 328. Ea... | coin_exchange | subset_sum | 26 | [19, 19, 19, 4, 11, 33, 32, 20, 8, 11, 15, 19, 18, 31, 22, 20, 27] | 98 | 0.053559064865112305 | 17 | 43 | 43 | [[4, 17, 14, 12, 1, 3, 12, 10, 14, 9, 30, 20, 11, 17, 11, 16, 22, 17, 30, 5, 10, 16, 19, 27, 6, 18, 20, 19, 32, 25, 30, 15, 30, 21, 19, 25, 31, 33, 19, 10, 8, 16, 8]] | [[4, 17, 14, 12, 1, 3, 12, 10, 14, 9, 30, 20, 11, 17, 11, 16, 22, 17, 30, 5, 10, 16, 19, 27, 6, 18, 20, 19, 32, 25, 30, 15, 30, 21, 19, 25, 31, 33, 19, 10, 8, 16, 8], {"1": 1, "31": 13, "25": 13, "11": 3, "3": 1, "10": 8, "33": 14, "8": 4, "9": 9, "4": 1, "20": 4, "12": 8, "27": 13, "30": 14, "16": 10, "18": 9, "32": 5... | ["[4, 17, 14, 12, 1, 3, 12, 10, 14, 9, 30, 20, 11, 17, 11, 16, 22, 17, 30, 5, 10, 16, 19, 27, 6, 18, 20, 19, 32, 25, 30, 15, 30, 21, 19, 25, 31, 33, 19, 10, 8, 16, 8]", "{1: 1, 31: 13, 25: 13, 11: 3, 3: 1, 10: 8, 33: 14, 8: 4, 9: 9, 4: 1, 20: 4, 12: 8, 27: 13, 30: 14, 16: 10, 18: 9, 32: 5, 21: 20, 6: 4, 5: 5, 22: 11, 1... |
54 | The game of 'Sort It' begins with 3 tubes, each filled with 5 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 | 9 | [[0, 2], [1, 0], [1, 2], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 1], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1]] | 24 | 54.056875705718994 | 24 | 6 | 15 | [[["Red", "Green", "Blue", "Red", "Green"], ["Green", "Red", "Green", "Red", "Blue"], ["Blue", "Red", "Green", "Blue", "Blue"]], 8] | [[["Red", "Green", "Blue", "Red", "Green"], ["Green", "Red", "Green", "Red", "Blue"], ["Blue", "Red", "Green", "Blue", "Blue"]], 8] | ["[['Red', 'Green', 'Blue', 'Red', 'Green'], ['Green', 'Red', 'Green', 'Red', 'Blue'], ['Blue', 'Red', 'Green', 'Blue', 'Blue']]", "8"] |
54 | We have a 4x4 numerical grid, with numbers ranging from 13 to 53 (13 included in the range but 53 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 0, 17], [0, 1, 18], [1, 0, 16], [1, 1, 19], [2, 1, 20], [2, 3, 35], [3, 2, 36], [3, 3, 37]] | 326 | 138.72793531417847 | 8 | 40 | 16 | ["[['', '', '25', '28'], ['', '', '28', '31'], ['15', '', '34', ''], ['13', '34', '', '']]", 13, 53] | ["[['', '', '25', '28'], ['', '', '28', '31'], ['15', '', '34', ''], ['13', '34', '', '']]", 13, 53] | ["[['', '', '25', '28'], ['', '', '28', '31'], ['15', '', '34', ''], ['13', '34', '', '']]", "13", "53"] |
54 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 28 to 59. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 208, 157, None for columns 1 to 2 respectively, and the sums of rows must be None, 196, 162, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 1, 48], [0, 2, 34], [1, 2, 54], [1, 3, 45], [2, 0, 31], [2, 1, 47], [3, 0, 28], [3, 1, 57], [3, 2, 40]] | 674 | 18.105977296829224 | 9 | 49 | 9 | ["[['30', '', '', '37'], ['41', '56', '', ''], ['', '', '29', '55'], ['', '', '', '42']]", 4, 28, 59] | ["[['30', '', '', '37'], ['41', '56', '', ''], ['', '', '29', '55'], ['', '', '', '42']]", 28, 59, [1, 3], [1, 3], [208, 157], [196, 162], 166] | ["[['30', '', '', '37'], ['41', '56', '', ''], ['', '', '29', '55'], ['', '', '', '42']]", "28", "59", "[None, 208, 157, None]", "[None, 196, 162, None]", "166"] |
54 | 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 | [[3, 6], [5, 6], [1, 7], [5, 7], [2, 0], [2, 4], [5, 4], [5, 0], [2, 5], [2, 7], [3, 0], [3, 5], [3, 6], [3, 0], [2, 3], [1, 2], [1, 5], [1, 2], [1, 7], [3, 6], [4, 2], [4, 2]] | 116 | 0.24997472763061523 | 22 | 56 | 20 | [[[], ["Green", "Yellow", "Blue", "Yellow", "Green"], ["Black", "Yellow", "Blue", "Green", "Red"], ["Red", "Black", "Blue", "Red", "Black"], [], ["Red", "Green", "Yellow", "Black", "Blue"], [], []], 5, {"0": 8, "1": 8, "2": 2, "3": 7, "4": 9, "5": 5, "6": 2, "7": 7}] | [[[], ["Green", "Yellow", "Blue", "Yellow", "Green"], ["Black", "Yellow", "Blue", "Green", "Red"], ["Red", "Black", "Blue", "Red", "Black"], [], ["Red", "Green", "Yellow", "Black", "Blue"], [], []], 5, {"0": 8, "1": 8, "2": 2, "3": 7, "4": 9, "5": 5, "6": 2, "7": 7}, 4] | ["[[], ['Green', 'Yellow', 'Blue', 'Yellow', 'Green'], ['Black', 'Yellow', 'Blue', 'Green', 'Red'], ['Red', 'Black', 'Blue', 'Red', 'Black'], [], ['Red', 'Green', 'Yellow', 'Black', 'Blue'], [], []]", "{0: 8, 1: 8, 2: 2, 3: 7, 4: 9, 5: 5, 6: 2, 7: 7}", "5", "4"] |
54 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 11) to his destination workshop at index (9, 2), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[4, 11], [3, 11], [4, 11], [4, 10], [5, 10], [6, 10], [7, 10], [7, 9], [7, 8], [8, 8], [9, 8], [10, 8], [10, 7], [10, 6], [10, 5], [9, 5], [9, 4], [9, 3], [9, 2]] | 165 | 0.02228689193725586 | 19 | 4 | 4 | [[["19", "14", "16", "4", "15", "16", "15", "x", "9", "x", "x", "x"], ["x", "7", "12", "6", "x", "12", "x", "3", "x", "14", "5", "9"], ["1", "12", "x", "x", "12", "x", "x", "x", "x", "x", "10", "1"], ["x", "1", "15", "14", "x", "2", "13", "x", "x", "x", "10", "9"], ["7", "x", "13", "x", "14", "1", "14", "8", "x", "x", ... | [[["19", "14", "16", "4", "15", "16", "15", "x", "9", "x", "x", "x"], ["x", "7", "12", "6", "x", "12", "x", "3", "x", "14", "5", "9"], ["1", "12", "x", "x", "12", "x", "x", "x", "x", "x", "10", "1"], ["x", "1", "15", "14", "x", "2", "13", "x", "x", "x", "10", "9"], ["7", "x", "13", "x", "14", "1", "14", "8", "x", "x", ... | ["[['19', '14', '16', '4', '15', '16', '15', 'x', '9', 'x', 'x', 'x'], ['x', '7', '12', '6', 'x', '12', 'x', '3', 'x', '14', '5', '9'], ['1', '12', 'x', 'x', '12', 'x', 'x', 'x', 'x', 'x', '10', '1'], ['x', '1', '15', '14', 'x', '2', '13', 'x', 'x', 'x', '10', '9'], ['7', 'x', '13', 'x', '14', '1', '14', '8', 'x', 'x',... |
54 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. 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 | 12 | [[1, 7], [2, 6], [3, 5], [4, 5], [5, 5], [6, 5], [7, 4], [7, 3], [8, 2], [8, 1], [9, 1], [9, 0], [10, 0]] | 13 | 0.029400348663330078 | 13 | 8 | 2 | ["[[1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, ... | ["[[1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, ... | ["[[1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, ... |
54 | Given 9 labeled water jugs with capacities 45, 67, 134, 133, 86, 66, 107, 94, 124, 122 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 229, 303, 307 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 | [["+", 66, 3], ["+", 107, 3], ["+", 134, 3], ["+", 124, 2], ["+", 134, 2], ["+", 45, 2], ["+", 107, 1], ["+", 122, 1]] | 8 | 0.02436041831970215 | 8 | 60 | 3 | [[45, 67, 134, 133, 86, 66, 107, 94, 124, 122], [229, 303, 307]] | [[45, 67, 134, 133, 86, 66, 107, 94, 124, 122], [229, 303, 307]] | ["[45, 67, 134, 133, 86, 66, 107, 94, 124, 122]", "[229, 303, 307]"] |
55 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [18, 68, 46, 18, 65, 47, 5, 20, 18, 65, 47, 7, 53, 12, 34, 46, 65, 47, 20, 18, 47, 65, 68, 53, 7, 20, 53, 34, 46, 68, 65, 53, 20, 5] | 34 | 3.4830353260040283 | 34 | 4 | 12 | [[[34, 68, 46, 20], [12, 18, "_", 5], [53, 7, 65, 47]]] | [[[34, 68, 46, 20], [12, 18, "_", 5], [53, 7, 65, 47]]] | ["[[34, 68, 46, 20], [12, 18, '_', 5], [53, 7, 65, 47]]"] |
55 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-left", "up-right", "down-right", "down-left", "up-left", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 14 | 0.19336867332458496 | 14 | 4 | 20 | [[["o", "n", "s", "t"], ["t", "e", "s", "w"], ["i", "l", "s", "p"], ["s", "g", "a", "f"], ["b", "o", "_", "n"]]] | [[["o", "n", "s", "t"], ["t", "e", "s", "w"], ["i", "l", "s", "p"], ["s", "g", "a", "f"], ["b", "o", "_", "n"]], ["net", "toss", "flip", "swag", "bosn"]] | ["[['o', 'n', 's', 't'], ['t', 'e', 's', 'w'], ['i', 'l', 's', 'p'], ['s', 'g', 'a', 'f'], ['b', 'o', '_', 'n']]", "['net', 'toss', 'flip', 'swag', 'bosn']"] |
55 | 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 | 13 | ["H", "Q", "L", "B", "X", "T", "B", "X"] | 8 | 0.04383373260498047 | 8 | 13 | 16 | [[[0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, ... | [[[0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, ... | ["[[0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0,... |
55 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 26, 9, 14, 11, 25, 28, 17, 18, 18, 9, 16, 2, 11, 31, 25, 4, 23, 9, 3, 24, 22, 3, 14, 32, 30, 19, 7, 4, 22, 33, 13, 25, 15, 14, 28, 20, 3, 4, 3, 32, 10, 6, 29, 25], such that the sum of the chosen coins adds up to 325.... | coin_exchange | subset_sum | 27 | [30, 28, 26, 6, 13, 15, 17, 29, 33, 32, 28, 18, 19, 31] | 101 | 0.05463528633117676 | 14 | 45 | 45 | [[12, 26, 9, 14, 11, 25, 28, 17, 18, 18, 9, 16, 2, 11, 31, 25, 4, 23, 9, 3, 24, 22, 3, 14, 32, 30, 19, 7, 4, 22, 33, 13, 25, 15, 14, 28, 20, 3, 4, 3, 32, 10, 6, 29, 25]] | [[12, 26, 9, 14, 11, 25, 28, 17, 18, 18, 9, 16, 2, 11, 31, 25, 4, 23, 9, 3, 24, 22, 3, 14, 32, 30, 19, 7, 4, 22, 33, 13, 25, 15, 14, 28, 20, 3, 4, 3, 32, 10, 6, 29, 25], {"29": 2, "9": 7, "17": 4, "18": 9, "26": 6, "33": 11, "16": 12, "4": 3, "31": 12, "6": 2, "11": 8, "23": 14, "7": 1, "30": 8, "12": 8, "13": 2, "20":... | ["[12, 26, 9, 14, 11, 25, 28, 17, 18, 18, 9, 16, 2, 11, 31, 25, 4, 23, 9, 3, 24, 22, 3, 14, 32, 30, 19, 7, 4, 22, 33, 13, 25, 15, 14, 28, 20, 3, 4, 3, 32, 10, 6, 29, 25]", "{29: 2, 9: 7, 17: 4, 18: 9, 26: 6, 33: 11, 16: 12, 4: 3, 31: 12, 6: 2, 11: 8, 23: 14, 7: 1, 30: 8, 12: 8, 13: 2, 20: 13, 24: 16, 14: 8, 19: 8, 10: ... |
55 | The game of 'Sort It' begins with 3 tubes, each filled with 5 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 | 9 | [[0, 2], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [0, 1], [2, 0], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0]] | 21 | 12.931140422821045 | 21 | 6 | 15 | [[["Green", "Blue", "Blue", "Red", "Red"], ["Green", "Red", "Blue", "Green", "Green"], ["Red", "Green", "Blue", "Blue", "Red"]], 8] | [[["Green", "Blue", "Blue", "Red", "Red"], ["Green", "Red", "Blue", "Green", "Green"], ["Red", "Green", "Blue", "Blue", "Red"]], 8] | ["[['Green', 'Blue', 'Blue', 'Red', 'Red'], ['Green', 'Red', 'Blue', 'Green', 'Green'], ['Red', 'Green', 'Blue', 'Blue', 'Red']]", "8"] |
55 | We have a 4x4 numerical grid, with numbers ranging from 10 to 50 (10 included in the range but 50 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 13 | [[0, 0, 39], [0, 3, 10], [1, 1, 31], [1, 2, 32], [1, 3, 33], [2, 0, 12], [2, 2, 34], [3, 0, 11], [3, 1, 13]] | 385 | 2.9997804164886475 | 9 | 40 | 16 | ["[['', '38', '19', ''], ['22', '', '', ''], ['', '30', '', '42'], ['', '', '35', '45']]", 10, 50] | ["[['', '38', '19', ''], ['22', '', '', ''], ['', '30', '', '42'], ['', '', '35', '45']]", 10, 50] | ["[['', '38', '19', ''], ['22', '', '', ''], ['', '30', '', '42'], ['', '', '35', '45']]", "10", "50"] |
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