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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
55 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 28 to 59. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 162, 195, None for columns 1 to 2 respectively, and the sums of rows must be None, 168, 168, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 1, 29], [1, 0, 31], [1, 1, 39], [1, 3, 44], [2, 0, 35], [2, 1, 41], [2, 2, 49], [2, 3, 43], [3, 3, 30]] | 659 | 0.8985345363616943 | 9 | 49 | 9 | ["[['46', '', '58', '45'], ['', '', '54', ''], ['', '', '', ''], ['28', '53', '34', '']]", 4, 28, 59] | ["[['46', '', '58', '45'], ['', '', '54', ''], ['', '', '', ''], ['28', '53', '34', '']]", 28, 59, [1, 3], [1, 3], [162, 195], [168, 168], 168] | ["[['46', '', '58', '45'], ['', '', '54', ''], ['', '', '', ''], ['28', '53', '34', '']]", "28", "59", "[None, 162, 195, None]", "[None, 168, 168, None]", "168"] |
55 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[5, 6], [5, 3], [5, 6], [5, 2], [7, 3], [7, 5], [7, 3], [7, 6], [7, 3], [1, 6], [0, 7], [0, 7], [0, 7], [1, 7], [1, 5], [2, 1], [0, 5], [0, 1]] | 70 | 14.086882591247559 | 18 | 56 | 20 | [[["Red", "Red", "Red", "Green", "Yellow"], ["Black", "Red", "Green", "Yellow", "Yellow"], [], [], [], ["Black", "Blue", "Black", "Yellow", "Green"], [], ["Blue", "Green", "Blue", "Black", "Blue"]], 5, {"0": 8, "1": 2, "2": 7, "3": 6, "4": 7, "5": 1, "6": 5, "7": 3}] | [[["Red", "Red", "Red", "Green", "Yellow"], ["Black", "Red", "Green", "Yellow", "Yellow"], [], [], [], ["Black", "Blue", "Black", "Yellow", "Green"], [], ["Blue", "Green", "Blue", "Black", "Blue"]], 5, {"0": 8, "1": 2, "2": 7, "3": 6, "4": 7, "5": 1, "6": 5, "7": 3}, 4] | ["[['Red', 'Red', 'Red', 'Green', 'Yellow'], ['Black', 'Red', 'Green', 'Yellow', 'Yellow'], [], [], [], ['Black', 'Blue', 'Black', 'Yellow', 'Green'], [], ['Blue', 'Green', 'Blue', 'Black', 'Blue']]", "{0: 8, 1: 2, 2: 7, 3: 6, 4: 7, 5: 1, 6: 5, 7: 3}", "5", "4"] |
55 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 9) to his destination workshop at index (7, 1), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[3, 9], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [7, 9], [8, 9], [9, 9], [9, 8], [9, 7], [9, 6], [9, 5], [9, 4], [9, 3], [8, 3], [8, 2], [7, 2], [7, 1]] | 130 | 0.02777552604675293 | 19 | 4 | 4 | [[["9", "4", "16", "7", "x", "2", "x", "x", "14", "x", "x", "x"], ["x", "15", "10", "5", "12", "16", "x", "x", "x", "3", "12", "18"], ["12", "x", "x", "x", "9", "16", "3", "9", "x", "x", "x", "7"], ["10", "6", "3", "10", "x", "x", "1", "17", "x", "12", "12", "x"], ["11", "8", "15", "x", "8", "16", "x", "x", "5", "15", ... | [[["9", "4", "16", "7", "x", "2", "x", "x", "14", "x", "x", "x"], ["x", "15", "10", "5", "12", "16", "x", "x", "x", "3", "12", "18"], ["12", "x", "x", "x", "9", "16", "3", "9", "x", "x", "x", "7"], ["10", "6", "3", "10", "x", "x", "1", "17", "x", "12", "12", "x"], ["11", "8", "15", "x", "8", "16", "x", "x", "5", "15", ... | ["[['9', '4', '16', '7', 'x', '2', 'x', 'x', '14', 'x', 'x', 'x'], ['x', '15', '10', '5', '12', '16', 'x', 'x', 'x', '3', '12', '18'], ['12', 'x', 'x', 'x', '9', '16', '3', '9', 'x', 'x', 'x', '7'], ['10', '6', '3', '10', 'x', 'x', '1', '17', 'x', '12', '12', 'x'], ['11', '8', '15', 'x', '8', '16', 'x', 'x', '5', '15',... |
55 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[1, 11], [0, 10], [0, 9], [0, 8], [0, 7], [0, 6], [0, 5], [1, 5], [1, 4], [2, 3], [3, 2], [4, 2], [5, 2], [6, 2], [6, 1], [7, 0], [8, 0], [9, 0]] | 18 | 0.029353857040405273 | 18 | 8 | 2 | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, ... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, ... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1], [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, ... |
55 | Given 5 labeled water jugs with capacities 33, 87, 48, 30, 61, 60 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 170, 225, 238, 317 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wa... | water_jug | subset_sum | 5 | [["+", 60, 4], ["+", 61, 4], ["+", 87, 4], ["+", 48, 4], ["+", 61, 4], ["+", 60, 3], ["+", 61, 3], ["+", 30, 3], ["+", 87, 3], ["+", 48, 2], ["+", 60, 2], ["+", 87, 2], ["+", 30, 2], ["+", 61, 1], ["+", 61, 1], ["+", 48, 1]] | 16 | 0.039655208587646484 | 16 | 48 | 3 | [[33, 87, 48, 30, 61, 60], [170, 225, 238, 317]] | [[33, 87, 48, 30, 61, 60], [170, 225, 238, 317]] | ["[33, 87, 48, 30, 61, 60]", "[170, 225, 238, 317]"] |
56 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [15, 84, 100, 10, 24, 100, 84, 80, 33, 96, 100, 84, 80, 33, 22, 79, 66, 100, 84, 80, 33, 15, 10, 24, 80, 84, 96, 66, 79, 22, 15, 10] | 32 | 1.4827980995178223 | 32 | 4 | 12 | [[[66, 96, 24, 10], [79, 33, 84, 100], [22, 80, 15, "_"]]] | [[[66, 96, 24, 10], [79, 33, 84, 100], [22, 80, 15, "_"]]] | ["[[66, 96, 24, 10], [79, 33, 84, 100], [22, 80, 15, '_']]"] |
56 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-right", "up-left", "up-left"] | 12 | 0.2367854118347168 | 12 | 4 | 20 | [[["a", "n", "x", "e"], ["c", "y", "l", "a"], ["r", "e", "_", "n"], ["j", "h", "o", "a"], ["e", "x", "b", "m"]]] | [[["a", "n", "x", "e"], ["c", "y", "l", "a"], ["r", "e", "_", "n"], ["j", "h", "o", "a"], ["e", "x", "b", "m"]], ["nye", "calx", "hern", "jaob", "exam"]] | ["[['a', 'n', 'x', 'e'], ['c', 'y', 'l', 'a'], ['r', 'e', '_', 'n'], ['j', 'h', 'o', 'a'], ['e', 'x', 'b', 'm']]", "['nye', 'calx', 'hern', 'jaob', 'exam']"] |
56 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["C", "D", "B", "K", "M", "L", "F", "I", "L", "W", "B"] | 11 | 0.1076192855834961 | 11 | 13 | 16 | [[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, ... | [[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, ... | ["[[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0,... |
56 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [4, 33, 14, 32, 9, 32, 2, 35, 25, 10, 11, 6, 8, 26, 10, 25, 34, 21, 13, 15, 3, 15, 25, 3, 16, 3, 2, 25, 15, 23, 31, 35, 13, 14, 5, 7, 2, 18, 10, 8, 25, 30, 13, 35, 3, 26, 33, 2, 5, 26, 26, 28, 6], such that the sum of the ... | coin_exchange | subset_sum | 28 | [34, 32, 26, 2, 35, 32, 30, 26, 35, 26, 35, 26, 16] | 64 | 0.06210756301879883 | 13 | 53 | 53 | [[4, 33, 14, 32, 9, 32, 2, 35, 25, 10, 11, 6, 8, 26, 10, 25, 34, 21, 13, 15, 3, 15, 25, 3, 16, 3, 2, 25, 15, 23, 31, 35, 13, 14, 5, 7, 2, 18, 10, 8, 25, 30, 13, 35, 3, 26, 33, 2, 5, 26, 26, 28, 6]] | [[4, 33, 14, 32, 9, 32, 2, 35, 25, 10, 11, 6, 8, 26, 10, 25, 34, 21, 13, 15, 3, 15, 25, 3, 16, 3, 2, 25, 15, 23, 31, 35, 13, 14, 5, 7, 2, 18, 10, 8, 25, 30, 13, 35, 3, 26, 33, 2, 5, 26, 26, 28, 6], {"26": 4, "34": 4, "7": 5, "28": 11, "35": 8, "18": 13, "25": 19, "14": 10, "23": 7, "6": 1, "10": 5, "21": 8, "13": 13, "... | ["[4, 33, 14, 32, 9, 32, 2, 35, 25, 10, 11, 6, 8, 26, 10, 25, 34, 21, 13, 15, 3, 15, 25, 3, 16, 3, 2, 25, 15, 23, 31, 35, 13, 14, 5, 7, 2, 18, 10, 8, 25, 30, 13, 35, 3, 26, 33, 2, 5, 26, 26, 28, 6]", "{26: 4, 34: 4, 7: 5, 28: 11, 35: 8, 18: 13, 25: 19, 14: 10, 23: 7, 6: 1, 10: 5, 21: 8, 13: 13, 2: 1, 3: 1, 30: 5, 4: 4,... |
56 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[2, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 2], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1]] | 24 | 51.796597480773926 | 24 | 6 | 15 | [[["Green", "Red", "Green", "Blue", "Red"], ["Red", "Green", "Red", "Blue", "Blue"], ["Green", "Blue", "Red", "Green", "Blue"]], 8] | [[["Green", "Red", "Green", "Blue", "Red"], ["Red", "Green", "Red", "Blue", "Blue"], ["Green", "Blue", "Red", "Green", "Blue"]], 8] | ["[['Green', 'Red', 'Green', 'Blue', 'Red'], ['Red', 'Green', 'Red', 'Blue', 'Blue'], ['Green', 'Blue', 'Red', 'Green', 'Blue']]", "8"] |
56 | We have a 4x4 numerical grid, with numbers ranging from 40 to 80 (40 included in the range but 80 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 13 | [[0, 0, 45], [0, 1, 54], [0, 3, 74], [1, 0, 44], [2, 0, 43], [2, 1, 47], [2, 3, 69], [3, 1, 46], [3, 2, 48]] | 742 | 13.670685529708862 | 9 | 40 | 16 | ["[['', '', '63', ''], ['', '53', '57', '73'], ['', '', '56', ''], ['42', '', '', '68']]", 40, 80] | ["[['', '', '63', ''], ['', '53', '57', '73'], ['', '', '56', ''], ['42', '', '', '68']]", 40, 80] | ["[['', '', '63', ''], ['', '53', '57', '73'], ['', '', '56', ''], ['42', '', '', '68']]", "40", "80"] |
56 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 28 to 59. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 134, 166, None for columns 1 to 2 respectively, and the sums of rows must be None, 185, 162, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 1, 28], [0, 2, 33], [1, 0, 41], [1, 1, 43], [1, 3, 57], [2, 1, 34], [2, 3, 32], [3, 1, 29], [3, 2, 40]] | 652 | 10.336912631988525 | 9 | 49 | 9 | ["[['50', '', '', '42'], ['', '', '44', ''], ['47', '', '49', ''], ['53', '', '', '30']]", 4, 28, 59] | ["[['50', '', '', '42'], ['', '', '44', ''], ['47', '', '49', ''], ['53', '', '', '30']]", 28, 59, [1, 3], [1, 3], [134, 166], [185, 162], 173] | ["[['50', '', '', '42'], ['', '', '44', ''], ['47', '', '49', ''], ['53', '', '', '30']]", "28", "59", "[None, 134, 166, None]", "[None, 185, 162, None]", "173"] |
56 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[4, 0], [4, 2], [5, 0], [5, 3], [7, 3], [7, 0], [4, 3], [4, 3], [7, 4], [7, 2], [7, 4], [1, 7], [1, 2], [1, 4], [1, 7], [5, 7], [5, 2], [5, 7], [1, 0]] | 103 | 0.03519558906555176 | 19 | 56 | 20 | [[[], ["Yellow", "Red", "Black", "Yellow", "Green"], [], [], ["Green", "Red", "Blue", "Blue", "Black"], ["Green", "Blue", "Yellow", "Red", "Yellow"], [], ["Blue", "Green", "Black", "Red", "Black"]], 5, {"0": 5, "1": 5, "2": 5, "3": 6, "4": 5, "5": 5, "6": 9, "7": 6}] | [[[], ["Yellow", "Red", "Black", "Yellow", "Green"], [], [], ["Green", "Red", "Blue", "Blue", "Black"], ["Green", "Blue", "Yellow", "Red", "Yellow"], [], ["Blue", "Green", "Black", "Red", "Black"]], 5, {"0": 5, "1": 5, "2": 5, "3": 6, "4": 5, "5": 5, "6": 9, "7": 6}, 4] | ["[[], ['Yellow', 'Red', 'Black', 'Yellow', 'Green'], [], [], ['Green', 'Red', 'Blue', 'Blue', 'Black'], ['Green', 'Blue', 'Yellow', 'Red', 'Yellow'], [], ['Blue', 'Green', 'Black', 'Red', 'Black']]", "{0: 5, 1: 5, 2: 5, 3: 6, 4: 5, 5: 5, 6: 9, 7: 6}", "5", "4"] |
56 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (6, 9) to his destination workshop at index (3, 0), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[6, 9], [6, 8], [6, 7], [6, 6], [7, 6], [6, 6], [6, 5], [5, 5], [4, 5], [3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [3, 0]] | 121 | 0.02821516990661621 | 15 | 4 | 4 | [[["2", "x", "x", "14", "x", "19", "6", "x", "x", "14", "18", "x"], ["x", "10", "1", "15", "x", "x", "x", "x", "17", "2", "9", "12"], ["13", "14", "x", "2", "x", "x", "10", "10", "x", "x", "x", "x"], ["9", "17", "3", "15", "4", "4", "x", "9", "15", "16", "x", "9"], ["10", "7", "3", "8", "x", "7", "x", "16", "3", "7", "... | [[["2", "x", "x", "14", "x", "19", "6", "x", "x", "14", "18", "x"], ["x", "10", "1", "15", "x", "x", "x", "x", "17", "2", "9", "12"], ["13", "14", "x", "2", "x", "x", "10", "10", "x", "x", "x", "x"], ["9", "17", "3", "15", "4", "4", "x", "9", "15", "16", "x", "9"], ["10", "7", "3", "8", "x", "7", "x", "16", "3", "7", "... | ["[['2', 'x', 'x', '14', 'x', '19', '6', 'x', 'x', '14', '18', 'x'], ['x', '10', '1', '15', 'x', 'x', 'x', 'x', '17', '2', '9', '12'], ['13', '14', 'x', '2', 'x', 'x', '10', '10', 'x', 'x', 'x', 'x'], ['9', '17', '3', '15', '4', '4', 'x', '9', '15', '16', 'x', '9'], ['10', '7', '3', '8', 'x', '7', 'x', '16', '3', '7', ... |
56 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[11, 7], [10, 6], [10, 5], [9, 4], [8, 3], [7, 2], [7, 1], [7, 0], [6, 0], [5, 0], [4, 0], [4, 1], [3, 1], [2, 1], [2, 0]] | 15 | 0.029215574264526367 | 15 | 8 | 2 | ["[[0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 1, 0, ... | ["[[0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 1, 0, ... | ["[[0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 1, 1, 0, ... |
56 | Given 5 labeled water jugs with capacities 12, 88, 148, 87, 143, 131 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 260, 295, 331, 394 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of... | water_jug | subset_sum | 5 | [["+", 87, 4], ["+", 148, 4], ["+", 148, 4], ["-", 88, 4], ["+", 87, 4], ["+", 12, 4], ["+", 88, 3], ["+", 88, 3], ["+", 12, 3], ["+", 143, 3], ["+", 131, 2], ["-", 12, 2], ["+", 88, 2], ["+", 88, 2], ["+", 12, 1], ["+", 88, 1], ["+", 148, 1], ["+", 12, 1]] | 18 | 0.03827953338623047 | 18 | 48 | 3 | [[12, 88, 148, 87, 143, 131], [260, 295, 331, 394]] | [[12, 88, 148, 87, 143, 131], [260, 295, 331, 394]] | ["[12, 88, 148, 87, 143, 131]", "[260, 295, 331, 394]"] |
57 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [28, 12, 68, 28, 22, 90, 28, 68, 12, 22, 90, 42, 78, 90, 68, 28, 42, 78, 71, 79, 90, 68, 78, 71, 79, 90, 68, 58, 22, 12, 28, 42, 71, 78, 42, 28] | 36 | 6.940868616104126 | 36 | 4 | 12 | [[[71, 42, 22, 90], [79, 78, "_", 68], [25, 58, 28, 12]]] | [[[71, 42, 22, 90], [79, 78, "_", 68], [25, 58, 28, 12]]] | ["[[71, 42, 22, 90], [79, 78, '_', 68], [25, 58, 28, 12]]"] |
57 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "down-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "up-left", "up-right", "up-left"] | 24 | 0.5264327526092529 | 24 | 4 | 20 | [[["u", "t", "_", "e"], ["k", "a", "b", "m"], ["n", "e", "o", "g"], ["p", "u", "s", "o"], ["y", "o", "e", "p"]]] | [[["u", "t", "_", "e"], ["k", "a", "b", "m"], ["n", "e", "o", "g"], ["p", "u", "s", "o"], ["y", "o", "e", "p"]], ["toe", "kuba", "meng", "peso", "youp"]] | ["[['u', 't', '_', 'e'], ['k', 'a', 'b', 'm'], ['n', 'e', 'o', 'g'], ['p', 'u', 's', 'o'], ['y', 'o', 'e', 'p']]", "['toe', 'kuba', 'meng', 'peso', 'youp']"] |
57 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["T", "X", "I", "V", "C", "J", "I", "V"] | 8 | 0.030387163162231445 | 8 | 13 | 16 | [[[0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, ... | [[[0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, ... | ["[[0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 0,... |
57 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [25, 22, 28, 23, 5, 14, 28, 14, 20, 6, 22, 1, 25, 18, 30, 10, 19, 12, 17, 17, 6, 28, 21, 28, 21, 2, 20, 2, 19, 14, 31, 31, 14, 7, 20, 13, 7, 18, 22, 15, 6, 6, 21, 9, 18, 11, 20, 26, 15], such that the sum of the chosen coi... | coin_exchange | subset_sum | 29 | [7, 9, 11, 19, 19, 25, 25, 31, 22, 31, 26, 22, 23, 22, 14, 10, 6] | 61 | 0.05817842483520508 | 17 | 49 | 49 | [[25, 22, 28, 23, 5, 14, 28, 14, 20, 6, 22, 1, 25, 18, 30, 10, 19, 12, 17, 17, 6, 28, 21, 28, 21, 2, 20, 2, 19, 14, 31, 31, 14, 7, 20, 13, 7, 18, 22, 15, 6, 6, 21, 9, 18, 11, 20, 26, 15]] | [[25, 22, 28, 23, 5, 14, 28, 14, 20, 6, 22, 1, 25, 18, 30, 10, 19, 12, 17, 17, 6, 28, 21, 28, 21, 2, 20, 2, 19, 14, 31, 31, 14, 7, 20, 13, 7, 18, 22, 15, 6, 6, 21, 9, 18, 11, 20, 26, 15], {"11": 1, "14": 4, "7": 2, "25": 4, "12": 5, "20": 19, "13": 6, "15": 11, "30": 18, "1": 1, "2": 2, "31": 6, "10": 2, "23": 1, "6": ... | ["[25, 22, 28, 23, 5, 14, 28, 14, 20, 6, 22, 1, 25, 18, 30, 10, 19, 12, 17, 17, 6, 28, 21, 28, 21, 2, 20, 2, 19, 14, 31, 31, 14, 7, 20, 13, 7, 18, 22, 15, 6, 6, 21, 9, 18, 11, 20, 26, 15]", "{11: 1, 14: 4, 7: 2, 25: 4, 12: 5, 20: 19, 13: 6, 15: 11, 30: 18, 1: 1, 2: 2, 31: 6, 10: 2, 23: 1, 6: 2, 21: 18, 18: 8, 28: 15, 1... |
57 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1], [2, 0], [2, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0]] | 17 | 1.3616485595703125 | 17 | 6 | 15 | [[["Red", "Green", "Blue", "Green", "Green"], ["Green", "Red", "Blue", "Blue", "Blue"], ["Red", "Red", "Blue", "Green", "Red"]], 8] | [[["Red", "Green", "Blue", "Green", "Green"], ["Green", "Red", "Blue", "Blue", "Blue"], ["Red", "Red", "Blue", "Green", "Red"]], 8] | ["[['Red', 'Green', 'Blue', 'Green', 'Green'], ['Green', 'Red', 'Blue', 'Blue', 'Blue'], ['Red', 'Red', 'Blue', 'Green', 'Red']]", "8"] |
57 | We have a 4x4 numerical grid, with numbers ranging from 7 to 47 (7 included in the range but 47 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid cell... | consecutive_grid | underdetermined_system | 13 | [[0, 2, 15], [0, 3, 39], [1, 1, 16], [1, 2, 17], [2, 0, 13], [2, 1, 18], [2, 2, 19], [3, 1, 26], [3, 2, 27]] | 306 | 88.0573205947876 | 9 | 40 | 16 | ["[['11', '14', '', ''], ['12', '', '', '38'], ['', '', '', '36'], ['25', '', '', '34']]", 7, 47] | ["[['11', '14', '', ''], ['12', '', '', '38'], ['', '', '', '36'], ['25', '', '', '34']]", 7, 47] | ["[['11', '14', '', ''], ['12', '', '', '38'], ['', '', '', '36'], ['25', '', '', '34']]", "7", "47"] |
57 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 28 to 59. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 170, 162, None for columns 1 to 2 respectively, and the sums of rows must be None, 191, 157, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 1, 29], [0, 3, 31], [1, 0, 34], [1, 2, 51], [1, 3, 58], [2, 0, 36], [3, 0, 50], [3, 1, 54], [3, 3, 28]] | 663 | 3.644191026687622 | 9 | 26 | 16 | ["[['42', '', '41', ''], ['', '48', '', ''], ['', '39', '30', '52'], ['', '', '40', '']]", 4, 28, 59] | ["[['42', '', '41', ''], ['', '48', '', ''], ['', '39', '30', '52'], ['', '', '40', '']]", 28, 59, [1, 3], [1, 3], [170, 162], [191, 157], 171] | ["[['42', '', '41', ''], ['', '48', '', ''], ['', '39', '30', '52'], ['', '', '40', '']]", "28", "59", "[None, 170, 162, None]", "[None, 191, 157, None]", "171"] |
57 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[2, 0], [2, 1], [7, 1], [7, 0], [7, 0], [7, 1], [2, 7], [3, 5], [4, 5], [4, 5], [4, 5], [4, 1], [4, 7], [3, 4], [3, 4], [3, 0], [3, 7], [2, 4], [2, 4]] | 75 | 0.13939952850341797 | 19 | 56 | 20 | [[[], [], ["Green", "Red", "Black", "Blue", "Blue"], ["Yellow", "Blue", "Blue", "Green", "Black"], ["Yellow", "Yellow", "Yellow", "Red", "Black"], [], [], ["Red", "Green", "Green", "Red", "Black"]], 5, {"0": 2, "1": 3, "2": 9, "3": 8, "4": 3, "5": 7, "6": 9, "7": 5}] | [[[], [], ["Green", "Red", "Black", "Blue", "Blue"], ["Yellow", "Blue", "Blue", "Green", "Black"], ["Yellow", "Yellow", "Yellow", "Red", "Black"], [], [], ["Red", "Green", "Green", "Red", "Black"]], 5, {"0": 2, "1": 3, "2": 9, "3": 8, "4": 3, "5": 7, "6": 9, "7": 5}, 4] | ["[[], [], ['Green', 'Red', 'Black', 'Blue', 'Blue'], ['Yellow', 'Blue', 'Blue', 'Green', 'Black'], ['Yellow', 'Yellow', 'Yellow', 'Red', 'Black'], [], [], ['Red', 'Green', 'Green', 'Red', 'Black']]", "{0: 2, 1: 3, 2: 9, 3: 8, 4: 3, 5: 7, 6: 9, 7: 5}", "5", "4"] |
57 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (7, 0) to his destination workshop at index (3, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [3, 1], [3, 2], [3, 3], [4, 3], [5, 3], [5, 4], [5, 5], [4, 5], [4, 6], [3, 6], [3, 7], [3, 8]] | 138 | 0.02782440185546875 | 17 | 4 | 4 | [[["17", "9", "11", "5", "19", "4", "18", "x", "5", "8", "x", "x"], ["6", "13", "x", "9", "2", "20", "11", "20", "7", "x", "x", "3"], ["4", "17", "x", "18", "2", "10", "x", "16", "x", "18", "x", "x"], ["12", "10", "9", "14", "x", "x", "12", "6", "1", "2", "x", "x"], ["5", "x", "x", "3", "x", "4", "9", "14", "8", "x", "... | [[["17", "9", "11", "5", "19", "4", "18", "x", "5", "8", "x", "x"], ["6", "13", "x", "9", "2", "20", "11", "20", "7", "x", "x", "3"], ["4", "17", "x", "18", "2", "10", "x", "16", "x", "18", "x", "x"], ["12", "10", "9", "14", "x", "x", "12", "6", "1", "2", "x", "x"], ["5", "x", "x", "3", "x", "4", "9", "14", "8", "x", "... | ["[['17', '9', '11', '5', '19', '4', '18', 'x', '5', '8', 'x', 'x'], ['6', '13', 'x', '9', '2', '20', '11', '20', '7', 'x', 'x', '3'], ['4', '17', 'x', '18', '2', '10', 'x', '16', 'x', '18', 'x', 'x'], ['12', '10', '9', '14', 'x', 'x', '12', '6', '1', '2', 'x', 'x'], ['5', 'x', 'x', '3', 'x', '4', '9', '14', '8', 'x', ... |
57 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[11, 2], [10, 2], [10, 3], [9, 4], [8, 4], [8, 5], [7, 5], [6, 5], [5, 6], [5, 7], [5, 8], [6, 9], [5, 10], [4, 10], [3, 10]] | 15 | 0.03331708908081055 | 15 | 8 | 2 | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, ... | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, ... | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1], [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, ... |
57 | Given 5 labeled water jugs with capacities 15, 20, 141, 104, 67, 14 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 230, 267, 278, 318 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ... | water_jug | subset_sum | 5 | [["+", 67, 4], ["+", 104, 4], ["+", 141, 4], ["-", 14, 4], ["+", 20, 4], ["+", 67, 3], ["+", 67, 3], ["+", 104, 3], ["+", 20, 3], ["+", 20, 3], ["+", 141, 2], ["-", 15, 2], ["+", 141, 2], ["+", 104, 1], ["-", 15, 1], ["+", 141, 1]] | 16 | 0.03609800338745117 | 16 | 48 | 3 | [[15, 20, 141, 104, 67, 14], [230, 267, 278, 318]] | [[15, 20, 141, 104, 67, 14], [230, 267, 278, 318]] | ["[15, 20, 141, 104, 67, 14]", "[230, 267, 278, 318]"] |
58 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [86, 91, 92, 86, 91, 58, 73, 75, 10, 46, 86, 91, 58, 6, 12, 73, 75, 10, 46, 58, 6, 75, 73, 12, 75, 73, 10, 6, 58, 46] | 30 | 1.039477825164795 | 30 | 4 | 12 | [[[94, 91, 92, 46], [6, 86, "_", 10], [12, 58, 73, 75]]] | [[[94, 91, 92, 46], [6, 86, "_", 10], [12, 58, 73, 75]]] | ["[[94, 91, 92, 46], [6, 86, '_', 10], [12, 58, 73, 75]]"] |
58 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-left", "up-right", "down-right", "down-left", "down-right", "down-left", "up-left", "up-left", "up-right", "up-left"] | 10 | 0.1858220100402832 | 10 | 4 | 20 | [[["i", "e", "e", "d"], ["v", "t", "n", "l"], ["o", "d", "_", "a"], ["p", "r", "c", "e"], ["p", "i", "o", "l"]]] | [[["i", "e", "e", "d"], ["v", "t", "n", "l"], ["o", "d", "_", "a"], ["p", "r", "c", "e"], ["p", "i", "o", "l"]], ["eld", "vint", "edea", "poco", "pirl"]] | ["[['i', 'e', 'e', 'd'], ['v', 't', 'n', 'l'], ['o', 'd', '_', 'a'], ['p', 'r', 'c', 'e'], ['p', 'i', 'o', 'l']]", "['eld', 'vint', 'edea', 'poco', 'pirl']"] |
58 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["S", "K", "X", "V", "B", "J", "T", "V", "B"] | 9 | 0.03627133369445801 | 9 | 13 | 16 | [[[0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, ... | [[[0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, ... | ["[[0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0,... |
58 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [10, 16, 2, 18, 10, 16, 17, 32, 18, 33, 23, 20, 21, 25, 32, 24, 10, 27, 13, 27, 30, 13, 19, 20, 4, 5, 15, 8, 8, 34, 21, 14, 3, 20, 10, 18, 3, 14, 28, 6, 4, 8, 15, 4, 30, 30, 12, 20, 14, 10], such that the sum of the chosen... | coin_exchange | subset_sum | 30 | [32, 28, 8, 17, 21, 18, 21, 18, 12, 8, 19, 18, 8, 4, 13, 4, 13, 33, 32, 30] | 73 | 0.05944538116455078 | 20 | 50 | 50 | [[10, 16, 2, 18, 10, 16, 17, 32, 18, 33, 23, 20, 21, 25, 32, 24, 10, 27, 13, 27, 30, 13, 19, 20, 4, 5, 15, 8, 8, 34, 21, 14, 3, 20, 10, 18, 3, 14, 28, 6, 4, 8, 15, 4, 30, 30, 12, 20, 14, 10]] | [[10, 16, 2, 18, 10, 16, 17, 32, 18, 33, 23, 20, 21, 25, 32, 24, 10, 27, 13, 27, 30, 13, 19, 20, 4, 5, 15, 8, 8, 34, 21, 14, 3, 20, 10, 18, 3, 14, 28, 6, 4, 8, 15, 4, 30, 30, 12, 20, 14, 10], {"30": 12, "20": 19, "16": 7, "24": 14, "12": 3, "13": 4, "8": 2, "2": 1, "21": 2, "23": 12, "34": 13, "27": 16, "3": 3, "28": 3... | ["[10, 16, 2, 18, 10, 16, 17, 32, 18, 33, 23, 20, 21, 25, 32, 24, 10, 27, 13, 27, 30, 13, 19, 20, 4, 5, 15, 8, 8, 34, 21, 14, 3, 20, 10, 18, 3, 14, 28, 6, 4, 8, 15, 4, 30, 30, 12, 20, 14, 10]", "{30: 12, 20: 19, 16: 7, 24: 14, 12: 3, 13: 4, 8: 2, 2: 1, 21: 2, 23: 12, 34: 13, 27: 16, 3: 3, 28: 3, 14: 13, 6: 4, 33: 17, 1... |
58 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 0], [2, 1]] | 22 | 19.447868585586548 | 22 | 6 | 15 | [[["Red", "Blue", "Green", "Blue", "Blue"], ["Green", "Red", "Green", "Red", "Blue"], ["Blue", "Green", "Red", "Red", "Green"]], 8] | [[["Red", "Blue", "Green", "Blue", "Blue"], ["Green", "Red", "Green", "Red", "Blue"], ["Blue", "Green", "Red", "Red", "Green"]], 8] | ["[['Red', 'Blue', 'Green', 'Blue', 'Blue'], ['Green', 'Red', 'Green', 'Red', 'Blue'], ['Blue', 'Green', 'Red', 'Red', 'Green']]", "8"] |
58 | We have a 4x4 numerical grid, with numbers ranging from 42 to 82 (42 included in the range but 82 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 14 | [[0, 0, 23], [0, 1, 31], [0, 3, 39], [1, 0, 21], [1, 2, 40], [1, 3, 41], [2, 1, 24], [2, 3, 45], [3, 0, 19], [3, 2, 46]] | 467 | 127.71580004692078 | 10 | 40 | 16 | ["[['', '', '38', ''], ['', '30', '', ''], ['20', '', '44', ''], ['', '22', '', '57']]", 19, 59] | ["[['', '', '38', ''], ['', '30', '', ''], ['20', '', '44', ''], ['', '22', '', '57']]", 19, 59] | ["[['', '', '38', ''], ['', '30', '', ''], ['20', '', '44', ''], ['', '22', '', '57']]", "19", "59"] |
58 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 53. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 137, 162, None for columns 1 to 2 respectively, and the sums of rows must be None, 141, 135, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 0, 23], [0, 1, 27], [0, 2, 31], [1, 2, 44], [1, 3, 26], [2, 0, 25], [2, 2, 45], [3, 0, 24], [3, 1, 30], [3, 2, 42]] | 540 | 180.21373414993286 | 10 | 26 | 16 | ["[['', '', '', '40'], ['34', '37', '', ''], ['', '43', '', '22'], ['', '', '', '47']]", 4, 22, 53] | ["[['', '', '', '40'], ['34', '37', '', ''], ['', '43', '', '22'], ['', '', '', '47']]", 22, 53, [1, 3], [1, 3], [137, 162], [141, 135], 151] | ["[['', '', '', '40'], ['34', '37', '', ''], ['', '43', '', '22'], ['', '', '', '47']]", "22", "53", "[None, 137, 162, None]", "[None, 141, 135, None]", "151"] |
58 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[1, 0], [7, 0], [1, 5], [4, 1], [4, 5], [3, 0], [3, 5], [3, 0], [3, 2], [7, 3], [7, 5], [4, 3], [4, 7], [2, 7], [3, 4], [3, 4], [3, 4]] | 106 | 0.03409838676452637 | 17 | 56 | 20 | [[[], ["Green", "Yellow", "Red", "Red", "Red"], [], ["Green", "Yellow", "Green", "Blue", "Black"], ["Red", "Yellow", "Black", "Blue", "Black"], [], [], ["Green", "Black", "Yellow", "Blue", "Blue"]], 5, {"0": 4, "1": 8, "2": 9, "3": 9, "4": 5, "5": 7, "6": 9, "7": 6}] | [[[], ["Green", "Yellow", "Red", "Red", "Red"], [], ["Green", "Yellow", "Green", "Blue", "Black"], ["Red", "Yellow", "Black", "Blue", "Black"], [], [], ["Green", "Black", "Yellow", "Blue", "Blue"]], 5, {"0": 4, "1": 8, "2": 9, "3": 9, "4": 5, "5": 7, "6": 9, "7": 6}, 4] | ["[[], ['Green', 'Yellow', 'Red', 'Red', 'Red'], [], ['Green', 'Yellow', 'Green', 'Blue', 'Black'], ['Red', 'Yellow', 'Black', 'Blue', 'Black'], [], [], ['Green', 'Black', 'Yellow', 'Blue', 'Blue']]", "{0: 4, 1: 8, 2: 9, 3: 9, 4: 5, 5: 7, 6: 9, 7: 6}", "5", "4"] |
58 | Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (1, 3) to his destination workshop at index (6, 10), indexing from 0. Ben's car can mov... | traffic | pathfinding | 4 | [[1, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 11], [5, 11], [5, 10], [6, 10]] | 141 | 0.027864456176757812 | 15 | 4 | 4 | [[["x", "x", "x", "6", "9", "x", "x", "10", "14", "7", "3", "12"], ["x", "11", "x", "3", "14", "16", "17", "1", "4", "14", "8", "16"], ["3", "x", "x", "x", "6", "1", "18", "16", "x", "6", "3", "11"], ["x", "x", "11", "4", "8", "x", "x", "1", "3", "9", "8", "7"], ["x", "x", "3", "x", "x", "x", "8", "14", "18", "x", "x",... | [[["x", "x", "x", "6", "9", "x", "x", "10", "14", "7", "3", "12"], ["x", "11", "x", "3", "14", "16", "17", "1", "4", "14", "8", "16"], ["3", "x", "x", "x", "6", "1", "18", "16", "x", "6", "3", "11"], ["x", "x", "11", "4", "8", "x", "x", "1", "3", "9", "8", "7"], ["x", "x", "3", "x", "x", "x", "8", "14", "18", "x", "x",... | ["[['x', 'x', 'x', '6', '9', 'x', 'x', '10', '14', '7', '3', '12'], ['x', '11', 'x', '3', '14', '16', '17', '1', '4', '14', '8', '16'], ['3', 'x', 'x', 'x', '6', '1', '18', '16', 'x', '6', '3', '11'], ['x', 'x', '11', '4', '8', 'x', 'x', '1', '3', '9', '8', '7'], ['x', 'x', '3', 'x', 'x', 'x', '8', '14', '18', 'x', 'x'... |
58 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[1, 1], [2, 1], [3, 1], [4, 2], [5, 3], [5, 4], [5, 5], [5, 6], [6, 7], [7, 7], [8, 7], [9, 8], [10, 8]] | 13 | 0.0319523811340332 | 13 | 8 | 2 | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, ... | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, ... | ["[[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0], [1, 1, 0, 0, ... |
58 | Given 5 labeled water jugs with capacities 59, 20, 21, 62, 61, 60 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 149, 156, 173, 186 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wa... | water_jug | subset_sum | 5 | [["+", 62, 4], ["+", 62, 4], ["+", 62, 4], ["+", 59, 3], ["+", 59, 3], ["-", 21, 3], ["+", 59, 3], ["-", 62, 3], ["+", 20, 3], ["+", 59, 3], ["+", 59, 2], ["+", 59, 2], ["-", 21, 2], ["+", 59, 2], ["+", 20, 1], ["+", 61, 1], ["+", 62, 1], ["-", 59, 1], ["+", 62, 1], ["-", 59, 1], ["+", 62, 1]] | 21 | 0.03367137908935547 | 21 | 48 | 3 | [[59, 20, 21, 62, 61, 60], [149, 156, 173, 186]] | [[59, 20, 21, 62, 61, 60], [149, 156, 173, 186]] | ["[59, 20, 21, 62, 61, 60]", "[149, 156, 173, 186]"] |
59 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [58, 67, 21, 3, 53, 98, 10, 96, 73, 14, 60, 58, 67, 21, 3, 53, 14, 10, 98, 14, 10, 60, 58, 73, 96, 98, 60, 58, 53, 3] | 30 | 0.15825581550598145 | 30 | 4 | 12 | [[[10, 96, 60, "_"], [98, 73, 14, 58], [53, 3, 21, 67]]] | [[[10, 96, 60, "_"], [98, 73, 14, 58], [53, 3, 21, 67]]] | ["[[10, 96, 60, '_'], [98, 73, 14, 58], [53, 3, 21, 67]]"] |
59 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "up-left"] | 18 | 0.20941829681396484 | 18 | 4 | 20 | [[["r", "f", "_", "e"], ["t", "a", "a", "f"], ["a", "e", "f", "t"], ["f", "i", "n", "h"], ["d", "a", "e", "f"]]] | [[["r", "f", "_", "e"], ["t", "a", "a", "f"], ["a", "e", "f", "t"], ["f", "i", "n", "h"], ["d", "a", "e", "f"]], ["fae", "trah", "feat", "fine", "daff"]] | ["[['r', 'f', '_', 'e'], ['t', 'a', 'a', 'f'], ['a', 'e', 'f', 't'], ['f', 'i', 'n', 'h'], ['d', 'a', 'e', 'f']]", "['fae', 'trah', 'feat', 'fine', 'daff']"] |
59 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["K", "H", "L", "F", "M", "L", "S", "Y", "D", "I", "Q", "D"] | 12 | 0.11734938621520996 | 12 | 13 | 16 | [[[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, ... | [[[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, ... | ["[[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 0, 0, 0, 0,... |
59 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [23, 27, 20, 21, 8, 2, 2, 3, 21, 26, 16, 33, 22, 3, 25, 17, 5, 31, 3, 9, 12, 30, 11, 10, 7, 13, 2, 21, 8, 16, 5, 18, 32, 27, 7, 32, 7, 10, 11, 33, 18, 30, 7, 24, 21, 4, 25, 4, 23, 21, 23, 15, 26, 10], such that the sum of ... | coin_exchange | subset_sum | 31 | [9, 21, 21, 21, 21, 18, 21, 18, 16, 33, 32, 22, 33, 32, 16] | 25 | 0.05468130111694336 | 15 | 54 | 54 | [[23, 27, 20, 21, 8, 2, 2, 3, 21, 26, 16, 33, 22, 3, 25, 17, 5, 31, 3, 9, 12, 30, 11, 10, 7, 13, 2, 21, 8, 16, 5, 18, 32, 27, 7, 32, 7, 10, 11, 33, 18, 30, 7, 24, 21, 4, 25, 4, 23, 21, 23, 15, 26, 10]] | [[23, 27, 20, 21, 8, 2, 2, 3, 21, 26, 16, 33, 22, 3, 25, 17, 5, 31, 3, 9, 12, 30, 11, 10, 7, 13, 2, 21, 8, 16, 5, 18, 32, 27, 7, 32, 7, 10, 11, 33, 18, 30, 7, 24, 21, 4, 25, 4, 23, 21, 23, 15, 26, 10], {"16": 1, "18": 1, "9": 1, "11": 5, "5": 3, "2": 1, "21": 1, "33": 3, "7": 1, "4": 1, "30": 8, "23": 10, "17": 8, "15"... | ["[23, 27, 20, 21, 8, 2, 2, 3, 21, 26, 16, 33, 22, 3, 25, 17, 5, 31, 3, 9, 12, 30, 11, 10, 7, 13, 2, 21, 8, 16, 5, 18, 32, 27, 7, 32, 7, 10, 11, 33, 18, 30, 7, 24, 21, 4, 25, 4, 23, 21, 23, 15, 26, 10]", "{16: 1, 18: 1, 9: 1, 11: 5, 5: 3, 2: 1, 21: 1, 33: 3, 7: 1, 4: 1, 30: 8, 23: 10, 17: 8, 15: 7, 13: 6, 20: 8, 32: 4,... |
59 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[0, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [2, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2]] | 24 | 45.59880995750427 | 24 | 6 | 15 | [[["Blue", "Red", "Red", "Blue", "Red"], ["Green", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Red", "Green", "Green"]], 8] | [[["Blue", "Red", "Red", "Blue", "Red"], ["Green", "Blue", "Blue", "Red", "Green"], ["Blue", "Green", "Red", "Green", "Green"]], 8] | ["[['Blue', 'Red', 'Red', 'Blue', 'Red'], ['Green', 'Blue', 'Blue', 'Red', 'Green'], ['Blue', 'Green', 'Red', 'Green', 'Green']]", "8"] |
59 | We have a 4x4 numerical grid, with numbers ranging from 19 to 59 (19 included in the range but 59 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 | 14 | [[0, 0, 24], [0, 1, 25], [0, 2, 26], [0, 3, 27], [1, 1, 38], [1, 3, 52], [2, 0, 39], [2, 2, 50], [2, 3, 53], [3, 1, 45]] | 468 | 132.53104043006897 | 10 | 40 | 16 | ["[['', '', '', ''], ['37', '', '49', ''], ['', '44', '', ''], ['42', '', '51', '61']]", 24, 64] | ["[['', '', '', ''], ['37', '', '49', ''], ['', '44', '', ''], ['42', '', '51', '61']]", 24, 64] | ["[['', '', '', ''], ['37', '', '49', ''], ['', '44', '', ''], ['42', '', '51', '61']]", "24", "64"] |
59 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 22 to 53. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 148, 157, None for columns 1 to 2 respectively, and the sums of rows must be None, 138, 149, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 1, 28], [0, 3, 25], [1, 0, 24], [1, 1, 42], [1, 2, 49], [2, 0, 34], [3, 0, 27], [3, 1, 46], [3, 2, 26], [3, 3, 22]] | 547 | 42.003302574157715 | 10 | 26 | 16 | ["[['35', '', '51', ''], ['', '', '', '23'], ['', '32', '31', '52'], ['', '', '', '']]", 4, 22, 53] | ["[['35', '', '51', ''], ['', '', '', '23'], ['', '32', '31', '52'], ['', '', '', '']]", 22, 53, [1, 3], [1, 3], [148, 157], [138, 149], 133] | ["[['35', '', '51', ''], ['', '', '', '23'], ['', '32', '31', '52'], ['', '', '', '']]", "22", "53", "[None, 148, 157, None]", "[None, 138, 149, None]", "133"] |
59 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[0, 5], [0, 3], [0, 5], [2, 1], [2, 1], [2, 5], [7, 2], [7, 3], [7, 1], [7, 1], [7, 5], [4, 3], [4, 0], [4, 2], [4, 0], [4, 3]] | 72 | 6.510378360748291 | 16 | 56 | 20 | [[["Green", "Blue", "Green", "Yellow", "Yellow"], [], ["Red", "Red", "Green", "Black", "Black"], [], ["Blue", "Yellow", "Black", "Yellow", "Blue"], [], [], ["Black", "Blue", "Red", "Red", "Green"]], 5, {"0": 1, "1": 5, "2": 5, "3": 4, "4": 8, "5": 6, "6": 8, "7": 9}] | [[["Green", "Blue", "Green", "Yellow", "Yellow"], [], ["Red", "Red", "Green", "Black", "Black"], [], ["Blue", "Yellow", "Black", "Yellow", "Blue"], [], [], ["Black", "Blue", "Red", "Red", "Green"]], 5, {"0": 1, "1": 5, "2": 5, "3": 4, "4": 8, "5": 6, "6": 8, "7": 9}, 4] | ["[['Green', 'Blue', 'Green', 'Yellow', 'Yellow'], [], ['Red', 'Red', 'Green', 'Black', 'Black'], [], ['Blue', 'Yellow', 'Black', 'Yellow', 'Blue'], [], [], ['Black', 'Blue', 'Red', 'Red', 'Green']]", "{0: 1, 1: 5, 2: 5, 3: 4, 4: 8, 5: 6, 6: 8, 7: 9}", "5", "4"] |
59 | 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 (7, 8), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[2, 0], [2, 1], [2, 2], [1, 2], [1, 3], [1, 4], [1, 5], [2, 5], [2, 6], [3, 6], [4, 6], [4, 7], [4, 8], [5, 8], [6, 8], [7, 8]] | 97 | 0.027582406997680664 | 16 | 4 | 4 | [[["4", "1", "20", "15", "9", "x", "8", "6", "x", "x", "14", "x"], ["5", "11", "9", "12", "10", "4", "15", "18", "7", "x", "x", "13"], ["15", "9", "1", "x", "18", "3", "1", "19", "x", "x", "17", "17"], ["x", "17", "11", "10", "x", "19", "8", "x", "x", "x", "x", "7"], ["5", "x", "1", "x", "14", "13", "4", "8", "5", "x",... | [[["4", "1", "20", "15", "9", "x", "8", "6", "x", "x", "14", "x"], ["5", "11", "9", "12", "10", "4", "15", "18", "7", "x", "x", "13"], ["15", "9", "1", "x", "18", "3", "1", "19", "x", "x", "17", "17"], ["x", "17", "11", "10", "x", "19", "8", "x", "x", "x", "x", "7"], ["5", "x", "1", "x", "14", "13", "4", "8", "5", "x",... | ["[['4', '1', '20', '15', '9', 'x', '8', '6', 'x', 'x', '14', 'x'], ['5', '11', '9', '12', '10', '4', '15', '18', '7', 'x', 'x', '13'], ['15', '9', '1', 'x', '18', '3', '1', '19', 'x', 'x', '17', '17'], ['x', '17', '11', '10', 'x', '19', '8', 'x', 'x', 'x', 'x', '7'], ['5', 'x', '1', 'x', '14', '13', '4', '8', '5', 'x'... |
59 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[0, 9], [1, 8], [1, 7], [1, 6], [2, 6], [3, 6], [3, 5], [4, 4], [4, 3], [4, 2], [5, 2], [5, 1], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 1], [11, 2]] | 19 | 0.03089118003845215 | 19 | 8 | 2 | ["[[1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 1, 1, 1, ... | ["[[1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 1, 1, 1, ... | ["[[1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 1, 1, 1, ... |
59 | Given 5 labeled water jugs with capacities 128, 67, 44, 31, 127, 15 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 258, 261, 415, 430 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ... | water_jug | subset_sum | 5 | [["+", 31, 4], ["+", 128, 4], ["+", 128, 4], ["+", 128, 4], ["+", 15, 4], ["+", 31, 3], ["+", 128, 3], ["+", 128, 3], ["+", 128, 3], ["+", 67, 2], ["+", 67, 2], ["+", 127, 2], ["+", 128, 1], ["+", 128, 1], ["-", 44, 1], ["+", 15, 1], ["+", 31, 1]] | 17 | 0.06383585929870605 | 17 | 48 | 3 | [[128, 67, 44, 31, 127, 15], [258, 261, 415, 430]] | [[128, 67, 44, 31, 127, 15], [258, 261, 415, 430]] | ["[128, 67, 44, 31, 127, 15]", "[258, 261, 415, 430]"] |
60 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 7 | [28, 42, 72, 69, 67, 72, 35, 87, 31, 92, 72, 67, 69, 35, 67, 72, 87, 67, 42, 28, 53, 31, 67, 53, 28, 19] | 26 | 0.2203352451324463 | 26 | 4 | 12 | [[[31, 92, 67, 69], [87, 35, 42, 72], [53, "_", 28, 19]]] | [[[31, 92, 67, 69], [87, 35, 42, 72], [53, "_", 28, 19]]] | ["[[31, 92, 67, 69], [87, 35, 42, 72], [53, '_', 28, 19]]"] |
60 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["up-left", "up-left", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "up-left", "up-left"] | 16 | 0.18634486198425293 | 16 | 4 | 20 | [[["e", "b", "a", "n"], ["z", "e", "e", "d"], ["o", "a", "d", "y"], ["m", "u", "t", "z"], ["m", "a", "_", "n"]]] | [[["e", "b", "a", "n"], ["z", "e", "e", "d"], ["o", "a", "d", "y"], ["m", "u", "t", "z"], ["m", "a", "_", "n"]], ["ban", "zeed", "dazy", "mote", "maun"]] | ["[['e', 'b', 'a', 'n'], ['z', 'e', 'e', 'd'], ['o', 'a', 'd', 'y'], ['m', 'u', 't', 'z'], ['m', 'a', '_', 'n']]", "['ban', 'zeed', 'dazy', 'mote', 'maun']"] |
60 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["I", "H", "N", "U", "X", "U", "G", "F", "Q", "F"] | 10 | 0.046558380126953125 | 10 | 13 | 16 | [[[0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, ... | [[[0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, ... | ["[[0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 1, 1, 0, 0, 0, 0, 1,... |
60 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [28, 2, 4, 7, 11, 26, 14, 8, 23, 29, 18, 13, 26, 21, 10, 26, 8, 33, 9, 15, 4, 21, 19, 3, 7, 10, 4, 7, 16, 16, 11, 33, 12, 23, 5, 3, 26, 7, 17, 30, 22, 22, 6, 16, 18, 25, 26, 11, 13, 23, 17, 11, 20, 12], such that the sum o... | coin_exchange | subset_sum | 32 | [28, 12, 23, 12, 13, 23, 22, 8, 23, 22, 25, 29, 26, 20, 8, 13, 15, 17] | 72 | 0.06408143043518066 | 18 | 54 | 54 | [[28, 2, 4, 7, 11, 26, 14, 8, 23, 29, 18, 13, 26, 21, 10, 26, 8, 33, 9, 15, 4, 21, 19, 3, 7, 10, 4, 7, 16, 16, 11, 33, 12, 23, 5, 3, 26, 7, 17, 30, 22, 22, 6, 16, 18, 25, 26, 11, 13, 23, 17, 11, 20, 12]] | [[28, 2, 4, 7, 11, 26, 14, 8, 23, 29, 18, 13, 26, 21, 10, 26, 8, 33, 9, 15, 4, 21, 19, 3, 7, 10, 4, 7, 16, 16, 11, 33, 12, 23, 5, 3, 26, 7, 17, 30, 22, 22, 6, 16, 18, 25, 26, 11, 13, 23, 17, 11, 20, 12], {"10": 6, "18": 17, "33": 15, "16": 16, "3": 2, "30": 18, "13": 3, "21": 17, "23": 4, "12": 1, "7": 6, "17": 7, "4":... | ["[28, 2, 4, 7, 11, 26, 14, 8, 23, 29, 18, 13, 26, 21, 10, 26, 8, 33, 9, 15, 4, 21, 19, 3, 7, 10, 4, 7, 16, 16, 11, 33, 12, 23, 5, 3, 26, 7, 17, 30, 22, 22, 6, 16, 18, 25, 26, 11, 13, 23, 17, 11, 20, 12]", "{10: 6, 18: 17, 33: 15, 16: 16, 3: 2, 30: 18, 13: 3, 21: 17, 23: 4, 12: 1, 7: 6, 17: 7, 4: 2, 6: 5, 2: 2, 11: 5, ... |
60 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[1, 0], [2, 1], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1], [0, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2]] | 26 | 132.6773865222931 | 26 | 6 | 15 | [[["Green", "Red", "Blue", "Blue", "Green"], ["Red", "Green", "Blue", "Red", "Green"], ["Blue", "Red", "Blue", "Green", "Red"]], 8] | [[["Green", "Red", "Blue", "Blue", "Green"], ["Red", "Green", "Blue", "Red", "Green"], ["Blue", "Red", "Blue", "Green", "Red"]], 8] | ["[['Green', 'Red', 'Blue', 'Blue', 'Green'], ['Red', 'Green', 'Blue', 'Red', 'Green'], ['Blue', 'Red', 'Blue', 'Green', 'Red']]", "8"] |
60 | We have a 4x4 numerical grid, with numbers ranging from 24 to 64 (24 included in the range but 64 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 | 14 | [[0, 0, 36], [0, 1, 37], [0, 3, 47], [1, 0, 38], [2, 1, 58], [3, 2, 76]] | 678 | 0.18999671936035156 | 6 | 40 | 16 | ["[['', '', '46', ''], ['', '57', '59', '70'], ['56', '', '69', '73'], ['57', '75', '', '80']]", 36, 81] | ["[['', '', '46', ''], ['', '57', '59', '70'], ['56', '', '69', '73'], ['57', '75', '', '80']]", 36, 81] | ["[['', '', '46', ''], ['', '57', '59', '70'], ['56', '', '69', '73'], ['57', '75', '', '80']]", "36", "81"] |
60 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 23 to 54. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 173, 166, None for columns 1 to 2 respectively, and the sums of rows must be None, 166, 165, None for rows 1 to... | magic_square | underdetermined_system | 7 | [[0, 2, 26], [0, 3, 23], [1, 0, 30], [1, 1, 50], [1, 2, 37], [1, 3, 49], [2, 1, 36], [2, 2, 51], [2, 3, 31], [3, 1, 34], [3, 3, 24]] | 623 | 225.59702444076538 | 11 | 26 | 16 | ["[['45', '53', '', ''], ['', '', '', ''], ['47', '', '', ''], ['35', '', '52', '']]", 4, 23, 54] | ["[['45', '53', '', ''], ['', '', '', ''], ['47', '', '', ''], ['35', '', '52', '']]", 23, 54, [1, 3], [1, 3], [173, 166], [166, 165], 131] | ["[['45', '53', '', ''], ['', '', '', ''], ['47', '', '', ''], ['35', '', '52', '']]", "23", "54", "[None, 173, 166, None]", "[None, 166, 165, None]", "131"] |
60 | In 'Restricted Sorting', there are 8 stacks each with a capacity of 5 blocks, with 4 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 4 blocks of a single shade. The player can only transfer one bl... | restricted_sorting | sorting | 2 | [[0, 1], [0, 5], [0, 5], [2, 1], [2, 5], [2, 0], [2, 5], [3, 4], [3, 0], [3, 7], [3, 7], [6, 4], [6, 7], [6, 1], [6, 7], [2, 4], [3, 1], [6, 4]] | 48 | 7.157405853271484 | 18 | 56 | 20 | [[["Yellow", "Green", "Green", "Black", "Black"], [], ["Yellow", "Green", "Black", "Green", "Red"], ["Red", "Black", "Blue", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Blue", "Red"], []], 5, {"0": 6, "1": 1, "2": 8, "3": 8, "4": 1, "5": 6, "6": 4, "7": 1}] | [[["Yellow", "Green", "Green", "Black", "Black"], [], ["Yellow", "Green", "Black", "Green", "Red"], ["Red", "Black", "Blue", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Blue", "Red"], []], 5, {"0": 6, "1": 1, "2": 8, "3": 8, "4": 1, "5": 6, "6": 4, "7": 1}, 4] | ["[['Yellow', 'Green', 'Green', 'Black', 'Black'], [], ['Yellow', 'Green', 'Black', 'Green', 'Red'], ['Red', 'Black', 'Blue', 'Blue', 'Yellow'], [], [], ['Red', 'Blue', 'Yellow', 'Blue', 'Red'], []]", "{0: 6, 1: 1, 2: 8, 3: 8, 4: 1, 5: 6, 6: 4, 7: 1}", "5", "4"] |
60 | 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, 0) to his destination workshop at index (9, 7), indexing from 0. Ben's car can move... | traffic | pathfinding | 4 | [[3, 0], [4, 0], [5, 0], [5, 1], [5, 2], [6, 2], [7, 2], [7, 3], [7, 4], [7, 5], [8, 5], [9, 5], [10, 5], [10, 6], [10, 7], [9, 7]] | 119 | 0.021150827407836914 | 16 | 4 | 4 | [[["16", "x", "5", "6", "x", "14", "12", "x", "x", "x", "6", "x"], ["17", "x", "x", "x", "5", "x", "5", "7", "x", "x", "8", "x"], ["3", "19", "x", "x", "x", "x", "18", "x", "13", "7", "x", "x"], ["13", "x", "4", "x", "x", "8", "7", "4", "x", "15", "x", "x"], ["5", "17", "18", "12", "3", "x", "14", "2", "4", "18", "x", ... | [[["16", "x", "5", "6", "x", "14", "12", "x", "x", "x", "6", "x"], ["17", "x", "x", "x", "5", "x", "5", "7", "x", "x", "8", "x"], ["3", "19", "x", "x", "x", "x", "18", "x", "13", "7", "x", "x"], ["13", "x", "4", "x", "x", "8", "7", "4", "x", "15", "x", "x"], ["5", "17", "18", "12", "3", "x", "14", "2", "4", "18", "x", ... | ["[['16', 'x', '5', '6', 'x', '14', '12', 'x', 'x', 'x', '6', 'x'], ['17', 'x', 'x', 'x', '5', 'x', '5', '7', 'x', 'x', '8', 'x'], ['3', '19', 'x', 'x', 'x', 'x', '18', 'x', '13', '7', 'x', 'x'], ['13', 'x', '4', 'x', 'x', '8', '7', '4', 'x', '15', 'x', 'x'], ['5', '17', '18', '12', '3', 'x', '14', '2', '4', '18', 'x',... |
60 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 12x12. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are... | trampoline_matrix | pathfinding | 12 | [[1, 0], [2, 1], [3, 1], [3, 2], [4, 2], [5, 2], [6, 2], [6, 3], [7, 3], [7, 4], [8, 4], [9, 5], [10, 6], [11, 7]] | 14 | 0.02705216407775879 | 14 | 8 | 2 | ["[[0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, ... | ["[[0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, ... | ["[[0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, ... |
60 | Given 5 labeled water jugs with capacities 78, 68, 49, 82, 77, 88 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 176, 189, 251, 285 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wa... | water_jug | subset_sum | 5 | [["+", 77, 4], ["+", 77, 4], ["+", 49, 4], ["+", 82, 4], ["+", 68, 3], ["+", 68, 3], ["+", 82, 3], ["-", 49, 3], ["+", 82, 3], ["+", 68, 2], ["+", 82, 2], ["-", 49, 2], ["+", 88, 2], ["+", 88, 1], ["+", 88, 1]] | 15 | 0.06066584587097168 | 15 | 48 | 3 | [[78, 68, 49, 82, 77, 88], [176, 189, 251, 285]] | [[78, 68, 49, 82, 77, 88], [176, 189, 251, 285]] | ["[78, 68, 49, 82, 77, 88]", "[176, 189, 251, 285]"] |
61 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 4 | [12, 92, 54, 9, 8, 19, 60, 12, 92, 54, 12, 50, 83, 92, 54, 12, 9, 8, 19, 60, 21, 67, 60, 19] | 24 | 0.06862807273864746 | 24 | 4 | 15 | [[[93, 83, 50, 21, 67], [59, "_", 60, 19, 8], [14, 12, 92, 54, 9]]] | [[[93, 83, 50, 21, 67], [59, "_", 60, 19, 8], [14, 12, 92, 54, 9]]] | ["[[93, 83, 50, 21, 67], [59, '_', 60, 19, 8], [14, 12, 92, 54, 9]]"] |
61 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "down-left", "down-right", "up-right", "up-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"] | 12 | 0.19978690147399902 | 12 | 4 | 20 | [[["u", "a", "_", "r"], ["h", "e", "m", "e"], ["m", "i", "i", "p"], ["v", "a", "v", "j"], ["f", "i", "m", "i"]]] | [[["u", "a", "_", "r"], ["h", "e", "m", "e"], ["m", "i", "i", "p"], ["v", "a", "v", "j"], ["f", "i", "m", "i"]], ["aer", "hume", "mimp", "viva", "fiji"]] | ["[['u', 'a', '_', 'r'], ['h', 'e', 'm', 'e'], ['m', 'i', 'i', 'p'], ['v', 'a', 'v', 'j'], ['f', 'i', 'm', 'i']]", "['aer', 'hume', 'mimp', 'viva', 'fiji']"] |
61 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["J", "N", "Z", "M", "F", "U", "Z", "M"] | 8 | 0.040180206298828125 | 8 | 13 | 16 | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, ... | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, ... | ["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0,... |
61 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [30, 4, 10, 25, 2, 20, 23, 22, 29, 13, 21, 23, 23, 24, 3, 26, 29, 27, 15, 18, 28, 10, 22, 24, 2, 22, 13, 32, 8, 28, 31, 13, 27, 6, 35, 2, 20, 25, 24, 2, 16, 31, 3, 5, 23, 32, 24, 20, 13, 7, 11, 12], such that the sum of th... | coin_exchange | subset_sum | 33 | [28, 24, 18, 21, 25, 24, 25, 24, 6, 13, 13, 13, 35, 28, 26, 24, 4] | 72 | 0.058156728744506836 | 17 | 52 | 52 | [[30, 4, 10, 25, 2, 20, 23, 22, 29, 13, 21, 23, 23, 24, 3, 26, 29, 27, 15, 18, 28, 10, 22, 24, 2, 22, 13, 32, 8, 28, 31, 13, 27, 6, 35, 2, 20, 25, 24, 2, 16, 31, 3, 5, 23, 32, 24, 20, 13, 7, 11, 12]] | [[30, 4, 10, 25, 2, 20, 23, 22, 29, 13, 21, 23, 23, 24, 3, 26, 29, 27, 15, 18, 28, 10, 22, 24, 2, 22, 13, 32, 8, 28, 31, 13, 27, 6, 35, 2, 20, 25, 24, 2, 16, 31, 3, 5, 23, 32, 24, 20, 13, 7, 11, 12], {"10": 8, "32": 8, "25": 5, "7": 2, "30": 9, "18": 3, "5": 2, "35": 14, "2": 1, "15": 10, "12": 6, "29": 14, "23": 12, "... | ["[30, 4, 10, 25, 2, 20, 23, 22, 29, 13, 21, 23, 23, 24, 3, 26, 29, 27, 15, 18, 28, 10, 22, 24, 2, 22, 13, 32, 8, 28, 31, 13, 27, 6, 35, 2, 20, 25, 24, 2, 16, 31, 3, 5, 23, 32, 24, 20, 13, 7, 11, 12]", "{10: 8, 32: 8, 25: 5, 7: 2, 30: 9, 18: 3, 5: 2, 35: 14, 2: 1, 15: 10, 12: 6, 29: 14, 23: 12, 31: 14, 11: 3, 8: 7, 21:... |
61 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 0], [2, 1], [2, 1], [0, 2]] | 24 | 50.06358861923218 | 24 | 6 | 15 | [[["Red", "Green", "Green", "Red", "Blue"], ["Red", "Blue", "Green", "Red", "Green"], ["Green", "Blue", "Blue", "Blue", "Red"]], 8] | [[["Red", "Green", "Green", "Red", "Blue"], ["Red", "Blue", "Green", "Red", "Green"], ["Green", "Blue", "Blue", "Blue", "Red"]], 8] | ["[['Red', 'Green', 'Green', 'Red', 'Blue'], ['Red', 'Blue', 'Green', 'Red', 'Green'], ['Green', 'Blue', 'Blue', 'Blue', 'Red']]", "8"] |
61 | We have a 4x4 numerical grid, with numbers ranging from 36 to 81 (36 included in the range but 81 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, 2, 71], [0, 3, 76], [1, 2, 68], [2, 2, 65], [2, 3, 67], [3, 1, 49]] | 796 | 0.5532352924346924 | 6 | 45 | 16 | ["[['69', '70', '', ''], ['64', '66', '', '75'], ['62', '64', '', ''], ['60', '', '48', '46']]", 41, 86] | ["[['69', '70', '', ''], ['64', '66', '', '75'], ['62', '64', '', ''], ['60', '', '48', '46']]", 41, 86] | ["[['69', '70', '', ''], ['64', '66', '', '75'], ['62', '64', '', ''], ['60', '', '48', '46']]", "41", "86"] |
61 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 23 to 54. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 135, 149, None for columns 1 to 2 respectively, and the sums of rows must be None, 156, 156, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 25], [0, 2, 24], [0, 3, 26], [1, 0, 28], [1, 1, 23], [1, 2, 53], [1, 3, 52], [2, 0, 34], [2, 1, 32], [2, 3, 48], [3, 0, 38]] | 562 | 323.3269555568695 | 11 | 26 | 16 | ["[['', '31', '', ''], ['', '', '', ''], ['', '', '42', ''], ['', '49', '30', '27']]", 4, 23, 54] | ["[['', '31', '', ''], ['', '', '', ''], ['', '', '42', ''], ['', '49', '30', '27']]", 23, 54, [1, 3], [1, 3], [135, 149], [156, 156], 149] | ["[['', '31', '', ''], ['', '', '', ''], ['', '', '42', ''], ['', '49', '30', '27']]", "23", "54", "[None, 135, 149, None]", "[None, 156, 156, None]", "149"] |
61 | In 'Restricted Sorting', there are 10 stacks each with a capacity of 6 blocks, with 5 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 5 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 3 | [[2, 0], [2, 3], [8, 6], [9, 7], [9, 6], [9, 0], [9, 3], [9, 0], [4, 3], [4, 3], [4, 7], [4, 1], [9, 7], [4, 9], [4, 6], [2, 4], [2, 0], [2, 6], [2, 4], [8, 4], [8, 2], [8, 4], [8, 7], [5, 8], [5, 7], [5, 3], [5, 8], [5, 8], [2, 6], [5, 0], [1, 4], [9, 8]] | 256 | 0.2655496597290039 | 32 | 90 | 30 | [[[], [], ["Green", "Red", "White", "Green", "Black", "White"], [], ["Red", "Red", "Yellow", "White", "Blue", "Black"], ["Blue", "Yellow", "Red", "Blue", "Blue", "Green"], [], [], ["Black", "White", "Black", "White", "Yellow", "Blue"], ["Yellow", "Black", "Green", "Red", "Green", "Yellow"]], 6, {"0": 7, "1": 11, "2": 8... | [[[], [], ["Green", "Red", "White", "Green", "Black", "White"], [], ["Red", "Red", "Yellow", "White", "Blue", "Black"], ["Blue", "Yellow", "Red", "Blue", "Blue", "Green"], [], [], ["Black", "White", "Black", "White", "Yellow", "Blue"], ["Yellow", "Black", "Green", "Red", "Green", "Yellow"]], 6, {"0": 7, "1": 11, "2": 8... | ["[[], [], ['Green', 'Red', 'White', 'Green', 'Black', 'White'], [], ['Red', 'Red', 'Yellow', 'White', 'Blue', 'Black'], ['Blue', 'Yellow', 'Red', 'Blue', 'Blue', 'Green'], [], [], ['Black', 'White', 'Black', 'White', 'Yellow', 'Blue'], ['Yellow', 'Black', 'Green', 'Red', 'Green', 'Yellow']]", "{0: 7, 1: 11, 2: 8, 3: 1... |
61 | 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, 12) to his destination workshop at index (6, 2), indexing from 0. Ben's car can mov... | traffic | pathfinding | 5 | [[3, 12], [2, 12], [2, 11], [1, 11], [1, 10], [1, 9], [2, 9], [3, 9], [3, 8], [4, 8], [4, 7], [5, 7], [5, 6], [5, 5], [5, 4], [6, 4], [6, 3], [6, 2]] | 118 | 0.02977895736694336 | 18 | 4 | 4 | [[["13", "13", "16", "8", "x", "19", "1", "18", "13", "8", "x", "7", "x"], ["x", "13", "x", "15", "x", "12", "20", "1", "13", "19", "4", "17", "x"], ["x", "12", "9", "11", "13", "12", "2", "12", "19", "5", "19", "16", "8"], ["x", "12", "18", "19", "x", "7", "x", "12", "3", "2", "x", "16", "11"], ["x", "7", "x", "x", "8... | [[["13", "13", "16", "8", "x", "19", "1", "18", "13", "8", "x", "7", "x"], ["x", "13", "x", "15", "x", "12", "20", "1", "13", "19", "4", "17", "x"], ["x", "12", "9", "11", "13", "12", "2", "12", "19", "5", "19", "16", "8"], ["x", "12", "18", "19", "x", "7", "x", "12", "3", "2", "x", "16", "11"], ["x", "7", "x", "x", "8... | ["[['13', '13', '16', '8', 'x', '19', '1', '18', '13', '8', 'x', '7', 'x'], ['x', '13', 'x', '15', 'x', '12', '20', '1', '13', '19', '4', '17', 'x'], ['x', '12', '9', '11', '13', '12', '2', '12', '19', '5', '19', '16', '8'], ['x', '12', '18', '19', 'x', '7', 'x', '12', '3', '2', 'x', '16', '11'], ['x', '7', 'x', 'x', '... |
61 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. 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 | 13 | [[0, 11], [0, 10], [1, 10], [2, 9], [3, 9], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [5, 3], [6, 2], [6, 1], [7, 1]] | 14 | 0.03135824203491211 | 14 | 8 | 2 | ["[[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1,... | ["[[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1,... | ["[[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1,... |
61 | Given 5 labeled water jugs with capacities 56, 92, 66, 85, 65, 136 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 209, 293, 326, 379 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of w... | water_jug | subset_sum | 5 | [["+", 66, 4], ["+", 85, 4], ["+", 92, 4], ["+", 136, 4], ["+", 85, 3], ["+", 85, 3], ["+", 136, 3], ["-", 65, 3], ["+", 85, 3], ["+", 65, 2], ["+", 92, 2], ["+", 136, 2], ["+", 66, 1], ["+", 92, 1], ["-", 85, 1], ["+", 136, 1]] | 16 | 0.05174422264099121 | 16 | 48 | 3 | [[56, 92, 66, 85, 65, 136], [209, 293, 326, 379]] | [[56, 92, 66, 85, 65, 136], [209, 293, 326, 379]] | ["[56, 92, 66, 85, 65, 136]", "[209, 293, 326, 379]"] |
62 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 4 | [68, 37, 7, 78, 35, 7, 78, 68, 37, 78, 64, 41, 15, 19, 49, 79, 78, 37, 68, 64, 37, 68, 64, 35] | 24 | 0.16290855407714844 | 24 | 4 | 15 | [[[87, 49, 79, 68, "_"], [56, 19, 64, 37, 7], [27, 15, 41, 35, 78]]] | [[[87, 49, 79, 68, "_"], [56, 19, 64, 37, 7], [27, 15, 41, 35, 78]]] | ["[[87, 49, 79, 68, '_'], [56, 19, 64, 37, 7], [27, 15, 41, 35, 78]]"] |
62 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "up-left"] | 8 | 0.20729756355285645 | 8 | 4 | 20 | [[["u", "m", "a", "n"], ["c", "d", "t", "e"], ["o", "a", "_", "y"], ["d", "n", "w", "y"], ["o", "r", "z", "x"]]] | [[["u", "m", "a", "n"], ["c", "d", "t", "e"], ["o", "a", "_", "y"], ["d", "n", "w", "y"], ["o", "r", "z", "x"]], ["man", "cute", "dazy", "down", "oryx"]] | ["[['u', 'm', 'a', 'n'], ['c', 'd', 't', 'e'], ['o', 'a', '_', 'y'], ['d', 'n', 'w', 'y'], ['o', 'r', 'z', 'x']]", "['man', 'cute', 'dazy', 'down', 'oryx']"] |
62 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["K", "A", "Z", "U", "O", "U", "M", "Y", "B", "Y"] | 10 | 0.049027204513549805 | 10 | 13 | 16 | [[[0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, ... | [[[0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, ... | ["[[0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0,... |
62 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [35, 14, 9, 23, 25, 24, 21, 20, 12, 17, 12, 5, 2, 17, 25, 25, 26, 31, 7, 21, 10, 2, 27, 19, 32, 29, 11, 33, 3, 27, 17, 3, 18, 14, 2, 32, 14, 21, 12, 8, 3, 34, 13, 12, 2, 23, 13, 3, 3, 31, 23, 23, 6, 30, 30, 11, 21], such t... | coin_exchange | subset_sum | 34 | [7, 9, 33, 14, 31, 26, 14, 31, 14, 25, 25, 25, 35, 34, 10, 23] | 103 | 0.07300186157226562 | 16 | 57 | 57 | [[35, 14, 9, 23, 25, 24, 21, 20, 12, 17, 12, 5, 2, 17, 25, 25, 26, 31, 7, 21, 10, 2, 27, 19, 32, 29, 11, 33, 3, 27, 17, 3, 18, 14, 2, 32, 14, 21, 12, 8, 3, 34, 13, 12, 2, 23, 13, 3, 3, 31, 23, 23, 6, 30, 30, 11, 21]] | [[35, 14, 9, 23, 25, 24, 21, 20, 12, 17, 12, 5, 2, 17, 25, 25, 26, 31, 7, 21, 10, 2, 27, 19, 32, 29, 11, 33, 3, 27, 17, 3, 18, 14, 2, 32, 14, 21, 12, 8, 3, 34, 13, 12, 2, 23, 13, 3, 3, 31, 23, 23, 6, 30, 30, 11, 21], {"3": 1, "32": 16, "6": 5, "20": 13, "13": 5, "31": 9, "23": 10, "35": 14, "24": 17, "11": 11, "9": 1, ... | ["[35, 14, 9, 23, 25, 24, 21, 20, 12, 17, 12, 5, 2, 17, 25, 25, 26, 31, 7, 21, 10, 2, 27, 19, 32, 29, 11, 33, 3, 27, 17, 3, 18, 14, 2, 32, 14, 21, 12, 8, 3, 34, 13, 12, 2, 23, 13, 3, 3, 31, 23, 23, 6, 30, 30, 11, 21]", "{3: 1, 32: 16, 6: 5, 20: 13, 13: 5, 31: 9, 23: 10, 35: 14, 24: 17, 11: 11, 9: 1, 12: 10, 5: 3, 8: 5,... |
62 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[2, 1], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 2], [1, 0], [1, 0], [2, 1], [2, 0], [2, 0]] | 20 | 7.412998199462891 | 20 | 6 | 15 | [[["Blue", "Green", "Green", "Blue", "Green"], ["Red", "Blue", "Green", "Blue", "Green"], ["Red", "Blue", "Red", "Red", "Red"]], 8] | [[["Blue", "Green", "Green", "Blue", "Green"], ["Red", "Blue", "Green", "Blue", "Green"], ["Red", "Blue", "Red", "Red", "Red"]], 8] | ["[['Blue', 'Green', 'Green', 'Blue', 'Green'], ['Red', 'Blue', 'Green', 'Blue', 'Green'], ['Red', 'Blue', 'Red', 'Red', 'Red']]", "8"] |
62 | We have a 4x4 numerical grid, with numbers ranging from 41 to 86 (41 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, 2, 38], [1, 2, 53], [2, 0, 45], [3, 0, 46], [3, 1, 54], [3, 3, 66]] | 629 | 24.031245946884155 | 6 | 45 | 16 | ["[['33', '37', '', '58'], ['44', '51', '', '63'], ['', '52', '62', '64'], ['', '', '65', '']]", 33, 78] | ["[['33', '37', '', '58'], ['44', '51', '', '63'], ['', '52', '62', '64'], ['', '', '65', '']]", 33, 78] | ["[['33', '37', '', '58'], ['44', '51', '', '63'], ['', '52', '62', '64'], ['', '', '65', '']]", "33", "78"] |
62 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 66. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 199, 194, None for columns 1 to 2 respectively, and the sums of rows must be None, 164, 210, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 30], [0, 1, 31], [0, 2, 61], [0, 3, 37], [2, 1, 65], [2, 3, 41], [3, 0, 63], [3, 1, 64]] | 754 | 73.30463027954102 | 8 | 26 | 16 | ["[['', '', '', ''], ['40', '39', '32', '53'], ['46', '', '58', ''], ['', '', '43', '51']]", 4, 30, 66] | ["[['', '', '', ''], ['40', '39', '32', '53'], ['46', '', '58', ''], ['', '', '43', '51']]", 30, 66, [1, 3], [1, 3], [199, 194], [164, 210], 197] | ["[['', '', '', ''], ['40', '39', '32', '53'], ['46', '', '58', ''], ['', '', '43', '51']]", "30", "66", "[None, 199, 194, None]", "[None, 164, 210, None]", "197"] |
62 | In 'Restricted Sorting', there are 10 stacks each with a capacity of 6 blocks, with 5 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 5 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 3 | [[5, 8], [9, 8], [3, 4], [3, 0], [9, 0], [9, 0], [9, 4], [3, 1], [3, 8], [3, 8], [5, 6], [9, 1], [2, 4], [9, 3], [2, 9], [2, 8], [5, 3], [5, 9], [5, 3], [5, 0], [2, 5], [2, 3], [7, 5], [7, 9], [7, 0], [7, 5], [7, 5], [1, 9], [1, 9], [6, 5], [2, 4], [7, 4]] | 187 | 0.27761077880859375 | 32 | 90 | 30 | [[[], [], ["Blue", "Yellow", "Red", "Black", "White", "Blue"], ["Blue", "Green", "Yellow", "Red", "Red", "White"], [], ["Red", "Black", "White", "Yellow", "White", "Green"], [], ["Black", "Yellow", "Green", "Black", "Black", "Blue"], [], ["Red", "Green", "Green", "Blue", "Yellow", "White"]], 6, {"0": 6, "1": 10, "2": 8... | [[[], [], ["Blue", "Yellow", "Red", "Black", "White", "Blue"], ["Blue", "Green", "Yellow", "Red", "Red", "White"], [], ["Red", "Black", "White", "Yellow", "White", "Green"], [], ["Black", "Yellow", "Green", "Black", "Black", "Blue"], [], ["Red", "Green", "Green", "Blue", "Yellow", "White"]], 6, {"0": 6, "1": 10, "2": 8... | ["[[], [], ['Blue', 'Yellow', 'Red', 'Black', 'White', 'Blue'], ['Blue', 'Green', 'Yellow', 'Red', 'Red', 'White'], [], ['Red', 'Black', 'White', 'Yellow', 'White', 'Green'], [], ['Black', 'Yellow', 'Green', 'Black', 'Black', 'Blue'], [], ['Red', 'Green', 'Green', 'Blue', 'Yellow', 'White']]", "{0: 6, 1: 10, 2: 8, 3: 3... |
62 | 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, 2) to his destination workshop at index (2, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 5 | [[8, 2], [8, 3], [7, 3], [6, 3], [5, 3], [5, 4], [4, 4], [4, 5], [3, 5], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9]] | 100 | 0.019217967987060547 | 14 | 4 | 4 | [[["5", "15", "15", "5", "6", "19", "x", "9", "2", "x", "16", "x", "15"], ["16", "x", "x", "7", "5", "x", "x", "x", "5", "2", "19", "x", "3"], ["x", "11", "2", "19", "17", "5", "11", "6", "3", "18", "15", "16", "x"], ["2", "x", "12", "x", "20", "11", "7", "19", "2", "x", "4", "14", "x"], ["3", "x", "19", "x", "11", "19... | [[["5", "15", "15", "5", "6", "19", "x", "9", "2", "x", "16", "x", "15"], ["16", "x", "x", "7", "5", "x", "x", "x", "5", "2", "19", "x", "3"], ["x", "11", "2", "19", "17", "5", "11", "6", "3", "18", "15", "16", "x"], ["2", "x", "12", "x", "20", "11", "7", "19", "2", "x", "4", "14", "x"], ["3", "x", "19", "x", "11", "19... | ["[['5', '15', '15', '5', '6', '19', 'x', '9', '2', 'x', '16', 'x', '15'], ['16', 'x', 'x', '7', '5', 'x', 'x', 'x', '5', '2', '19', 'x', '3'], ['x', '11', '2', '19', '17', '5', '11', '6', '3', '18', '15', '16', 'x'], ['2', 'x', '12', 'x', '20', '11', '7', '19', '2', 'x', '4', '14', 'x'], ['3', 'x', '19', 'x', '11', '1... |
62 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. 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 | 13 | [[11, 8], [10, 8], [9, 7], [9, 6], [9, 5], [8, 4], [7, 5], [6, 4], [5, 4], [5, 3], [5, 2], [4, 2], [3, 2], [3, 1], [2, 1], [1, 1], [1, 0]] | 17 | 0.032764434814453125 | 17 | 8 | 2 | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 0, 1,... | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 0, 1,... | ["[[1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1], [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 1, 0, 1,... |
62 | Given 5 labeled water jugs with capacities 54, 89, 26, 70, 71, 128 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 240, 242, 246, 329 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of w... | water_jug | subset_sum | 5 | [["+", 54, 4], ["+", 128, 4], ["+", 128, 4], ["-", 70, 4], ["+", 89, 4], ["+", 70, 3], ["+", 70, 3], ["+", 89, 3], ["-", 54, 3], ["+", 71, 3], ["+", 70, 2], ["+", 70, 2], ["-", 26, 2], ["+", 128, 2], ["+", 54, 1], ["+", 71, 1], ["+", 89, 1], ["+", 26, 1]] | 18 | 0.041527748107910156 | 18 | 48 | 3 | [[54, 89, 26, 70, 71, 128], [240, 242, 246, 329]] | [[54, 89, 26, 70, 71, 128], [240, 242, 246, 329]] | ["[54, 89, 26, 70, 71, 128]", "[240, 242, 246, 329]"] |
63 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 4 | [65, 49, 24, 65, 91, 41, 80, 93, 65, 91, 49, 43, 12, 88, 41, 80, 91, 49, 88, 41, 80, 88, 43, 12] | 24 | 0.1251230239868164 | 24 | 4 | 15 | [[[98, 80, 41, 91, 88], [75, 93, 24, "_", 12], [38, 37, 49, 65, 43]]] | [[[98, 80, 41, 91, 88], [75, 93, 24, "_", 12], [38, 37, 49, 65, 43]]] | ["[[98, 80, 41, 91, 88], [75, 93, 24, '_', 12], [38, 37, 49, 65, 43]]"] |
63 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "up-left", "up-left"] | 16 | 0.22672724723815918 | 16 | 4 | 20 | [[["o", "l", "_", "z"], ["c", "i", "o", "s"], ["e", "n", "o", "s"], ["c", "e", "z", "o"], ["g", "a", "s", "t"]]] | [[["o", "l", "_", "z"], ["c", "i", "o", "s"], ["e", "n", "o", "s"], ["c", "e", "z", "o"], ["g", "a", "s", "t"]], ["liz", "coos", "enos", "coze", "gast"]] | ["[['o', 'l', '_', 'z'], ['c', 'i', 'o', 's'], ['e', 'n', 'o', 's'], ['c', 'e', 'z', 'o'], ['g', 'a', 's', 't']]", "['liz', 'coos', 'enos', 'coze', 'gast']"] |
63 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["F", "L", "O", "J", "U", "J", "I", "S", "N", "Z", "R", "N"] | 12 | 0.05983471870422363 | 12 | 13 | 16 | [[[0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, ... | [[[0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, ... | ["[[0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0,... |
63 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 12, 5, 32, 25, 3, 23, 49, 31, 6, 12, 23, 20, 14, 34, 17, 16, 16, 21, 18, 7, 30, 7, 27, 29, 14, 5, 9, 48, 33, 5, 18, 15, 29, 2, 28, 29, 25, 26, 6, 4, 4, 6, 8, 16, 5, 4, 4, 20, 25, 10, 6, 3, 24, 19], such that the sum o... | coin_exchange | subset_sum | 35 | [48, 34, 2, 25, 25, 6, 25, 6, 49, 6, 15, 19, 16, 6, 23, 10, 33] | 76 | 0.07342052459716797 | 17 | 55 | 55 | [[12, 12, 5, 32, 25, 3, 23, 49, 31, 6, 12, 23, 20, 14, 34, 17, 16, 16, 21, 18, 7, 30, 7, 27, 29, 14, 5, 9, 48, 33, 5, 18, 15, 29, 2, 28, 29, 25, 26, 6, 4, 4, 6, 8, 16, 5, 4, 4, 20, 25, 10, 6, 3, 24, 19]] | [[12, 12, 5, 32, 25, 3, 23, 49, 31, 6, 12, 23, 20, 14, 34, 17, 16, 16, 21, 18, 7, 30, 7, 27, 29, 14, 5, 9, 48, 33, 5, 18, 15, 29, 2, 28, 29, 25, 26, 6, 4, 4, 6, 8, 16, 5, 4, 4, 20, 25, 10, 6, 3, 24, 19], {"20": 18, "16": 6, "19": 2, "27": 12, "25": 2, "6": 2, "26": 16, "23": 9, "28": 12, "49": 16, "33": 13, "30": 12, "... | ["[12, 12, 5, 32, 25, 3, 23, 49, 31, 6, 12, 23, 20, 14, 34, 17, 16, 16, 21, 18, 7, 30, 7, 27, 29, 14, 5, 9, 48, 33, 5, 18, 15, 29, 2, 28, 29, 25, 26, 6, 4, 4, 6, 8, 16, 5, 4, 4, 20, 25, 10, 6, 3, 24, 19]", "{20: 18, 16: 6, 19: 2, 27: 12, 25: 2, 6: 2, 26: 16, 23: 9, 28: 12, 49: 16, 33: 13, 30: 12, 8: 6, 21: 18, 31: 16, ... |
63 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[1, 0], [2, 1], [2, 0], [2, 1], [2, 1], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [0, 2], [0, 1], [0, 1], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2]] | 26 | 131.11853456497192 | 26 | 6 | 15 | [[["Blue", "Green", "Blue", "Red", "Green"], ["Blue", "Green", "Green", "Red", "Blue"], ["Red", "Blue", "Red", "Red", "Green"]], 8] | [[["Blue", "Green", "Blue", "Red", "Green"], ["Blue", "Green", "Green", "Red", "Blue"], ["Red", "Blue", "Red", "Red", "Green"]], 8] | ["[['Blue', 'Green', 'Blue', 'Red', 'Green'], ['Blue', 'Green', 'Green', 'Red', 'Blue'], ['Red', 'Blue', 'Red', 'Red', 'Green']]", "8"] |
63 | We have a 4x4 numerical grid, with numbers ranging from 33 to 78 (33 included in the range but 78 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, 48], [0, 3, 75], [1, 1, 49], [2, 0, 42], [2, 2, 51], [2, 3, 55], [3, 2, 50]] | 728 | 4.985894441604614 | 7 | 45 | 16 | ["[['', '73', '74', ''], ['46', '', '63', '72'], ['', '47', '', ''], ['41', '45', '', '54']]", 35, 80] | ["[['', '73', '74', ''], ['46', '', '63', '72'], ['', '47', '', ''], ['41', '45', '', '54']]", 35, 80] | ["[['', '73', '74', ''], ['46', '', '63', '72'], ['', '47', '', ''], ['41', '45', '', '54']]", "35", "80"] |
63 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 66. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 207, 208, None for columns 1 to 2 respectively, and the sums of rows must be None, 173, 208, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 0, 30], [0, 1, 58], [0, 3, 32], [1, 0, 31], [1, 2, 62], [2, 1, 53], [2, 2, 45], [3, 0, 54]] | 772 | 65.37240958213806 | 8 | 26 | 16 | ["[['', '', '63', ''], ['', '44', '', '36'], ['50', '', '', '60'], ['', '52', '38', '64']]", 4, 30, 66] | ["[['', '', '63', ''], ['', '44', '', '36'], ['50', '', '', '60'], ['', '52', '38', '64']]", 30, 66, [1, 3], [1, 3], [207, 208], [173, 208], 201] | ["[['', '', '63', ''], ['', '44', '', '36'], ['50', '', '', '60'], ['', '52', '38', '64']]", "30", "66", "[None, 207, 208, None]", "[None, 173, 208, None]", "201"] |
63 | In 'Restricted Sorting', there are 10 stacks each with a capacity of 6 blocks, with 5 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 5 blocks of a single shade. The player can only transfer one b... | restricted_sorting | sorting | 3 | [[3, 8], [3, 8], [2, 0], [4, 1], [6, 1], [4, 9], [4, 8], [4, 5], [4, 0], [7, 5], [7, 8], [7, 8], [7, 0], [7, 1], [3, 0], [3, 1], [3, 0], [6, 9], [6, 9], [6, 1], [2, 4], [2, 4], [3, 7], [2, 3], [2, 4], [3, 4], [6, 9], [6, 9], [2, 7], [5, 7], [5, 7]] | 207 | 13.576901912689209 | 31 | 90 | 30 | [[[], [], ["Blue", "Yellow", "Yellow", "Yellow", "Yellow", "Black"], ["Red", "Red", "Blue", "White", "Blue", "Black"], ["White", "Green", "Red", "Black", "Blue", "Yellow"], [], ["White", "Green", "Green", "White", "Green", "Green"], ["Black", "Red", "Red", "Blue", "White", "Black"], [], []], 6, {"0": 7, "1": 7, "2": 8,... | [[[], [], ["Blue", "Yellow", "Yellow", "Yellow", "Yellow", "Black"], ["Red", "Red", "Blue", "White", "Blue", "Black"], ["White", "Green", "Red", "Black", "Blue", "Yellow"], [], ["White", "Green", "Green", "White", "Green", "Green"], ["Black", "Red", "Red", "Blue", "White", "Black"], [], []], 6, {"0": 7, "1": 7, "2": 8,... | ["[[], [], ['Blue', 'Yellow', 'Yellow', 'Yellow', 'Yellow', 'Black'], ['Red', 'Red', 'Blue', 'White', 'Blue', 'Black'], ['White', 'Green', 'Red', 'Black', 'Blue', 'Yellow'], [], ['White', 'Green', 'Green', 'White', 'Green', 'Green'], ['Black', 'Red', 'Red', 'Blue', 'White', 'Black'], [], []]", "{0: 7, 1: 7, 2: 8, 3: 5,... |
63 | 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, 0) to his destination workshop at index (8, 9), indexing from 0. Ben's car can move... | traffic | pathfinding | 5 | [[3, 0], [4, 0], [4, 1], [5, 1], [6, 1], [6, 2], [7, 2], [8, 2], [9, 2], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9]] | 102 | 0.01901412010192871 | 17 | 4 | 4 | [[["16", "9", "19", "14", "16", "19", "6", "x", "x", "x", "16", "18", "x"], ["19", "x", "x", "9", "9", "x", "17", "16", "3", "x", "x", "14", "x"], ["x", "x", "11", "x", "5", "x", "15", "15", "17", "10", "x", "13", "5"], ["2", "12", "9", "18", "7", "x", "x", "x", "4", "x", "10", "x", "3"], ["8", "9", "19", "1", "x", "4"... | [[["16", "9", "19", "14", "16", "19", "6", "x", "x", "x", "16", "18", "x"], ["19", "x", "x", "9", "9", "x", "17", "16", "3", "x", "x", "14", "x"], ["x", "x", "11", "x", "5", "x", "15", "15", "17", "10", "x", "13", "5"], ["2", "12", "9", "18", "7", "x", "x", "x", "4", "x", "10", "x", "3"], ["8", "9", "19", "1", "x", "4"... | ["[['16', '9', '19', '14', '16', '19', '6', 'x', 'x', 'x', '16', '18', 'x'], ['19', 'x', 'x', '9', '9', 'x', '17', '16', '3', 'x', 'x', '14', 'x'], ['x', 'x', '11', 'x', '5', 'x', '15', '15', '17', '10', 'x', '13', '5'], ['2', '12', '9', '18', '7', 'x', 'x', 'x', '4', 'x', '10', 'x', '3'], ['8', '9', '19', '1', 'x', '4... |
63 | Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. 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 | 13 | [[4, 0], [4, 1], [4, 2], [5, 3], [5, 4], [5, 5], [5, 6], [6, 6], [7, 6], [7, 7], [8, 7], [8, 8], [8, 9], [9, 9], [10, 10], [11, 11], [12, 12]] | 17 | 0.03172564506530762 | 17 | 8 | 2 | ["[[1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0,... | ["[[1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0,... | ["[[1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 0, 0, 1, 0,... |
63 | Given 5 labeled water jugs with capacities 123, 124, 133, 85, 74 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 276, 277, 355, 425 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wat... | water_jug | subset_sum | 5 | [["+", 85, 4], ["+", 133, 4], ["+", 74, 4], ["+", 133, 4], ["+", 74, 3], ["+", 74, 3], ["+", 74, 3], ["+", 133, 3], ["+", 85, 2], ["+", 133, 2], ["-", 74, 2], ["+", 133, 2], ["+", 133, 1], ["+", 133, 1], ["-", 123, 1], ["+", 133, 1]] | 16 | 0.024725675582885742 | 16 | 40 | 3 | [[123, 124, 133, 85, 74], [276, 277, 355, 425]] | [[123, 124, 133, 85, 74], [276, 277, 355, 425]] | ["[123, 124, 133, 85, 74]", "[276, 277, 355, 425]"] |
64 | In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ... | 8_puzzle | puzzle | 4 | [36, 44, 38, 36, 44, 14, 19, 54, 100, 91, 80, 74, 36, 38, 13, 10] | 16 | 0.03679513931274414 | 16 | 4 | 15 | [[[54, 100, 91, 80, 56], [19, "_", 38, 74, 29], [14, 36, 44, 13, 10]]] | [[[54, 100, 91, 80, 56], [19, "_", 38, 74, 29], [14, 36, 44, 13, 10]]] | ["[[54, 100, 91, 80, 56], [19, '_', 38, 74, 29], [14, 36, 44, 13, 10]]"] |
64 | In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ... | 8_puzzle_words | puzzle | 2 | ["down-left", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "up-left"] | 20 | 0.3210330009460449 | 20 | 4 | 20 | [[["u", "t", "_", "e"], ["j", "d", "d", "u"], ["o", "e", "z", "n"], ["b", "i", "r", "y"], ["w", "i", "r", "y"]]] | [[["u", "t", "_", "e"], ["j", "d", "d", "u"], ["o", "e", "z", "n"], ["b", "i", "r", "y"], ["w", "i", "r", "y"]], ["tue", "judy", "zein", "bord", "wiry"]] | ["[['u', 't', '_', 'e'], ['j', 'd', 'd', 'u'], ['o', 'e', 'z', 'n'], ['b', 'i', 'r', 'y'], ['w', 'i', 'r', 'y']]", "['tue', 'judy', 'zein', 'bord', 'wiry']"] |
64 | We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw... | city_directed_graph | pathfinding | 13 | ["Y", "T", "D", "A", "D", "L", "R", "Z", "R"] | 9 | 0.04733538627624512 | 9 | 13 | 16 | [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 0, 1, 1, 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, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 0, 1, 1, 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, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1,... |
64 | In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [14, 8, 11, 30, 3, 3, 27, 16, 19, 4, 6, 14, 7, 2, 39, 103, 15, 100, 27, 36, 7, 36, 13, 7, 18, 39, 14, 3, 28], such that the sum of the chosen coins adds up to 410. Each coin in the list is unique and can only be used once.... | coin_exchange | subset_sum | 15 | [7, 7, 19, 39, 103, 100, 28, 39, 36, 6, 7, 11, 8] | 83 | 0.03669548034667969 | 13 | 29 | 29 | [[14, 8, 11, 30, 3, 3, 27, 16, 19, 4, 6, 14, 7, 2, 39, 103, 15, 100, 27, 36, 7, 36, 13, 7, 18, 39, 14, 3, 28]] | [[14, 8, 11, 30, 3, 3, 27, 16, 19, 4, 6, 14, 7, 2, 39, 103, 15, 100, 27, 36, 7, 36, 13, 7, 18, 39, 14, 3, 28], {"13": 11, "18": 8, "36": 15, "11": 4, "6": 1, "16": 8, "100": 12, "39": 10, "28": 9, "27": 20, "103": 6, "19": 5, "30": 14, "2": 1, "4": 3, "3": 3, "15": 10, "8": 5, "7": 2, "14": 14}, 410] | ["[14, 8, 11, 30, 3, 3, 27, 16, 19, 4, 6, 14, 7, 2, 39, 103, 15, 100, 27, 36, 7, 36, 13, 7, 18, 39, 14, 3, 28]", "{13: 11, 18: 8, 36: 15, 11: 4, 6: 1, 16: 8, 100: 12, 39: 10, 28: 9, 27: 20, 103: 6, 19: 5, 30: 14, 2: 1, 4: 3, 3: 3, 15: 10, 8: 5, 7: 2, 14: 14}", "410"] |
64 | The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number... | color_sorting | sorting | 9 | [[0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1]] | 14 | 0.2936434745788574 | 14 | 6 | 15 | [[["Red", "Blue", "Red", "Red", "Red"], ["Blue", "Blue", "Blue", "Green", "Green"], ["Red", "Green", "Green", "Green", "Blue"]], 8] | [[["Red", "Blue", "Red", "Red", "Red"], ["Blue", "Blue", "Blue", "Green", "Green"], ["Red", "Green", "Green", "Green", "Blue"]], 8] | ["[['Red', 'Blue', 'Red', 'Red', 'Red'], ['Blue', 'Blue', 'Blue', 'Green', 'Green'], ['Red', 'Green', 'Green', 'Green', 'Blue']]", "8"] |
64 | We have a 4x4 numerical grid, with numbers ranging from 35 to 80 (35 included in the range but 80 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce... | consecutive_grid | underdetermined_system | 12 | [[0, 0, 31], [0, 3, 72], [1, 0, 32], [1, 1, 47], [1, 3, 63], [2, 1, 46], [2, 3, 59]] | 685 | 41.66590666770935 | 7 | 45 | 16 | ["[['', '68', '71', ''], ['', '', '62', ''], ['43', '', '55', ''], ['44', '45', '52', '58']]", 31, 76] | ["[['', '68', '71', ''], ['', '', '62', ''], ['43', '', '55', ''], ['44', '45', '52', '58']]", 31, 76] | ["[['', '68', '71', ''], ['', '', '62', ''], ['43', '', '55', ''], ['44', '45', '52', '58']]", "31", "76"] |
64 | In the magic square problem, a 4x4 grid is filled with unique integers ranging from 30 to 66. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 154, 157, None for columns 1 to 2 respectively, and the sums of rows must be None, 173, 194, None for rows 1 to... | magic_square | underdetermined_system | 8 | [[0, 2, 42], [1, 1, 32], [1, 2, 45], [2, 0, 35], [2, 1, 58], [2, 3, 64], [3, 0, 56], [3, 3, 31]] | 688 | 0.30200624465942383 | 8 | 26 | 16 | ["[['46', '30', '', '49'], ['43', '', '', '53'], ['', '', '37', ''], ['', '34', '33', '']]", 4, 30, 66] | ["[['46', '30', '', '49'], ['43', '', '', '53'], ['', '', '37', ''], ['', '34', '33', '']]", 30, 66, [1, 3], [1, 3], [154, 157], [173, 194], 208] | ["[['46', '30', '', '49'], ['43', '', '', '53'], ['', '', '37', ''], ['', '34', '33', '']]", "30", "66", "[None, 154, 157, None]", "[None, 173, 194, None]", "208"] |
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