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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
19 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["E", "M", "Y", "T", "B", "R", "Y", "T"] | 8 | 0.022693395614624023 | 8 | 11 | 14 | [[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0,... | [[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0,... | ["[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0... |
19 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11], such that the sum of th... | coin_exchange | subset_sum | 33 | [20, 23, 22, 20, 16, 8, 11, 10, 8, 11, 10, 8, 13, 10, 8, 4, 2, 9, 8, 4, 2, 7, 4, 5] | 63 | 0.05074810981750488 | 24 | 55 | 55 | [[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11]] | [[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11], {"20": 3, "9": 2, "23": 1, "10": 3, "5": 4, "21": 14, "22": 5, "18": 7, "16": 4, "13": 5, "2": 1, "8": 2, "19": 16, "7":... | ["[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11]", "{20: 3, 9: 2, 23: 1, 10: 3, 5: 4, 21: 14, 22: 5, 18: 7, 16: 4, 13: 5, 2: 1, 8: 2, 19: 16, 7: 3, 6: 6, 11: 3, 14: 8, 4... |
19 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[0, 1], [0, 2], [0, 2], [0, 1], [2, 0], [2, 0], [1, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0]] | 21 | 4.620145320892334 | 21 | 6 | 12 | [[["Blue", "Green", "Green", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Red", "Green", "Blue"]], 6] | [[["Blue", "Green", "Green", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Red", "Green", "Blue"]], 6] | ["[['Blue', 'Green', 'Green', 'Red'], ['Red', 'Blue', 'Green', 'Red'], ['Blue', 'Red', 'Green', 'Blue']]", "6"] |
19 | We have a 3x3 numerical grid, with numbers ranging from 48 to 91 (48 included in the range but 91 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 0, 48], [0, 1, 49], [1, 1, 60], [2, 0, 75]] | 577 | 0.17565202713012695 | 4 | 43 | 9 | ["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", 48, 91] | ["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", 48, 91] | ["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", "48", "91"] |
19 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 234, and sum of row 1 must be 201. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 2, 51], [1, 0, 52], [1, 1, 83], [1, 2, 66], [2, 0, 79], [2, 1, 73], [2, 2, 50]] | 596 | 7.28009295463562 | 7 | 29 | 9 | ["[['64', '78', ''], ['', '', ''], ['', '', '']]", 3, 50, 84] | ["[['64', '78', ''], ['', '', ''], ['', '', '']]", 50, 84, [1, 2], [1, 2], [234], [201], 213] | ["[['64', '78', ''], ['', '', ''], ['', '', '']]", "50", "84", "[None, 234, None]", "[None, 201, None]", "213"] |
19 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[5, 0], [2, 0], [2, 1], [2, 0], [5, 3], [5, 1], [4, 3], [4, 3], [4, 2], [5, 2], [4, 1]] | 48 | 0.03397560119628906 | 11 | 30 | 12 | [[[], [], ["Green", "Blue", "Green", "Yellow"], [], ["Red", "Red", "Yellow", "Blue"], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 2, "1": 4, "2": 6, "3": 6, "4": 6, "5": 7}] | [[[], [], ["Green", "Blue", "Green", "Yellow"], [], ["Red", "Red", "Yellow", "Blue"], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 2, "1": 4, "2": 6, "3": 6, "4": 6, "5": 7}, 3] | ["[[], [], ['Green', 'Blue', 'Green', 'Yellow'], [], ['Red', 'Red', 'Yellow', 'Blue'], ['Green', 'Red', 'Blue', 'Yellow']]", "{0: 2, 1: 4, 2: 6, 3: 6, 4: 6, 5: 7}", "4", "3"] |
19 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 0) to his destination workshop at index (3, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 0], [6, 0], [6, 1], [6, 2], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [4, 8], [4, 9], [3, 9]] | 122 | 0.027219295501708984 | 14 | 4 | 4 | [[["x", "16", "15", "14", "2", "12", "3", "x", "7", "7"], ["11", "x", "x", "x", "4", "10", "5", "x", "x", "x"], ["12", "x", "3", "x", "x", "19", "x", "13", "x", "x"], ["16", "15", "13", "x", "12", "x", "x", "1", "x", "7"], ["2", "6", "x", "5", "x", "14", "7", "x", "8", "18"], ["19", "17", "2", "11", "8", "17", "12", "8... | [[["x", "16", "15", "14", "2", "12", "3", "x", "7", "7"], ["11", "x", "x", "x", "4", "10", "5", "x", "x", "x"], ["12", "x", "3", "x", "x", "19", "x", "13", "x", "x"], ["16", "15", "13", "x", "12", "x", "x", "1", "x", "7"], ["2", "6", "x", "5", "x", "14", "7", "x", "8", "18"], ["19", "17", "2", "11", "8", "17", "12", "8... | ["[['x', '16', '15', '14', '2', '12', '3', 'x', '7', '7'], ['11', 'x', 'x', 'x', '4', '10', '5', 'x', 'x', 'x'], ['12', 'x', '3', 'x', 'x', '19', 'x', '13', 'x', 'x'], ['16', '15', '13', 'x', '12', 'x', 'x', '1', 'x', '7'], ['2', '6', 'x', '5', 'x', '14', '7', 'x', '8', '18'], ['19', '17', '2', '11', '8', '17', '12', '... |
19 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[1, 9], [1, 8], [1, 7], [1, 6], [0, 5], [0, 4], [1, 4], [1, 3], [1, 2], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1], [6, 1], [7, 1]] | 16 | 0.029511690139770508 | 16 | 8 | 2 | ["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1... | ["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1... | ["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1... |
19 | Given 7 labeled water jugs with capacities 21, 62, 98, 143, 61, 110, 140, 40 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 280, 338, 353 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount... | water_jug | subset_sum | 5 | [["+", 110, 3], ["+", 140, 3], ["-", 40, 3], ["+", 143, 3], ["+", 140, 2], ["+", 140, 2], ["-", 40, 2], ["+", 98, 2], ["+", 140, 1], ["+", 140, 1]] | 10 | 0.0442960262298584 | 10 | 48 | 3 | [[21, 62, 98, 143, 61, 110, 140, 40], [280, 338, 353]] | [[21, 62, 98, 143, 61, 110, 140, 40], [280, 338, 353]] | ["[21, 62, 98, 143, 61, 110, 140, 40]", "[280, 338, 353]"] |
20 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 5 | [99, 49, 92, 91, 25, 99, 49, 92, 91, 46, 50, 91, 99, 25, 46, 50, 91, 99, 50, 91, 99, 97, 92, 49] | 24 | 0.10476183891296387 | 24 | 4 | 9 | [[[46, 50, 97], [92, 49, 99], [91, 25, "_"]]] | [[[46, 50, 97], [92, 49, 99], [91, 25, "_"]]] | ["[[46, 50, 97], [92, 49, 99], [91, 25, '_']]"] |
20 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 16 | 0.2547872066497803 | 16 | 4 | 20 | [[["r", "s", "w", "o", "g"], ["t", "n", "e", "m", "a"], ["m", "o", "_", "u", "s"], ["a", "w", "i", "r", "i"]]] | [[["r", "s", "w", "o", "g"], ["t", "n", "e", "m", "a"], ["m", "o", "_", "u", "s"], ["a", "w", "i", "r", "i"]], ["snog", "trema", "mosur", "awiwi"]] | ["[['r', 's', 'w', 'o', 'g'], ['t', 'n', 'e', 'm', 'a'], ['m', 'o', '_', 'u', 's'], ['a', 'w', 'i', 'r', 'i']]", "['snog', 'trema', 'mosur', 'awiwi']"] |
20 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["F", "D", "Y", "N", "C", "I", "R", "M", "N", "X", "Q", "I"] | 12 | 0.029342174530029297 | 12 | 11 | 14 | [[[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, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0,... | [[[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, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0,... | ["[[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, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0... |
20 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15], such that the sum of th... | coin_exchange | subset_sum | 34 | [24, 22, 2, 5, 11, 2, 5, 11, 2, 5, 5, 5, 7, 6, 21, 16, 14, 12, 23, 22, 18, 8] | 65 | 0.05625104904174805 | 22 | 56 | 56 | [[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15]] | [[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15], {"20": 14, "15": 15, "6": 1, "14": 1, "7": 2, "18": 5, "2": 1, "16": 5, "21": 9, "3": 3, "12": 3, "17": 10, "22": 4, "10... | ["[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15]", "{20: 14, 15: 15, 6: 1, 14: 1, 7: 2, 18: 5, 2: 1, 16: 5, 21: 9, 3: 3, 12: 3, 17: 10, 22: 4, 10: 9, 4: 3, 11: 1, 5: 1, ... |
20 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[1, 2], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]] | 18 | 1.1464557647705078 | 18 | 6 | 12 | [[["Red", "Red", "Green", "Blue"], ["Green", "Green", "Red", "Green"], ["Blue", "Blue", "Red", "Blue"]], 6] | [[["Red", "Red", "Green", "Blue"], ["Green", "Green", "Red", "Green"], ["Blue", "Blue", "Red", "Blue"]], 6] | ["[['Red', 'Red', 'Green', 'Blue'], ['Green', 'Green', 'Red', 'Green'], ['Blue', 'Blue', 'Red', 'Blue']]", "6"] |
20 | We have a 3x3 numerical grid, with numbers ranging from 48 to 91 (48 included in the range but 91 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 1, 49], [0, 2, 48], [1, 1, 57], [2, 1, 58]] | 578 | 0.17241978645324707 | 4 | 43 | 9 | ["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", 48, 91] | ["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", 48, 91] | ["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", "48", "91"] |
20 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 233, and sum of row 1 must be 207. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 2, 50], [1, 0, 53], [1, 1, 83], [1, 2, 71], [2, 0, 52], [2, 1, 68], [2, 2, 51]] | 572 | 3.969967842102051 | 7 | 29 | 9 | ["[['62', '82', ''], ['', '', ''], ['', '', '']]", 3, 50, 84] | ["[['62', '82', ''], ['', '', ''], ['', '', '']]", 50, 84, [1, 2], [1, 2], [233], [207], 185] | ["[['62', '82', ''], ['', '', ''], ['', '', '']]", "50", "84", "[None, 233, None]", "[None, 207, None]", "185"] |
20 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[1, 2], [1, 0], [3, 0], [4, 0], [1, 5], [3, 1], [4, 5], [4, 1], [3, 5], [2, 3], [4, 3]] | 28 | 0.036955833435058594 | 11 | 30 | 12 | [[[], ["Green", "Red", "Yellow", "Blue"], [], ["Red", "Blue", "Yellow", "Green"], ["Red", "Yellow", "Blue", "Green"], []], 4, {"0": 4, "1": 2, "2": 5, "3": 2, "4": 4, "5": 1}] | [[[], ["Green", "Red", "Yellow", "Blue"], [], ["Red", "Blue", "Yellow", "Green"], ["Red", "Yellow", "Blue", "Green"], []], 4, {"0": 4, "1": 2, "2": 5, "3": 2, "4": 4, "5": 1}, 3] | ["[[], ['Green', 'Red', 'Yellow', 'Blue'], [], ['Red', 'Blue', 'Yellow', 'Green'], ['Red', 'Yellow', 'Blue', 'Green'], []]", "{0: 4, 1: 2, 2: 5, 3: 2, 4: 4, 5: 1}", "4", "3"] |
20 | 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, 0) to his destination workshop at index (4, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[6, 0], [5, 0], [4, 0], [4, 1], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 8], [4, 9]] | 141 | 0.029550790786743164 | 14 | 4 | 4 | [[["19", "x", "7", "x", "12", "x", "15", "5", "19", "14"], ["17", "x", "3", "5", "7", "x", "x", "x", "17", "20"], ["x", "11", "15", "8", "x", "16", "4", "x", "1", "1"], ["x", "8", "19", "4", "3", "3", "3", "17", "8", "15"], ["13", "10", "17", "17", "6", "1", "x", "8", "13", "20"], ["20", "x", "x", "x", "x", "4", "18", ... | [[["19", "x", "7", "x", "12", "x", "15", "5", "19", "14"], ["17", "x", "3", "5", "7", "x", "x", "x", "17", "20"], ["x", "11", "15", "8", "x", "16", "4", "x", "1", "1"], ["x", "8", "19", "4", "3", "3", "3", "17", "8", "15"], ["13", "10", "17", "17", "6", "1", "x", "8", "13", "20"], ["20", "x", "x", "x", "x", "4", "18", ... | ["[['19', 'x', '7', 'x', '12', 'x', '15', '5', '19', '14'], ['17', 'x', '3', '5', '7', 'x', 'x', 'x', '17', '20'], ['x', '11', '15', '8', 'x', '16', '4', 'x', '1', '1'], ['x', '8', '19', '4', '3', '3', '3', '17', '8', '15'], ['13', '10', '17', '17', '6', '1', 'x', '8', '13', '20'], ['20', 'x', 'x', 'x', 'x', '4', '18',... |
20 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[0, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 2], [6, 3], [7, 4], [7, 5], [7, 6]] | 11 | 0.03641462326049805 | 11 | 8 | 2 | ["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1... | ["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1... | ["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1... |
20 | Given 7 labeled water jugs with capacities 76, 48, 35, 94, 93, 115, 16, 53 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 247, 261, 273 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 48, 3], ["+", 94, 3], ["+", 16, 3], ["+", 115, 3], ["+", 93, 2], ["+", 115, 2], ["+", 53, 2], ["+", 76, 1], ["+", 93, 1], ["-", 16, 1], ["+", 94, 1]] | 11 | 0.03790163993835449 | 11 | 48 | 3 | [[76, 48, 35, 94, 93, 115, 16, 53], [247, 261, 273]] | [[76, 48, 35, 94, 93, 115, 16, 53], [247, 261, 273]] | ["[76, 48, 35, 94, 93, 115, 16, 53]", "[247, 261, 273]"] |
21 | 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 | [53, 94, 61, 25, 71, 58, 94, 61, 18, 50, 25, 71, 58, 94, 61, 53, 50, 18, 71, 58, 94, 71, 53, 50] | 24 | 0.061148881912231445 | 24 | 4 | 9 | [[[25, 71, 58], [61, 94, 53], [50, 18, "_"]]] | [[[25, 71, 58], [61, 94, 53], [50, 18, "_"]]] | ["[[25, 71, 58], [61, 94, 53], [50, 18, '_']]"] |
21 | 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", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left"] | 18 | 0.25868940353393555 | 18 | 4 | 20 | [[["m", "p", "l", "s", "s"], ["s", "a", "o", "s", "e"], ["c", "a", "_", "e", "k"], ["h", "i", "r", "o", "m"]]] | [[["m", "p", "l", "s", "s"], ["s", "a", "o", "s", "e"], ["c", "a", "_", "e", "k"], ["h", "i", "r", "o", "m"]], ["poss", "smoke", "casel", "hiram"]] | ["[['m', 'p', 'l', 's', 's'], ['s', 'a', 'o', 's', 'e'], ['c', 'a', '_', 'e', 'k'], ['h', 'i', 'r', 'o', 'm']]", "['poss', 'smoke', 'casel', 'hiram']"] |
21 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["Y", "K", "M", "I", "H", "Q", "R", "Q", "W", "I"] | 10 | 0.020466327667236328 | 10 | 11 | 14 | [[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1,... | [[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1,... | ["[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1... |
21 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15], such that the sum of the cho... | coin_exchange | subset_sum | 35 | [20, 16, 6, 15, 15, 15, 15, 14, 6, 4, 13, 13, 4, 21, 16, 4, 2, 7, 4] | 56 | 0.052184104919433594 | 19 | 55 | 55 | [[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15]] | [[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15], {"9": 9, "6": 1, "13": 4, "2": 1, "16": 3, "14": 4, "19": 16, "20": 2, "15": 3, "7": 3, "18": 14, "17": 15, "4": 2, "5": 5, "... | ["[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15]", "{9: 9, 6: 1, 13: 4, 2: 1, 16: 3, 14: 4, 19: 16, 20: 2, 15: 3, 7: 3, 18: 14, 17: 15, 4: 2, 5: 5, 8: 8, 21: 10, 12: 11, 11: ... |
21 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]] | 18 | 1.3162987232208252 | 18 | 6 | 12 | [[["Green", "Red", "Blue", "Green"], ["Red", "Blue", "Red", "Blue"], ["Red", "Blue", "Green", "Green"]], 6] | [[["Green", "Red", "Blue", "Green"], ["Red", "Blue", "Red", "Blue"], ["Red", "Blue", "Green", "Green"]], 6] | ["[['Green', 'Red', 'Blue', 'Green'], ['Red', 'Blue', 'Red', 'Blue'], ['Red', 'Blue', 'Green', 'Green']]", "6"] |
21 | We have a 3x3 numerical grid, with numbers ranging from 15 to 58 (15 included in the range but 58 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 7 | [[0, 1, 16], [0, 2, 15], [2, 0, 17], [2, 1, 34]] | 284 | 0.16371726989746094 | 4 | 43 | 9 | ["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", 15, 58] | ["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", 15, 58] | ["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", "15", "58"] |
21 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 212, and sum of row 1 must be 193. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 50], [0, 1, 51], [1, 0, 52], [1, 1, 83], [1, 2, 58], [2, 0, 72], [2, 1, 78]] | 562 | 155.01593708992004 | 7 | 29 | 9 | ["[['', '', '62'], ['', '', ''], ['', '', '56']]", 3, 50, 84] | ["[['', '', '62'], ['', '', ''], ['', '', '56']]", 50, 84, [1, 2], [1, 2], [212], [193], 217] | ["[['', '', '62'], ['', '', ''], ['', '', '56']]", "50", "84", "[None, 212, None]", "[None, 193, None]", "217"] |
21 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 2], [5, 4], [5, 2], [5, 1], [0, 4], [0, 5], [3, 1], [3, 5], [3, 1], [0, 4], [3, 2]] | 43 | 0.025786161422729492 | 11 | 30 | 12 | [[["Red", "Yellow", "Blue", "Yellow"], [], [], ["Green", "Blue", "Green", "Red"], [], ["Yellow", "Red", "Green", "Blue"]], 4, {"0": 4, "1": 5, "2": 3, "3": 3, "4": 3, "5": 5}] | [[["Red", "Yellow", "Blue", "Yellow"], [], [], ["Green", "Blue", "Green", "Red"], [], ["Yellow", "Red", "Green", "Blue"]], 4, {"0": 4, "1": 5, "2": 3, "3": 3, "4": 3, "5": 5}, 3] | ["[['Red', 'Yellow', 'Blue', 'Yellow'], [], [], ['Green', 'Blue', 'Green', 'Red'], [], ['Yellow', 'Red', 'Green', 'Blue']]", "{0: 4, 1: 5, 2: 3, 3: 3, 4: 3, 5: 5}", "4", "3"] |
21 | 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, 9) to his destination workshop at index (6, 3), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[1, 9], [1, 8], [2, 8], [3, 8], [3, 7], [4, 7], [4, 6], [5, 6], [6, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5], [4, 4], [5, 4], [5, 3], [6, 3]] | 120 | 0.022410869598388672 | 18 | 4 | 4 | [[["15", "4", "9", "10", "19", "x", "12", "4", "x", "15"], ["12", "19", "11", "x", "x", "x", "x", "7", "6", "3"], ["4", "x", "8", "x", "x", "19", "x", "11", "1", "6"], ["x", "x", "5", "x", "x", "x", "12", "6", "6", "x"], ["x", "14", "x", "x", "14", "11", "2", "9", "6", "14"], ["8", "8", "5", "17", "7", "x", "1", "2", "... | [[["15", "4", "9", "10", "19", "x", "12", "4", "x", "15"], ["12", "19", "11", "x", "x", "x", "x", "7", "6", "3"], ["4", "x", "8", "x", "x", "19", "x", "11", "1", "6"], ["x", "x", "5", "x", "x", "x", "12", "6", "6", "x"], ["x", "14", "x", "x", "14", "11", "2", "9", "6", "14"], ["8", "8", "5", "17", "7", "x", "1", "2", "... | ["[['15', '4', '9', '10', '19', 'x', '12', '4', 'x', '15'], ['12', '19', '11', 'x', 'x', 'x', 'x', '7', '6', '3'], ['4', 'x', '8', 'x', 'x', '19', 'x', '11', '1', '6'], ['x', 'x', '5', 'x', 'x', 'x', '12', '6', '6', 'x'], ['x', '14', 'x', 'x', '14', '11', '2', '9', '6', '14'], ['8', '8', '5', '17', '7', 'x', '1', '2', ... |
21 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[1, 9], [1, 8], [2, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [5, 2], [5, 1], [5, 0]] | 11 | 0.029159069061279297 | 11 | 8 | 2 | ["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1... | ["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1... | ["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1... |
21 | Given 7 labeled water jugs with capacities 52, 131, 82, 132, 117, 65 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 357, 384, 522 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wate... | water_jug | subset_sum | 5 | [["+", 117, 3], ["+", 117, 3], ["+", 52, 3], ["+", 52, 3], ["+", 52, 3], ["+", 132, 3], ["+", 82, 2], ["+", 131, 2], ["+", 52, 2], ["+", 52, 2], ["-", 65, 2], ["+", 132, 2], ["+", 65, 1], ["+", 131, 1], ["+", 131, 1], ["-", 52, 1], ["+", 82, 1]] | 17 | 0.047934532165527344 | 17 | 36 | 3 | [[52, 131, 82, 132, 117, 65], [357, 384, 522]] | [[52, 131, 82, 132, 117, 65], [357, 384, 522]] | ["[52, 131, 82, 132, 117, 65]", "[357, 384, 522]"] |
22 | 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, 41, 61, 19, 41, 61, 39, 14, 25, 56, 61, 39, 14] | 14 | 0.019939899444580078 | 14 | 4 | 9 | [[[81, 25, "_"], [19, 56, 14], [61, 41, 39]]] | [[[81, 25, "_"], [19, 56, 14], [61, 41, 39]]] | ["[[81, 25, '_'], [19, 56, 14], [61, 41, 39]]"] |
22 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-left"] | 16 | 0.13087821006774902 | 16 | 4 | 20 | [[["o", "j", "_", "h", "u"], ["w", "l", "r", "e", "y"], ["n", "i", "l", "t", "a"], ["i", "y", "i", "m", "l"]]] | [[["o", "j", "_", "h", "u"], ["w", "l", "r", "e", "y"], ["n", "i", "l", "t", "a"], ["i", "y", "i", "m", "l"]], ["jehu", "wormy", "linty", "ilial"]] | ["[['o', 'j', '_', 'h', 'u'], ['w', 'l', 'r', 'e', 'y'], ['n', 'i', 'l', 't', 'a'], ['i', 'y', 'i', 'm', 'l']]", "['jehu', 'wormy', 'linty', 'ilial']"] |
22 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["X", "Z", "V", "T", "E", "J", "M", "T", "E"] | 9 | 0.029807567596435547 | 9 | 11 | 14 | [[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0,... | [[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0,... | ["[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0... |
22 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10], such that the sum of the chosen coins adds up to 268. Each coin in the list is unique and can only be used once. Also... | coin_exchange | subset_sum | 15 | [9, 13, 10, 69, 66, 16, 10, 19, 25, 12, 15, 4] | 96 | 0.04047846794128418 | 12 | 28 | 28 | [[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10]] | [[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10], {"66": 17, "9": 3, "15": 10, "7": 6, "3": 3, "13": 7, "11": 10, "25": 14, "22": 18, "24": 17, "12": 6, "23": 18, "2": 2, "10": 5, "19": 10, "20": 19, "5": 4, "16": 1, "21": 20, "69": 14, "4": 4}, 268] | ["[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10]", "{66: 17, 9: 3, 15: 10, 7: 6, 3: 3, 13: 7, 11: 10, 25: 14, 22: 18, 24: 17, 12: 6, 23: 18, 2: 2, 10: 5, 19: 10, 20: 19, 5: 4, 16: 1, 21: 20, 69: 14, 4: 4}", "268"] |
22 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[0, 2], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]] | 19 | 2.2448041439056396 | 19 | 6 | 12 | [[["Blue", "Red", "Blue", "Green"], ["Red", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red"]], 6] | [[["Blue", "Red", "Blue", "Green"], ["Red", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red"]], 6] | ["[['Blue', 'Red', 'Blue', 'Green'], ['Red', 'Blue', 'Green', 'Red'], ['Blue', 'Green', 'Green', 'Red']]", "6"] |
22 | We have a 3x3 numerical grid, with numbers ranging from 13 to 56 (13 included in the range but 56 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 1, 14], [0, 2, 13], [1, 2, 35], [2, 0, 47], [2, 2, 36]] | 213 | 7.270275831222534 | 5 | 43 | 9 | ["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", 13, 56] | ["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", 13, 56] | ["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", "13", "56"] |
22 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 12 to 46. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 120, and sum of row 1 must be 105. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 7 | [[0, 0, 12], [0, 1, 32], [0, 2, 14], [1, 0, 16], [1, 1, 45], [1, 2, 44], [2, 0, 40], [2, 2, 13]] | 259 | 92.43742489814758 | 8 | 29 | 9 | ["[['', '', ''], ['', '', ''], ['', '43', '']]", 3, 12, 46] | ["[['', '', ''], ['', '', ''], ['', '43', '']]", 12, 46, [1, 2], [1, 2], [120], [105], 99] | ["[['', '', ''], ['', '', ''], ['', '43', '']]", "12", "46", "[None, 120, None]", "[None, 105, None]", "99"] |
22 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[5, 3], [5, 3], [4, 5], [1, 2], [4, 2], [1, 0], [1, 2], [4, 1], [0, 1], [3, 0], [3, 0], [4, 0]] | 38 | 0.09250640869140625 | 12 | 30 | 12 | [[[], ["Blue", "Yellow", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Green"], ["Green", "Green", "Red", "Red"]], 4, {"0": 1, "1": 4, "2": 2, "3": 7, "4": 6, "5": 6}] | [[[], ["Blue", "Yellow", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Green"], ["Green", "Green", "Red", "Red"]], 4, {"0": 1, "1": 4, "2": 2, "3": 7, "4": 6, "5": 6}, 3] | ["[[], ['Blue', 'Yellow', 'Blue', 'Yellow'], [], [], ['Red', 'Blue', 'Yellow', 'Green'], ['Green', 'Green', 'Red', 'Red']]", "{0: 1, 1: 4, 2: 2, 3: 7, 4: 6, 5: 6}", "4", "3"] |
22 | 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 (5, 7), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[1, 0], [2, 0], [3, 0], [3, 1], [3, 2], [3, 3], [4, 3], [4, 4], [4, 5], [4, 6], [4, 7], [5, 7]] | 116 | 0.020702600479125977 | 12 | 4 | 4 | [[["2", "2", "3", "x", "2", "10", "x", "8", "6", "x"], ["6", "11", "x", "x", "x", "x", "x", "16", "x", "7"], ["17", "17", "7", "12", "13", "15", "5", "6", "10", "13"], ["1", "15", "13", "3", "x", "x", "x", "14", "x", "9"], ["14", "x", "x", "6", "15", "2", "12", "18", "x", "18"], ["11", "19", "1", "19", "10", "8", "x", ... | [[["2", "2", "3", "x", "2", "10", "x", "8", "6", "x"], ["6", "11", "x", "x", "x", "x", "x", "16", "x", "7"], ["17", "17", "7", "12", "13", "15", "5", "6", "10", "13"], ["1", "15", "13", "3", "x", "x", "x", "14", "x", "9"], ["14", "x", "x", "6", "15", "2", "12", "18", "x", "18"], ["11", "19", "1", "19", "10", "8", "x", ... | ["[['2', '2', '3', 'x', '2', '10', 'x', '8', '6', 'x'], ['6', '11', 'x', 'x', 'x', 'x', 'x', '16', 'x', '7'], ['17', '17', '7', '12', '13', '15', '5', '6', '10', '13'], ['1', '15', '13', '3', 'x', 'x', 'x', '14', 'x', '9'], ['14', 'x', 'x', '6', '15', '2', '12', '18', 'x', '18'], ['11', '19', '1', '19', '10', '8', 'x',... |
22 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[8, 1], [9, 2], [9, 3], [8, 3], [8, 4], [7, 4], [6, 4], [5, 5], [5, 6], [5, 7], [4, 8], [4, 9], [3, 9], [2, 9], [1, 9]] | 15 | 0.02926492691040039 | 15 | 8 | 2 | ["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0... | ["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0... | ["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0... |
22 | Given 7 labeled water jugs with capacities 16, 124, 57, 40, 99, 45, 72, 98 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 263, 341, 360 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 98, 3], ["+", 124, 3], ["+", 40, 3], ["+", 98, 3], ["+", 45, 2], ["+", 98, 2], ["+", 99, 2], ["+", 99, 2], ["+", 40, 1], ["+", 99, 1], ["+", 124, 1]] | 11 | 0.04340982437133789 | 11 | 48 | 3 | [[16, 124, 57, 40, 99, 45, 72, 98], [263, 341, 360]] | [[16, 124, 57, 40, 99, 45, 72, 98], [263, 341, 360]] | ["[16, 124, 57, 40, 99, 45, 72, 98]", "[263, 341, 360]"] |
23 | 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 | [53, 28, 43, 34, 59, 29, 76, 53, 28, 43, 34, 59, 29, 76, 53, 29, 43, 34, 59, 62, 76, 53, 29, 28] | 24 | 0.11378741264343262 | 24 | 4 | 9 | [[[62, 43, 28], [59, 34, 53], [29, 76, "_"]]] | [[[62, 43, 28], [59, 34, 53], [29, 76, "_"]]] | ["[[62, 43, 28], [59, 34, 53], [29, 76, '_']]"] |
23 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-left"] | 8 | 0.1897449493408203 | 8 | 4 | 20 | [[["m", "s", "_", "n", "g"], ["a", "o", "i", "e", "h"], ["h", "i", "p", "e", "s"], ["a", "g", "l", "r", "y"]]] | [[["m", "s", "_", "n", "g"], ["a", "o", "i", "e", "h"], ["h", "i", "p", "e", "s"], ["a", "g", "l", "r", "y"]], ["song", "amish", "hiper", "agley"]] | ["[['m', 's', '_', 'n', 'g'], ['a', 'o', 'i', 'e', 'h'], ['h', 'i', 'p', 'e', 's'], ['a', 'g', 'l', 'r', 'y']]", "['song', 'amish', 'hiper', 'agley']"] |
23 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["K", "E", "N", "X", "P", "W", "P", "N"] | 8 | 0.02664780616760254 | 8 | 11 | 14 | [[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0,... | [[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0,... | ["[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0... |
23 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6], such that the sum of the chosen coins adds up to 309. Each coin in the list is unique and can only be used once. Also coi... | coin_exchange | subset_sum | 16 | [84, 28, 10, 13, 17, 4, 5, 15, 85, 30, 14, 4] | 62 | 0.03924393653869629 | 12 | 27 | 27 | [[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6]] | [[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6], {"15": 2, "18": 9, "28": 4, "84": 10, "2": 1, "24": 19, "30": 12, "5": 2, "9": 9, "21": 9, "11": 10, "16": 14, "4": 2, "17": 2, "85": 18, "6": 5, "8": 6, "13": 2, "10": 4, "25": 11, "20": 19, "14": 2}, 309] | ["[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6]", "{15: 2, 18: 9, 28: 4, 84: 10, 2: 1, 24: 19, 30: 12, 5: 2, 9: 9, 21: 9, 11: 10, 16: 14, 4: 2, 17: 2, 85: 18, 6: 5, 8: 6, 13: 2, 10: 4, 25: 11, 20: 19, 14: 2}", "309"] |
23 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1]] | 13 | 0.13763999938964844 | 13 | 6 | 12 | [[["Red", "Red", "Blue", "Green"], ["Blue", "Green", "Blue", "Blue"], ["Red", "Green", "Green", "Red"]], 6] | [[["Red", "Red", "Blue", "Green"], ["Blue", "Green", "Blue", "Blue"], ["Red", "Green", "Green", "Red"]], 6] | ["[['Red', 'Red', 'Blue', 'Green'], ['Blue', 'Green', 'Blue', 'Blue'], ['Red', 'Green', 'Green', 'Red']]", "6"] |
23 | We have a 3x3 numerical grid, with numbers ranging from 23 to 66 (23 included in the range but 66 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 0, 23], [0, 1, 24], [1, 0, 25], [1, 1, 26], [1, 2, 48]] | 352 | 1.0622022151947021 | 5 | 43 | 9 | ["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", 23, 66] | ["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", 23, 66] | ["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", "23", "66"] |
23 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 12 to 46. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 71, and sum of row 1 must be 82. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 7 | [[0, 0, 13], [0, 1, 14], [0, 2, 12], [1, 0, 17], [1, 1, 42], [1, 2, 23], [2, 0, 16], [2, 1, 15]] | 171 | 8.869033575057983 | 8 | 29 | 9 | ["[['', '', ''], ['', '', ''], ['', '', '19']]", 3, 12, 46] | ["[['', '', ''], ['', '', ''], ['', '', '19']]", 12, 46, [1, 2], [1, 2], [71], [82], 70] | ["[['', '', ''], ['', '', ''], ['', '', '19']]", "12", "46", "[None, 71, None]", "[None, 82, None]", "70"] |
23 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[3, 2], [0, 2], [0, 2], [0, 5], [1, 5], [1, 0], [1, 4], [3, 4], [3, 0], [3, 4], [1, 5]] | 43 | 0.04391932487487793 | 11 | 30 | 12 | [[["Green", "Green", "Blue", "Red"], ["Blue", "Red", "Yellow", "Blue"], [], ["Green", "Yellow", "Red", "Yellow"], [], []], 4, {"0": 2, "1": 7, "2": 4, "3": 7, "4": 6, "5": 3}] | [[["Green", "Green", "Blue", "Red"], ["Blue", "Red", "Yellow", "Blue"], [], ["Green", "Yellow", "Red", "Yellow"], [], []], 4, {"0": 2, "1": 7, "2": 4, "3": 7, "4": 6, "5": 3}, 3] | ["[['Green', 'Green', 'Blue', 'Red'], ['Blue', 'Red', 'Yellow', 'Blue'], [], ['Green', 'Yellow', 'Red', 'Yellow'], [], []]", "{0: 2, 1: 7, 2: 4, 3: 7, 4: 6, 5: 3}", "4", "3"] |
23 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 8) to his destination workshop at index (3, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 8], [4, 8], [4, 7], [4, 6], [3, 6], [3, 5], [2, 5], [2, 4], [3, 4], [3, 3], [4, 3], [4, 2], [4, 1], [3, 1], [3, 0]] | 105 | 0.02059459686279297 | 15 | 4 | 4 | [[["x", "x", "x", "x", "x", "8", "x", "15", "18", "10"], ["4", "5", "10", "6", "20", "2", "12", "x", "x", "x"], ["19", "6", "19", "7", "6", "2", "x", "15", "x", "14"], ["16", "17", "x", "2", "3", "7", "4", "x", "18", "6"], ["x", "2", "1", "19", "7", "10", "18", "5", "3", "19"], ["8", "5", "x", "1", "x", "10", "17", "x"... | [[["x", "x", "x", "x", "x", "8", "x", "15", "18", "10"], ["4", "5", "10", "6", "20", "2", "12", "x", "x", "x"], ["19", "6", "19", "7", "6", "2", "x", "15", "x", "14"], ["16", "17", "x", "2", "3", "7", "4", "x", "18", "6"], ["x", "2", "1", "19", "7", "10", "18", "5", "3", "19"], ["8", "5", "x", "1", "x", "10", "17", "x"... | ["[['x', 'x', 'x', 'x', 'x', '8', 'x', '15', '18', '10'], ['4', '5', '10', '6', '20', '2', '12', 'x', 'x', 'x'], ['19', '6', '19', '7', '6', '2', 'x', '15', 'x', '14'], ['16', '17', 'x', '2', '3', '7', '4', 'x', '18', '6'], ['x', '2', '1', '19', '7', '10', '18', '5', '3', '19'], ['8', '5', 'x', '1', 'x', '10', '17', 'x... |
23 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[1, 9], [2, 8], [3, 8], [4, 7], [5, 6], [5, 5], [6, 5], [6, 4], [6, 3], [7, 3], [8, 3]] | 11 | 0.028395891189575195 | 11 | 8 | 2 | ["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0... | ["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0... | ["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0... |
23 | Given 7 labeled water jugs with capacities 118, 15, 88, 145, 84, 14, 107, 31 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 226, 258, 296 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount... | water_jug | subset_sum | 5 | [["+", 31, 3], ["+", 118, 3], ["+", 15, 3], ["+", 118, 3], ["+", 14, 3], ["+", 15, 2], ["+", 84, 2], ["+", 145, 2], ["+", 14, 2], ["+", 88, 1], ["+", 107, 1], ["+", 31, 1]] | 12 | 0.05219745635986328 | 12 | 48 | 3 | [[118, 15, 88, 145, 84, 14, 107, 31], [226, 258, 296]] | [[118, 15, 88, 145, 84, 14, 107, 31], [226, 258, 296]] | ["[118, 15, 88, 145, 84, 14, 107, 31]", "[226, 258, 296]"] |
24 | 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 | [92, 35, 32, 97, 75, 44, 97, 32, 35, 97, 94, 58, 44, 75, 32, 35, 97, 94, 75, 32, 35, 75, 58, 44] | 24 | 0.1467905044555664 | 24 | 4 | 9 | [[[35, 92, "_"], [32, 44, 94], [97, 75, 58]]] | [[[35, 92, "_"], [32, 44, 94], [97, 75, 58]]] | ["[[35, 92, '_'], [32, 44, 94], [97, 75, 58]]"] |
24 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 8 | 0.184800386428833 | 8 | 4 | 20 | [[["_", "p", "h", "m", "p"], ["s", "a", "d", "r", "e"], ["i", "u", "n", "i", "r"], ["u", "a", "z", "e", "n"]]] | [[["_", "p", "h", "m", "p"], ["s", "a", "d", "r", "e"], ["i", "u", "n", "i", "r"], ["u", "a", "z", "e", "n"]], ["pimp", "sadhe", "aurir", "unzen"]] | ["[['_', 'p', 'h', 'm', 'p'], ['s', 'a', 'd', 'r', 'e'], ['i', 'u', 'n', 'i', 'r'], ['u', 'a', 'z', 'e', 'n']]", "['pimp', 'sadhe', 'aurir', 'unzen']"] |
24 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["D", "H", "A", "B", "W", "L", "J", "L", "O", "B"] | 10 | 0.0295867919921875 | 10 | 11 | 14 | [[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0,... | [[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0,... | ["[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0... |
24 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2], such that the sum of the chosen coins adds up to 305. Each coin in the list is unique and can only be used once. Also coin... | coin_exchange | subset_sum | 17 | [98, 16, 29, 24, 16, 23, 99] | 54 | 0.034387826919555664 | 7 | 27 | 27 | [[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2]] | [[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2], {"24": 5, "26": 16, "28": 20, "2": 1, "22": 16, "25": 11, "27": 7, "11": 4, "6": 3, "99": 17, "8": 5, "7": 5, "5": 3, "23": 5, "4": 4, "98": 16, "16": 3, "29": 5, "20": 19}, 305] | ["[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2]", "{24: 5, 26: 16, 28: 20, 2: 1, 22: 16, 25: 11, 27: 7, 11: 4, 6: 3, 99: 17, 8: 5, 7: 5, 5: 3, 23: 5, 4: 4, 98: 16, 16: 3, 29: 5, 20: 19}", "305"] |
24 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 2], [1, 2], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1]] | 21 | 3.7056467533111572 | 21 | 6 | 12 | [[["Red", "Blue", "Green", "Blue"], ["Red", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Green"]], 6] | [[["Red", "Blue", "Green", "Blue"], ["Red", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Green"]], 6] | ["[['Red', 'Blue', 'Green', 'Blue'], ['Red', 'Red', 'Red', 'Green'], ['Blue', 'Green', 'Blue', 'Green']]", "6"] |
24 | We have a 3x3 numerical grid, with numbers ranging from 50 to 93 (50 included in the range but 93 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 8 | [[0, 1, 51], [0, 2, 50], [1, 2, 69], [2, 0, 52], [2, 1, 70]] | 578 | 0.18818449974060059 | 5 | 43 | 9 | ["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", 50, 93] | ["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", 50, 93] | ["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", "50", "93"] |
24 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 9 to 48. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 115, and sum of row 1 must be 95. Also, the sum of the numbers in the diagonal from the top right to the... | magic_square | underdetermined_system | 7 | [[0, 0, 9], [0, 1, 23], [0, 2, 44], [1, 0, 11], [1, 1, 47], [1, 2, 37], [2, 2, 10]] | 268 | 97.89336490631104 | 7 | 29 | 9 | ["[['', '', ''], ['', '', ''], ['42', '45', '']]", 3, 9, 48] | ["[['', '', ''], ['', '', ''], ['42', '45', '']]", 9, 48, [1, 2], [1, 2], [115], [95], 133] | ["[['', '', ''], ['', '', ''], ['42', '45', '']]", "9", "48", "[None, 115, None]", "[None, 95, None]", "133"] |
24 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[3, 4], [2, 4], [2, 0], [2, 4], [3, 2], [5, 1], [5, 2], [5, 0], [3, 1], [3, 0], [5, 1]] | 51 | 0.07999825477600098 | 11 | 30 | 12 | [[[], [], ["Green", "Yellow", "Green", "Red"], ["Green", "Red", "Blue", "Yellow"], [], ["Blue", "Red", "Yellow", "Blue"]], 4, {"0": 5, "1": 1, "2": 6, "3": 7, "4": 7, "5": 7}] | [[[], [], ["Green", "Yellow", "Green", "Red"], ["Green", "Red", "Blue", "Yellow"], [], ["Blue", "Red", "Yellow", "Blue"]], 4, {"0": 5, "1": 1, "2": 6, "3": 7, "4": 7, "5": 7}, 3] | ["[[], [], ['Green', 'Yellow', 'Green', 'Red'], ['Green', 'Red', 'Blue', 'Yellow'], [], ['Blue', 'Red', 'Yellow', 'Blue']]", "{0: 5, 1: 1, 2: 6, 3: 7, 4: 7, 5: 7}", "4", "3"] |
24 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 1) to his destination workshop at index (3, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 1], [5, 2], [5, 3], [5, 4], [4, 4], [4, 5], [4, 6], [4, 7], [3, 7], [3, 8], [3, 9]] | 56 | 0.020661354064941406 | 11 | 4 | 4 | [[["18", "19", "9", "x", "x", "x", "3", "x", "8", "x"], ["13", "2", "3", "15", "3", "x", "8", "9", "x", "x"], ["x", "6", "18", "1", "20", "7", "16", "8", "1", "19"], ["x", "x", "x", "20", "14", "x", "19", "11", "9", "6"], ["2", "x", "x", "6", "5", "6", "7", "1", "x", "8"], ["17", "9", "5", "3", "3", "x", "16", "18", "x... | [[["18", "19", "9", "x", "x", "x", "3", "x", "8", "x"], ["13", "2", "3", "15", "3", "x", "8", "9", "x", "x"], ["x", "6", "18", "1", "20", "7", "16", "8", "1", "19"], ["x", "x", "x", "20", "14", "x", "19", "11", "9", "6"], ["2", "x", "x", "6", "5", "6", "7", "1", "x", "8"], ["17", "9", "5", "3", "3", "x", "16", "18", "x... | ["[['18', '19', '9', 'x', 'x', 'x', '3', 'x', '8', 'x'], ['13', '2', '3', '15', '3', 'x', '8', '9', 'x', 'x'], ['x', '6', '18', '1', '20', '7', '16', '8', '1', '19'], ['x', 'x', 'x', '20', '14', 'x', '19', '11', '9', '6'], ['2', 'x', 'x', '6', '5', '6', '7', '1', 'x', '8'], ['17', '9', '5', '3', '3', 'x', '16', '18', '... |
24 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[9, 9], [9, 8], [8, 7], [7, 6], [7, 5], [7, 4], [7, 3], [6, 2], [6, 1], [5, 1], [4, 1]] | 11 | 0.030521631240844727 | 11 | 8 | 2 | ["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0... | ["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0... | ["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0... |
24 | Given 7 labeled water jugs with capacities 33, 56, 108, 53, 65, 54, 52, 59 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 168, 239, 307 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 59, 3], ["+", 108, 3], ["+", 108, 3], ["-", 33, 3], ["+", 65, 3], ["+", 108, 2], ["+", 108, 2], ["-", 33, 2], ["+", 56, 2], ["+", 53, 1], ["+", 56, 1], ["+", 59, 1]] | 12 | 0.04154396057128906 | 12 | 48 | 3 | [[33, 56, 108, 53, 65, 54, 52, 59], [168, 239, 307]] | [[33, 56, 108, 53, 65, 54, 52, 59], [168, 239, 307]] | ["[33, 56, 108, 53, 65, 54, 52, 59]", "[168, 239, 307]"] |
25 | 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 | [76, 41, 13, 76, 41, 13, 66, 85, 21, 74, 13, 41, 76, 45, 85, 66, 74, 13, 41, 74, 45, 76, 74, 41] | 24 | 0.10150957107543945 | 24 | 4 | 9 | [[[45, 13, "_"], [66, 41, 76], [85, 21, 74]]] | [[[45, 13, "_"], [66, 41, 76], [85, 21, 74]]] | ["[[45, 13, '_'], [66, 41, 76], [85, 21, 74]]"] |
25 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 8 | 0.21672630310058594 | 8 | 4 | 20 | [[["i", "g", "u", "h", "a"], ["n", "o", "s", "u", "s"], ["c", "n", "g", "a", "_"], ["j", "u", "u", "p", "h"]]] | [[["i", "g", "u", "h", "a"], ["n", "o", "s", "u", "s"], ["c", "n", "g", "a", "_"], ["j", "u", "u", "p", "h"]], ["guha", "nisus", "uncap", "jough"]] | ["[['i', 'g', 'u', 'h', 'a'], ['n', 'o', 's', 'u', 's'], ['c', 'n', 'g', 'a', '_'], ['j', 'u', 'u', 'p', 'h']]", "['guha', 'nisus', 'uncap', 'jough']"] |
25 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["M", "V", "F", "Y", "O", "L", "X", "J", "X", "K", "Y"] | 11 | 0.02562737464904785 | 11 | 11 | 14 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1,... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1,... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1... |
25 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12], such that the sum of the chosen coins adds up to 284. Each coin in the list is unique an... | coin_exchange | subset_sum | 18 | [7, 13, 21, 23, 25, 65, 28, 22, 23, 22, 27, 8] | 52 | 0.03629875183105469 | 12 | 35 | 35 | [[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12]] | [[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12], {"20": 12, "21": 3, "5": 2, "3": 2, "7": 1, "15": 8, "8": 7, "27": 6, "17": 8, "18": 14, "28": 5, "13": 1, "23": 4, "65": 8, "26": 8, "22": 5, "25": 3, "11": 11, "12": 8, "19": 19, "10"... | ["[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12]", "{20: 12, 21: 3, 5: 2, 3: 2, 7: 1, 15: 8, 8: 7, 27: 6, 17: 8, 18: 14, 28: 5, 13: 1, 23: 4, 65: 8, 26: 8, 22: 5, 25: 3, 11: 11, 12: 8, 19: 19, 10: 7}", "284"] |
25 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 7 | [[2, 0], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0]] | 10 | 0.04879570007324219 | 10 | 6 | 12 | [[["Green", "Green", "Red", "Red"], ["Blue", "Blue", "Blue", "Blue"], ["Green", "Red", "Green", "Red"]], 6] | [[["Green", "Green", "Red", "Red"], ["Blue", "Blue", "Blue", "Blue"], ["Green", "Red", "Green", "Red"]], 6] | ["[['Green', 'Green', 'Red', 'Red'], ['Blue', 'Blue', 'Blue', 'Blue'], ['Green', 'Red', 'Green', 'Red']]", "6"] |
25 | We have a 3x3 numerical grid, with numbers ranging from 29 to 72 (29 included in the range but 72 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 0, 29], [0, 1, 31], [0, 2, 53], [1, 1, 40], [2, 1, 41], [2, 2, 30]] | 347 | 36.68832039833069 | 6 | 43 | 9 | ["[['', '', ''], ['39', '', '52'], ['60', '', '']]", 29, 72] | ["[['', '', ''], ['39', '', '52'], ['60', '', '']]", 29, 72] | ["[['', '', ''], ['39', '', '52'], ['60', '', '']]", "29", "72"] |
25 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 9 to 48. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 67, and sum of row 1 must be 60. Also, the sum of the numbers in the diagonal from the top right to the ... | magic_square | underdetermined_system | 6 | [[0, 0, 9], [0, 2, 10], [1, 0, 12], [1, 1, 34], [1, 2, 14], [2, 1, 17], [2, 2, 11]] | 168 | 0.5386793613433838 | 7 | 34 | 9 | ["[['', '16', ''], ['', '', ''], ['45', '', '']]", 3, 9, 48] | ["[['', '16', ''], ['', '', ''], ['45', '', '']]", 9, 48, [1, 2], [1, 2], [67], [60], 89] | ["[['', '16', ''], ['', '', ''], ['45', '', '']]", "9", "48", "[None, 67, None]", "[None, 60, None]", "89"] |
25 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[2, 0], [4, 3], [4, 5], [4, 0], [2, 4], [2, 4], [2, 3], [1, 2], [1, 3], [1, 0], [1, 2], [5, 2]] | 39 | 0.023729562759399414 | 12 | 30 | 12 | [[[], ["Green", "Blue", "Yellow", "Green"], ["Yellow", "Red", "Red", "Blue"], [], ["Blue", "Green", "Yellow", "Red"], []], 4, {"0": 4, "1": 3, "2": 2, "3": 4, "4": 2, "5": 5}] | [[[], ["Green", "Blue", "Yellow", "Green"], ["Yellow", "Red", "Red", "Blue"], [], ["Blue", "Green", "Yellow", "Red"], []], 4, {"0": 4, "1": 3, "2": 2, "3": 4, "4": 2, "5": 5}, 3] | ["[[], ['Green', 'Blue', 'Yellow', 'Green'], ['Yellow', 'Red', 'Red', 'Blue'], [], ['Blue', 'Green', 'Yellow', 'Red'], []]", "{0: 4, 1: 3, 2: 2, 3: 4, 4: 2, 5: 5}", "4", "3"] |
25 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 9) to his destination workshop at index (5, 2), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[2, 9], [2, 8], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [4, 2], [5, 2]] | 105 | 0.022072553634643555 | 11 | 4 | 4 | [[["x", "x", "6", "x", "x", "x", "x", "15", "x", "x"], ["x", "17", "13", "13", "x", "12", "x", "3", "10", "2"], ["x", "5", "13", "15", "4", "x", "x", "20", "6", "2"], ["x", "9", "x", "6", "2", "16", "18", "9", "13", "x"], ["x", "x", "15", "17", "x", "10", "11", "x", "x", "x"], ["3", "x", "3", "17", "8", "x", "1", "x", ... | [[["x", "x", "6", "x", "x", "x", "x", "15", "x", "x"], ["x", "17", "13", "13", "x", "12", "x", "3", "10", "2"], ["x", "5", "13", "15", "4", "x", "x", "20", "6", "2"], ["x", "9", "x", "6", "2", "16", "18", "9", "13", "x"], ["x", "x", "15", "17", "x", "10", "11", "x", "x", "x"], ["3", "x", "3", "17", "8", "x", "1", "x", ... | ["[['x', 'x', '6', 'x', 'x', 'x', 'x', '15', 'x', 'x'], ['x', '17', '13', '13', 'x', '12', 'x', '3', '10', '2'], ['x', '5', '13', '15', '4', 'x', 'x', '20', '6', '2'], ['x', '9', 'x', '6', '2', '16', '18', '9', '13', 'x'], ['x', 'x', '15', '17', 'x', '10', '11', 'x', 'x', 'x'], ['3', 'x', '3', '17', '8', 'x', '1', 'x',... |
25 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[0, 0], [1, 0], [1, 1], [2, 1], [3, 2], [4, 2], [4, 3], [4, 4], [5, 4], [6, 5], [7, 6]] | 11 | 0.031239748001098633 | 11 | 8 | 2 | ["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1... | ["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1... | ["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1... |
25 | Given 7 labeled water jugs with capacities 75, 20, 64, 106, 88, 13, 107, 131 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 287, 394, 455 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount... | water_jug | subset_sum | 5 | [["+", 75, 3], ["+", 131, 3], ["+", 131, 3], ["-", 13, 3], ["+", 131, 3], ["+", 106, 2], ["+", 106, 2], ["+", 75, 2], ["+", 107, 2], ["+", 75, 1], ["+", 106, 1], ["+", 106, 1]] | 12 | 0.05149412155151367 | 12 | 48 | 3 | [[75, 20, 64, 106, 88, 13, 107, 131], [287, 394, 455]] | [[75, 20, 64, 106, 88, 13, 107, 131], [287, 394, 455]] | ["[75, 20, 64, 106, 88, 13, 107, 131]", "[287, 394, 455]"] |
26 | 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 | [79, 89, 94, 79, 89, 94, 43, 56, 94, 89, 79, 43, 52, 25] | 14 | 0.0211181640625 | 14 | 4 | 9 | [[[56, 79, "_"], [43, 89, 94], [36, 52, 25]]] | [[[56, 79, "_"], [43, 89, 94], [36, 52, 25]]] | ["[[56, 79, '_'], [43, 89, 94], [36, 52, 25]]"] |
26 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-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-left", "down-left", "up-left", "up-left"] | 18 | 0.2016615867614746 | 18 | 4 | 20 | [[["t", "w", "y", "l", "_"], ["s", "a", "u", "f", "t"], ["o", "a", "e", "m", "n"], ["f", "l", "d", "m", "d"]]] | [[["t", "w", "y", "l", "_"], ["s", "a", "u", "f", "t"], ["o", "a", "e", "m", "n"], ["f", "l", "d", "m", "d"]], ["wolf", "stunt", "lammy", "faded"]] | ["[['t', 'w', 'y', 'l', '_'], ['s', 'a', 'u', 'f', 't'], ['o', 'a', 'e', 'm', 'n'], ['f', 'l', 'd', 'm', 'd']]", "['wolf', 'stunt', 'lammy', 'faded']"] |
26 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["I", "T", "L", "K", "H", "W", "R", "W", "C", "L"] | 10 | 0.03812885284423828 | 10 | 11 | 14 | [[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1,... | [[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1,... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1... |
26 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2], such that the sum of the chosen coins adds up to 307. Each coin in the list is unique and can o... | coin_exchange | subset_sum | 19 | [6, 9, 25, 25, 71, 6, 19, 8, 23, 23, 23, 6, 7, 9, 15, 15, 17] | 51 | 0.04102158546447754 | 17 | 34 | 34 | [[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2]] | [[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2], {"24": 14, "2": 1, "25": 2, "26": 14, "18": 12, "27": 15, "29": 19, "19": 3, "15": 7, "9": 1, "8": 1, "21": 18, "6": 1, "71": 3, "23": 4, "17": 7, "7": 2, "22": 11, "3": 1}, 307] | ["[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2]", "{24: 14, 2: 1, 25: 2, 26: 14, 18: 12, 27: 15, 29: 19, 19: 3, 15: 7, 9: 1, 8: 1, 21: 18, 6: 1, 71: 3, 23: 4, 17: 7, 7: 2, 22: 11, 3: 1}", "307"] |
26 | The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 8 | [[0, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2]] | 13 | 0.2634403705596924 | 13 | 6 | 12 | [[["Red", "Blue", "Blue", "Red"], ["Green", "Green", "Blue", "Blue"], ["Green", "Green", "Red", "Red"]], 7] | [[["Red", "Blue", "Blue", "Red"], ["Green", "Green", "Blue", "Blue"], ["Green", "Green", "Red", "Red"]], 7] | ["[['Red', 'Blue', 'Blue', 'Red'], ['Green', 'Green', 'Blue', 'Blue'], ['Green', 'Green', 'Red', 'Red']]", "7"] |
26 | We have a 3x3 numerical grid, with numbers ranging from 17 to 60 (17 included in the range but 60 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 1, 18], [0, 2, 17], [1, 0, 30], [1, 1, 20], [1, 2, 19], [2, 2, 56]] | 261 | 27.528469800949097 | 6 | 43 | 9 | ["[['29', '', ''], ['', '', ''], ['36', '55', '']]", 17, 60] | ["[['29', '', ''], ['', '', ''], ['36', '55', '']]", 17, 60] | ["[['29', '', ''], ['', '', ''], ['36', '55', '']]", "17", "60"] |
26 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 26 to 65. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 150, and sum of row 1 must be 135. Also, the sum of the numbers in the diagonal from the top right to t... | magic_square | underdetermined_system | 6 | [[0, 0, 26], [0, 1, 54], [0, 2, 27], [1, 0, 30], [1, 1, 64], [1, 2, 41], [2, 0, 28], [2, 2, 29]] | 331 | 25.04846739768982 | 8 | 34 | 9 | ["[['', '', ''], ['', '', ''], ['', '32', '']]", 3, 26, 65] | ["[['', '', ''], ['', '', ''], ['', '32', '']]", 26, 65, [1, 2], [1, 2], [150], [135], 119] | ["[['', '', ''], ['', '', ''], ['', '32', '']]", "26", "65", "[None, 150, None]", "[None, 135, None]", "119"] |
26 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 4], [1, 5], [2, 4], [2, 5], [2, 3], [0, 2], [3, 4], [0, 3], [0, 2], [1, 0], [1, 5], [0, 1], [3, 1]] | 73 | 0.024808883666992188 | 13 | 30 | 12 | [[["Blue", "Yellow", "Red", "Yellow"], ["Green", "Red", "Green", "Red"], ["Blue", "Green", "Blue", "Yellow"], [], [], []], 4, {"0": 4, "1": 4, "2": 7, "3": 7, "4": 5, "5": 6}] | [[["Blue", "Yellow", "Red", "Yellow"], ["Green", "Red", "Green", "Red"], ["Blue", "Green", "Blue", "Yellow"], [], [], []], 4, {"0": 4, "1": 4, "2": 7, "3": 7, "4": 5, "5": 6}, 3] | ["[['Blue', 'Yellow', 'Red', 'Yellow'], ['Green', 'Red', 'Green', 'Red'], ['Blue', 'Green', 'Blue', 'Yellow'], [], [], []]", "{0: 4, 1: 4, 2: 7, 3: 7, 4: 5, 5: 6}", "4", "3"] |
26 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 9) to his destination workshop at index (3, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[5, 9], [5, 8], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [3, 4], [3, 3], [3, 2], [3, 1]] | 67 | 0.02885293960571289 | 11 | 4 | 4 | [[["7", "x", "19", "11", "6", "x", "4", "15", "9", "3"], ["x", "x", "13", "x", "8", "17", "x", "x", "12", "16"], ["x", "x", "2", "x", "15", "8", "x", "13", "4", "x"], ["13", "11", "3", "3", "3", "x", "x", "x", "x", "x"], ["1", "16", "14", "6", "14", "17", "4", "9", "1", "x"], ["x", "4", "9", "x", "17", "17", "x", "13",... | [[["7", "x", "19", "11", "6", "x", "4", "15", "9", "3"], ["x", "x", "13", "x", "8", "17", "x", "x", "12", "16"], ["x", "x", "2", "x", "15", "8", "x", "13", "4", "x"], ["13", "11", "3", "3", "3", "x", "x", "x", "x", "x"], ["1", "16", "14", "6", "14", "17", "4", "9", "1", "x"], ["x", "4", "9", "x", "17", "17", "x", "13",... | ["[['7', 'x', '19', '11', '6', 'x', '4', '15', '9', '3'], ['x', 'x', '13', 'x', '8', '17', 'x', 'x', '12', '16'], ['x', 'x', '2', 'x', '15', '8', 'x', '13', '4', 'x'], ['13', '11', '3', '3', '3', 'x', 'x', 'x', 'x', 'x'], ['1', '16', '14', '6', '14', '17', '4', '9', '1', 'x'], ['x', '4', '9', 'x', '17', '17', 'x', '13'... |
26 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[8, 6], [7, 5], [7, 4], [6, 3], [5, 3], [4, 3], [3, 3], [2, 2], [1, 2], [0, 2], [0, 1]] | 11 | 0.030196428298950195 | 11 | 8 | 2 | ["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0... | ["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0... | ["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0... |
26 | Given 7 labeled water jugs with capacities 24, 132, 149, 62, 120, 61, 42 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 298, 430, 468 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ... | water_jug | subset_sum | 5 | [["+", 42, 3], ["+", 132, 3], ["+", 132, 3], ["+", 42, 3], ["+", 120, 3], ["+", 132, 2], ["+", 149, 2], ["+", 149, 2], ["+", 149, 1], ["+", 149, 1]] | 10 | 0.0418705940246582 | 10 | 42 | 3 | [[24, 132, 149, 62, 120, 61, 42], [298, 430, 468]] | [[24, 132, 149, 62, 120, 61, 42], [298, 430, 468]] | ["[24, 132, 149, 62, 120, 61, 42]", "[298, 430, 468]"] |
27 | 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 | [99, 23, 50, 14, 73, 50, 79, 99, 23, 63, 14, 73, 50, 79, 73, 50, 79, 85, 99, 73, 63, 14] | 22 | 0.036279916763305664 | 22 | 4 | 9 | [[[85, 73, 14], [79, 23, 50], ["_", 99, 63]]] | [[[85, 73, 14], [79, 23, 50], ["_", 99, 63]]] | ["[[85, 73, 14], [79, 23, 50], ['_', 99, 63]]"] |
27 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-right", "down-right", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"] | 20 | 0.26288700103759766 | 20 | 4 | 20 | [[["_", "b", "p", "i", "s"], ["d", "u", "r", "n", "c"], ["l", "i", "o", "e", "n"], ["s", "n", "e", "o", "t"]]] | [[["_", "b", "p", "i", "s"], ["d", "u", "r", "n", "c"], ["l", "i", "o", "e", "n"], ["s", "n", "e", "o", "t"]], ["bois", "duroc", "linen", "spent"]] | ["[['_', 'b', 'p', 'i', 's'], ['d', 'u', 'r', 'n', 'c'], ['l', 'i', 'o', 'e', 'n'], ['s', 'n', 'e', 'o', 't']]", "['bois', 'duroc', 'linen', 'spent']"] |
27 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["D", "I", "Z", "J", "X", "H", "B", "Z", "W", "H"] | 10 | 0.03222942352294922 | 10 | 11 | 14 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1,... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1,... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1... |
27 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14], such that the sum of the chosen coins adds up to 301. Each coin in the list is unique and can only ... | coin_exchange | subset_sum | 20 | [22, 10, 15, 10, 8, 15, 161, 28, 22, 10] | 38 | 0.0371396541595459 | 10 | 32 | 32 | [[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14]] | [[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14], {"15": 2, "17": 10, "10": 3, "12": 10, "21": 12, "4": 2, "22": 1, "11": 6, "26": 9, "14": 7, "24": 12, "161": 16, "20": 15, "9": 8, "8": 1, "13": 10, "28": 6, "7": 6, "25": 6, "19": 15}, 301] | ["[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14]", "{15: 2, 17: 10, 10: 3, 12: 10, 21: 12, 4: 2, 22: 1, 11: 6, 26: 9, 14: 7, 24: 12, 161: 16, 20: 15, 9: 8, 8: 1, 13: 10, 28: 6, 7: 6, 25: 6, 19: 15}", "301"] |
27 | 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], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1]] | 16 | 1.1768579483032227 | 16 | 6 | 12 | [[["Blue", "Red", "Red", "Blue"], ["Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Green"]], 7] | [[["Blue", "Red", "Red", "Blue"], ["Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Green"]], 7] | ["[['Blue', 'Red', 'Red', 'Blue'], ['Green', 'Red', 'Red', 'Green'], ['Blue', 'Blue', 'Green', 'Green']]", "7"] |
27 | We have a 3x3 numerical grid, with numbers ranging from 46 to 89 (46 included in the range but 89 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ... | consecutive_grid | underdetermined_system | 9 | [[0, 1, 47], [0, 2, 46], [1, 1, 51], [1, 2, 53], [2, 0, 48], [2, 1, 54]] | 485 | 0.19235539436340332 | 6 | 43 | 9 | ["[['52', '', ''], ['50', '', ''], ['', '', '69']]", 46, 89] | ["[['52', '', ''], ['50', '', ''], ['', '', '69']]", 46, 89] | ["[['52', '', ''], ['50', '', ''], ['', '', '69']]", "46", "89"] |
27 | In the magic square problem, a 3x3 grid is filled with unique integers ranging from 26 to 65. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 93, and sum of row 1 must be 135. Also, the sum of the numbers in the diagonal from the top right to th... | magic_square | underdetermined_system | 6 | [[0, 1, 26], [0, 2, 29], [1, 0, 31], [1, 1, 40], [1, 2, 64], [2, 0, 37], [2, 1, 27], [2, 2, 28]] | 329 | 29.752150774002075 | 8 | 34 | 9 | ["[['47', '', ''], ['', '', ''], ['', '', '']]", 3, 26, 65] | ["[['47', '', ''], ['', '', ''], ['', '', '']]", 26, 65, [1, 2], [1, 2], [93], [135], 106] | ["[['47', '', ''], ['', '', ''], ['', '', '']]", "26", "65", "[None, 93, None]", "[None, 135, None]", "106"] |
27 | In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 1 | [[0, 2], [5, 3], [5, 2], [0, 4], [0, 3], [0, 5], [1, 0], [1, 0], [1, 3], [4, 0], [1, 2]] | 38 | 0.03287506103515625 | 11 | 30 | 12 | [[["Red", "Blue", "Green", "Yellow"], ["Blue", "Blue", "Green", "Red"], [], [], [], ["Green", "Red", "Yellow", "Yellow"]], 4, {"0": 3, "1": 6, "2": 2, "3": 4, "4": 6, "5": 5}] | [[["Red", "Blue", "Green", "Yellow"], ["Blue", "Blue", "Green", "Red"], [], [], [], ["Green", "Red", "Yellow", "Yellow"]], 4, {"0": 3, "1": 6, "2": 2, "3": 4, "4": 6, "5": 5}, 3] | ["[['Red', 'Blue', 'Green', 'Yellow'], ['Blue', 'Blue', 'Green', 'Red'], [], [], [], ['Green', 'Red', 'Yellow', 'Yellow']]", "{0: 3, 1: 6, 2: 2, 3: 4, 4: 6, 5: 5}", "4", "3"] |
27 | 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, 8) to his destination workshop at index (6, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 2 | [[3, 8], [2, 8], [2, 7], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [5, 3], [5, 2], [5, 1], [5, 0], [6, 0]] | 154 | 0.028217792510986328 | 14 | 4 | 4 | [[["19", "x", "3", "x", "x", "x", "13", "x", "12", "x"], ["x", "x", "8", "x", "15", "18", "11", "12", "x", "7"], ["x", "8", "x", "x", "15", "20", "17", "12", "2", "8"], ["x", "x", "4", "13", "2", "14", "19", "13", "15", "19"], ["13", "2", "x", "8", "x", "17", "13", "x", "x", "12"], ["2", "20", "20", "14", "x", "x", "15... | [[["19", "x", "3", "x", "x", "x", "13", "x", "12", "x"], ["x", "x", "8", "x", "15", "18", "11", "12", "x", "7"], ["x", "8", "x", "x", "15", "20", "17", "12", "2", "8"], ["x", "x", "4", "13", "2", "14", "19", "13", "15", "19"], ["13", "2", "x", "8", "x", "17", "13", "x", "x", "12"], ["2", "20", "20", "14", "x", "x", "15... | ["[['19', 'x', '3', 'x', 'x', 'x', '13', 'x', '12', 'x'], ['x', 'x', '8', 'x', '15', '18', '11', '12', 'x', '7'], ['x', '8', 'x', 'x', '15', '20', '17', '12', '2', '8'], ['x', 'x', '4', '13', '2', '14', '19', '13', '15', '19'], ['13', '2', 'x', '8', 'x', '17', '13', 'x', 'x', '12'], ['2', '20', '20', '14', 'x', 'x', '1... |
27 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 10 | [[7, 9], [7, 8], [7, 7], [7, 6], [7, 5], [7, 4], [6, 3], [5, 2], [4, 1], [4, 0], [3, 0]] | 11 | 0.030271291732788086 | 11 | 8 | 2 | ["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0... | ["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0... | ["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0... |
27 | Given 7 labeled water jugs with capacities 80, 76, 132, 60, 83, 28, 75, 26 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 337, 378, 398 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o... | water_jug | subset_sum | 5 | [["+", 28, 3], ["+", 80, 3], ["+", 132, 3], ["+", 75, 3], ["+", 83, 3], ["+", 80, 2], ["+", 83, 2], ["+", 83, 2], ["+", 132, 2], ["+", 28, 1], ["+", 83, 1], ["+", 83, 1], ["+", 83, 1], ["+", 60, 1]] | 14 | 0.05565452575683594 | 14 | 48 | 3 | [[80, 76, 132, 60, 83, 28, 75, 26], [337, 378, 398]] | [[80, 76, 132, 60, 83, 28, 75, 26], [337, 378, 398]] | ["[80, 76, 132, 60, 83, 28, 75, 26]", "[337, 378, 398]"] |
28 | 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 | [45, 36, 87, 10, 81, 74, 10, 87, 36, 10, 72, 46, 74, 81, 87, 72, 46, 45] | 18 | 0.023023605346679688 | 18 | 4 | 9 | [[[10, 81, 46], [87, 74, 72], [36, 45, "_"]]] | [[[10, 81, 46], [87, 74, 72], [36, 45, "_"]]] | ["[[10, 81, 46], [87, 74, 72], [36, 45, '_']]"] |
28 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "down-right", "up-right", "up-left", "up-left", "down-left", "up-left"] | 16 | 0.22631430625915527 | 16 | 4 | 20 | [[["a", "a", "e", "e", "y"], ["h", "a", "i", "t", "h"], ["_", "r", "k", "n", "t"], ["m", "k", "n", "o", "o"]]] | [[["a", "a", "e", "e", "y"], ["h", "a", "i", "t", "h"], ["_", "r", "k", "n", "t"], ["m", "k", "n", "o", "o"]], ["akey", "haikh", "trone", "manto"]] | ["[['a', 'a', 'e', 'e', 'y'], ['h', 'a', 'i', 't', 'h'], ['_', 'r', 'k', 'n', 't'], ['m', 'k', 'n', 'o', 'o']]", "['akey', 'haikh', 'trone', 'manto']"] |
28 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 11 | ["B", "G", "N", "P", "E", "A", "E", "M", "N"] | 9 | 0.029226064682006836 | 9 | 11 | 14 | [[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0,... | [[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0,... | ["[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0... |
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