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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
92 | 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 | [26, 47, 73, 44, 64, 73, 16, 17, 44, 64, 73, 46, 74, 75, 56, 53, 29, 39, 59, 56, 53, 26, 17, 16, 46, 73, 64, 44] | 28 | 0.7006855010986328 | 28 | 4 | 18 | [[[92, 79, 74, 46, 64, 44], [39, 59, 75, 26, 47, 73], [29, 53, 56, "_", 16, 17]]] | [[[92, 79, 74, 46, 64, 44], [39, 59, 75, 26, 47, 73], [29, 53, 56, "_", 16, 17]]] | ["[[92, 79, 74, 46, 64, 44], [39, 59, 75, 26, 47, 73], [29, 53, 56, '_', 16, 17]]"] |
92 | 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 | 4 | ["down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-right", "down-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up... | 28 | 23.219958066940308 | 28 | 4 | 30 | [[["e", "s", "_", "r", "k", "w"], ["b", "c", "d", "d", "r", "a"], ["c", "u", "e", "c", "e", "s"], ["b", "r", "n", "h", "e", "a"], ["h", "o", "e", "k", "r", "r"]]] | [[["e", "s", "_", "r", "k", "w"], ["b", "c", "d", "d", "r", "a"], ["c", "u", "e", "c", "e", "s"], ["b", "r", "n", "h", "e", "a"], ["h", "o", "e", "k", "r", "r"]], ["shrew", "bedark", "curcas", "bender", "hocker"]] | ["[['e', 's', '_', 'r', 'k', 'w'], ['b', 'c', 'd', 'd', 'r', 'a'], ['c', 'u', 'e', 'c', 'e', 's'], ['b', 'r', 'n', 'h', 'e', 'a'], ['h', 'o', 'e', 'k', 'r', 'r']]", "['shrew', 'bedark', 'curcas', 'bender', 'hocker']"] |
92 | 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 | 15 | ["F", "H", "S", "J", "S", "Q", "C", "R", "W", "R"] | 10 | 0.05547213554382324 | 10 | 15 | 18 | [[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,... | [[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,... | ["[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0... |
92 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [19, 11, 35, 3, 12, 23, 42, 45, 8, 12, 32, 82, 39, 12, 45, 12, 40, 38, 28, 6, 32, 37, 39, 9, 43, 12, 38, 4, 42, 44, 41, 37, 83, 5, 38], such that the sum of the chosen coins adds up to 466. Each coin in the list is unique ... | coin_exchange | subset_sum | 22 | [3, 39, 83, 42, 40, 6, 37, 37, 39, 41, 45, 42, 12] | 54 | 0.05336928367614746 | 13 | 35 | 35 | [[19, 11, 35, 3, 12, 23, 42, 45, 8, 12, 32, 82, 39, 12, 45, 12, 40, 38, 28, 6, 32, 37, 39, 9, 43, 12, 38, 4, 42, 44, 41, 37, 83, 5, 38]] | [[19, 11, 35, 3, 12, 23, 42, 45, 8, 12, 32, 82, 39, 12, 45, 12, 40, 38, 28, 6, 32, 37, 39, 9, 43, 12, 38, 4, 42, 44, 41, 37, 83, 5, 38], {"37": 6, "43": 18, "32": 16, "4": 4, "83": 4, "8": 5, "23": 18, "12": 6, "82": 16, "44": 20, "39": 1, "19": 8, "35": 7, "38": 11, "11": 3, "42": 5, "45": 12, "3": 1, "6": 2, "41": 3,... | ["[19, 11, 35, 3, 12, 23, 42, 45, 8, 12, 32, 82, 39, 12, 45, 12, 40, 38, 28, 6, 32, 37, 39, 9, 43, 12, 38, 4, 42, 44, 41, 37, 83, 5, 38]", "{37: 6, 43: 18, 32: 16, 4: 4, 83: 4, 8: 5, 23: 18, 12: 6, 82: 16, 44: 20, 39: 1, 19: 8, 35: 7, 38: 11, 11: 3, 42: 5, 45: 12, 3: 1, 6: 2, 41: 3, 28: 18, 40: 2, 9: 6, 5: 4}", "466"] |
92 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[1, 2], [1, 0], [1, 2], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [0, 1]] | 35 | 174.02124547958374 | 35 | 6 | 18 | [[["Red", "Green", "Blue", "Red", "Red", "Blue"], ["Green", "Red", "Green", "Green", "Blue", "Red"], ["Green", "Blue", "Green", "Blue", "Blue", "Red"]], 9] | [[["Red", "Green", "Blue", "Red", "Red", "Blue"], ["Green", "Red", "Green", "Green", "Blue", "Red"], ["Green", "Blue", "Green", "Blue", "Blue", "Red"]], 9] | ["[['Red', 'Green', 'Blue', 'Red', 'Red', 'Blue'], ['Green', 'Red', 'Green', 'Green', 'Blue', 'Red'], ['Green', 'Blue', 'Green', 'Blue', 'Blue', 'Red']]", "9"] |
92 | We have a 4x4 numerical grid, with numbers ranging from 31 to 86 (31 included in the range but 86 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 11 | [[0, 0, 30], [0, 3, 6], [1, 0, 29], [1, 2, 12], [1, 3, 7], [2, 1, 16], [2, 2, 17], [3, 0, 8], [3, 1, 9], [3, 2, 18]] | 308 | 15.29494833946228 | 10 | 55 | 16 | ["[['', '28', '11', ''], ['', '27', '', ''], ['15', '', '', '46'], ['', '', '', '50']]", 6, 61] | ["[['', '28', '11', ''], ['', '27', '', ''], ['15', '', '', '46'], ['', '', '', '50']]", 6, 61] | ["[['', '28', '11', ''], ['', '27', '', ''], ['15', '', '', '46'], ['', '', '', '50']]", "6", "61"] |
92 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 41 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 240, 266, None for columns 1 to 2 respectively, and the sums of rows must be None, 298, 222, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 42], [0, 3, 87], [1, 0, 45], [1, 2, 89], [2, 0, 44], [2, 2, 59], [3, 1, 83], [3, 2, 51]] | 1057 | 14.704439878463745 | 8 | 36 | 16 | ["[['', '41', '67', ''], ['', '73', '', '91'], ['', '43', '', '76'], ['80', '', '', '86']]", 4, 41, 92] | ["[['', '41', '67', ''], ['', '73', '', '91'], ['', '43', '', '76'], ['80', '', '', '86']]", 41, 92, [1, 3], [1, 3], [240, 266], [298, 222], 299] | ["[['', '41', '67', ''], ['', '73', '', '91'], ['', '43', '', '76'], ['80', '', '', '86']]", "41", "92", "[None, 240, 266, None]", "[None, 298, 222, None]", "299"] |
92 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (7, 14) to his destination workshop at index (2, 4), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[7, 14], [6, 14], [6, 13], [5, 13], [4, 13], [4, 12], [3, 12], [3, 11], [2, 11], [1, 11], [1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [1, 5], [2, 5], [2, 4]] | 140 | 0.030504465103149414 | 18 | 4 | 4 | [[["15", "1", "x", "3", "x", "9", "15", "8", "17", "x", "x", "6", "x", "12", "3"], ["x", "x", "x", "14", "x", "7", "18", "6", "14", "2", "19", "15", "x", "x", "x"], ["4", "3", "x", "10", "8", "4", "16", "13", "6", "x", "18", "10", "14", "x", "x"], ["x", "x", "x", "10", "x", "14", "10", "7", "x", "x", "x", "4", "2", "19... | [[["15", "1", "x", "3", "x", "9", "15", "8", "17", "x", "x", "6", "x", "12", "3"], ["x", "x", "x", "14", "x", "7", "18", "6", "14", "2", "19", "15", "x", "x", "x"], ["4", "3", "x", "10", "8", "4", "16", "13", "6", "x", "18", "10", "14", "x", "x"], ["x", "x", "x", "10", "x", "14", "10", "7", "x", "x", "x", "4", "2", "19... | ["[['15', '1', 'x', '3', 'x', '9', '15', '8', '17', 'x', 'x', '6', 'x', '12', '3'], ['x', 'x', 'x', '14', 'x', '7', '18', '6', '14', '2', '19', '15', 'x', 'x', 'x'], ['4', '3', 'x', '10', '8', '4', '16', '13', '6', 'x', '18', '10', '14', 'x', 'x'], ['x', 'x', 'x', '10', 'x', '14', '10', '7', 'x', 'x', 'x', '4', '2', '1... |
92 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[10, 0], [9, 1], [8, 2], [7, 2], [7, 3], [6, 3], [5, 3], [4, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [2, 9], [2, 10], [1, 11], [1, 12]] | 17 | 0.029998064041137695 | 17 | 8 | 2 | ["[[1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1... | ["[[1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1... | ["[[1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1... |
92 | Given 9 labeled water jugs with capacities 143, 34, 117, 130, 50, 142, 144, 150, 29, 78 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 307, 316, 325, 622 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time e... | water_jug | subset_sum | 7 | [["+", 143, 4], ["+", 150, 4], ["+", 150, 4], ["+", 150, 4], ["+", 29, 4], ["+", 78, 3], ["+", 117, 3], ["+", 130, 3], ["+", 143, 2], ["+", 144, 2], ["+", 29, 2], ["+", 130, 1], ["+", 143, 1], ["+", 34, 1]] | 14 | 0.04768729209899902 | 14 | 80 | 3 | [[143, 34, 117, 130, 50, 142, 144, 150, 29, 78], [307, 316, 325, 622]] | [[143, 34, 117, 130, 50, 142, 144, 150, 29, 78], [307, 316, 325, 622]] | ["[143, 34, 117, 130, 50, 142, 144, 150, 29, 78]", "[307, 316, 325, 622]"] |
93 | 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 | [94, 87, 69, 86, 65, 18, 35, 69, 87, 94, 69, 65, 61, 57, 4, 79, 75, 55, 53, 4, 55, 53] | 22 | 0.032526254653930664 | 22 | 4 | 18 | [[[94, 87, 69, 81, 4, 79], ["_", 35, 86, 61, 57, 75], [41, 18, 65, 9, 53, 55]]] | [[[94, 87, 69, 81, 4, 79], ["_", 35, 86, 61, 57, 75], [41, 18, 65, 9, 53, 55]]] | ["[[94, 87, 69, 81, 4, 79], ['_', 35, 86, 61, 57, 75], [41, 18, 65, 9, 53, 55]]"] |
93 | 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 | 4 | ["down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "down-right", "up-right", "up-left", "up-right", "up-... | 38 | 502.2531027793884 | 38 | 4 | 30 | [[["d", "h", "_", "l", "e", "n"], ["a", "a", "e", "b", "e", "u"], ["m", "u", "i", "b", "e", "e"], ["i", "o", "d", "m", "s", "l"], ["t", "r", "l", "l", "l", "o"]]] | [[["d", "h", "_", "l", "e", "n"], ["a", "a", "e", "b", "e", "u"], ["m", "u", "i", "b", "e", "e"], ["i", "o", "d", "m", "s", "l"], ["t", "r", "l", "l", "l", "o"]], ["helen", "adelea", "bumble", "iodism", "trullo"]] | ["[['d', 'h', '_', 'l', 'e', 'n'], ['a', 'a', 'e', 'b', 'e', 'u'], ['m', 'u', 'i', 'b', 'e', 'e'], ['i', 'o', 'd', 'm', 's', 'l'], ['t', 'r', 'l', 'l', 'l', 'o']]", "['helen', 'adelea', 'bumble', 'iodism', 'trullo']"] |
93 | 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 | 15 | ["M", "A", "Y", "B", "D", "K", "P", "Y", "O", "K"] | 10 | 0.10736274719238281 | 10 | 15 | 18 | [[[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 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, 0, 0, 1,... | [[[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 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, 0, 0, 1,... | ["[[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 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, 0, 0, 1... |
93 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [43, 41, 23, 24, 40, 11, 12, 9, 32, 32, 6, 15, 16, 20, 6, 39, 9, 12, 4, 251, 43, 24, 27, 20, 39, 37, 7, 43, 9, 13, 45, 27, 9, 15, 41, 25], such that the sum of the chosen coins adds up to 471. Each coin in the list is uniq... | coin_exchange | subset_sum | 23 | [7, 45, 20, 12, 23, 12, 251, 40, 20, 41] | 34 | 0.04783797264099121 | 10 | 36 | 36 | [[43, 41, 23, 24, 40, 11, 12, 9, 32, 32, 6, 15, 16, 20, 6, 39, 9, 12, 4, 251, 43, 24, 27, 20, 39, 37, 7, 43, 9, 13, 45, 27, 9, 15, 41, 25]] | [[43, 41, 23, 24, 40, 11, 12, 9, 32, 32, 6, 15, 16, 20, 6, 39, 9, 12, 4, 251, 43, 24, 27, 20, 39, 37, 7, 43, 9, 13, 45, 27, 9, 15, 41, 25], {"9": 7, "32": 17, "24": 17, "15": 11, "4": 3, "39": 18, "41": 9, "25": 14, "27": 5, "40": 5, "43": 8, "11": 9, "20": 1, "45": 2, "16": 15, "251": 12, "37": 10, "13": 1, "23": 1, "... | ["[43, 41, 23, 24, 40, 11, 12, 9, 32, 32, 6, 15, 16, 20, 6, 39, 9, 12, 4, 251, 43, 24, 27, 20, 39, 37, 7, 43, 9, 13, 45, 27, 9, 15, 41, 25]", "{9: 7, 32: 17, 24: 17, 15: 11, 4: 3, 39: 18, 41: 9, 25: 14, 27: 5, 40: 5, 43: 8, 11: 9, 20: 1, 45: 2, 16: 15, 251: 12, 37: 10, 13: 1, 23: 1, 7: 1, 12: 1, 6: 5}", "471"] |
93 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[2, 1], [0, 1], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 0], [2, 0], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 2]] | 27 | 151.82125544548035 | 27 | 6 | 18 | [[["Red", "Green", "Red", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Green", "Blue", "Blue"], ["Red", "Blue", "Blue", "Green", "Red", "Green"]], 9] | [[["Red", "Green", "Red", "Green", "Blue", "Red"], ["Red", "Blue", "Green", "Green", "Blue", "Blue"], ["Red", "Blue", "Blue", "Green", "Red", "Green"]], 9] | ["[['Red', 'Green', 'Red', 'Green', 'Blue', 'Red'], ['Red', 'Blue', 'Green', 'Green', 'Blue', 'Blue'], ['Red', 'Blue', 'Blue', 'Green', 'Red', 'Green']]", "9"] |
93 | We have a 4x4 numerical grid, with numbers ranging from 36 to 91 (36 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 > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 11 | [[0, 0, 62], [0, 1, 63], [0, 3, 76], [1, 1, 64], [2, 0, 52], [2, 1, 65]] | 916 | 0.2937626838684082 | 6 | 55 | 16 | ["[['', '', '74', ''], ['61', '', '80', '88'], ['', '', '82', '89'], ['51', '75', '83', '90']]", 50, 110] | ["[['', '', '74', ''], ['61', '', '80', '88'], ['', '', '82', '89'], ['51', '75', '83', '90']]", 50, 110] | ["[['', '', '74', ''], ['61', '', '80', '88'], ['', '', '82', '89'], ['51', '75', '83', '90']]", "50", "110"] |
93 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 41 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 244, 295, None for columns 1 to 2 respectively, and the sums of rows must be None, 266, 261, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 2, 61], [0, 3, 58], [1, 2, 55], [2, 3, 60], [3, 0, 90], [3, 1, 47], [3, 2, 91], [3, 3, 41]] | 1025 | 1.733626127243042 | 8 | 36 | 16 | ["[['53', '57', '', ''], ['77', '78', '', '56'], ['51', '62', '88', ''], ['', '', '', '']]", 4, 41, 92] | ["[['53', '57', '', ''], ['77', '78', '', '56'], ['51', '62', '88', ''], ['', '', '', '']]", 41, 92, [1, 3], [1, 3], [244, 295], [266, 261], 265] | ["[['53', '57', '', ''], ['77', '78', '', '56'], ['51', '62', '88', ''], ['', '', '', '']]", "41", "92", "[None, 244, 295, None]", "[None, 266, 261, None]", "265"] |
93 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 14) to his destination workshop at index (7, 1), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[4, 14], [4, 13], [4, 12], [5, 12], [5, 11], [5, 10], [5, 9], [5, 8], [6, 8], [6, 7], [7, 7], [7, 6], [8, 6], [8, 5], [8, 4], [7, 4], [7, 3], [7, 2], [7, 1]] | 131 | 0.028059959411621094 | 19 | 4 | 4 | [[["x", "x", "x", "x", "2", "19", "x", "x", "15", "x", "x", "2", "17", "18", "18"], ["x", "x", "2", "18", "3", "17", "1", "x", "x", "x", "6", "x", "x", "7", "9"], ["x", "x", "2", "10", "3", "x", "6", "11", "5", "7", "8", "17", "x", "12", "6"], ["x", "14", "13", "9", "3", "x", "18", "x", "17", "16", "14", "8", "9", "x",... | [[["x", "x", "x", "x", "2", "19", "x", "x", "15", "x", "x", "2", "17", "18", "18"], ["x", "x", "2", "18", "3", "17", "1", "x", "x", "x", "6", "x", "x", "7", "9"], ["x", "x", "2", "10", "3", "x", "6", "11", "5", "7", "8", "17", "x", "12", "6"], ["x", "14", "13", "9", "3", "x", "18", "x", "17", "16", "14", "8", "9", "x",... | ["[['x', 'x', 'x', 'x', '2', '19', 'x', 'x', '15', 'x', 'x', '2', '17', '18', '18'], ['x', 'x', '2', '18', '3', '17', '1', 'x', 'x', 'x', '6', 'x', 'x', '7', '9'], ['x', 'x', '2', '10', '3', 'x', '6', '11', '5', '7', '8', '17', 'x', '12', '6'], ['x', '14', '13', '9', '3', 'x', '18', 'x', '17', '16', '14', '8', '9', 'x'... |
93 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[14, 10], [14, 9], [14, 8], [13, 7], [13, 6], [12, 5], [11, 4], [11, 3], [10, 2], [9, 1], [8, 1], [7, 1], [6, 1], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1]] | 19 | 0.024536848068237305 | 19 | 8 | 2 | ["[[1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1... | ["[[1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1... | ["[[1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1... |
93 | Given 9 labeled water jugs with capacities 39, 110, 41, 54, 47, 33, 136, 40, 100 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 192, 459, 473, 493 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed t... | water_jug | subset_sum | 7 | [["+", 100, 4], ["+", 100, 4], ["+", 47, 4], ["+", 110, 4], ["+", 136, 4], ["+", 47, 3], ["+", 136, 3], ["+", 136, 3], ["+", 54, 3], ["+", 100, 3], ["+", 33, 2], ["+", 136, 2], ["+", 136, 2], ["+", 54, 2], ["+", 100, 2], ["+", 41, 1], ["+", 41, 1], ["+", 110, 1]] | 18 | 0.06568336486816406 | 18 | 72 | 3 | [[39, 110, 41, 54, 47, 33, 136, 40, 100], [192, 459, 473, 493]] | [[39, 110, 41, 54, 47, 33, 136, 40, 100], [192, 459, 473, 493]] | ["[39, 110, 41, 54, 47, 33, 136, 40, 100]", "[192, 459, 473, 493]"] |
94 | 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 | [15, 40, 59, 44, 61, 50, 68, 30, 85, 68, 50, 81, 24, 48, 30, 50, 81, 47, 44, 61, 68, 81, 48, 24, 22, 15] | 26 | 0.07562923431396484 | 26 | 4 | 18 | [[[98, 30, 85, 44, 59, 40], [56, 68, 50, 61, 47, 15], [37, 48, 24, 81, 22, "_"]]] | [[[98, 30, 85, 44, 59, 40], [56, 68, 50, 61, 47, 15], [37, 48, 24, 81, 22, "_"]]] | ["[[98, 30, 85, 44, 59, 40], [56, 68, 50, 61, 47, 15], [37, 48, 24, 81, 22, '_']]"] |
94 | 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 | 4 | ["down-right", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "up-left", "up-right", "up-left"] | 20 | 0.9841225147247314 | 20 | 4 | 30 | [[["_", "d", "a", "u", "n", "k"], ["a", "r", "m", "r", "r", "e"], ["d", "i", "u", "l", "l", "t"], ["c", "d", "u", "r", "a", "c"], ["m", "i", "g", "a", "o", "h"]]] | [[["_", "d", "a", "u", "n", "k"], ["a", "r", "m", "r", "r", "e"], ["d", "i", "u", "l", "l", "t"], ["c", "d", "u", "r", "a", "c"], ["m", "i", "g", "a", "o", "h"]], ["drunk", "armure", "diglot", "caudal", "mirach"]] | ["[['_', 'd', 'a', 'u', 'n', 'k'], ['a', 'r', 'm', 'r', 'r', 'e'], ['d', 'i', 'u', 'l', 'l', 't'], ['c', 'd', 'u', 'r', 'a', 'c'], ['m', 'i', 'g', 'a', 'o', 'h']]", "['drunk', 'armure', 'diglot', 'caudal', 'mirach']"] |
94 | 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 | 15 | ["I", "B", "H", "F", "R", "O", "M", "H", "Q", "R"] | 10 | 0.04136967658996582 | 10 | 15 | 18 | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,... | [[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,... | ["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0... |
94 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [21, 13, 10, 18, 21, 43, 42, 29, 14, 19, 9, 2, 15, 19, 32, 45, 24, 31, 25, 7, 21, 24, 29, 29, 4, 36, 29, 19, 29, 12, 3, 44, 40, 46, 33, 3, 28, 44, 25, 6, 36, 3, 4, 19, 31], such that the sum of the chosen coins adds up to ... | coin_exchange | subset_sum | 24 | [46, 44, 40, 28, 24, 2, 3, 3, 3, 33, 24, 18, 43, 42, 45, 44, 32] | 105 | 0.08423256874084473 | 17 | 45 | 45 | [[21, 13, 10, 18, 21, 43, 42, 29, 14, 19, 9, 2, 15, 19, 32, 45, 24, 31, 25, 7, 21, 24, 29, 29, 4, 36, 29, 19, 29, 12, 3, 44, 40, 46, 33, 3, 28, 44, 25, 6, 36, 3, 4, 19, 31]] | [[21, 13, 10, 18, 21, 43, 42, 29, 14, 19, 9, 2, 15, 19, 32, 45, 24, 31, 25, 7, 21, 24, 29, 29, 4, 36, 29, 19, 29, 12, 3, 44, 40, 46, 33, 3, 28, 44, 25, 6, 36, 3, 4, 19, 31], {"6": 3, "9": 7, "13": 11, "19": 11, "36": 17, "32": 11, "46": 1, "4": 3, "21": 14, "3": 1, "18": 5, "29": 18, "12": 9, "2": 2, "15": 14, "43": 11... | ["[21, 13, 10, 18, 21, 43, 42, 29, 14, 19, 9, 2, 15, 19, 32, 45, 24, 31, 25, 7, 21, 24, 29, 29, 4, 36, 29, 19, 29, 12, 3, 44, 40, 46, 33, 3, 28, 44, 25, 6, 36, 3, 4, 19, 31]", "{6: 3, 9: 7, 13: 11, 19: 11, 36: 17, 32: 11, 46: 1, 4: 3, 21: 14, 3: 1, 18: 5, 29: 18, 12: 9, 2: 2, 15: 14, 43: 11, 24: 5, 25: 15, 14: 10, 42: ... |
94 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[1, 0], [2, 0], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 2], [1, 2], [1, 0], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 0], [2, 0]] | 33 | 79.31269884109497 | 33 | 6 | 18 | [[["Red", "Green", "Blue", "Blue", "Green", "Blue"], ["Red", "Green", "Green", "Blue", "Green", "Blue"], ["Red", "Red", "Blue", "Red", "Green", "Red"]], 9] | [[["Red", "Green", "Blue", "Blue", "Green", "Blue"], ["Red", "Green", "Green", "Blue", "Green", "Blue"], ["Red", "Red", "Blue", "Red", "Green", "Red"]], 9] | ["[['Red', 'Green', 'Blue', 'Blue', 'Green', 'Blue'], ['Red', 'Green', 'Green', 'Blue', 'Green', 'Blue'], ['Red', 'Red', 'Blue', 'Red', 'Green', 'Red']]", "9"] |
94 | We have a 4x4 numerical grid, with numbers ranging from 39 to 94 (39 included in the range but 94 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 0, 24], [1, 0, 23], [1, 1, 37], [1, 3, 72], [2, 0, 22], [3, 2, 54]] | 679 | 0.5468931198120117 | 6 | 55 | 16 | ["[['', '36', '71', '79'], ['', '', '69', ''], ['', '50', '63', '70'], ['21', '53', '', '62']]", 20, 80] | ["[['', '36', '71', '79'], ['', '', '69', ''], ['', '50', '63', '70'], ['21', '53', '', '62']]", 20, 80] | ["[['', '36', '71', '79'], ['', '', '69', ''], ['', '50', '63', '70'], ['21', '53', '', '62']]", "20", "80"] |
94 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 41 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 267, 236, None for columns 1 to 2 respectively, and the sums of rows must be None, 270, 234, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 1, 49], [0, 2, 52], [0, 3, 66], [1, 1, 86], [1, 2, 89], [1, 3, 41], [2, 0, 43], [3, 3, 42]] | 962 | 2.9558627605438232 | 8 | 36 | 16 | ["[['48', '', '', ''], ['54', '', '', ''], ['', '64', '44', '83'], ['82', '68', '51', '']]", 4, 41, 92] | ["[['48', '', '', ''], ['54', '', '', ''], ['', '64', '44', '83'], ['82', '68', '51', '']]", 41, 92, [1, 3], [1, 3], [267, 236], [270, 234], 301] | ["[['48', '', '', ''], ['54', '', '', ''], ['', '64', '44', '83'], ['82', '68', '51', '']]", "41", "92", "[None, 267, 236, None]", "[None, 270, 234, None]", "301"] |
94 | 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, 2) to his destination workshop at index (7, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[3, 2], [2, 2], [2, 3], [2, 4], [2, 5], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 11], [5, 11], [6, 11], [6, 12], [7, 12], [7, 13]] | 185 | 0.026812314987182617 | 18 | 4 | 4 | [[["x", "2", "x", "12", "3", "8", "x", "1", "5", "x", "x", "14", "x", "5", "x"], ["5", "x", "x", "9", "19", "10", "10", "x", "x", "14", "16", "x", "x", "17", "x"], ["7", "4", "7", "18", "2", "7", "16", "x", "7", "x", "9", "x", "x", "6", "x"], ["9", "x", "14", "x", "x", "14", "7", "9", "18", "11", "14", "8", "13", "14",... | [[["x", "2", "x", "12", "3", "8", "x", "1", "5", "x", "x", "14", "x", "5", "x"], ["5", "x", "x", "9", "19", "10", "10", "x", "x", "14", "16", "x", "x", "17", "x"], ["7", "4", "7", "18", "2", "7", "16", "x", "7", "x", "9", "x", "x", "6", "x"], ["9", "x", "14", "x", "x", "14", "7", "9", "18", "11", "14", "8", "13", "14",... | ["[['x', '2', 'x', '12', '3', '8', 'x', '1', '5', 'x', 'x', '14', 'x', '5', 'x'], ['5', 'x', 'x', '9', '19', '10', '10', 'x', 'x', '14', '16', 'x', 'x', '17', 'x'], ['7', '4', '7', '18', '2', '7', '16', 'x', '7', 'x', '9', 'x', 'x', '6', 'x'], ['9', 'x', '14', 'x', 'x', '14', '7', '9', '18', '11', '14', '8', '13', '14'... |
94 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[13, 1], [12, 2], [11, 3], [10, 4], [10, 5], [10, 6], [10, 7], [9, 8], [8, 8], [8, 9], [8, 10], [7, 11], [6, 11], [6, 12], [6, 13], [5, 13], [4, 13]] | 17 | 0.023047924041748047 | 17 | 8 | 2 | ["[[1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0... | ["[[1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0... | ["[[1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0... |
94 | Given 9 labeled water jugs with capacities 81, 56, 41, 88, 137, 14, 149, 120, 87, 104 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 377, 456, 512, 541 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exc... | water_jug | subset_sum | 7 | [["+", 81, 4], ["+", 149, 4], ["+", 149, 4], ["+", 81, 4], ["+", 81, 4], ["+", 81, 3], ["+", 120, 3], ["+", 149, 3], ["+", 81, 3], ["+", 81, 3], ["+", 41, 2], ["+", 137, 2], ["+", 149, 2], ["+", 88, 2], ["+", 41, 2], ["+", 120, 1], ["+", 120, 1], ["+", 137, 1]] | 18 | 0.09543561935424805 | 18 | 80 | 3 | [[81, 56, 41, 88, 137, 14, 149, 120, 87, 104], [377, 456, 512, 541]] | [[81, 56, 41, 88, 137, 14, 149, 120, 87, 104], [377, 456, 512, 541]] | ["[81, 56, 41, 88, 137, 14, 149, 120, 87, 104]", "[377, 456, 512, 541]"] |
95 | 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 | [58, 27, 63, 65, 67, 72, 92, 93, 72, 67, 65, 83, 62, 24, 74, 62, 24, 79, 83, 63, 27, 24, 62, 58] | 24 | 0.20434069633483887 | 24 | 4 | 18 | [[[92, 72, 91, 79, 62, 24], [93, 67, 65, 63, 83, 74], [41, 34, 29, 27, 58, "_"]]] | [[[92, 72, 91, 79, 62, 24], [93, 67, 65, 63, 83, 74], [41, 34, 29, 27, 58, "_"]]] | ["[[92, 72, 91, 79, 62, 24], [93, 67, 65, 63, 83, 74], [41, 34, 29, 27, 58, '_']]"] |
95 | 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 | 4 | ["up-left", "up-right", "down-right", "up-right", "down-right", "down-left", "down-left", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "up-left", "down-left", "up-left"] | 20 | 0.4562370777130127 | 20 | 4 | 30 | [[["y", "t", "s", "n", "a", "r"], ["m", "r", "r", "t", "o", "e"], ["l", "o", "_", "d", "l", "n"], ["e", "u", "v", "i", "r", "a"], ["h", "e", "l", "m", "a", "n"]]] | [[["y", "t", "s", "n", "a", "r"], ["m", "r", "r", "t", "o", "e"], ["l", "o", "_", "d", "l", "n"], ["e", "u", "v", "i", "r", "a"], ["h", "e", "l", "m", "a", "n"]], ["tuner", "myrtol", "soldan", "elvira", "herman"]] | ["[['y', 't', 's', 'n', 'a', 'r'], ['m', 'r', 'r', 't', 'o', 'e'], ['l', 'o', '_', 'd', 'l', 'n'], ['e', 'u', 'v', 'i', 'r', 'a'], ['h', 'e', 'l', 'm', 'a', 'n']]", "['tuner', 'myrtol', 'soldan', 'elvira', 'herman']"] |
95 | 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 | 15 | ["C", "O", "N", "Q", "E", "R", "Q", "E"] | 8 | 0.034786224365234375 | 8 | 15 | 18 | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,... | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0... |
95 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [26, 8, 19, 9, 36, 23, 42, 40, 13, 34, 40, 25, 11, 38, 10, 41, 19, 34, 91, 18, 14, 27, 14, 43, 42, 13, 2, 27, 90, 13, 3, 4, 44, 7, 48, 40, 35, 40, 10, 12, 25], such that the sum of the chosen coins adds up to 488. Each coi... | coin_exchange | subset_sum | 25 | [23, 27, 27, 12, 19, 91, 90, 36, 41, 40, 43, 10, 19, 10] | 63 | 0.06218409538269043 | 14 | 41 | 41 | [[26, 8, 19, 9, 36, 23, 42, 40, 13, 34, 40, 25, 11, 38, 10, 41, 19, 34, 91, 18, 14, 27, 14, 43, 42, 13, 2, 27, 90, 13, 3, 4, 44, 7, 48, 40, 35, 40, 10, 12, 25]] | [[26, 8, 19, 9, 36, 23, 42, 40, 13, 34, 40, 25, 11, 38, 10, 41, 19, 34, 91, 18, 14, 27, 14, 43, 42, 13, 2, 27, 90, 13, 3, 4, 44, 7, 48, 40, 35, 40, 10, 12, 25], {"44": 20, "11": 4, "19": 3, "4": 4, "10": 3, "14": 9, "90": 18, "48": 12, "91": 5, "8": 4, "7": 5, "9": 5, "12": 2, "42": 18, "36": 6, "35": 10, "34": 12, "25... | ["[26, 8, 19, 9, 36, 23, 42, 40, 13, 34, 40, 25, 11, 38, 10, 41, 19, 34, 91, 18, 14, 27, 14, 43, 42, 13, 2, 27, 90, 13, 3, 4, 44, 7, 48, 40, 35, 40, 10, 12, 25]", "{44: 20, 11: 4, 19: 3, 4: 4, 10: 3, 14: 9, 90: 18, 48: 12, 91: 5, 8: 4, 7: 5, 9: 5, 12: 2, 42: 18, 36: 6, 35: 10, 34: 12, 25: 7, 27: 1, 3: 2, 26: 15, 40: 8,... |
95 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 2], [1, 0]] | 27 | 145.94300484657288 | 27 | 6 | 18 | [[["Green", "Green", "Green", "Red", "Blue", "Blue"], ["Blue", "Red", "Red", "Red", "Green", "Green"], ["Blue", "Green", "Blue", "Red", "Red", "Blue"]], 9] | [[["Green", "Green", "Green", "Red", "Blue", "Blue"], ["Blue", "Red", "Red", "Red", "Green", "Green"], ["Blue", "Green", "Blue", "Red", "Red", "Blue"]], 9] | ["[['Green', 'Green', 'Green', 'Red', 'Blue', 'Blue'], ['Blue', 'Red', 'Red', 'Red', 'Green', 'Green'], ['Blue', 'Green', 'Blue', 'Red', 'Red', 'Blue']]", "9"] |
95 | We have a 4x4 numerical grid, with numbers ranging from 39 to 94 (39 included in the range but 94 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 0, 13], [0, 1, 14], [0, 2, 43], [0, 3, 47], [2, 1, 33], [3, 0, 28]] | 418 | 1.5906620025634766 | 6 | 55 | 16 | ["[['', '', '', ''], ['25', '32', '40', '46'], ['27', '', '39', '42'], ['', '34', '38', '41']]", 13, 73] | ["[['', '', '', ''], ['25', '32', '40', '46'], ['27', '', '39', '42'], ['', '34', '38', '41']]", 13, 73] | ["[['', '', '', ''], ['25', '32', '40', '46'], ['27', '', '39', '42'], ['', '34', '38', '41']]", "13", "73"] |
95 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 41 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 262, 272, None for columns 1 to 2 respectively, and the sums of rows must be None, 291, 301, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[1, 0, 42], [1, 2, 87], [2, 0, 88], [2, 1, 63], [2, 2, 90], [3, 0, 41], [3, 1, 58], [3, 2, 48]] | 1053 | 13.726203918457031 | 8 | 36 | 16 | ["[['68', '50', '47', '65'], ['', '91', '', '71'], ['', '', '', '60'], ['', '', '', '84']]", 4, 41, 92] | ["[['68', '50', '47', '65'], ['', '91', '', '71'], ['', '', '', '60'], ['', '', '', '84']]", 41, 92, [1, 3], [1, 3], [262, 272], [291, 301], 256] | ["[['68', '50', '47', '65'], ['', '91', '', '71'], ['', '', '', '60'], ['', '', '', '84']]", "41", "92", "[None, 262, 272, None]", "[None, 291, 301, None]", "256"] |
95 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 2) to his destination workshop at index (9, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [4, 6], [5, 6], [5, 7], [5, 8], [6, 8], [6, 9], [7, 9], [7, 10], [8, 10], [9, 10], [9, 11], [10, 11], [10, 12], [10, 13], [9, 13]] | 134 | 0.029214859008789062 | 20 | 4 | 4 | [[["x", "x", "x", "x", "9", "x", "14", "17", "x", "13", "3", "x", "13", "10", "18"], ["1", "x", "11", "12", "14", "13", "8", "x", "5", "7", "x", "x", "x", "x", "x"], ["3", "x", "x", "18", "11", "16", "x", "x", "x", "x", "1", "x", "15", "12", "10"], ["x", "10", "x", "3", "2", "15", "14", "x", "x", "x", "17", "x", "6", "... | [[["x", "x", "x", "x", "9", "x", "14", "17", "x", "13", "3", "x", "13", "10", "18"], ["1", "x", "11", "12", "14", "13", "8", "x", "5", "7", "x", "x", "x", "x", "x"], ["3", "x", "x", "18", "11", "16", "x", "x", "x", "x", "1", "x", "15", "12", "10"], ["x", "10", "x", "3", "2", "15", "14", "x", "x", "x", "17", "x", "6", "... | ["[['x', 'x', 'x', 'x', '9', 'x', '14', '17', 'x', '13', '3', 'x', '13', '10', '18'], ['1', 'x', '11', '12', '14', '13', '8', 'x', '5', '7', 'x', 'x', 'x', 'x', 'x'], ['3', 'x', 'x', '18', '11', '16', 'x', 'x', 'x', 'x', '1', 'x', '15', '12', '10'], ['x', '10', 'x', '3', '2', '15', '14', 'x', 'x', 'x', '17', 'x', '6', ... |
95 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[0, 13], [0, 12], [1, 11], [2, 10], [2, 9], [2, 8], [3, 7], [3, 6], [4, 6], [4, 5], [5, 5], [6, 5], [7, 5], [8, 6], [9, 6], [10, 6], [11, 6], [12, 6], [13, 5]] | 19 | 0.029097557067871094 | 19 | 8 | 2 | ["[[1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0... | ["[[1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0... | ["[[1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0... |
95 | Given 9 labeled water jugs with capacities 146, 45, 136, 13, 148, 17, 42, 137, 141, 31 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 307, 384, 555, 575 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time ex... | water_jug | subset_sum | 7 | [["+", 136, 4], ["+", 137, 4], ["+", 141, 4], ["+", 148, 4], ["+", 13, 4], ["+", 136, 3], ["+", 136, 3], ["+", 137, 3], ["+", 146, 3], ["+", 45, 2], ["+", 45, 2], ["+", 146, 2], ["+", 148, 2], ["+", 146, 1], ["+", 148, 1], ["+", 13, 1]] | 16 | 0.049184560775756836 | 16 | 80 | 3 | [[146, 45, 136, 13, 148, 17, 42, 137, 141, 31], [307, 384, 555, 575]] | [[146, 45, 136, 13, 148, 17, 42, 137, 141, 31], [307, 384, 555, 575]] | ["[146, 45, 136, 13, 148, 17, 42, 137, 141, 31]", "[307, 384, 555, 575]"] |
96 | 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, 37, 16, 48, 18, 19, 57, 53, 48, 16] | 10 | 0.02994561195373535 | 10 | 4 | 18 | [[[99, 98, 87, 84, 72, 64], [60, 59, 19, 57, "_", 53], [33, 22, 18, 48, 16, 37]]] | [[[99, 98, 87, 84, 72, 64], [60, 59, 19, 57, "_", 53], [33, 22, 18, 48, 16, 37]]] | ["[[99, 98, 87, 84, 72, 64], [60, 59, 19, 57, '_', 53], [33, 22, 18, 48, 16, 37]]"] |
96 | 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 | 4 | ["up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "up-right", "up-left", "down-left", "up-left"] | 20 | 0.39241790771484375 | 20 | 4 | 30 | [[["o", "s", "n", "e", "d", "a"], ["l", "k", "c", "c", "e", "h"], ["t", "o", "_", "c", "n", "e"], ["c", "i", "l", "a", "i", "c"], ["b", "l", "e", "n", "c", "o"]]] | [[["o", "s", "n", "e", "d", "a"], ["l", "k", "c", "c", "e", "h"], ["t", "o", "_", "c", "n", "e"], ["c", "i", "l", "a", "i", "c"], ["b", "l", "e", "n", "c", "o"]], ["siena", "locked", "conche", "celtic", "blanco"]] | ["[['o', 's', 'n', 'e', 'd', 'a'], ['l', 'k', 'c', 'c', 'e', 'h'], ['t', 'o', '_', 'c', 'n', 'e'], ['c', 'i', 'l', 'a', 'i', 'c'], ['b', 'l', 'e', 'n', 'c', 'o']]", "['siena', 'locked', 'conche', 'celtic', 'blanco']"] |
96 | 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 | 15 | ["O", "T", "J", "K", "X", "J", "K"] | 7 | 0.03685426712036133 | 7 | 15 | 18 | [[[0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,... | [[[0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,... | ["[[0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0... |
96 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [22, 25, 37, 5, 46, 10, 23, 23, 3, 6, 34, 32, 34, 2, 3, 8, 4, 28, 32, 24, 15, 38, 17, 35, 9, 12, 12, 22, 34, 48, 39, 30, 7, 18, 10, 46, 30, 36, 49, 27, 22, 19, 9, 24, 43, 15], such that the sum of the chosen coins adds up ... | coin_exchange | subset_sum | 26 | [46, 22, 27, 22, 43, 22, 12, 15, 15, 37, 39, 34, 49, 46, 34] | 66 | 0.06879425048828125 | 15 | 46 | 46 | [[22, 25, 37, 5, 46, 10, 23, 23, 3, 6, 34, 32, 34, 2, 3, 8, 4, 28, 32, 24, 15, 38, 17, 35, 9, 12, 12, 22, 34, 48, 39, 30, 7, 18, 10, 46, 30, 36, 49, 27, 22, 19, 9, 24, 43, 15]] | [[22, 25, 37, 5, 46, 10, 23, 23, 3, 6, 34, 32, 34, 2, 3, 8, 4, 28, 32, 24, 15, 38, 17, 35, 9, 12, 12, 22, 34, 48, 39, 30, 7, 18, 10, 46, 30, 36, 49, 27, 22, 19, 9, 24, 43, 15], {"18": 11, "17": 7, "7": 6, "43": 2, "22": 3, "24": 11, "9": 3, "36": 10, "46": 4, "10": 3, "39": 5, "5": 5, "35": 15, "28": 8, "15": 2, "34": ... | ["[22, 25, 37, 5, 46, 10, 23, 23, 3, 6, 34, 32, 34, 2, 3, 8, 4, 28, 32, 24, 15, 38, 17, 35, 9, 12, 12, 22, 34, 48, 39, 30, 7, 18, 10, 46, 30, 36, 49, 27, 22, 19, 9, 24, 43, 15]", "{18: 11, 17: 7, 7: 6, 43: 2, 22: 3, 24: 11, 9: 3, 36: 10, 46: 4, 10: 3, 39: 5, 5: 5, 35: 15, 28: 8, 15: 2, 34: 6, 27: 3, 38: 11, 30: 20, 23:... |
96 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[1, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 0], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1]] | 31 | 507.0654656887054 | 31 | 6 | 18 | [[["Blue", "Green", "Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Blue", "Red", "Red"], ["Green", "Green", "Green", "Blue", "Red", "Red"]], 9] | [[["Blue", "Green", "Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Blue", "Red", "Red"], ["Green", "Green", "Green", "Blue", "Red", "Red"]], 9] | ["[['Blue', 'Green', 'Red', 'Red', 'Green', 'Blue'], ['Green', 'Blue', 'Blue', 'Blue', 'Red', 'Red'], ['Green', 'Green', 'Green', 'Blue', 'Red', 'Red']]", "9"] |
96 | We have a 4x4 numerical grid, with numbers ranging from 28 to 83 (28 included in the range but 83 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 0, 25], [0, 2, 64], [1, 0, 24], [2, 0, 23], [2, 1, 44], [2, 2, 46], [3, 2, 45]] | 696 | 10.49123215675354 | 7 | 55 | 16 | ["[['', '58', '', '77'], ['', '49', '63', '70'], ['', '', '', '69'], ['22', '43', '', '68']]", 22, 82] | ["[['', '58', '', '77'], ['', '49', '63', '70'], ['', '', '', '69'], ['22', '43', '', '68']]", 22, 82] | ["[['', '58', '', '77'], ['', '49', '63', '70'], ['', '', '', '69'], ['22', '43', '', '68']]", "22", "82"] |
96 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 11 to 62. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 148, 109, None for columns 1 to 2 respectively, and the sums of rows must be None, 105, 115, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 14], [0, 1, 22], [0, 2, 24], [0, 3, 47], [1, 0, 15], [1, 3, 18], [2, 2, 49], [2, 3, 12], [3, 1, 61]] | 469 | 202.49410438537598 | 9 | 36 | 16 | ["[['', '', '', ''], ['', '52', '20', ''], ['41', '13', '', ''], ['54', '', '16', '11']]", 4, 11, 62] | ["[['', '', '', ''], ['', '52', '20', ''], ['41', '13', '', ''], ['54', '', '16', '11']]", 11, 62, [1, 3], [1, 3], [148, 109], [105, 115], 134] | ["[['', '', '', ''], ['', '52', '20', ''], ['41', '13', '', ''], ['54', '', '16', '11']]", "11", "62", "[None, 148, 109, None]", "[None, 105, 115, None]", "134"] |
96 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (8, 13) to his destination workshop at index (3, 3), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[8, 13], [8, 12], [7, 12], [7, 11], [6, 11], [5, 11], [4, 11], [4, 10], [3, 10], [3, 9], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3]] | 146 | 0.02926325798034668 | 16 | 4 | 4 | [[["x", "9", "x", "10", "x", "11", "13", "5", "4", "x", "x", "19", "13", "x", "x"], ["x", "6", "3", "8", "18", "8", "1", "5", "2", "x", "x", "17", "x", "x", "x"], ["x", "x", "11", "5", "x", "11", "13", "20", "7", "x", "x", "x", "x", "15", "4"], ["x", "3", "x", "14", "4", "20", "4", "15", "12", "12", "4", "x", "8", "4",... | [[["x", "9", "x", "10", "x", "11", "13", "5", "4", "x", "x", "19", "13", "x", "x"], ["x", "6", "3", "8", "18", "8", "1", "5", "2", "x", "x", "17", "x", "x", "x"], ["x", "x", "11", "5", "x", "11", "13", "20", "7", "x", "x", "x", "x", "15", "4"], ["x", "3", "x", "14", "4", "20", "4", "15", "12", "12", "4", "x", "8", "4",... | ["[['x', '9', 'x', '10', 'x', '11', '13', '5', '4', 'x', 'x', '19', '13', 'x', 'x'], ['x', '6', '3', '8', '18', '8', '1', '5', '2', 'x', 'x', '17', 'x', 'x', 'x'], ['x', 'x', '11', '5', 'x', '11', '13', '20', '7', 'x', 'x', 'x', 'x', '15', '4'], ['x', '3', 'x', '14', '4', '20', '4', '15', '12', '12', '4', 'x', '8', '4'... |
96 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[3, 10], [4, 9], [5, 9], [6, 9], [7, 8], [8, 7], [8, 6], [8, 5], [8, 4], [9, 4], [9, 3], [9, 2], [10, 1], [11, 1], [12, 1], [13, 0]] | 16 | 0.02433037757873535 | 16 | 8 | 2 | ["[[1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0... | ["[[1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0... | ["[[1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0... |
96 | Given 9 labeled water jugs with capacities 90, 21, 104, 111, 97, 22, 34, 15, 62, 52 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 177, 263, 294, 462 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time excee... | water_jug | subset_sum | 7 | [["+", 52, 4], ["+", 62, 4], ["+", 111, 4], ["+", 111, 4], ["+", 104, 4], ["+", 22, 4], ["+", 90, 3], ["+", 90, 3], ["+", 52, 3], ["+", 62, 3], ["+", 90, 2], ["+", 111, 2], ["+", 62, 2], ["+", 52, 1], ["+", 104, 1], ["+", 21, 1]] | 16 | 0.06696057319641113 | 16 | 80 | 3 | [[90, 21, 104, 111, 97, 22, 34, 15, 62, 52], [177, 263, 294, 462]] | [[90, 21, 104, 111, 97, 22, 34, 15, 62, 52], [177, 263, 294, 462]] | ["[90, 21, 104, 111, 97, 22, 34, 15, 62, 52]", "[177, 263, 294, 462]"] |
97 | 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 | [6, 82, 93, 50, 48, 10, 76, 74, 24, 6, 74, 76, 9, 48, 50, 93, 82, 74, 76, 24, 6, 19, 74, 76, 24, 6] | 26 | 1.0652458667755127 | 26 | 4 | 18 | [[[100, 96, 93, 82, 6, 19], [68, 53, 50, 9, "_", 24], [16, 15, 48, 10, 76, 74]]] | [[[100, 96, 93, 82, 6, 19], [68, 53, 50, 9, "_", 24], [16, 15, 48, 10, 76, 74]]] | ["[[100, 96, 93, 82, 6, 19], [68, 53, 50, 9, '_', 24], [16, 15, 48, 10, 76, 74]]"] |
97 | 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 | 4 | ["down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "down-left", "up-left", "up-right", "up-left"] | 20 | 0.3242766857147217 | 20 | 4 | 30 | [[["e", "b", "v", "r", "l", "t"], ["m", "u", "r", "m", "i", "r"], ["h", "o", "a", "a", "_", "e"], ["c", "n", "i", "s", "e", "s"], ["t", "i", "l", "p", "y", "h"]]] | [[["e", "b", "v", "r", "l", "t"], ["m", "u", "r", "m", "i", "r"], ["h", "o", "a", "a", "_", "e"], ["c", "n", "i", "s", "e", "s"], ["t", "i", "l", "p", "y", "h"]], ["burst", "merril", "monase", "chivey", "tilpah"]] | ["[['e', 'b', 'v', 'r', 'l', 't'], ['m', 'u', 'r', 'm', 'i', 'r'], ['h', 'o', 'a', 'a', '_', 'e'], ['c', 'n', 'i', 's', 'e', 's'], ['t', 'i', 'l', 'p', 'y', 'h']]", "['burst', 'merril', 'monase', 'chivey', 'tilpah']"] |
97 | 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 | 15 | ["Q", "E", "Y", "A", "N", "Y", "X", "N"] | 8 | 0.03821444511413574 | 8 | 15 | 18 | [[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,... | [[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,... | ["[[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0... |
97 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [39, 3, 38, 10, 3, 5, 6, 14, 32, 7, 30, 28, 17, 9, 8, 13, 17, 41, 25, 6, 19, 36, 5, 36, 8, 38, 6, 19, 25, 3, 22, 18, 3, 21, 57, 37, 42, 30, 54, 13, 36, 6, 13, 17, 10, 4, 36], such that the sum of the chosen coins adds up t... | coin_exchange | subset_sum | 27 | [38, 18, 25, 37, 4, 13, 13, 25, 8, 13, 57, 54, 38, 28, 8, 41, 32] | 70 | 0.06327366828918457 | 17 | 47 | 47 | [[39, 3, 38, 10, 3, 5, 6, 14, 32, 7, 30, 28, 17, 9, 8, 13, 17, 41, 25, 6, 19, 36, 5, 36, 8, 38, 6, 19, 25, 3, 22, 18, 3, 21, 57, 37, 42, 30, 54, 13, 36, 6, 13, 17, 10, 4, 36]] | [[39, 3, 38, 10, 3, 5, 6, 14, 32, 7, 30, 28, 17, 9, 8, 13, 17, 41, 25, 6, 19, 36, 5, 36, 8, 38, 6, 19, 25, 3, 22, 18, 3, 21, 57, 37, 42, 30, 54, 13, 36, 6, 13, 17, 10, 4, 36], {"37": 2, "38": 4, "30": 18, "39": 18, "14": 1, "18": 1, "4": 1, "10": 8, "21": 10, "6": 5, "42": 13, "32": 10, "25": 2, "17": 15, "13": 2, "9":... | ["[39, 3, 38, 10, 3, 5, 6, 14, 32, 7, 30, 28, 17, 9, 8, 13, 17, 41, 25, 6, 19, 36, 5, 36, 8, 38, 6, 19, 25, 3, 22, 18, 3, 21, 57, 37, 42, 30, 54, 13, 36, 6, 13, 17, 10, 4, 36]", "{37: 2, 38: 4, 30: 18, 39: 18, 14: 1, 18: 1, 4: 1, 10: 8, 21: 10, 6: 5, 42: 13, 32: 10, 25: 2, 17: 15, 13: 2, 9: 4, 22: 17, 7: 5, 3: 2, 54: 7... |
97 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[1, 0], [1, 0], [2, 1], [0, 1], [2, 1], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [0, 1], [0, 2], [1, 0], [2, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 0], [2, 1]] | 36 | 382.4207499027252 | 36 | 6 | 18 | [[["Red", "Red", "Blue", "Red", "Blue", "Green"], ["Red", "Green", "Blue", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red", "Blue", "Green"]], 9] | [[["Red", "Red", "Blue", "Red", "Blue", "Green"], ["Red", "Green", "Blue", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red", "Blue", "Green"]], 9] | ["[['Red', 'Red', 'Blue', 'Red', 'Blue', 'Green'], ['Red', 'Green', 'Blue', 'Blue', 'Green', 'Red'], ['Blue', 'Green', 'Green', 'Red', 'Blue', 'Green']]", "9"] |
97 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 11 to 62. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 117, 160, None for columns 1 to 2 respectively, and the sums of rows must be None, 175, 114, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[0, 2, 11], [0, 3, 14], [1, 0, 12], [1, 1, 60], [1, 2, 61], [1, 3, 42], [2, 0, 18], [2, 2, 35], [3, 0, 17]] | 506 | 231.75803446769714 | 9 | 36 | 16 | ["[['58', '19', '', ''], ['', '', '', ''], ['', '22', '', '39'], ['', '16', '53', '29']]", 4, 11, 62] | ["[['58', '19', '', ''], ['', '', '', ''], ['', '22', '', '39'], ['', '16', '53', '29']]", 11, 62, [1, 3], [1, 3], [117, 160], [175, 114], 114] | ["[['58', '19', '', ''], ['', '', '', ''], ['', '22', '', '39'], ['', '16', '53', '29']]", "11", "62", "[None, 117, 160, None]", "[None, 175, 114, None]", "114"] |
97 | 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 (9, 1) to his destination workshop at index (7, 14), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[9, 1], [9, 2], [9, 3], [9, 4], [8, 4], [7, 4], [6, 4], [6, 5], [6, 6], [6, 7], [6, 8], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [6, 14], [7, 14]] | 202 | 0.027507543563842773 | 20 | 4 | 4 | [[["17", "8", "x", "3", "x", "13", "x", "x", "14", "11", "x", "x", "x", "x", "x"], ["x", "x", "x", "7", "x", "x", "13", "x", "x", "x", "x", "x", "16", "x", "13"], ["x", "x", "2", "x", "x", "12", "10", "x", "x", "x", "2", "x", "x", "5", "17"], ["4", "3", "x", "14", "x", "x", "16", "x", "x", "x", "1", "x", "x", "x", "x"]... | [[["17", "8", "x", "3", "x", "13", "x", "x", "14", "11", "x", "x", "x", "x", "x"], ["x", "x", "x", "7", "x", "x", "13", "x", "x", "x", "x", "x", "16", "x", "13"], ["x", "x", "2", "x", "x", "12", "10", "x", "x", "x", "2", "x", "x", "5", "17"], ["4", "3", "x", "14", "x", "x", "16", "x", "x", "x", "1", "x", "x", "x", "x"]... | ["[['17', '8', 'x', '3', 'x', '13', 'x', 'x', '14', '11', 'x', 'x', 'x', 'x', 'x'], ['x', 'x', 'x', '7', 'x', 'x', '13', 'x', 'x', 'x', 'x', 'x', '16', 'x', '13'], ['x', 'x', '2', 'x', 'x', '12', '10', 'x', 'x', 'x', '2', 'x', 'x', '5', '17'], ['4', '3', 'x', '14', 'x', 'x', '16', 'x', 'x', 'x', '1', 'x', 'x', 'x', 'x'... |
97 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[4, 14], [5, 13], [5, 12], [6, 12], [7, 11], [7, 10], [7, 9], [7, 8], [7, 7], [7, 6], [7, 5], [7, 4], [7, 3], [8, 3], [9, 2], [10, 1], [11, 0]] | 17 | 0.02439427375793457 | 17 | 8 | 2 | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1... | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1... | ["[[1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1... |
97 | Given 9 labeled water jugs with capacities 59, 104, 79, 23, 20, 60, 14, 15, 119, 105 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 215, 403, 420, 504 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exce... | water_jug | subset_sum | 7 | [["+", 14, 4], ["+", 119, 4], ["+", 119, 4], ["+", 119, 4], ["+", 119, 4], ["+", 14, 4], ["+", 105, 3], ["+", 105, 3], ["+", 105, 3], ["+", 105, 3], ["+", 60, 2], ["+", 105, 2], ["+", 119, 2], ["+", 119, 2], ["+", 119, 1], ["-", 23, 1], ["+", 119, 1]] | 17 | 0.03369307518005371 | 17 | 80 | 3 | [[59, 104, 79, 23, 20, 60, 14, 15, 119, 105], [215, 403, 420, 504]] | [[59, 104, 79, 23, 20, 60, 14, 15, 119, 105], [215, 403, 420, 504]] | ["[59, 104, 79, 23, 20, 60, 14, 15, 119, 105]", "[215, 403, 420, 504]"] |
98 | 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 | [19, 54, 14, 78, 67, 61, 62, 88, 89, 92, 48, 63, 32, 48, 63, 62, 61, 57, 79, 67, 78, 53, 67, 78, 54, 14] | 26 | 0.06994152069091797 | 26 | 4 | 18 | [[[89, 88, 62, 57, 79, 53], [92, 48, 61, 67, 78, 14], [32, 63, 27, "_", 19, 54]]] | [[[89, 88, 62, 57, 79, 53], [92, 48, 61, 67, 78, 14], [32, 63, 27, "_", 19, 54]]] | ["[[89, 88, 62, 57, 79, 53], [92, 48, 61, 67, 78, 14], [32, 63, 27, '_', 19, 54]]"] |
98 | 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 | 4 | ["down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left... | 28 | 5.565536260604858 | 28 | 4 | 30 | [[["a", "r", "o", "f", "n", "y"], ["l", "g", "p", "p", "e", "a"], ["a", "n", "n", "i", "_", "a"], ["l", "t", "n", "d", "s", "e"], ["a", "c", "a", "i", "d", "a"]]] | [[["a", "r", "o", "f", "n", "y"], ["l", "g", "p", "p", "e", "a"], ["a", "n", "n", "i", "_", "a"], ["l", "t", "n", "d", "s", "e"], ["a", "c", "a", "i", "d", "a"]], ["rafty", "lapped", "angina", "lanose", "acnida"]] | ["[['a', 'r', 'o', 'f', 'n', 'y'], ['l', 'g', 'p', 'p', 'e', 'a'], ['a', 'n', 'n', 'i', '_', 'a'], ['l', 't', 'n', 'd', 's', 'e'], ['a', 'c', 'a', 'i', 'd', 'a']]", "['rafty', 'lapped', 'angina', 'lanose', 'acnida']"] |
98 | 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 | 15 | ["D", "B", "X", "K", "A", "X", "H", "J", "Q", "J"] | 10 | 0.061826229095458984 | 10 | 15 | 18 | [[[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,... | [[[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,... | ["[[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0... |
98 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [35, 14, 15, 111, 8, 4, 6, 37, 14, 33, 45, 32, 46, 41, 38, 19, 34, 14, 2, 4, 24, 36, 46, 33, 12, 2, 14, 28, 12, 21, 34, 26, 28, 27, 25, 4, 23, 43, 43, 20, 10, 13, 5, 36, 27, 36], such that the sum of the chosen coins adds ... | coin_exchange | subset_sum | 28 | [46, 38, 14, 111, 46, 14, 12, 4, 19, 14, 4, 45, 28, 14, 12, 4, 37] | 59 | 0.07613182067871094 | 17 | 46 | 46 | [[35, 14, 15, 111, 8, 4, 6, 37, 14, 33, 45, 32, 46, 41, 38, 19, 34, 14, 2, 4, 24, 36, 46, 33, 12, 2, 14, 28, 12, 21, 34, 26, 28, 27, 25, 4, 23, 43, 43, 20, 10, 13, 5, 36, 27, 36]] | [[35, 14, 15, 111, 8, 4, 6, 37, 14, 33, 45, 32, 46, 41, 38, 19, 34, 14, 2, 4, 24, 36, 46, 33, 12, 2, 14, 28, 12, 21, 34, 26, 28, 27, 25, 4, 23, 43, 43, 20, 10, 13, 5, 36, 27, 36], {"33": 16, "21": 14, "4": 1, "13": 9, "23": 8, "2": 2, "12": 2, "41": 15, "46": 6, "45": 2, "34": 16, "24": 15, "19": 4, "5": 4, "35": 14, "... | ["[35, 14, 15, 111, 8, 4, 6, 37, 14, 33, 45, 32, 46, 41, 38, 19, 34, 14, 2, 4, 24, 36, 46, 33, 12, 2, 14, 28, 12, 21, 34, 26, 28, 27, 25, 4, 23, 43, 43, 20, 10, 13, 5, 36, 27, 36]", "{33: 16, 21: 14, 4: 1, 13: 9, 23: 8, 2: 2, 12: 2, 41: 15, 46: 6, 45: 2, 34: 16, 24: 15, 19: 4, 5: 4, 35: 14, 6: 6, 37: 13, 26: 16, 43: 20... |
98 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[0, 1], [0, 2], [0, 1], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0]] | 29 | 370.69857454299927 | 29 | 6 | 18 | [[["Blue", "Red", "Blue", "Red", "Blue", "Red"], ["Blue", "Blue", "Red", "Green", "Green", "Green"], ["Green", "Red", "Green", "Blue", "Green", "Red"]], 9] | [[["Blue", "Red", "Blue", "Red", "Blue", "Red"], ["Blue", "Blue", "Red", "Green", "Green", "Green"], ["Green", "Red", "Green", "Blue", "Green", "Red"]], 9] | ["[['Blue', 'Red', 'Blue', 'Red', 'Blue', 'Red'], ['Blue', 'Blue', 'Red', 'Green', 'Green', 'Green'], ['Green', 'Red', 'Green', 'Blue', 'Green', 'Red']]", "9"] |
98 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 33 to 84. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 189, 204, None for columns 1 to 2 respectively, and the sums of rows must be None, 229, 249, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[0, 1, 34], [0, 2, 48], [1, 1, 80], [1, 2, 39], [1, 3, 36], [2, 0, 46], [2, 1, 38], [2, 3, 83], [3, 1, 37], [3, 3, 33]] | 875 | 49.4717218875885 | 10 | 36 | 16 | ["[['68', '', '', '76'], ['74', '', '', ''], ['', '', '82', ''], ['66', '', '35', '']]", 4, 33, 84] | ["[['68', '', '', '76'], ['74', '', '', ''], ['', '', '82', ''], ['66', '', '35', '']]", 33, 84, [1, 3], [1, 3], [189, 204], [229, 249], 219] | ["[['68', '', '', '76'], ['74', '', '', ''], ['', '', '82', ''], ['66', '', '35', '']]", "33", "84", "[None, 189, 204, None]", "[None, 229, 249, None]", "219"] |
98 | 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 (9, 3) to his destination workshop at index (4, 14), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[9, 3], [8, 3], [7, 3], [6, 3], [6, 4], [6, 5], [5, 5], [4, 5], [4, 6], [4, 7], [3, 7], [3, 8], [2, 8], [2, 9], [2, 10], [1, 10], [1, 11], [1, 12], [2, 12], [3, 12], [3, 13], [3, 14], [4, 14]] | 212 | 0.02391839027404785 | 23 | 4 | 4 | [[["x", "19", "4", "x", "17", "11", "x", "x", "18", "7", "x", "8", "20", "x", "1"], ["x", "16", "x", "1", "9", "1", "x", "8", "16", "x", "15", "7", "1", "x", "x"], ["7", "x", "9", "9", "9", "x", "18", "x", "15", "13", "10", "x", "19", "16", "9"], ["x", "x", "x", "6", "x", "x", "7", "10", "18", "17", "x", "8", "9", "6",... | [[["x", "19", "4", "x", "17", "11", "x", "x", "18", "7", "x", "8", "20", "x", "1"], ["x", "16", "x", "1", "9", "1", "x", "8", "16", "x", "15", "7", "1", "x", "x"], ["7", "x", "9", "9", "9", "x", "18", "x", "15", "13", "10", "x", "19", "16", "9"], ["x", "x", "x", "6", "x", "x", "7", "10", "18", "17", "x", "8", "9", "6",... | ["[['x', '19', '4', 'x', '17', '11', 'x', 'x', '18', '7', 'x', '8', '20', 'x', '1'], ['x', '16', 'x', '1', '9', '1', 'x', '8', '16', 'x', '15', '7', '1', 'x', 'x'], ['7', 'x', '9', '9', '9', 'x', '18', 'x', '15', '13', '10', 'x', '19', '16', '9'], ['x', 'x', 'x', '6', 'x', 'x', '7', '10', '18', '17', 'x', '8', '9', '6'... |
98 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[1, 2], [1, 3], [1, 4], [0, 4], [0, 5], [1, 6], [2, 6], [3, 6], [3, 7], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [9, 8], [10, 9], [11, 10], [12, 11]] | 18 | 0.02712726593017578 | 18 | 8 | 2 | ["[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0... | ["[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0... | ["[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0... |
98 | Given 9 labeled water jugs with capacities 137, 100, 82, 25, 21, 101, 118, 117, 26, 131 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 272, 439, 458, 590 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time e... | water_jug | subset_sum | 7 | [["+", 82, 4], ["+", 117, 4], ["+", 117, 4], ["+", 137, 4], ["+", 137, 4], ["+", 26, 3], ["+", 137, 3], ["+", 137, 3], ["+", 137, 3], ["+", 21, 3], ["+", 100, 2], ["+", 101, 2], ["+", 101, 2], ["+", 137, 2], ["+", 117, 1], ["+", 137, 1], ["-", 82, 1], ["+", 100, 1]] | 18 | 0.05659294128417969 | 18 | 80 | 3 | [[137, 100, 82, 25, 21, 101, 118, 117, 26, 131], [272, 439, 458, 590]] | [[137, 100, 82, 25, 21, 101, 118, 117, 26, 131], [272, 439, 458, 590]] | ["[137, 100, 82, 25, 21, 101, 118, 117, 26, 131]", "[272, 439, 458, 590]"] |
99 | 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 | [34, 64, 92, 75, 100, 61, 90, 20, 43, 87, 86, 83, 42, 5, 20, 55, 64, 92, 75, 100, 92, 64, 61, 90, 87, 86, 83, 42] | 28 | 0.13985705375671387 | 28 | 4 | 18 | [[[92, 75, 100, 61, 43, 87], [64, 34, 55, 90, 20, 86], [36, "_", 32, 5, 42, 83]]] | [[[92, 75, 100, 61, 43, 87], [64, 34, 55, 90, 20, 86], [36, "_", 32, 5, 42, 83]]] | ["[[92, 75, 100, 61, 43, 87], [64, 34, 55, 90, 20, 86], [36, '_', 32, 5, 42, 83]]"] |
99 | 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 | 4 | ["up-right", "up-left", "up-left", "up-left", "down-left", "down-right", "down-left", "down-right", "up-right", "down-right", "up-right", "up-left", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-right", "down-right", "down-lef... | 30 | 13.15977692604065 | 30 | 4 | 30 | [[["o", "c", "a", "a", "n", "k"], ["h", "m", "r", "l", "i", "g"], ["h", "i", "o", "t", "u", "g"], ["t", "n", "r", "t", "a", "c"], ["z", "y", "t", "h", "_", "m"]]] | [[["o", "c", "a", "a", "n", "k"], ["h", "m", "r", "l", "i", "g"], ["h", "i", "o", "t", "u", "g"], ["t", "n", "r", "t", "a", "c"], ["z", "y", "t", "h", "_", "m"]], ["chank", "hormic", "tigtag", "tornal", "zythum"]] | ["[['o', 'c', 'a', 'a', 'n', 'k'], ['h', 'm', 'r', 'l', 'i', 'g'], ['h', 'i', 'o', 't', 'u', 'g'], ['t', 'n', 'r', 't', 'a', 'c'], ['z', 'y', 't', 'h', '_', 'm']]", "['chank', 'hormic', 'tigtag', 'tornal', 'zythum']"] |
99 | 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 | 15 | ["L", "U", "P", "W", "E", "D", "P", "W"] | 8 | 0.04042506217956543 | 8 | 15 | 18 | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,... | [[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0... |
99 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [37, 4, 1, 15, 2, 7, 8, 33, 35, 14, 47, 36, 41, 44, 13, 31, 3, 7, 27, 25, 26, 38, 10, 19, 7, 18, 32, 45, 29, 35, 44, 17, 40, 13, 14, 40, 28, 15, 23, 11, 7, 16, 7, 35, 31, 45, 14, 22, 7, 36, 31], such that the sum of the ch... | coin_exchange | subset_sum | 29 | [44, 40, 26, 14, 23, 14, 41, 40, 28, 14, 45, 44, 45, 47] | 69 | 0.07292604446411133 | 14 | 51 | 51 | [[37, 4, 1, 15, 2, 7, 8, 33, 35, 14, 47, 36, 41, 44, 13, 31, 3, 7, 27, 25, 26, 38, 10, 19, 7, 18, 32, 45, 29, 35, 44, 17, 40, 13, 14, 40, 28, 15, 23, 11, 7, 16, 7, 35, 31, 45, 14, 22, 7, 36, 31]] | [[37, 4, 1, 15, 2, 7, 8, 33, 35, 14, 47, 36, 41, 44, 13, 31, 3, 7, 27, 25, 26, 38, 10, 19, 7, 18, 32, 45, 29, 35, 44, 17, 40, 13, 14, 40, 28, 15, 23, 11, 7, 16, 7, 35, 31, 45, 14, 22, 7, 36, 31], {"44": 2, "1": 1, "36": 14, "26": 2, "22": 10, "33": 13, "16": 12, "23": 1, "41": 6, "8": 6, "18": 3, "13": 5, "2": 2, "7": ... | ["[37, 4, 1, 15, 2, 7, 8, 33, 35, 14, 47, 36, 41, 44, 13, 31, 3, 7, 27, 25, 26, 38, 10, 19, 7, 18, 32, 45, 29, 35, 44, 17, 40, 13, 14, 40, 28, 15, 23, 11, 7, 16, 7, 35, 31, 45, 14, 22, 7, 36, 31]", "{44: 2, 1: 1, 36: 14, 26: 2, 22: 10, 33: 13, 16: 12, 23: 1, 41: 6, 8: 6, 18: 3, 13: 5, 2: 2, 7: 5, 29: 13, 25: 19, 3: 1, ... |
99 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[2, 1], [0, 1], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [2, 1]] | 33 | 52.178091049194336 | 33 | 6 | 18 | [[["Blue", "Red", "Red", "Green", "Blue", "Green"], ["Blue", "Red", "Red", "Red", "Green", "Green"], ["Blue", "Red", "Blue", "Blue", "Green", "Green"]], 9] | [[["Blue", "Red", "Red", "Green", "Blue", "Green"], ["Blue", "Red", "Red", "Red", "Green", "Green"], ["Blue", "Red", "Blue", "Blue", "Green", "Green"]], 9] | ["[['Blue', 'Red', 'Red', 'Green', 'Blue', 'Green'], ['Blue', 'Red', 'Red', 'Red', 'Green', 'Green'], ['Blue', 'Red', 'Blue', 'Blue', 'Green', 'Green']]", "9"] |
99 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 86. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 239, 192, None for columns 1 to 2 respectively, and the sums of rows must be None, 220, 184, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[0, 0, 31], [0, 1, 51], [0, 2, 53], [1, 1, 49], [2, 1, 54], [2, 3, 30], [3, 0, 46], [3, 1, 85]] | 845 | 26.860548496246338 | 8 | 36 | 16 | ["[['', '', '', '67'], ['62', '', '32', '77'], ['66', '', '34', ''], ['', '', '73', '35']]", 4, 30, 86] | ["[['', '', '', '67'], ['62', '', '32', '77'], ['66', '', '34', ''], ['', '', '73', '35']]", 30, 86, [1, 3], [1, 3], [239, 192], [220, 184], 199] | ["[['', '', '', '67'], ['62', '', '32', '77'], ['66', '', '34', ''], ['', '', '73', '35']]", "30", "86", "[None, 239, 192, None]", "[None, 220, 184, None]", "199"] |
99 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 14) to his destination workshop at index (8, 3), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[4, 14], [4, 13], [4, 12], [4, 11], [4, 10], [4, 9], [4, 8], [5, 8], [6, 8], [7, 8], [7, 7], [7, 6], [7, 5], [7, 4], [8, 4], [8, 3]] | 125 | 0.02839803695678711 | 16 | 4 | 4 | [[["7", "6", "11", "x", "x", "x", "19", "x", "9", "15", "12", "8", "10", "15", "5"], ["9", "14", "x", "x", "x", "x", "x", "x", "x", "x", "18", "2", "11", "x", "10"], ["14", "5", "x", "x", "4", "4", "12", "x", "18", "x", "17", "11", "3", "18", "19"], ["18", "17", "x", "8", "x", "x", "9", "x", "x", "8", "19", "10", "x", ... | [[["7", "6", "11", "x", "x", "x", "19", "x", "9", "15", "12", "8", "10", "15", "5"], ["9", "14", "x", "x", "x", "x", "x", "x", "x", "x", "18", "2", "11", "x", "10"], ["14", "5", "x", "x", "4", "4", "12", "x", "18", "x", "17", "11", "3", "18", "19"], ["18", "17", "x", "8", "x", "x", "9", "x", "x", "8", "19", "10", "x", ... | ["[['7', '6', '11', 'x', 'x', 'x', '19', 'x', '9', '15', '12', '8', '10', '15', '5'], ['9', '14', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', '18', '2', '11', 'x', '10'], ['14', '5', 'x', 'x', '4', '4', '12', 'x', '18', 'x', '17', '11', '3', '18', '19'], ['18', '17', 'x', '8', 'x', 'x', '9', 'x', 'x', '8', '19', '10', 'x',... |
99 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[11, 1], [10, 2], [9, 1], [8, 1], [7, 0], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [5, 4], [4, 4], [4, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [2, 12]] | 20 | 0.03243589401245117 | 20 | 8 | 2 | ["[[0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1... | ["[[0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1... | ["[[0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1... |
99 | Given 9 labeled water jugs with capacities 32, 73, 55, 68, 61, 107, 44, 45, 74, 113 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 203, 429, 433, 477 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time excee... | water_jug | subset_sum | 7 | [["+", 74, 4], ["+", 74, 4], ["+", 74, 4], ["+", 113, 4], ["+", 68, 4], ["+", 74, 4], ["+", 68, 3], ["+", 107, 3], ["+", 113, 3], ["+", 113, 3], ["+", 32, 3], ["+", 61, 2], ["+", 113, 2], ["+", 113, 2], ["+", 74, 2], ["+", 68, 2], ["+", 61, 1], ["+", 74, 1], ["+", 68, 1]] | 19 | 0.048816680908203125 | 19 | 80 | 3 | [[32, 73, 55, 68, 61, 107, 44, 45, 74, 113], [203, 429, 433, 477]] | [[32, 73, 55, 68, 61, 107, 44, 45, 74, 113], [203, 429, 433, 477]] | ["[32, 73, 55, 68, 61, 107, 44, 45, 74, 113]", "[203, 429, 433, 477]"] |
100 | 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 | [37, 17, 55, 19, 26, 34, 44, 29, 74, 44, 29, 69, 34, 29, 17, 26, 29, 17, 44, 37, 76, 55, 19, 29, 26, 19, 55, 91, 93, 61, 67, 32, 29, 26, 19, 44, 37, 74, 69, 34] | 40 | 21.31004285812378 | 40 | 4 | 18 | [[[94, 91, 76, "_", 74, 29], [61, 93, 17, 37, 34, 44], [67, 32, 55, 19, 26, 69]]] | [[[94, 91, 76, "_", 74, 29], [61, 93, 17, 37, 34, 44], [67, 32, 55, 19, 26, 69]]] | ["[[94, 91, 76, '_', 74, 29], [61, 93, 17, 37, 34, 44], [67, 32, 55, 19, 26, 69]]"] |
100 | 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 | 4 | ["down-right", "up-right", "up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "down-right", "up-right", "down-right", "up-right", "up-left", "up-left", "down-left", "down-left", "up-le... | 28 | 19.604556798934937 | 28 | 4 | 30 | [[["o", "k", "s", "t", "a", "r"], ["b", "y", "n", "i", "a", "a"], ["s", "a", "_", "b", "a", "r"], ["m", "o", "p", "e", "n", "u"], ["v", "o", "m", "e", "a", "r"]]] | [[["o", "k", "s", "t", "a", "r"], ["b", "y", "n", "i", "a", "a"], ["s", "a", "_", "b", "a", "r"], ["m", "o", "p", "e", "n", "u"], ["v", "o", "m", "e", "a", "r"]], ["katar", "bonsai", "sambar", "mopane", "voyeur"]] | ["[['o', 'k', 's', 't', 'a', 'r'], ['b', 'y', 'n', 'i', 'a', 'a'], ['s', 'a', '_', 'b', 'a', 'r'], ['m', 'o', 'p', 'e', 'n', 'u'], ['v', 'o', 'm', 'e', 'a', 'r']]", "['katar', 'bonsai', 'sambar', 'mopane', 'voyeur']"] |
100 | 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 | 15 | ["R", "K", "N", "H", "X", "L", "X", "A", "N"] | 9 | 0.15291357040405273 | 9 | 15 | 18 | [[[0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,... | [[[0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,... | ["[[0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0... |
100 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [19, 11, 3, 37, 9, 29, 42, 12, 2, 13, 15, 11, 25, 14, 31, 17, 24, 45, 5, 18, 42, 21, 28, 23, 26, 40, 27, 42, 12, 13, 16, 14, 31, 38, 9, 24, 27, 36, 13, 27, 15, 43, 9, 14, 34, 7, 15, 12, 31, 44], such that the sum of the ch... | coin_exchange | subset_sum | 30 | [27, 27, 31, 31, 14, 27, 31, 43, 42, 45, 44, 42, 36, 2, 7] | 41 | 0.05939221382141113 | 15 | 50 | 50 | [[19, 11, 3, 37, 9, 29, 42, 12, 2, 13, 15, 11, 25, 14, 31, 17, 24, 45, 5, 18, 42, 21, 28, 23, 26, 40, 27, 42, 12, 13, 16, 14, 31, 38, 9, 24, 27, 36, 13, 27, 15, 43, 9, 14, 34, 7, 15, 12, 31, 44]] | [[19, 11, 3, 37, 9, 29, 42, 12, 2, 13, 15, 11, 25, 14, 31, 17, 24, 45, 5, 18, 42, 21, 28, 23, 26, 40, 27, 42, 12, 13, 16, 14, 31, 38, 9, 24, 27, 36, 13, 27, 15, 43, 9, 14, 34, 7, 15, 12, 31, 44], {"37": 7, "45": 7, "29": 6, "27": 2, "2": 2, "40": 6, "13": 9, "17": 2, "9": 2, "15": 12, "36": 2, "26": 18, "44": 5, "42": ... | ["[19, 11, 3, 37, 9, 29, 42, 12, 2, 13, 15, 11, 25, 14, 31, 17, 24, 45, 5, 18, 42, 21, 28, 23, 26, 40, 27, 42, 12, 13, 16, 14, 31, 38, 9, 24, 27, 36, 13, 27, 15, 43, 9, 14, 34, 7, 15, 12, 31, 44]", "{37: 7, 45: 7, 29: 6, 27: 2, 2: 2, 40: 6, 13: 9, 17: 2, 9: 2, 15: 12, 36: 2, 26: 18, 44: 5, 42: 4, 38: 8, 43: 2, 12: 4, 2... |
100 | The game of 'Sort It' begins with 3 tubes, each filled with 6 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 | 10 | [[0, 2], [1, 2], [0, 2], [0, 1], [0, 1], [2, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2]] | 35 | 125.36433982849121 | 35 | 6 | 18 | [[["Blue", "Green", "Red", "Red", "Blue", "Green"], ["Blue", "Red", "Green", "Green", "Green", "Red"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"]], 9] | [[["Blue", "Green", "Red", "Red", "Blue", "Green"], ["Blue", "Red", "Green", "Green", "Green", "Red"], ["Blue", "Blue", "Blue", "Red", "Red", "Green"]], 9] | ["[['Blue', 'Green', 'Red', 'Red', 'Blue', 'Green'], ['Blue', 'Red', 'Green', 'Green', 'Green', 'Red'], ['Blue', 'Blue', 'Blue', 'Red', 'Red', 'Green']]", "9"] |
100 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 86. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 295, 204, None for columns 1 to 2 respectively, and the sums of rows must be None, 244, 251, None for rows 1 to... | magic_square | underdetermined_system | 9 | [[0, 3, 33], [1, 0, 35], [1, 2, 80], [1, 3, 46], [2, 0, 72], [3, 0, 47], [3, 2, 30], [3, 3, 31]] | 839 | 14.697113037109375 | 8 | 36 | 16 | ["[['32', '75', '36', ''], ['', '83', '', ''], ['', '77', '58', '44'], ['', '60', '', '']]", 4, 30, 86] | ["[['32', '75', '36', ''], ['', '83', '', ''], ['', '77', '58', '44'], ['', '60', '', '']]", 30, 86, [1, 3], [1, 3], [295, 204], [244, 251], 237] | ["[['32', '75', '36', ''], ['', '83', '', ''], ['', '77', '58', '44'], ['', '60', '', '']]", "30", "86", "[None, 295, 204, None]", "[None, 244, 251, None]", "237"] |
100 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 0) to his destination workshop at index (9, 11), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[4, 0], [5, 0], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [7, 4], [7, 5], [8, 5], [8, 6], [8, 7], [9, 7], [9, 8], [9, 9], [10, 9], [9, 9], [9, 10], [9, 11]] | 170 | 0.028670310974121094 | 19 | 4 | 4 | [[["x", "2", "16", "x", "9", "x", "14", "x", "8", "x", "16", "x", "x", "4", "8"], ["9", "x", "4", "x", "x", "7", "11", "x", "x", "13", "x", "x", "6", "11", "x"], ["x", "x", "10", "14", "x", "x", "18", "x", "x", "x", "x", "x", "6", "16", "x"], ["x", "14", "x", "1", "x", "7", "5", "16", "x", "19", "x", "x", "10", "7", "x... | [[["x", "2", "16", "x", "9", "x", "14", "x", "8", "x", "16", "x", "x", "4", "8"], ["9", "x", "4", "x", "x", "7", "11", "x", "x", "13", "x", "x", "6", "11", "x"], ["x", "x", "10", "14", "x", "x", "18", "x", "x", "x", "x", "x", "6", "16", "x"], ["x", "14", "x", "1", "x", "7", "5", "16", "x", "19", "x", "x", "10", "7", "x... | ["[['x', '2', '16', 'x', '9', 'x', '14', 'x', '8', 'x', '16', 'x', 'x', '4', '8'], ['9', 'x', '4', 'x', 'x', '7', '11', 'x', 'x', '13', 'x', 'x', '6', '11', 'x'], ['x', 'x', '10', '14', 'x', 'x', '18', 'x', 'x', 'x', 'x', 'x', '6', '16', 'x'], ['x', '14', 'x', '1', 'x', '7', '5', '16', 'x', '19', 'x', 'x', '10', '7', '... |
100 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[2, 2], [1, 3], [0, 4], [0, 5], [1, 5], [2, 5], [2, 6], [3, 6], [3, 7], [3, 8], [4, 8], [4, 9], [4, 10], [4, 11], [5, 11], [6, 11], [7, 12], [8, 12], [9, 12], [10, 13], [11, 13], [12, 14], [13, 14]] | 23 | 0.03257179260253906 | 23 | 8 | 2 | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0... | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0... | ["[[1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0... |
100 | Given 9 labeled water jugs with capacities 126, 120, 127, 110, 54, 39, 38, 47, 139, 99 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 219, 240, 312, 411 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time ex... | water_jug | subset_sum | 7 | [["+", 99, 4], ["+", 139, 4], ["+", 47, 4], ["+", 126, 4], ["+", 47, 3], ["+", 126, 3], ["+", 139, 3], ["+", 120, 2], ["+", 120, 2], ["+", 99, 1], ["+", 120, 1]] | 11 | 0.045166015625 | 11 | 80 | 3 | [[126, 120, 127, 110, 54, 39, 38, 47, 139, 99], [219, 240, 312, 411]] | [[126, 120, 127, 110, 54, 39, 38, 47, 139, 99], [219, 240, 312, 411]] | ["[126, 120, 127, 110, 54, 39, 38, 47, 139, 99]", "[219, 240, 312, 411]"] |
101 | 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 | 15 | ["P", "E", "N", "B", "N", "R", "I", "F", "X", "I"] | 10 | 0.16242361068725586 | 10 | 15 | 18 | [[[0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1,... | [[[0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1,... | ["[[0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1... |
101 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [29, 25, 15, 12, 40, 23, 36, 22, 16, 24, 51, 34, 46, 29, 20, 14, 21, 27, 15, 31, 15, 17, 9, 42, 30, 45, 14, 14, 30, 16, 44, 32, 6, 15, 5, 41, 18, 43, 36, 31, 27, 26, 6, 44, 33, 23, 7, 19], such that the sum of the chosen c... | coin_exchange | subset_sum | 31 | [44, 36, 22, 23, 23, 29, 29, 33, 51, 44, 42, 36, 18, 31, 16] | 66 | 0.06806683540344238 | 15 | 48 | 48 | [[29, 25, 15, 12, 40, 23, 36, 22, 16, 24, 51, 34, 46, 29, 20, 14, 21, 27, 15, 31, 15, 17, 9, 42, 30, 45, 14, 14, 30, 16, 44, 32, 6, 15, 5, 41, 18, 43, 36, 31, 27, 26, 6, 44, 33, 23, 7, 19]] | [[29, 25, 15, 12, 40, 23, 36, 22, 16, 24, 51, 34, 46, 29, 20, 14, 21, 27, 15, 31, 15, 17, 9, 42, 30, 45, 14, 14, 30, 16, 44, 32, 6, 15, 5, 41, 18, 43, 36, 31, 27, 26, 6, 44, 33, 23, 7, 19], {"41": 15, "22": 3, "9": 4, "34": 9, "32": 11, "36": 5, "18": 5, "40": 9, "46": 11, "45": 17, "33": 3, "14": 9, "12": 12, "7": 2, ... | ["[29, 25, 15, 12, 40, 23, 36, 22, 16, 24, 51, 34, 46, 29, 20, 14, 21, 27, 15, 31, 15, 17, 9, 42, 30, 45, 14, 14, 30, 16, 44, 32, 6, 15, 5, 41, 18, 43, 36, 31, 27, 26, 6, 44, 33, 23, 7, 19]", "{41: 15, 22: 3, 9: 4, 34: 9, 32: 11, 36: 5, 18: 5, 40: 9, 46: 11, 45: 17, 33: 3, 14: 9, 12: 12, 7: 2, 43: 14, 25: 18, 31: 9, 51... |
101 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 86. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 260, 216, None for columns 1 to 2 respectively, and the sums of rows must be None, 183, 217, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 1, 76], [0, 3, 30], [1, 0, 31], [1, 3, 67], [2, 2, 72], [3, 0, 78], [3, 1, 85], [3, 2, 48]] | 905 | 50.447338819503784 | 8 | 36 | 16 | ["[['70', '', '50', ''], ['', '39', '46', ''], ['34', '60', '', '51'], ['', '', '', '68']]", 4, 30, 86] | ["[['70', '', '50', ''], ['', '39', '46', ''], ['34', '60', '', '51'], ['', '', '', '68']]", 30, 86, [1, 3], [1, 3], [260, 216], [183, 217], 214] | ["[['70', '', '50', ''], ['', '39', '46', ''], ['34', '60', '', '51'], ['', '', '', '68']]", "30", "86", "[None, 260, 216, None]", "[None, 183, 217, None]", "214"] |
101 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (7, 0) to his destination workshop at index (4, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[7, 0], [7, 1], [8, 1], [9, 1], [9, 2], [10, 2], [11, 2], [12, 2], [12, 3], [12, 4], [12, 5], [11, 5], [11, 6], [11, 7], [10, 7], [10, 8], [10, 9], [9, 9], [8, 9], [7, 9], [7, 10], [6, 10], [6, 11], [5, 11], [5, 12], [4, 12], [4, 13]] | 244 | 0.02743220329284668 | 27 | 4 | 4 | [[["x", "3", "1", "19", "8", "1", "4", "18", "15", "17", "4", "3", "x", "3", "x"], ["x", "11", "x", "x", "x", "12", "x", "19", "15", "4", "x", "x", "x", "x", "x"], ["4", "1", "x", "8", "x", "12", "17", "x", "14", "4", "9", "11", "13", "6", "19"], ["2", "x", "6", "14", "15", "x", "18", "9", "x", "10", "10", "x", "x", "1... | [[["x", "3", "1", "19", "8", "1", "4", "18", "15", "17", "4", "3", "x", "3", "x"], ["x", "11", "x", "x", "x", "12", "x", "19", "15", "4", "x", "x", "x", "x", "x"], ["4", "1", "x", "8", "x", "12", "17", "x", "14", "4", "9", "11", "13", "6", "19"], ["2", "x", "6", "14", "15", "x", "18", "9", "x", "10", "10", "x", "x", "1... | ["[['x', '3', '1', '19', '8', '1', '4', '18', '15', '17', '4', '3', 'x', '3', 'x'], ['x', '11', 'x', 'x', 'x', '12', 'x', '19', '15', '4', 'x', 'x', 'x', 'x', 'x'], ['4', '1', 'x', '8', 'x', '12', '17', 'x', '14', '4', '9', '11', '13', '6', '19'], ['2', 'x', '6', '14', '15', 'x', '18', '9', 'x', '10', '10', 'x', 'x', '... |
101 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[0, 3], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [9, 6], [10, 7], [11, 8], [12, 9], [13, 10], [14, 11]] | 18 | 0.027624130249023438 | 18 | 8 | 2 | ["[[1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1... | ["[[1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1... | ["[[1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1... |
102 | 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 | 15 | ["S", "J", "F", "C", "T", "V", "Z", "C", "T"] | 9 | 0.04518413543701172 | 9 | 15 | 18 | [[[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,... | [[[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,... | ["[[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0... |
102 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [14, 29, 39, 40, 16, 35, 17, 37, 43, 30, 28, 26, 13, 13, 42, 30, 10, 7, 44, 5, 34, 7, 32, 11, 40, 35, 12, 34, 35, 38, 29, 42, 33, 26, 4, 36, 41, 35, 26, 34, 16, 6, 38, 13, 41, 23, 20], such that the sum of the chosen coins... | coin_exchange | subset_sum | 32 | [26, 35, 26, 35, 26, 35, 34, 35, 34, 37, 36, 34, 28, 14, 10, 4] | 48 | 0.08744978904724121 | 16 | 47 | 47 | [[14, 29, 39, 40, 16, 35, 17, 37, 43, 30, 28, 26, 13, 13, 42, 30, 10, 7, 44, 5, 34, 7, 32, 11, 40, 35, 12, 34, 35, 38, 29, 42, 33, 26, 4, 36, 41, 35, 26, 34, 16, 6, 38, 13, 41, 23, 20]] | [[14, 29, 39, 40, 16, 35, 17, 37, 43, 30, 28, 26, 13, 13, 42, 30, 10, 7, 44, 5, 34, 7, 32, 11, 40, 35, 12, 34, 35, 38, 29, 42, 33, 26, 4, 36, 41, 35, 26, 34, 16, 6, 38, 13, 41, 23, 20], {"11": 4, "10": 3, "41": 9, "34": 4, "7": 2, "17": 16, "29": 8, "37": 1, "44": 8, "30": 13, "32": 9, "20": 18, "23": 8, "6": 4, "5": 3... | ["[14, 29, 39, 40, 16, 35, 17, 37, 43, 30, 28, 26, 13, 13, 42, 30, 10, 7, 44, 5, 34, 7, 32, 11, 40, 35, 12, 34, 35, 38, 29, 42, 33, 26, 4, 36, 41, 35, 26, 34, 16, 6, 38, 13, 41, 23, 20]", "{11: 4, 10: 3, 41: 9, 34: 4, 7: 2, 17: 16, 29: 8, 37: 1, 44: 8, 30: 13, 32: 9, 20: 18, 23: 8, 6: 4, 5: 3, 14: 3, 13: 7, 35: 4, 33: ... |
102 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 36 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 279, 306, None for columns 1 to 2 respectively, and the sums of rows must be None, 315, 234, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 1, 89], [0, 2, 59], [0, 3, 38], [1, 2, 82], [2, 0, 36], [2, 2, 78], [3, 0, 86], [3, 2, 87], [3, 3, 37]] | 1069 | 51.39947175979614 | 9 | 36 | 16 | ["[['44', '', '', ''], ['90', '52', '', '91'], ['', '58', '', '62'], ['', '80', '', '']]", 4, 36, 92] | ["[['44', '', '', ''], ['90', '52', '', '91'], ['', '58', '', '62'], ['', '80', '', '']]", 36, 92, [1, 3], [1, 3], [279, 306], [315, 234], 264] | ["[['44', '', '', ''], ['90', '52', '', '91'], ['', '58', '', '62'], ['', '80', '', '']]", "36", "92", "[None, 279, 306, None]", "[None, 315, 234, None]", "264"] |
102 | 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 (7, 13), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [6, 5], [7, 5], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9], [8, 10], [8, 11], [7, 11], [7, 12], [7, 13]] | 180 | 0.028650999069213867 | 18 | 4 | 4 | [[["x", "13", "x", "x", "x", "x", "3", "4", "x", "x", "9", "x", "18", "7", "2"], ["1", "10", "17", "x", "x", "x", "11", "13", "x", "10", "x", "9", "13", "x", "x"], ["x", "x", "7", "18", "x", "x", "x", "x", "7", "x", "x", "x", "1", "x", "16"], ["10", "x", "x", "x", "13", "x", "2", "9", "x", "x", "8", "x", "x", "5", "x"]... | [[["x", "13", "x", "x", "x", "x", "3", "4", "x", "x", "9", "x", "18", "7", "2"], ["1", "10", "17", "x", "x", "x", "11", "13", "x", "10", "x", "9", "13", "x", "x"], ["x", "x", "7", "18", "x", "x", "x", "x", "7", "x", "x", "x", "1", "x", "16"], ["10", "x", "x", "x", "13", "x", "2", "9", "x", "x", "8", "x", "x", "5", "x"]... | ["[['x', '13', 'x', 'x', 'x', 'x', '3', '4', 'x', 'x', '9', 'x', '18', '7', '2'], ['1', '10', '17', 'x', 'x', 'x', '11', '13', 'x', '10', 'x', '9', '13', 'x', 'x'], ['x', 'x', '7', '18', 'x', 'x', 'x', 'x', '7', 'x', 'x', 'x', '1', 'x', '16'], ['10', 'x', 'x', 'x', '13', 'x', '2', '9', 'x', 'x', '8', 'x', 'x', '5', 'x'... |
102 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[14, 13], [13, 13], [12, 13], [11, 13], [10, 13], [9, 12], [9, 11], [8, 10], [7, 10], [6, 10], [5, 10], [4, 9], [3, 8], [2, 7], [2, 6], [2, 5]] | 16 | 0.03172016143798828 | 16 | 8 | 2 | ["[[1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1... | ["[[1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1... | ["[[1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1... |
103 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [40, 28, 46, 16, 13, 15, 38, 39, 3, 8, 40, 41, 18, 48, 16, 25, 39, 14, 47, 46, 31, 16, 41, 45, 9, 26, 33, 46, 17, 23, 6, 46, 7, 43, 10, 28, 47, 15, 35, 20, 32, 4, 32, 9, 48, 7, 34, 46, 10, 39, 44], such that the sum of the... | coin_exchange | subset_sum | 33 | [44, 38, 14, 25, 31, 28, 10, 4, 43, 34, 28, 45, 40, 10, 17, 33, 41] | 91 | 0.0840153694152832 | 17 | 51 | 51 | [[40, 28, 46, 16, 13, 15, 38, 39, 3, 8, 40, 41, 18, 48, 16, 25, 39, 14, 47, 46, 31, 16, 41, 45, 9, 26, 33, 46, 17, 23, 6, 46, 7, 43, 10, 28, 47, 15, 35, 20, 32, 4, 32, 9, 48, 7, 34, 46, 10, 39, 44]] | [[40, 28, 46, 16, 13, 15, 38, 39, 3, 8, 40, 41, 18, 48, 16, 25, 39, 14, 47, 46, 31, 16, 41, 45, 9, 26, 33, 46, 17, 23, 6, 46, 7, 43, 10, 28, 47, 15, 35, 20, 32, 4, 32, 9, 48, 7, 34, 46, 10, 39, 44], {"44": 6, "39": 15, "4": 2, "23": 11, "7": 2, "40": 10, "13": 10, "34": 8, "45": 9, "10": 3, "35": 18, "14": 2, "28": 5, ... | ["[40, 28, 46, 16, 13, 15, 38, 39, 3, 8, 40, 41, 18, 48, 16, 25, 39, 14, 47, 46, 31, 16, 41, 45, 9, 26, 33, 46, 17, 23, 6, 46, 7, 43, 10, 28, 47, 15, 35, 20, 32, 4, 32, 9, 48, 7, 34, 46, 10, 39, 44]", "{44: 6, 39: 15, 4: 2, 23: 11, 7: 2, 40: 10, 13: 10, 34: 8, 45: 9, 10: 3, 35: 18, 14: 2, 28: 5, 46: 12, 25: 3, 26: 18, ... |
103 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 36 to 92. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 295, 200, None for columns 1 to 2 respectively, and the sums of rows must be None, 234, 271, None for rows 1 to... | magic_square | underdetermined_system | 10 | [[0, 2, 36], [0, 3, 42], [1, 0, 38], [1, 1, 88], [1, 2, 68], [2, 3, 67], [3, 0, 56], [3, 2, 37], [3, 3, 41]] | 881 | 8.308101177215576 | 9 | 36 | 16 | ["[['39', '47', '', ''], ['', '', '', '40'], ['63', '82', '59', ''], ['', '78', '', '']]", 4, 36, 92] | ["[['39', '47', '', ''], ['', '', '', '40'], ['63', '82', '59', ''], ['', '78', '', '']]", 36, 92, [1, 3], [1, 3], [295, 200], [234, 271], 248] | ["[['39', '47', '', ''], ['', '', '', '40'], ['63', '82', '59', ''], ['', '78', '', '']]", "36", "92", "[None, 295, 200, None]", "[None, 234, 271, None]", "248"] |
103 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 0) to his destination workshop at index (6, 14), indexing from 0. Ben's car can mov... | traffic | pathfinding | 7 | [[2, 0], [2, 1], [3, 1], [3, 2], [3, 3], [4, 3], [4, 4], [4, 5], [4, 6], [4, 7], [5, 7], [5, 8], [5, 9], [5, 10], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [7, 14], [8, 14], [9, 14], [8, 14], [7, 14], [6, 14]] | 208 | 0.028629302978515625 | 25 | 4 | 4 | [[["6", "6", "2", "x", "13", "x", "x", "x", "x", "11", "x", "x", "x", "3", "x"], ["6", "11", "x", "14", "x", "x", "x", "1", "5", "6", "1", "19", "2", "7", "14"], ["16", "4", "12", "13", "17", "4", "x", "x", "x", "14", "x", "x", "9", "9", "13"], ["x", "11", "6", "14", "x", "16", "x", "1", "10", "18", "11", "x", "x", "13... | [[["6", "6", "2", "x", "13", "x", "x", "x", "x", "11", "x", "x", "x", "3", "x"], ["6", "11", "x", "14", "x", "x", "x", "1", "5", "6", "1", "19", "2", "7", "14"], ["16", "4", "12", "13", "17", "4", "x", "x", "x", "14", "x", "x", "9", "9", "13"], ["x", "11", "6", "14", "x", "16", "x", "1", "10", "18", "11", "x", "x", "13... | ["[['6', '6', '2', 'x', '13', 'x', 'x', 'x', 'x', '11', 'x', 'x', 'x', '3', 'x'], ['6', '11', 'x', '14', 'x', 'x', 'x', '1', '5', '6', '1', '19', '2', '7', '14'], ['16', '4', '12', '13', '17', '4', 'x', 'x', 'x', '14', 'x', 'x', '9', '9', '13'], ['x', '11', '6', '14', 'x', '16', 'x', '1', '10', '18', '11', 'x', 'x', '1... |
103 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 15x15. 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 | 15 | [[10, 1], [9, 2], [9, 3], [9, 4], [8, 5], [7, 6], [6, 6], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [5, 12], [4, 12], [3, 13], [3, 14]] | 16 | 0.03287553787231445 | 16 | 8 | 2 | ["[[0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1], [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0... | ["[[0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1], [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0... | ["[[0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1], [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0... |
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