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stringclasses
105 values
problem_statement
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778
1.74k
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stringclasses
11 values
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stringclasses
5 values
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stringclasses
35 values
opt_solution
stringlengths
24
474
opt_solution_cost
stringlengths
1
4
opt_solution_compute_t
stringlengths
14
20
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stringclasses
40 values
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stringclasses
51 values
num_vars_per_state
stringclasses
47 values
is_feasible_args
stringlengths
43
1.24k
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stringlengths
43
1.26k
A*_args
stringlengths
46
1.27k
19
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["E", "M", "Y", "T", "B", "R", "Y", "T"]
8
0.022693395614624023
8
11
14
[[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0,...
[[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0,...
["[[0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0...
19
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11], such that the sum of th...
coin_exchange
subset_sum
33
[20, 23, 22, 20, 16, 8, 11, 10, 8, 11, 10, 8, 13, 10, 8, 4, 2, 9, 8, 4, 2, 7, 4, 5]
63
0.05074810981750488
24
55
55
[[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11]]
[[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11], {"20": 3, "9": 2, "23": 1, "10": 3, "5": 4, "21": 14, "22": 5, "18": 7, "16": 4, "13": 5, "2": 1, "8": 2, "19": 16, "7":...
["[9, 20, 4, 23, 10, 11, 8, 6, 20, 8, 20, 12, 15, 20, 18, 16, 19, 21, 5, 6, 4, 5, 14, 5, 4, 18, 22, 7, 8, 15, 5, 15, 8, 19, 14, 12, 2, 5, 5, 15, 2, 6, 10, 18, 14, 13, 8, 10, 21, 14, 5, 18, 16, 6, 11]", "{20: 3, 9: 2, 23: 1, 10: 3, 5: 4, 21: 14, 22: 5, 18: 7, 16: 4, 13: 5, 2: 1, 8: 2, 19: 16, 7: 3, 6: 6, 11: 3, 14: 8, 4...
19
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[0, 1], [0, 2], [0, 2], [0, 1], [2, 0], [2, 0], [1, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0]]
21
4.620145320892334
21
6
12
[[["Blue", "Green", "Green", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Red", "Green", "Blue"]], 6]
[[["Blue", "Green", "Green", "Red"], ["Red", "Blue", "Green", "Red"], ["Blue", "Red", "Green", "Blue"]], 6]
["[['Blue', 'Green', 'Green', 'Red'], ['Red', 'Blue', 'Green', 'Red'], ['Blue', 'Red', 'Green', 'Blue']]", "6"]
19
We have a 3x3 numerical grid, with numbers ranging from 48 to 91 (48 included in the range but 91 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
7
[[0, 0, 48], [0, 1, 49], [1, 1, 60], [2, 0, 75]]
577
0.17565202713012695
4
43
9
["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", 48, 91]
["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", 48, 91]
["[['', '', '85'], ['58', '', '84'], ['', '74', '59']]", "48", "91"]
19
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 234, and sum of row 1 must be 201. Also, the sum of the numbers in the diagonal from the top right to t...
magic_square
underdetermined_system
6
[[0, 2, 51], [1, 0, 52], [1, 1, 83], [1, 2, 66], [2, 0, 79], [2, 1, 73], [2, 2, 50]]
596
7.28009295463562
7
29
9
["[['64', '78', ''], ['', '', ''], ['', '', '']]", 3, 50, 84]
["[['64', '78', ''], ['', '', ''], ['', '', '']]", 50, 84, [1, 2], [1, 2], [234], [201], 213]
["[['64', '78', ''], ['', '', ''], ['', '', '']]", "50", "84", "[None, 234, None]", "[None, 201, None]", "213"]
19
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[5, 0], [2, 0], [2, 1], [2, 0], [5, 3], [5, 1], [4, 3], [4, 3], [4, 2], [5, 2], [4, 1]]
48
0.03397560119628906
11
30
12
[[[], [], ["Green", "Blue", "Green", "Yellow"], [], ["Red", "Red", "Yellow", "Blue"], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 2, "1": 4, "2": 6, "3": 6, "4": 6, "5": 7}]
[[[], [], ["Green", "Blue", "Green", "Yellow"], [], ["Red", "Red", "Yellow", "Blue"], ["Green", "Red", "Blue", "Yellow"]], 4, {"0": 2, "1": 4, "2": 6, "3": 6, "4": 6, "5": 7}, 3]
["[[], [], ['Green', 'Blue', 'Green', 'Yellow'], [], ['Red', 'Red', 'Yellow', 'Blue'], ['Green', 'Red', 'Blue', 'Yellow']]", "{0: 2, 1: 4, 2: 6, 3: 6, 4: 6, 5: 7}", "4", "3"]
19
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 0) to his destination workshop at index (3, 9), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[5, 0], [6, 0], [6, 1], [6, 2], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [4, 8], [4, 9], [3, 9]]
122
0.027219295501708984
14
4
4
[[["x", "16", "15", "14", "2", "12", "3", "x", "7", "7"], ["11", "x", "x", "x", "4", "10", "5", "x", "x", "x"], ["12", "x", "3", "x", "x", "19", "x", "13", "x", "x"], ["16", "15", "13", "x", "12", "x", "x", "1", "x", "7"], ["2", "6", "x", "5", "x", "14", "7", "x", "8", "18"], ["19", "17", "2", "11", "8", "17", "12", "8...
[[["x", "16", "15", "14", "2", "12", "3", "x", "7", "7"], ["11", "x", "x", "x", "4", "10", "5", "x", "x", "x"], ["12", "x", "3", "x", "x", "19", "x", "13", "x", "x"], ["16", "15", "13", "x", "12", "x", "x", "1", "x", "7"], ["2", "6", "x", "5", "x", "14", "7", "x", "8", "18"], ["19", "17", "2", "11", "8", "17", "12", "8...
["[['x', '16', '15', '14', '2', '12', '3', 'x', '7', '7'], ['11', 'x', 'x', 'x', '4', '10', '5', 'x', 'x', 'x'], ['12', 'x', '3', 'x', 'x', '19', 'x', '13', 'x', 'x'], ['16', '15', '13', 'x', '12', 'x', 'x', '1', 'x', '7'], ['2', '6', 'x', '5', 'x', '14', '7', 'x', '8', '18'], ['19', '17', '2', '11', '8', '17', '12', '...
19
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[1, 9], [1, 8], [1, 7], [1, 6], [0, 5], [0, 4], [1, 4], [1, 3], [1, 2], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1], [6, 1], [7, 1]]
16
0.029511690139770508
16
8
2
["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1...
["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1...
["[[1, 0, 1, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0, 1, 1...
19
Given 7 labeled water jugs with capacities 21, 62, 98, 143, 61, 110, 140, 40 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 280, 338, 353 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount...
water_jug
subset_sum
5
[["+", 110, 3], ["+", 140, 3], ["-", 40, 3], ["+", 143, 3], ["+", 140, 2], ["+", 140, 2], ["-", 40, 2], ["+", 98, 2], ["+", 140, 1], ["+", 140, 1]]
10
0.0442960262298584
10
48
3
[[21, 62, 98, 143, 61, 110, 140, 40], [280, 338, 353]]
[[21, 62, 98, 143, 61, 110, 140, 40], [280, 338, 353]]
["[21, 62, 98, 143, 61, 110, 140, 40]", "[280, 338, 353]"]
20
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
5
[99, 49, 92, 91, 25, 99, 49, 92, 91, 46, 50, 91, 99, 25, 46, 50, 91, 99, 50, 91, 99, 97, 92, 49]
24
0.10476183891296387
24
4
9
[[[46, 50, 97], [92, 49, 99], [91, 25, "_"]]]
[[[46, 50, 97], [92, 49, 99], [91, 25, "_"]]]
["[[46, 50, 97], [92, 49, 99], [91, 25, '_']]"]
20
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"]
16
0.2547872066497803
16
4
20
[[["r", "s", "w", "o", "g"], ["t", "n", "e", "m", "a"], ["m", "o", "_", "u", "s"], ["a", "w", "i", "r", "i"]]]
[[["r", "s", "w", "o", "g"], ["t", "n", "e", "m", "a"], ["m", "o", "_", "u", "s"], ["a", "w", "i", "r", "i"]], ["snog", "trema", "mosur", "awiwi"]]
["[['r', 's', 'w', 'o', 'g'], ['t', 'n', 'e', 'm', 'a'], ['m', 'o', '_', 'u', 's'], ['a', 'w', 'i', 'r', 'i']]", "['snog', 'trema', 'mosur', 'awiwi']"]
20
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["F", "D", "Y", "N", "C", "I", "R", "M", "N", "X", "Q", "I"]
12
0.029342174530029297
12
11
14
[[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0,...
[[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0,...
["[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [0...
20
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15], such that the sum of th...
coin_exchange
subset_sum
34
[24, 22, 2, 5, 11, 2, 5, 11, 2, 5, 5, 5, 7, 6, 21, 16, 14, 12, 23, 22, 18, 8]
65
0.05625104904174805
22
56
56
[[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15]]
[[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15], {"20": 14, "15": 15, "6": 1, "14": 1, "7": 2, "18": 5, "2": 1, "16": 5, "21": 9, "3": 3, "12": 3, "17": 10, "22": 4, "10...
["[12, 15, 3, 24, 10, 18, 10, 20, 21, 17, 9, 8, 2, 11, 5, 5, 3, 8, 6, 12, 20, 22, 4, 5, 17, 5, 14, 10, 15, 8, 9, 22, 4, 7, 15, 16, 4, 2, 5, 9, 24, 23, 3, 7, 20, 9, 12, 10, 4, 4, 8, 24, 11, 20, 2, 15]", "{20: 14, 15: 15, 6: 1, 14: 1, 7: 2, 18: 5, 2: 1, 16: 5, 21: 9, 3: 3, 12: 3, 17: 10, 22: 4, 10: 9, 4: 3, 11: 1, 5: 1, ...
20
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[1, 2], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]]
18
1.1464557647705078
18
6
12
[[["Red", "Red", "Green", "Blue"], ["Green", "Green", "Red", "Green"], ["Blue", "Blue", "Red", "Blue"]], 6]
[[["Red", "Red", "Green", "Blue"], ["Green", "Green", "Red", "Green"], ["Blue", "Blue", "Red", "Blue"]], 6]
["[['Red', 'Red', 'Green', 'Blue'], ['Green', 'Green', 'Red', 'Green'], ['Blue', 'Blue', 'Red', 'Blue']]", "6"]
20
We have a 3x3 numerical grid, with numbers ranging from 48 to 91 (48 included in the range but 91 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
7
[[0, 1, 49], [0, 2, 48], [1, 1, 57], [2, 1, 58]]
578
0.17241978645324707
4
43
9
["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", 48, 91]
["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", 48, 91]
["[['80', '', ''], ['56', '', '64'], ['51', '', '76']]", "48", "91"]
20
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 233, and sum of row 1 must be 207. Also, the sum of the numbers in the diagonal from the top right to t...
magic_square
underdetermined_system
6
[[0, 2, 50], [1, 0, 53], [1, 1, 83], [1, 2, 71], [2, 0, 52], [2, 1, 68], [2, 2, 51]]
572
3.969967842102051
7
29
9
["[['62', '82', ''], ['', '', ''], ['', '', '']]", 3, 50, 84]
["[['62', '82', ''], ['', '', ''], ['', '', '']]", 50, 84, [1, 2], [1, 2], [233], [207], 185]
["[['62', '82', ''], ['', '', ''], ['', '', '']]", "50", "84", "[None, 233, None]", "[None, 207, None]", "185"]
20
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[1, 2], [1, 0], [3, 0], [4, 0], [1, 5], [3, 1], [4, 5], [4, 1], [3, 5], [2, 3], [4, 3]]
28
0.036955833435058594
11
30
12
[[[], ["Green", "Red", "Yellow", "Blue"], [], ["Red", "Blue", "Yellow", "Green"], ["Red", "Yellow", "Blue", "Green"], []], 4, {"0": 4, "1": 2, "2": 5, "3": 2, "4": 4, "5": 1}]
[[[], ["Green", "Red", "Yellow", "Blue"], [], ["Red", "Blue", "Yellow", "Green"], ["Red", "Yellow", "Blue", "Green"], []], 4, {"0": 4, "1": 2, "2": 5, "3": 2, "4": 4, "5": 1}, 3]
["[[], ['Green', 'Red', 'Yellow', 'Blue'], [], ['Red', 'Blue', 'Yellow', 'Green'], ['Red', 'Yellow', 'Blue', 'Green'], []]", "{0: 4, 1: 2, 2: 5, 3: 2, 4: 4, 5: 1}", "4", "3"]
20
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (6, 0) to his destination workshop at index (4, 9), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[6, 0], [5, 0], [4, 0], [4, 1], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 8], [4, 9]]
141
0.029550790786743164
14
4
4
[[["19", "x", "7", "x", "12", "x", "15", "5", "19", "14"], ["17", "x", "3", "5", "7", "x", "x", "x", "17", "20"], ["x", "11", "15", "8", "x", "16", "4", "x", "1", "1"], ["x", "8", "19", "4", "3", "3", "3", "17", "8", "15"], ["13", "10", "17", "17", "6", "1", "x", "8", "13", "20"], ["20", "x", "x", "x", "x", "4", "18", ...
[[["19", "x", "7", "x", "12", "x", "15", "5", "19", "14"], ["17", "x", "3", "5", "7", "x", "x", "x", "17", "20"], ["x", "11", "15", "8", "x", "16", "4", "x", "1", "1"], ["x", "8", "19", "4", "3", "3", "3", "17", "8", "15"], ["13", "10", "17", "17", "6", "1", "x", "8", "13", "20"], ["20", "x", "x", "x", "x", "4", "18", ...
["[['19', 'x', '7', 'x', '12', 'x', '15', '5', '19', '14'], ['17', 'x', '3', '5', '7', 'x', 'x', 'x', '17', '20'], ['x', '11', '15', '8', 'x', '16', '4', 'x', '1', '1'], ['x', '8', '19', '4', '3', '3', '3', '17', '8', '15'], ['13', '10', '17', '17', '6', '1', 'x', '8', '13', '20'], ['20', 'x', 'x', 'x', 'x', '4', '18',...
20
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[0, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 2], [6, 3], [7, 4], [7, 5], [7, 6]]
11
0.03641462326049805
11
8
2
["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1...
["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1...
["[[0, 0, 1, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1, 1...
20
Given 7 labeled water jugs with capacities 76, 48, 35, 94, 93, 115, 16, 53 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 247, 261, 273 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o...
water_jug
subset_sum
5
[["+", 48, 3], ["+", 94, 3], ["+", 16, 3], ["+", 115, 3], ["+", 93, 2], ["+", 115, 2], ["+", 53, 2], ["+", 76, 1], ["+", 93, 1], ["-", 16, 1], ["+", 94, 1]]
11
0.03790163993835449
11
48
3
[[76, 48, 35, 94, 93, 115, 16, 53], [247, 261, 273]]
[[76, 48, 35, 94, 93, 115, 16, 53], [247, 261, 273]]
["[76, 48, 35, 94, 93, 115, 16, 53]", "[247, 261, 273]"]
21
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
5
[53, 94, 61, 25, 71, 58, 94, 61, 18, 50, 25, 71, 58, 94, 61, 53, 50, 18, 71, 58, 94, 71, 53, 50]
24
0.061148881912231445
24
4
9
[[[25, 71, 58], [61, 94, 53], [50, 18, "_"]]]
[[[25, 71, 58], [61, 94, 53], [50, 18, "_"]]]
["[[25, 71, 58], [61, 94, 53], [50, 18, '_']]"]
21
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left"]
18
0.25868940353393555
18
4
20
[[["m", "p", "l", "s", "s"], ["s", "a", "o", "s", "e"], ["c", "a", "_", "e", "k"], ["h", "i", "r", "o", "m"]]]
[[["m", "p", "l", "s", "s"], ["s", "a", "o", "s", "e"], ["c", "a", "_", "e", "k"], ["h", "i", "r", "o", "m"]], ["poss", "smoke", "casel", "hiram"]]
["[['m', 'p', 'l', 's', 's'], ['s', 'a', 'o', 's', 'e'], ['c', 'a', '_', 'e', 'k'], ['h', 'i', 'r', 'o', 'm']]", "['poss', 'smoke', 'casel', 'hiram']"]
21
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["Y", "K", "M", "I", "H", "Q", "R", "Q", "W", "I"]
10
0.020466327667236328
10
11
14
[[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1,...
[[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1,...
["[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [1...
21
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15], such that the sum of the cho...
coin_exchange
subset_sum
35
[20, 16, 6, 15, 15, 15, 15, 14, 6, 4, 13, 13, 4, 21, 16, 4, 2, 7, 4]
56
0.052184104919433594
19
55
55
[[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15]]
[[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15], {"9": 9, "6": 1, "13": 4, "2": 1, "16": 3, "14": 4, "19": 16, "20": 2, "15": 3, "7": 3, "18": 14, "17": 15, "4": 2, "5": 5, "...
["[17, 19, 5, 17, 13, 2, 12, 4, 4, 15, 19, 7, 18, 15, 4, 6, 9, 2, 4, 11, 21, 17, 20, 4, 8, 2, 19, 16, 2, 12, 8, 16, 18, 3, 18, 13, 3, 15, 7, 18, 4, 14, 3, 5, 8, 7, 19, 9, 17, 5, 17, 6, 3, 5, 15]", "{9: 9, 6: 1, 13: 4, 2: 1, 16: 3, 14: 4, 19: 16, 20: 2, 15: 3, 7: 3, 18: 14, 17: 15, 4: 2, 5: 5, 8: 8, 21: 10, 12: 11, 11: ...
21
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[1, 2], [0, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0]]
18
1.3162987232208252
18
6
12
[[["Green", "Red", "Blue", "Green"], ["Red", "Blue", "Red", "Blue"], ["Red", "Blue", "Green", "Green"]], 6]
[[["Green", "Red", "Blue", "Green"], ["Red", "Blue", "Red", "Blue"], ["Red", "Blue", "Green", "Green"]], 6]
["[['Green', 'Red', 'Blue', 'Green'], ['Red', 'Blue', 'Red', 'Blue'], ['Red', 'Blue', 'Green', 'Green']]", "6"]
21
We have a 3x3 numerical grid, with numbers ranging from 15 to 58 (15 included in the range but 58 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
7
[[0, 1, 16], [0, 2, 15], [2, 0, 17], [2, 1, 34]]
284
0.16371726989746094
4
43
9
["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", 15, 58]
["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", 15, 58]
["[['30', '', ''], ['28', '33', '43'], ['', '', '51']]", "15", "58"]
21
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 50 to 84. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 212, and sum of row 1 must be 193. Also, the sum of the numbers in the diagonal from the top right to t...
magic_square
underdetermined_system
7
[[0, 0, 50], [0, 1, 51], [1, 0, 52], [1, 1, 83], [1, 2, 58], [2, 0, 72], [2, 1, 78]]
562
155.01593708992004
7
29
9
["[['', '', '62'], ['', '', ''], ['', '', '56']]", 3, 50, 84]
["[['', '', '62'], ['', '', ''], ['', '', '56']]", 50, 84, [1, 2], [1, 2], [212], [193], 217]
["[['', '', '62'], ['', '', ''], ['', '', '56']]", "50", "84", "[None, 212, None]", "[None, 193, None]", "217"]
21
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[0, 2], [5, 4], [5, 2], [5, 1], [0, 4], [0, 5], [3, 1], [3, 5], [3, 1], [0, 4], [3, 2]]
43
0.025786161422729492
11
30
12
[[["Red", "Yellow", "Blue", "Yellow"], [], [], ["Green", "Blue", "Green", "Red"], [], ["Yellow", "Red", "Green", "Blue"]], 4, {"0": 4, "1": 5, "2": 3, "3": 3, "4": 3, "5": 5}]
[[["Red", "Yellow", "Blue", "Yellow"], [], [], ["Green", "Blue", "Green", "Red"], [], ["Yellow", "Red", "Green", "Blue"]], 4, {"0": 4, "1": 5, "2": 3, "3": 3, "4": 3, "5": 5}, 3]
["[['Red', 'Yellow', 'Blue', 'Yellow'], [], [], ['Green', 'Blue', 'Green', 'Red'], [], ['Yellow', 'Red', 'Green', 'Blue']]", "{0: 4, 1: 5, 2: 3, 3: 3, 4: 3, 5: 5}", "4", "3"]
21
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (1, 9) to his destination workshop at index (6, 3), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[1, 9], [1, 8], [2, 8], [3, 8], [3, 7], [4, 7], [4, 6], [5, 6], [6, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5], [4, 4], [5, 4], [5, 3], [6, 3]]
120
0.022410869598388672
18
4
4
[[["15", "4", "9", "10", "19", "x", "12", "4", "x", "15"], ["12", "19", "11", "x", "x", "x", "x", "7", "6", "3"], ["4", "x", "8", "x", "x", "19", "x", "11", "1", "6"], ["x", "x", "5", "x", "x", "x", "12", "6", "6", "x"], ["x", "14", "x", "x", "14", "11", "2", "9", "6", "14"], ["8", "8", "5", "17", "7", "x", "1", "2", "...
[[["15", "4", "9", "10", "19", "x", "12", "4", "x", "15"], ["12", "19", "11", "x", "x", "x", "x", "7", "6", "3"], ["4", "x", "8", "x", "x", "19", "x", "11", "1", "6"], ["x", "x", "5", "x", "x", "x", "12", "6", "6", "x"], ["x", "14", "x", "x", "14", "11", "2", "9", "6", "14"], ["8", "8", "5", "17", "7", "x", "1", "2", "...
["[['15', '4', '9', '10', '19', 'x', '12', '4', 'x', '15'], ['12', '19', '11', 'x', 'x', 'x', 'x', '7', '6', '3'], ['4', 'x', '8', 'x', 'x', '19', 'x', '11', '1', '6'], ['x', 'x', '5', 'x', 'x', 'x', '12', '6', '6', 'x'], ['x', '14', 'x', 'x', '14', '11', '2', '9', '6', '14'], ['8', '8', '5', '17', '7', 'x', '1', '2', ...
21
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[1, 9], [1, 8], [2, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [5, 2], [5, 1], [5, 0]]
11
0.029159069061279297
11
8
2
["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1...
["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1...
["[[0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1...
21
Given 7 labeled water jugs with capacities 52, 131, 82, 132, 117, 65 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 357, 384, 522 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of wate...
water_jug
subset_sum
5
[["+", 117, 3], ["+", 117, 3], ["+", 52, 3], ["+", 52, 3], ["+", 52, 3], ["+", 132, 3], ["+", 82, 2], ["+", 131, 2], ["+", 52, 2], ["+", 52, 2], ["-", 65, 2], ["+", 132, 2], ["+", 65, 1], ["+", 131, 1], ["+", 131, 1], ["-", 52, 1], ["+", 82, 1]]
17
0.047934532165527344
17
36
3
[[52, 131, 82, 132, 117, 65], [357, 384, 522]]
[[52, 131, 82, 132, 117, 65], [357, 384, 522]]
["[52, 131, 82, 132, 117, 65]", "[357, 384, 522]"]
22
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
5
[25, 56, 41, 61, 19, 41, 61, 39, 14, 25, 56, 61, 39, 14]
14
0.019939899444580078
14
4
9
[[[81, 25, "_"], [19, 56, 14], [61, 41, 39]]]
[[[81, 25, "_"], [19, 56, 14], [61, 41, 39]]]
["[[81, 25, '_'], [19, 56, 14], [61, 41, 39]]"]
22
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-left", "down-right", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-left"]
16
0.13087821006774902
16
4
20
[[["o", "j", "_", "h", "u"], ["w", "l", "r", "e", "y"], ["n", "i", "l", "t", "a"], ["i", "y", "i", "m", "l"]]]
[[["o", "j", "_", "h", "u"], ["w", "l", "r", "e", "y"], ["n", "i", "l", "t", "a"], ["i", "y", "i", "m", "l"]], ["jehu", "wormy", "linty", "ilial"]]
["[['o', 'j', '_', 'h', 'u'], ['w', 'l', 'r', 'e', 'y'], ['n', 'i', 'l', 't', 'a'], ['i', 'y', 'i', 'm', 'l']]", "['jehu', 'wormy', 'linty', 'ilial']"]
22
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["X", "Z", "V", "T", "E", "J", "M", "T", "E"]
9
0.029807567596435547
9
11
14
[[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0,...
[[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0,...
["[[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0...
22
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10], such that the sum of the chosen coins adds up to 268. Each coin in the list is unique and can only be used once. Also...
coin_exchange
subset_sum
15
[9, 13, 10, 69, 66, 16, 10, 19, 25, 12, 15, 4]
96
0.04047846794128418
12
28
28
[[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10]]
[[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10], {"66": 17, "9": 3, "15": 10, "7": 6, "3": 3, "13": 7, "11": 10, "25": 14, "22": 18, "24": 17, "12": 6, "23": 18, "2": 2, "10": 5, "19": 10, "20": 19, "5": 4, "16": 1, "21": 20, "69": 14, "4": 4}, 268]
["[10, 2, 5, 22, 15, 3, 4, 66, 3, 11, 21, 16, 69, 2, 19, 20, 9, 24, 24, 20, 12, 13, 21, 7, 7, 23, 25, 10]", "{66: 17, 9: 3, 15: 10, 7: 6, 3: 3, 13: 7, 11: 10, 25: 14, 22: 18, 24: 17, 12: 6, 23: 18, 2: 2, 10: 5, 19: 10, 20: 19, 5: 4, 16: 1, 21: 20, 69: 14, 4: 4}", "268"]
22
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[0, 2], [1, 0], [1, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [2, 1]]
19
2.2448041439056396
19
6
12
[[["Blue", "Red", "Blue", "Green"], ["Red", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red"]], 6]
[[["Blue", "Red", "Blue", "Green"], ["Red", "Blue", "Green", "Red"], ["Blue", "Green", "Green", "Red"]], 6]
["[['Blue', 'Red', 'Blue', 'Green'], ['Red', 'Blue', 'Green', 'Red'], ['Blue', 'Green', 'Green', 'Red']]", "6"]
22
We have a 3x3 numerical grid, with numbers ranging from 13 to 56 (13 included in the range but 56 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
8
[[0, 1, 14], [0, 2, 13], [1, 2, 35], [2, 0, 47], [2, 2, 36]]
213
7.270275831222534
5
43
9
["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", 13, 56]
["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", 13, 56]
["[['16', '', ''], ['28', '34', ''], ['', '46', '']]", "13", "56"]
22
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 12 to 46. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 120, and sum of row 1 must be 105. Also, the sum of the numbers in the diagonal from the top right to t...
magic_square
underdetermined_system
7
[[0, 0, 12], [0, 1, 32], [0, 2, 14], [1, 0, 16], [1, 1, 45], [1, 2, 44], [2, 0, 40], [2, 2, 13]]
259
92.43742489814758
8
29
9
["[['', '', ''], ['', '', ''], ['', '43', '']]", 3, 12, 46]
["[['', '', ''], ['', '', ''], ['', '43', '']]", 12, 46, [1, 2], [1, 2], [120], [105], 99]
["[['', '', ''], ['', '', ''], ['', '43', '']]", "12", "46", "[None, 120, None]", "[None, 105, None]", "99"]
22
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[5, 3], [5, 3], [4, 5], [1, 2], [4, 2], [1, 0], [1, 2], [4, 1], [0, 1], [3, 0], [3, 0], [4, 0]]
38
0.09250640869140625
12
30
12
[[[], ["Blue", "Yellow", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Green"], ["Green", "Green", "Red", "Red"]], 4, {"0": 1, "1": 4, "2": 2, "3": 7, "4": 6, "5": 6}]
[[[], ["Blue", "Yellow", "Blue", "Yellow"], [], [], ["Red", "Blue", "Yellow", "Green"], ["Green", "Green", "Red", "Red"]], 4, {"0": 1, "1": 4, "2": 2, "3": 7, "4": 6, "5": 6}, 3]
["[[], ['Blue', 'Yellow', 'Blue', 'Yellow'], [], [], ['Red', 'Blue', 'Yellow', 'Green'], ['Green', 'Green', 'Red', 'Red']]", "{0: 1, 1: 4, 2: 2, 3: 7, 4: 6, 5: 6}", "4", "3"]
22
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (1, 0) to his destination workshop at index (5, 7), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[1, 0], [2, 0], [3, 0], [3, 1], [3, 2], [3, 3], [4, 3], [4, 4], [4, 5], [4, 6], [4, 7], [5, 7]]
116
0.020702600479125977
12
4
4
[[["2", "2", "3", "x", "2", "10", "x", "8", "6", "x"], ["6", "11", "x", "x", "x", "x", "x", "16", "x", "7"], ["17", "17", "7", "12", "13", "15", "5", "6", "10", "13"], ["1", "15", "13", "3", "x", "x", "x", "14", "x", "9"], ["14", "x", "x", "6", "15", "2", "12", "18", "x", "18"], ["11", "19", "1", "19", "10", "8", "x", ...
[[["2", "2", "3", "x", "2", "10", "x", "8", "6", "x"], ["6", "11", "x", "x", "x", "x", "x", "16", "x", "7"], ["17", "17", "7", "12", "13", "15", "5", "6", "10", "13"], ["1", "15", "13", "3", "x", "x", "x", "14", "x", "9"], ["14", "x", "x", "6", "15", "2", "12", "18", "x", "18"], ["11", "19", "1", "19", "10", "8", "x", ...
["[['2', '2', '3', 'x', '2', '10', 'x', '8', '6', 'x'], ['6', '11', 'x', 'x', 'x', 'x', 'x', '16', 'x', '7'], ['17', '17', '7', '12', '13', '15', '5', '6', '10', '13'], ['1', '15', '13', '3', 'x', 'x', 'x', '14', 'x', '9'], ['14', 'x', 'x', '6', '15', '2', '12', '18', 'x', '18'], ['11', '19', '1', '19', '10', '8', 'x',...
22
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[8, 1], [9, 2], [9, 3], [8, 3], [8, 4], [7, 4], [6, 4], [5, 5], [5, 6], [5, 7], [4, 8], [4, 9], [3, 9], [2, 9], [1, 9]]
15
0.02926492691040039
15
8
2
["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0...
["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0...
["[[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1, 0, 1, 1, 0], [1, 1, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 1, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0...
22
Given 7 labeled water jugs with capacities 16, 124, 57, 40, 99, 45, 72, 98 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 263, 341, 360 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o...
water_jug
subset_sum
5
[["+", 98, 3], ["+", 124, 3], ["+", 40, 3], ["+", 98, 3], ["+", 45, 2], ["+", 98, 2], ["+", 99, 2], ["+", 99, 2], ["+", 40, 1], ["+", 99, 1], ["+", 124, 1]]
11
0.04340982437133789
11
48
3
[[16, 124, 57, 40, 99, 45, 72, 98], [263, 341, 360]]
[[16, 124, 57, 40, 99, 45, 72, 98], [263, 341, 360]]
["[16, 124, 57, 40, 99, 45, 72, 98]", "[263, 341, 360]"]
23
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
5
[53, 28, 43, 34, 59, 29, 76, 53, 28, 43, 34, 59, 29, 76, 53, 29, 43, 34, 59, 62, 76, 53, 29, 28]
24
0.11378741264343262
24
4
9
[[[62, 43, 28], [59, 34, 53], [29, 76, "_"]]]
[[[62, 43, 28], [59, 34, 53], [29, 76, "_"]]]
["[[62, 43, 28], [59, 34, 53], [29, 76, '_']]"]
23
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-left", "down-right", "up-right", "down-right", "down-left", "up-left", "up-left", "up-left"]
8
0.1897449493408203
8
4
20
[[["m", "s", "_", "n", "g"], ["a", "o", "i", "e", "h"], ["h", "i", "p", "e", "s"], ["a", "g", "l", "r", "y"]]]
[[["m", "s", "_", "n", "g"], ["a", "o", "i", "e", "h"], ["h", "i", "p", "e", "s"], ["a", "g", "l", "r", "y"]], ["song", "amish", "hiper", "agley"]]
["[['m', 's', '_', 'n', 'g'], ['a', 'o', 'i', 'e', 'h'], ['h', 'i', 'p', 'e', 's'], ['a', 'g', 'l', 'r', 'y']]", "['song', 'amish', 'hiper', 'agley']"]
23
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["K", "E", "N", "X", "P", "W", "P", "N"]
8
0.02664780616760254
8
11
14
[[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0,...
[[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0,...
["[[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], [0...
23
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6], such that the sum of the chosen coins adds up to 309. Each coin in the list is unique and can only be used once. Also coi...
coin_exchange
subset_sum
16
[84, 28, 10, 13, 17, 4, 5, 15, 85, 30, 14, 4]
62
0.03924393653869629
12
27
27
[[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6]]
[[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6], {"15": 2, "18": 9, "28": 4, "84": 10, "2": 1, "24": 19, "30": 12, "5": 2, "9": 9, "21": 9, "11": 10, "16": 14, "4": 2, "17": 2, "85": 18, "6": 5, "8": 6, "13": 2, "10": 4, "25": 11, "20": 19, "14": 2}, 309]
["[84, 2, 8, 16, 21, 10, 15, 4, 17, 16, 4, 85, 30, 13, 28, 2, 2, 11, 18, 9, 25, 5, 24, 14, 20, 30, 6]", "{15: 2, 18: 9, 28: 4, 84: 10, 2: 1, 24: 19, 30: 12, 5: 2, 9: 9, 21: 9, 11: 10, 16: 14, 4: 2, 17: 2, 85: 18, 6: 5, 8: 6, 13: 2, 10: 4, 25: 11, 20: 19, 14: 2}", "309"]
23
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1]]
13
0.13763999938964844
13
6
12
[[["Red", "Red", "Blue", "Green"], ["Blue", "Green", "Blue", "Blue"], ["Red", "Green", "Green", "Red"]], 6]
[[["Red", "Red", "Blue", "Green"], ["Blue", "Green", "Blue", "Blue"], ["Red", "Green", "Green", "Red"]], 6]
["[['Red', 'Red', 'Blue', 'Green'], ['Blue', 'Green', 'Blue', 'Blue'], ['Red', 'Green', 'Green', 'Red']]", "6"]
23
We have a 3x3 numerical grid, with numbers ranging from 23 to 66 (23 included in the range but 66 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
8
[[0, 0, 23], [0, 1, 24], [1, 0, 25], [1, 1, 26], [1, 2, 48]]
352
1.0622022151947021
5
43
9
["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", 23, 66]
["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", 23, 66]
["[['', '', '57'], ['', '', ''], ['33', '43', '47']]", "23", "66"]
23
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 12 to 46. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 71, and sum of row 1 must be 82. Also, the sum of the numbers in the diagonal from the top right to the...
magic_square
underdetermined_system
7
[[0, 0, 13], [0, 1, 14], [0, 2, 12], [1, 0, 17], [1, 1, 42], [1, 2, 23], [2, 0, 16], [2, 1, 15]]
171
8.869033575057983
8
29
9
["[['', '', ''], ['', '', ''], ['', '', '19']]", 3, 12, 46]
["[['', '', ''], ['', '', ''], ['', '', '19']]", 12, 46, [1, 2], [1, 2], [71], [82], 70]
["[['', '', ''], ['', '', ''], ['', '', '19']]", "12", "46", "[None, 71, None]", "[None, 82, None]", "70"]
23
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[3, 2], [0, 2], [0, 2], [0, 5], [1, 5], [1, 0], [1, 4], [3, 4], [3, 0], [3, 4], [1, 5]]
43
0.04391932487487793
11
30
12
[[["Green", "Green", "Blue", "Red"], ["Blue", "Red", "Yellow", "Blue"], [], ["Green", "Yellow", "Red", "Yellow"], [], []], 4, {"0": 2, "1": 7, "2": 4, "3": 7, "4": 6, "5": 3}]
[[["Green", "Green", "Blue", "Red"], ["Blue", "Red", "Yellow", "Blue"], [], ["Green", "Yellow", "Red", "Yellow"], [], []], 4, {"0": 2, "1": 7, "2": 4, "3": 7, "4": 6, "5": 3}, 3]
["[['Green', 'Green', 'Blue', 'Red'], ['Blue', 'Red', 'Yellow', 'Blue'], [], ['Green', 'Yellow', 'Red', 'Yellow'], [], []]", "{0: 2, 1: 7, 2: 4, 3: 7, 4: 6, 5: 3}", "4", "3"]
23
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 8) to his destination workshop at index (3, 0), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[5, 8], [4, 8], [4, 7], [4, 6], [3, 6], [3, 5], [2, 5], [2, 4], [3, 4], [3, 3], [4, 3], [4, 2], [4, 1], [3, 1], [3, 0]]
105
0.02059459686279297
15
4
4
[[["x", "x", "x", "x", "x", "8", "x", "15", "18", "10"], ["4", "5", "10", "6", "20", "2", "12", "x", "x", "x"], ["19", "6", "19", "7", "6", "2", "x", "15", "x", "14"], ["16", "17", "x", "2", "3", "7", "4", "x", "18", "6"], ["x", "2", "1", "19", "7", "10", "18", "5", "3", "19"], ["8", "5", "x", "1", "x", "10", "17", "x"...
[[["x", "x", "x", "x", "x", "8", "x", "15", "18", "10"], ["4", "5", "10", "6", "20", "2", "12", "x", "x", "x"], ["19", "6", "19", "7", "6", "2", "x", "15", "x", "14"], ["16", "17", "x", "2", "3", "7", "4", "x", "18", "6"], ["x", "2", "1", "19", "7", "10", "18", "5", "3", "19"], ["8", "5", "x", "1", "x", "10", "17", "x"...
["[['x', 'x', 'x', 'x', 'x', '8', 'x', '15', '18', '10'], ['4', '5', '10', '6', '20', '2', '12', 'x', 'x', 'x'], ['19', '6', '19', '7', '6', '2', 'x', '15', 'x', '14'], ['16', '17', 'x', '2', '3', '7', '4', 'x', '18', '6'], ['x', '2', '1', '19', '7', '10', '18', '5', '3', '19'], ['8', '5', 'x', '1', 'x', '10', '17', 'x...
23
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[1, 9], [2, 8], [3, 8], [4, 7], [5, 6], [5, 5], [6, 5], [6, 4], [6, 3], [7, 3], [8, 3]]
11
0.028395891189575195
11
8
2
["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0...
["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0...
["[[1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1], [1, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1, 0, 0, 1, 0...
23
Given 7 labeled water jugs with capacities 118, 15, 88, 145, 84, 14, 107, 31 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 226, 258, 296 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount...
water_jug
subset_sum
5
[["+", 31, 3], ["+", 118, 3], ["+", 15, 3], ["+", 118, 3], ["+", 14, 3], ["+", 15, 2], ["+", 84, 2], ["+", 145, 2], ["+", 14, 2], ["+", 88, 1], ["+", 107, 1], ["+", 31, 1]]
12
0.05219745635986328
12
48
3
[[118, 15, 88, 145, 84, 14, 107, 31], [226, 258, 296]]
[[118, 15, 88, 145, 84, 14, 107, 31], [226, 258, 296]]
["[118, 15, 88, 145, 84, 14, 107, 31]", "[226, 258, 296]"]
24
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
5
[92, 35, 32, 97, 75, 44, 97, 32, 35, 97, 94, 58, 44, 75, 32, 35, 97, 94, 75, 32, 35, 75, 58, 44]
24
0.1467905044555664
24
4
9
[[[35, 92, "_"], [32, 44, 94], [97, 75, 58]]]
[[[35, 92, "_"], [32, 44, 94], [97, 75, 58]]]
["[[35, 92, '_'], [32, 44, 94], [97, 75, 58]]"]
24
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-right", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"]
8
0.184800386428833
8
4
20
[[["_", "p", "h", "m", "p"], ["s", "a", "d", "r", "e"], ["i", "u", "n", "i", "r"], ["u", "a", "z", "e", "n"]]]
[[["_", "p", "h", "m", "p"], ["s", "a", "d", "r", "e"], ["i", "u", "n", "i", "r"], ["u", "a", "z", "e", "n"]], ["pimp", "sadhe", "aurir", "unzen"]]
["[['_', 'p', 'h', 'm', 'p'], ['s', 'a', 'd', 'r', 'e'], ['i', 'u', 'n', 'i', 'r'], ['u', 'a', 'z', 'e', 'n']]", "['pimp', 'sadhe', 'aurir', 'unzen']"]
24
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["D", "H", "A", "B", "W", "L", "J", "L", "O", "B"]
10
0.0295867919921875
10
11
14
[[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0,...
[[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0,...
["[[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1], [0...
24
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2], such that the sum of the chosen coins adds up to 305. Each coin in the list is unique and can only be used once. Also coin...
coin_exchange
subset_sum
17
[98, 16, 29, 24, 16, 23, 99]
54
0.034387826919555664
7
27
27
[[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2]]
[[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2], {"24": 5, "26": 16, "28": 20, "2": 1, "22": 16, "25": 11, "27": 7, "11": 4, "6": 3, "99": 17, "8": 5, "7": 5, "5": 3, "23": 5, "4": 4, "98": 16, "16": 3, "29": 5, "20": 19}, 305]
["[25, 29, 8, 11, 8, 25, 20, 16, 6, 4, 98, 7, 28, 24, 27, 16, 23, 26, 26, 99, 2, 7, 22, 7, 5, 24, 2]", "{24: 5, 26: 16, 28: 20, 2: 1, 22: 16, 25: 11, 27: 7, 11: 4, 6: 3, 99: 17, 8: 5, 7: 5, 5: 3, 23: 5, 4: 4, 98: 16, 16: 3, 29: 5, 20: 19}", "305"]
24
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 2], [1, 2], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1]]
21
3.7056467533111572
21
6
12
[[["Red", "Blue", "Green", "Blue"], ["Red", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Green"]], 6]
[[["Red", "Blue", "Green", "Blue"], ["Red", "Red", "Red", "Green"], ["Blue", "Green", "Blue", "Green"]], 6]
["[['Red', 'Blue', 'Green', 'Blue'], ['Red', 'Red', 'Red', 'Green'], ['Blue', 'Green', 'Blue', 'Green']]", "6"]
24
We have a 3x3 numerical grid, with numbers ranging from 50 to 93 (50 included in the range but 93 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
8
[[0, 1, 51], [0, 2, 50], [1, 2, 69], [2, 0, 52], [2, 1, 70]]
578
0.18818449974060059
5
43
9
["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", 50, 93]
["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", 50, 93]
["[['66', '', ''], ['65', '68', ''], ['', '', '79']]", "50", "93"]
24
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 9 to 48. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 115, and sum of row 1 must be 95. Also, the sum of the numbers in the diagonal from the top right to the...
magic_square
underdetermined_system
7
[[0, 0, 9], [0, 1, 23], [0, 2, 44], [1, 0, 11], [1, 1, 47], [1, 2, 37], [2, 2, 10]]
268
97.89336490631104
7
29
9
["[['', '', ''], ['', '', ''], ['42', '45', '']]", 3, 9, 48]
["[['', '', ''], ['', '', ''], ['42', '45', '']]", 9, 48, [1, 2], [1, 2], [115], [95], 133]
["[['', '', ''], ['', '', ''], ['42', '45', '']]", "9", "48", "[None, 115, None]", "[None, 95, None]", "133"]
24
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[3, 4], [2, 4], [2, 0], [2, 4], [3, 2], [5, 1], [5, 2], [5, 0], [3, 1], [3, 0], [5, 1]]
51
0.07999825477600098
11
30
12
[[[], [], ["Green", "Yellow", "Green", "Red"], ["Green", "Red", "Blue", "Yellow"], [], ["Blue", "Red", "Yellow", "Blue"]], 4, {"0": 5, "1": 1, "2": 6, "3": 7, "4": 7, "5": 7}]
[[[], [], ["Green", "Yellow", "Green", "Red"], ["Green", "Red", "Blue", "Yellow"], [], ["Blue", "Red", "Yellow", "Blue"]], 4, {"0": 5, "1": 1, "2": 6, "3": 7, "4": 7, "5": 7}, 3]
["[[], [], ['Green', 'Yellow', 'Green', 'Red'], ['Green', 'Red', 'Blue', 'Yellow'], [], ['Blue', 'Red', 'Yellow', 'Blue']]", "{0: 5, 1: 1, 2: 6, 3: 7, 4: 7, 5: 7}", "4", "3"]
24
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 1) to his destination workshop at index (3, 9), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[5, 1], [5, 2], [5, 3], [5, 4], [4, 4], [4, 5], [4, 6], [4, 7], [3, 7], [3, 8], [3, 9]]
56
0.020661354064941406
11
4
4
[[["18", "19", "9", "x", "x", "x", "3", "x", "8", "x"], ["13", "2", "3", "15", "3", "x", "8", "9", "x", "x"], ["x", "6", "18", "1", "20", "7", "16", "8", "1", "19"], ["x", "x", "x", "20", "14", "x", "19", "11", "9", "6"], ["2", "x", "x", "6", "5", "6", "7", "1", "x", "8"], ["17", "9", "5", "3", "3", "x", "16", "18", "x...
[[["18", "19", "9", "x", "x", "x", "3", "x", "8", "x"], ["13", "2", "3", "15", "3", "x", "8", "9", "x", "x"], ["x", "6", "18", "1", "20", "7", "16", "8", "1", "19"], ["x", "x", "x", "20", "14", "x", "19", "11", "9", "6"], ["2", "x", "x", "6", "5", "6", "7", "1", "x", "8"], ["17", "9", "5", "3", "3", "x", "16", "18", "x...
["[['18', '19', '9', 'x', 'x', 'x', '3', 'x', '8', 'x'], ['13', '2', '3', '15', '3', 'x', '8', '9', 'x', 'x'], ['x', '6', '18', '1', '20', '7', '16', '8', '1', '19'], ['x', 'x', 'x', '20', '14', 'x', '19', '11', '9', '6'], ['2', 'x', 'x', '6', '5', '6', '7', '1', 'x', '8'], ['17', '9', '5', '3', '3', 'x', '16', '18', '...
24
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[9, 9], [9, 8], [8, 7], [7, 6], [7, 5], [7, 4], [7, 3], [6, 2], [6, 1], [5, 1], [4, 1]]
11
0.030521631240844727
11
8
2
["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0...
["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0...
["[[1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1, 0, 0...
24
Given 7 labeled water jugs with capacities 33, 56, 108, 53, 65, 54, 52, 59 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 168, 239, 307 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o...
water_jug
subset_sum
5
[["+", 59, 3], ["+", 108, 3], ["+", 108, 3], ["-", 33, 3], ["+", 65, 3], ["+", 108, 2], ["+", 108, 2], ["-", 33, 2], ["+", 56, 2], ["+", 53, 1], ["+", 56, 1], ["+", 59, 1]]
12
0.04154396057128906
12
48
3
[[33, 56, 108, 53, 65, 54, 52, 59], [168, 239, 307]]
[[33, 56, 108, 53, 65, 54, 52, 59], [168, 239, 307]]
["[33, 56, 108, 53, 65, 54, 52, 59]", "[168, 239, 307]"]
25
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
6
[76, 41, 13, 76, 41, 13, 66, 85, 21, 74, 13, 41, 76, 45, 85, 66, 74, 13, 41, 74, 45, 76, 74, 41]
24
0.10150957107543945
24
4
9
[[[45, 13, "_"], [66, 41, 76], [85, 21, 74]]]
[[[45, 13, "_"], [66, 41, 76], [85, 21, 74]]]
["[[45, 13, '_'], [66, 41, 76], [85, 21, 74]]"]
25
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-left", "up-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"]
8
0.21672630310058594
8
4
20
[[["i", "g", "u", "h", "a"], ["n", "o", "s", "u", "s"], ["c", "n", "g", "a", "_"], ["j", "u", "u", "p", "h"]]]
[[["i", "g", "u", "h", "a"], ["n", "o", "s", "u", "s"], ["c", "n", "g", "a", "_"], ["j", "u", "u", "p", "h"]], ["guha", "nisus", "uncap", "jough"]]
["[['i', 'g', 'u', 'h', 'a'], ['n', 'o', 's', 'u', 's'], ['c', 'n', 'g', 'a', '_'], ['j', 'u', 'u', 'p', 'h']]", "['guha', 'nisus', 'uncap', 'jough']"]
25
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["M", "V", "F", "Y", "O", "L", "X", "J", "X", "K", "Y"]
11
0.02562737464904785
11
11
14
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1,...
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1,...
["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [1...
25
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12], such that the sum of the chosen coins adds up to 284. Each coin in the list is unique an...
coin_exchange
subset_sum
18
[7, 13, 21, 23, 25, 65, 28, 22, 23, 22, 27, 8]
52
0.03629875183105469
12
35
35
[[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12]]
[[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12], {"20": 12, "21": 3, "5": 2, "3": 2, "7": 1, "15": 8, "8": 7, "27": 6, "17": 8, "18": 14, "28": 5, "13": 1, "23": 4, "65": 8, "26": 8, "22": 5, "25": 3, "11": 11, "12": 8, "19": 19, "10"...
["[28, 5, 25, 22, 26, 13, 20, 20, 18, 28, 7, 20, 18, 19, 18, 5, 15, 23, 28, 27, 22, 10, 8, 17, 3, 8, 5, 11, 21, 17, 65, 23, 11, 3, 12]", "{20: 12, 21: 3, 5: 2, 3: 2, 7: 1, 15: 8, 8: 7, 27: 6, 17: 8, 18: 14, 28: 5, 13: 1, 23: 4, 65: 8, 26: 8, 22: 5, 25: 3, 11: 11, 12: 8, 19: 19, 10: 7}", "284"]
25
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
7
[[2, 0], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0]]
10
0.04879570007324219
10
6
12
[[["Green", "Green", "Red", "Red"], ["Blue", "Blue", "Blue", "Blue"], ["Green", "Red", "Green", "Red"]], 6]
[[["Green", "Green", "Red", "Red"], ["Blue", "Blue", "Blue", "Blue"], ["Green", "Red", "Green", "Red"]], 6]
["[['Green', 'Green', 'Red', 'Red'], ['Blue', 'Blue', 'Blue', 'Blue'], ['Green', 'Red', 'Green', 'Red']]", "6"]
25
We have a 3x3 numerical grid, with numbers ranging from 29 to 72 (29 included in the range but 72 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
9
[[0, 0, 29], [0, 1, 31], [0, 2, 53], [1, 1, 40], [2, 1, 41], [2, 2, 30]]
347
36.68832039833069
6
43
9
["[['', '', ''], ['39', '', '52'], ['60', '', '']]", 29, 72]
["[['', '', ''], ['39', '', '52'], ['60', '', '']]", 29, 72]
["[['', '', ''], ['39', '', '52'], ['60', '', '']]", "29", "72"]
25
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 9 to 48. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 67, and sum of row 1 must be 60. Also, the sum of the numbers in the diagonal from the top right to the ...
magic_square
underdetermined_system
6
[[0, 0, 9], [0, 2, 10], [1, 0, 12], [1, 1, 34], [1, 2, 14], [2, 1, 17], [2, 2, 11]]
168
0.5386793613433838
7
34
9
["[['', '16', ''], ['', '', ''], ['45', '', '']]", 3, 9, 48]
["[['', '16', ''], ['', '', ''], ['45', '', '']]", 9, 48, [1, 2], [1, 2], [67], [60], 89]
["[['', '16', ''], ['', '', ''], ['45', '', '']]", "9", "48", "[None, 67, None]", "[None, 60, None]", "89"]
25
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[2, 0], [4, 3], [4, 5], [4, 0], [2, 4], [2, 4], [2, 3], [1, 2], [1, 3], [1, 0], [1, 2], [5, 2]]
39
0.023729562759399414
12
30
12
[[[], ["Green", "Blue", "Yellow", "Green"], ["Yellow", "Red", "Red", "Blue"], [], ["Blue", "Green", "Yellow", "Red"], []], 4, {"0": 4, "1": 3, "2": 2, "3": 4, "4": 2, "5": 5}]
[[[], ["Green", "Blue", "Yellow", "Green"], ["Yellow", "Red", "Red", "Blue"], [], ["Blue", "Green", "Yellow", "Red"], []], 4, {"0": 4, "1": 3, "2": 2, "3": 4, "4": 2, "5": 5}, 3]
["[[], ['Green', 'Blue', 'Yellow', 'Green'], ['Yellow', 'Red', 'Red', 'Blue'], [], ['Blue', 'Green', 'Yellow', 'Red'], []]", "{0: 4, 1: 3, 2: 2, 3: 4, 4: 2, 5: 5}", "4", "3"]
25
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 9) to his destination workshop at index (5, 2), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[2, 9], [2, 8], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [4, 2], [5, 2]]
105
0.022072553634643555
11
4
4
[[["x", "x", "6", "x", "x", "x", "x", "15", "x", "x"], ["x", "17", "13", "13", "x", "12", "x", "3", "10", "2"], ["x", "5", "13", "15", "4", "x", "x", "20", "6", "2"], ["x", "9", "x", "6", "2", "16", "18", "9", "13", "x"], ["x", "x", "15", "17", "x", "10", "11", "x", "x", "x"], ["3", "x", "3", "17", "8", "x", "1", "x", ...
[[["x", "x", "6", "x", "x", "x", "x", "15", "x", "x"], ["x", "17", "13", "13", "x", "12", "x", "3", "10", "2"], ["x", "5", "13", "15", "4", "x", "x", "20", "6", "2"], ["x", "9", "x", "6", "2", "16", "18", "9", "13", "x"], ["x", "x", "15", "17", "x", "10", "11", "x", "x", "x"], ["3", "x", "3", "17", "8", "x", "1", "x", ...
["[['x', 'x', '6', 'x', 'x', 'x', 'x', '15', 'x', 'x'], ['x', '17', '13', '13', 'x', '12', 'x', '3', '10', '2'], ['x', '5', '13', '15', '4', 'x', 'x', '20', '6', '2'], ['x', '9', 'x', '6', '2', '16', '18', '9', '13', 'x'], ['x', 'x', '15', '17', 'x', '10', '11', 'x', 'x', 'x'], ['3', 'x', '3', '17', '8', 'x', '1', 'x',...
25
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[0, 0], [1, 0], [1, 1], [2, 1], [3, 2], [4, 2], [4, 3], [4, 4], [5, 4], [6, 5], [7, 6]]
11
0.031239748001098633
11
8
2
["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1...
["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1...
["[[0, 0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 0, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 1, 1...
25
Given 7 labeled water jugs with capacities 75, 20, 64, 106, 88, 13, 107, 131 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 287, 394, 455 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount...
water_jug
subset_sum
5
[["+", 75, 3], ["+", 131, 3], ["+", 131, 3], ["-", 13, 3], ["+", 131, 3], ["+", 106, 2], ["+", 106, 2], ["+", 75, 2], ["+", 107, 2], ["+", 75, 1], ["+", 106, 1], ["+", 106, 1]]
12
0.05149412155151367
12
48
3
[[75, 20, 64, 106, 88, 13, 107, 131], [287, 394, 455]]
[[75, 20, 64, 106, 88, 13, 107, 131], [287, 394, 455]]
["[75, 20, 64, 106, 88, 13, 107, 131]", "[287, 394, 455]"]
26
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
6
[79, 89, 94, 79, 89, 94, 43, 56, 94, 89, 79, 43, 52, 25]
14
0.0211181640625
14
4
9
[[[56, 79, "_"], [43, 89, 94], [36, 52, 25]]]
[[[56, 79, "_"], [43, 89, 94], [36, 52, 25]]]
["[[56, 79, '_'], [43, 89, 94], [36, 52, 25]]"]
26
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-left", "down-left", "up-left", "down-left", "down-right", "up-right", "down-right", "up-right", "up-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-left"]
18
0.2016615867614746
18
4
20
[[["t", "w", "y", "l", "_"], ["s", "a", "u", "f", "t"], ["o", "a", "e", "m", "n"], ["f", "l", "d", "m", "d"]]]
[[["t", "w", "y", "l", "_"], ["s", "a", "u", "f", "t"], ["o", "a", "e", "m", "n"], ["f", "l", "d", "m", "d"]], ["wolf", "stunt", "lammy", "faded"]]
["[['t', 'w', 'y', 'l', '_'], ['s', 'a', 'u', 'f', 't'], ['o', 'a', 'e', 'm', 'n'], ['f', 'l', 'd', 'm', 'd']]", "['wolf', 'stunt', 'lammy', 'faded']"]
26
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["I", "T", "L", "K", "H", "W", "R", "W", "C", "L"]
10
0.03812885284423828
10
11
14
[[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1,...
[[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1,...
["[[0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], [1...
26
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2], such that the sum of the chosen coins adds up to 307. Each coin in the list is unique and can o...
coin_exchange
subset_sum
19
[6, 9, 25, 25, 71, 6, 19, 8, 23, 23, 23, 6, 7, 9, 15, 15, 17]
51
0.04102158546447754
17
34
34
[[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2]]
[[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2], {"24": 14, "2": 1, "25": 2, "26": 14, "18": 12, "27": 15, "29": 19, "19": 3, "15": 7, "9": 1, "8": 1, "21": 18, "6": 1, "71": 3, "23": 4, "17": 7, "7": 2, "22": 11, "3": 1}, 307]
["[29, 29, 22, 23, 23, 3, 26, 9, 15, 8, 21, 15, 29, 25, 71, 27, 23, 6, 7, 9, 15, 21, 6, 8, 19, 17, 18, 6, 26, 24, 24, 3, 25, 2]", "{24: 14, 2: 1, 25: 2, 26: 14, 18: 12, 27: 15, 29: 19, 19: 3, 15: 7, 9: 1, 8: 1, 21: 18, 6: 1, 71: 3, 23: 4, 17: 7, 7: 2, 22: 11, 3: 1}", "307"]
26
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
8
[[0, 2], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [1, 2], [1, 2]]
13
0.2634403705596924
13
6
12
[[["Red", "Blue", "Blue", "Red"], ["Green", "Green", "Blue", "Blue"], ["Green", "Green", "Red", "Red"]], 7]
[[["Red", "Blue", "Blue", "Red"], ["Green", "Green", "Blue", "Blue"], ["Green", "Green", "Red", "Red"]], 7]
["[['Red', 'Blue', 'Blue', 'Red'], ['Green', 'Green', 'Blue', 'Blue'], ['Green', 'Green', 'Red', 'Red']]", "7"]
26
We have a 3x3 numerical grid, with numbers ranging from 17 to 60 (17 included in the range but 60 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
9
[[0, 1, 18], [0, 2, 17], [1, 0, 30], [1, 1, 20], [1, 2, 19], [2, 2, 56]]
261
27.528469800949097
6
43
9
["[['29', '', ''], ['', '', ''], ['36', '55', '']]", 17, 60]
["[['29', '', ''], ['', '', ''], ['36', '55', '']]", 17, 60]
["[['29', '', ''], ['', '', ''], ['36', '55', '']]", "17", "60"]
26
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 26 to 65. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 150, and sum of row 1 must be 135. Also, the sum of the numbers in the diagonal from the top right to t...
magic_square
underdetermined_system
6
[[0, 0, 26], [0, 1, 54], [0, 2, 27], [1, 0, 30], [1, 1, 64], [1, 2, 41], [2, 0, 28], [2, 2, 29]]
331
25.04846739768982
8
34
9
["[['', '', ''], ['', '', ''], ['', '32', '']]", 3, 26, 65]
["[['', '', ''], ['', '', ''], ['', '32', '']]", 26, 65, [1, 2], [1, 2], [150], [135], 119]
["[['', '', ''], ['', '', ''], ['', '32', '']]", "26", "65", "[None, 150, None]", "[None, 135, None]", "119"]
26
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[0, 4], [1, 5], [2, 4], [2, 5], [2, 3], [0, 2], [3, 4], [0, 3], [0, 2], [1, 0], [1, 5], [0, 1], [3, 1]]
73
0.024808883666992188
13
30
12
[[["Blue", "Yellow", "Red", "Yellow"], ["Green", "Red", "Green", "Red"], ["Blue", "Green", "Blue", "Yellow"], [], [], []], 4, {"0": 4, "1": 4, "2": 7, "3": 7, "4": 5, "5": 6}]
[[["Blue", "Yellow", "Red", "Yellow"], ["Green", "Red", "Green", "Red"], ["Blue", "Green", "Blue", "Yellow"], [], [], []], 4, {"0": 4, "1": 4, "2": 7, "3": 7, "4": 5, "5": 6}, 3]
["[['Blue', 'Yellow', 'Red', 'Yellow'], ['Green', 'Red', 'Green', 'Red'], ['Blue', 'Green', 'Blue', 'Yellow'], [], [], []]", "{0: 4, 1: 4, 2: 7, 3: 7, 4: 5, 5: 6}", "4", "3"]
26
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (5, 9) to his destination workshop at index (3, 1), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[5, 9], [5, 8], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [3, 4], [3, 3], [3, 2], [3, 1]]
67
0.02885293960571289
11
4
4
[[["7", "x", "19", "11", "6", "x", "4", "15", "9", "3"], ["x", "x", "13", "x", "8", "17", "x", "x", "12", "16"], ["x", "x", "2", "x", "15", "8", "x", "13", "4", "x"], ["13", "11", "3", "3", "3", "x", "x", "x", "x", "x"], ["1", "16", "14", "6", "14", "17", "4", "9", "1", "x"], ["x", "4", "9", "x", "17", "17", "x", "13",...
[[["7", "x", "19", "11", "6", "x", "4", "15", "9", "3"], ["x", "x", "13", "x", "8", "17", "x", "x", "12", "16"], ["x", "x", "2", "x", "15", "8", "x", "13", "4", "x"], ["13", "11", "3", "3", "3", "x", "x", "x", "x", "x"], ["1", "16", "14", "6", "14", "17", "4", "9", "1", "x"], ["x", "4", "9", "x", "17", "17", "x", "13",...
["[['7', 'x', '19', '11', '6', 'x', '4', '15', '9', '3'], ['x', 'x', '13', 'x', '8', '17', 'x', 'x', '12', '16'], ['x', 'x', '2', 'x', '15', '8', 'x', '13', '4', 'x'], ['13', '11', '3', '3', '3', 'x', 'x', 'x', 'x', 'x'], ['1', '16', '14', '6', '14', '17', '4', '9', '1', 'x'], ['x', '4', '9', 'x', '17', '17', 'x', '13'...
26
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[8, 6], [7, 5], [7, 4], [6, 3], [5, 3], [4, 3], [3, 3], [2, 2], [1, 2], [0, 2], [0, 1]]
11
0.030196428298950195
11
8
2
["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0...
["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0...
["[[1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0...
26
Given 7 labeled water jugs with capacities 24, 132, 149, 62, 120, 61, 42 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 298, 430, 468 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount of ...
water_jug
subset_sum
5
[["+", 42, 3], ["+", 132, 3], ["+", 132, 3], ["+", 42, 3], ["+", 120, 3], ["+", 132, 2], ["+", 149, 2], ["+", 149, 2], ["+", 149, 1], ["+", 149, 1]]
10
0.0418705940246582
10
42
3
[[24, 132, 149, 62, 120, 61, 42], [298, 430, 468]]
[[24, 132, 149, 62, 120, 61, 42], [298, 430, 468]]
["[24, 132, 149, 62, 120, 61, 42]", "[298, 430, 468]"]
27
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
6
[99, 23, 50, 14, 73, 50, 79, 99, 23, 63, 14, 73, 50, 79, 73, 50, 79, 85, 99, 73, 63, 14]
22
0.036279916763305664
22
4
9
[[[85, 73, 14], [79, 23, 50], ["_", 99, 63]]]
[[[85, 73, 14], [79, 23, 50], ["_", 99, 63]]]
["[[85, 73, 14], [79, 23, 50], ['_', 99, 63]]"]
27
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["down-right", "down-right", "down-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-right", "up-left", "down-left", "up-left"]
20
0.26288700103759766
20
4
20
[[["_", "b", "p", "i", "s"], ["d", "u", "r", "n", "c"], ["l", "i", "o", "e", "n"], ["s", "n", "e", "o", "t"]]]
[[["_", "b", "p", "i", "s"], ["d", "u", "r", "n", "c"], ["l", "i", "o", "e", "n"], ["s", "n", "e", "o", "t"]], ["bois", "duroc", "linen", "spent"]]
["[['_', 'b', 'p', 'i', 's'], ['d', 'u', 'r', 'n', 'c'], ['l', 'i', 'o', 'e', 'n'], ['s', 'n', 'e', 'o', 't']]", "['bois', 'duroc', 'linen', 'spent']"]
27
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["D", "I", "Z", "J", "X", "H", "B", "Z", "W", "H"]
10
0.03222942352294922
10
11
14
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1,...
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1,...
["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1...
27
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14], such that the sum of the chosen coins adds up to 301. Each coin in the list is unique and can only ...
coin_exchange
subset_sum
20
[22, 10, 15, 10, 8, 15, 161, 28, 22, 10]
38
0.0371396541595459
10
32
32
[[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14]]
[[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14], {"15": 2, "17": 10, "10": 3, "12": 10, "21": 12, "4": 2, "22": 1, "11": 6, "26": 9, "14": 7, "24": 12, "161": 16, "20": 15, "9": 8, "8": 1, "13": 10, "28": 6, "7": 6, "25": 6, "19": 15}, 301]
["[22, 4, 12, 26, 4, 9, 4, 28, 28, 8, 28, 19, 15, 20, 9, 161, 11, 28, 17, 10, 25, 15, 7, 28, 21, 24, 10, 13, 22, 4, 10, 14]", "{15: 2, 17: 10, 10: 3, 12: 10, 21: 12, 4: 2, 22: 1, 11: 6, 26: 9, 14: 7, 24: 12, 161: 16, 20: 15, 9: 8, 8: 1, 13: 10, 28: 6, 7: 6, 25: 6, 19: 15}", "301"]
27
The game of 'Sort It' begins with 3 tubes, each filled with 4 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
8
[[0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 2], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1]]
16
1.1768579483032227
16
6
12
[[["Blue", "Red", "Red", "Blue"], ["Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Green"]], 7]
[[["Blue", "Red", "Red", "Blue"], ["Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Green"]], 7]
["[['Blue', 'Red', 'Red', 'Blue'], ['Green', 'Red', 'Red', 'Green'], ['Blue', 'Blue', 'Green', 'Green']]", "7"]
27
We have a 3x3 numerical grid, with numbers ranging from 46 to 89 (46 included in the range but 89 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third or first < second < third in each row and column. If a grid cell is marked with ...
consecutive_grid
underdetermined_system
9
[[0, 1, 47], [0, 2, 46], [1, 1, 51], [1, 2, 53], [2, 0, 48], [2, 1, 54]]
485
0.19235539436340332
6
43
9
["[['52', '', ''], ['50', '', ''], ['', '', '69']]", 46, 89]
["[['52', '', ''], ['50', '', ''], ['', '', '69']]", 46, 89]
["[['52', '', ''], ['50', '', ''], ['', '', '69']]", "46", "89"]
27
In the magic square problem, a 3x3 grid is filled with unique integers ranging from 26 to 65. Some numbers are already given, while others are unknown and represented as 'x'. Sum of column 1 (counting from 0) must be 93, and sum of row 1 must be 135. Also, the sum of the numbers in the diagonal from the top right to th...
magic_square
underdetermined_system
6
[[0, 1, 26], [0, 2, 29], [1, 0, 31], [1, 1, 40], [1, 2, 64], [2, 0, 37], [2, 1, 27], [2, 2, 28]]
329
29.752150774002075
8
34
9
["[['47', '', ''], ['', '', ''], ['', '', '']]", 3, 26, 65]
["[['47', '', ''], ['', '', ''], ['', '', '']]", 26, 65, [1, 2], [1, 2], [93], [135], 106]
["[['47', '', ''], ['', '', ''], ['', '', '']]", "26", "65", "[None, 93, None]", "[None, 135, None]", "106"]
27
In 'Restricted Sorting', there are 6 stacks each with a capacity of 4 blocks, with 3 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 3 blocks of a single shade. The player can only transfer one bl...
restricted_sorting
sorting
1
[[0, 2], [5, 3], [5, 2], [0, 4], [0, 3], [0, 5], [1, 0], [1, 0], [1, 3], [4, 0], [1, 2]]
38
0.03287506103515625
11
30
12
[[["Red", "Blue", "Green", "Yellow"], ["Blue", "Blue", "Green", "Red"], [], [], [], ["Green", "Red", "Yellow", "Yellow"]], 4, {"0": 3, "1": 6, "2": 2, "3": 4, "4": 6, "5": 5}]
[[["Red", "Blue", "Green", "Yellow"], ["Blue", "Blue", "Green", "Red"], [], [], [], ["Green", "Red", "Yellow", "Yellow"]], 4, {"0": 3, "1": 6, "2": 2, "3": 4, "4": 6, "5": 5}, 3]
["[['Red', 'Blue', 'Green', 'Yellow'], ['Blue', 'Blue', 'Green', 'Red'], [], [], [], ['Green', 'Red', 'Yellow', 'Yellow']]", "{0: 3, 1: 6, 2: 2, 3: 4, 4: 6, 5: 5}", "4", "3"]
27
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 8) to his destination workshop at index (6, 0), indexing from 0. Ben's car can move...
traffic
pathfinding
2
[[3, 8], [2, 8], [2, 7], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 3], [5, 3], [5, 2], [5, 1], [5, 0], [6, 0]]
154
0.028217792510986328
14
4
4
[[["19", "x", "3", "x", "x", "x", "13", "x", "12", "x"], ["x", "x", "8", "x", "15", "18", "11", "12", "x", "7"], ["x", "8", "x", "x", "15", "20", "17", "12", "2", "8"], ["x", "x", "4", "13", "2", "14", "19", "13", "15", "19"], ["13", "2", "x", "8", "x", "17", "13", "x", "x", "12"], ["2", "20", "20", "14", "x", "x", "15...
[[["19", "x", "3", "x", "x", "x", "13", "x", "12", "x"], ["x", "x", "8", "x", "15", "18", "11", "12", "x", "7"], ["x", "8", "x", "x", "15", "20", "17", "12", "2", "8"], ["x", "x", "4", "13", "2", "14", "19", "13", "15", "19"], ["13", "2", "x", "8", "x", "17", "13", "x", "x", "12"], ["2", "20", "20", "14", "x", "x", "15...
["[['19', 'x', '3', 'x', 'x', 'x', '13', 'x', '12', 'x'], ['x', 'x', '8', 'x', '15', '18', '11', '12', 'x', '7'], ['x', '8', 'x', 'x', '15', '20', '17', '12', '2', '8'], ['x', 'x', '4', '13', '2', '14', '19', '13', '15', '19'], ['13', '2', 'x', '8', 'x', '17', '13', 'x', 'x', '12'], ['2', '20', '20', '14', 'x', 'x', '1...
27
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 10x10. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
10
[[7, 9], [7, 8], [7, 7], [7, 6], [7, 5], [7, 4], [6, 3], [5, 2], [4, 1], [4, 0], [3, 0]]
11
0.030271291732788086
11
8
2
["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0...
["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0...
["[[1, 1, 1, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 0...
27
Given 7 labeled water jugs with capacities 80, 76, 132, 60, 83, 28, 75, 26 liters, we aim to fill 3 unlabeled buckets, numbered 1 to 3 and arranged in a line in ascending order, with 337, 378, 398 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amount o...
water_jug
subset_sum
5
[["+", 28, 3], ["+", 80, 3], ["+", 132, 3], ["+", 75, 3], ["+", 83, 3], ["+", 80, 2], ["+", 83, 2], ["+", 83, 2], ["+", 132, 2], ["+", 28, 1], ["+", 83, 1], ["+", 83, 1], ["+", 83, 1], ["+", 60, 1]]
14
0.05565452575683594
14
48
3
[[80, 76, 132, 60, 83, 28, 75, 26], [337, 378, 398]]
[[80, 76, 132, 60, 83, 28, 75, 26], [337, 378, 398]]
["[80, 76, 132, 60, 83, 28, 75, 26]", "[337, 378, 398]"]
28
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
6
[45, 36, 87, 10, 81, 74, 10, 87, 36, 10, 72, 46, 74, 81, 87, 72, 46, 45]
18
0.023023605346679688
18
4
9
[[[10, 81, 46], [87, 74, 72], [36, 45, "_"]]]
[[[10, 81, 46], [87, 74, 72], [36, 45, "_"]]]
["[[10, 81, 46], [87, 74, 72], [36, 45, '_']]"]
28
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
2
["up-right", "down-right", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "down-right", "up-right", "up-left", "up-left", "down-left", "up-left"]
16
0.22631430625915527
16
4
20
[[["a", "a", "e", "e", "y"], ["h", "a", "i", "t", "h"], ["_", "r", "k", "n", "t"], ["m", "k", "n", "o", "o"]]]
[[["a", "a", "e", "e", "y"], ["h", "a", "i", "t", "h"], ["_", "r", "k", "n", "t"], ["m", "k", "n", "o", "o"]], ["akey", "haikh", "trone", "manto"]]
["[['a', 'a', 'e', 'e', 'y'], ['h', 'a', 'i', 't', 'h'], ['_', 'r', 'k', 'n', 't'], ['m', 'k', 'n', 'o', 'o']]", "['akey', 'haikh', 'trone', 'manto']"]
28
We have a map of cities, each represented by a letter, and they are connected by one-way roads. The adjacency matrix below shows the connections between the cities. Each row and column represents a city, and a '1' signifies a direct road from the city of the row to the city of the column. The travel time between any tw...
city_directed_graph
pathfinding
11
["B", "G", "N", "P", "E", "A", "E", "M", "N"]
9
0.029226064682006836
9
11
14
[[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0,...
[[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0,...
["[[0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0...