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stringclasses
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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
73
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 (8, 0), indexing from 0. Ben's car can move...
traffic
pathfinding
5
[[3, 8], [3, 7], [4, 7], [4, 6], [4, 5], [5, 5], [5, 4], [6, 4], [6, 3], [6, 2], [7, 2], [7, 1], [8, 1], [8, 0]]
109
0.018488407135009766
14
4
4
[[["x", "14", "15", "10", "x", "14", "x", "x", "18", "6", "x", "x", "4"], ["6", "x", "x", "x", "1", "x", "15", "x", "x", "2", "x", "17", "x"], ["x", "4", "x", "17", "3", "14", "4", "2", "x", "3", "x", "11", "x"], ["6", "6", "x", "19", "x", "13", "x", "11", "13", "6", "3", "x", "x"], ["3", "10", "11", "x", "x", "4", "4"...
[[["x", "14", "15", "10", "x", "14", "x", "x", "18", "6", "x", "x", "4"], ["6", "x", "x", "x", "1", "x", "15", "x", "x", "2", "x", "17", "x"], ["x", "4", "x", "17", "3", "14", "4", "2", "x", "3", "x", "11", "x"], ["6", "6", "x", "19", "x", "13", "x", "11", "13", "6", "3", "x", "x"], ["3", "10", "11", "x", "x", "4", "4"...
["[['x', '14', '15', '10', 'x', '14', 'x', 'x', '18', '6', 'x', 'x', '4'], ['6', 'x', 'x', 'x', '1', 'x', '15', 'x', 'x', '2', 'x', '17', 'x'], ['x', '4', 'x', '17', '3', '14', '4', '2', 'x', '3', 'x', '11', 'x'], ['6', '6', 'x', '19', 'x', '13', 'x', '11', '13', '6', '3', 'x', 'x'], ['3', '10', '11', 'x', 'x', '4', '4...
73
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
13
[[1, 12], [2, 11], [2, 10], [3, 10], [4, 9], [5, 8], [5, 7], [5, 6], [6, 5], [6, 4], [7, 4], [8, 4], [8, 3], [8, 2]]
14
0.024569988250732422
14
8
2
["[[1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1,...
["[[1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1,...
["[[1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 0, 1, 1, 0, 1,...
73
Given 7 labeled water jugs with capacities 56, 81, 132, 41, 86, 128, 57, 138 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 232, 401, 444, 451 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the a...
water_jug
subset_sum
6
[["+", 128, 4], ["+", 128, 4], ["+", 138, 4], ["+", 57, 4], ["+", 128, 3], ["+", 128, 3], ["+", 56, 3], ["+", 132, 3], ["+", 132, 2], ["+", 132, 2], ["+", 56, 2], ["+", 81, 2], ["+", 57, 1], ["+", 128, 1], ["-", 81, 1], ["+", 128, 1]]
16
0.05008697509765625
16
64
3
[[56, 81, 132, 41, 86, 128, 57, 138], [232, 401, 444, 451]]
[[56, 81, 132, 41, 86, 128, 57, 138], [232, 401, 444, 451]]
["[56, 81, 132, 41, 86, 128, 57, 138]", "[232, 401, 444, 451]"]
74
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
[81, 27, 41, 81, 52, 45, 16, 44, 72, 46, 44, 16, 45, 77, 20, 49, 81, 52, 77, 20, 78, 72, 46, 44, 16, 45, 20, 77, 49, 78, 77, 46, 45, 16]
34
2.7185001373291016
34
4
15
[[[49, 20, 77, 78, 57], [41, "_", 52, 44, 72], [27, 81, 45, 16, 46]]]
[[[49, 20, 77, 78, 57], [41, "_", 52, 44, 72], [27, 81, 45, 16, 46]]]
["[[49, 20, 77, 78, 57], [41, '_', 52, 44, 72], [27, 81, 45, 16, 46]]"]
74
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["up-left", "up-right", "down-right", "down-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "down-right", "down-left", "up-left", "up-right", "up-left", "up-left"]
16
0.29548144340515137
16
4
25
[[["u", "z", "s", "t", "a"], ["s", "e", "m", "o", "c"], ["a", "h", "_", "w", "y"], ["s", "a", "e", "m", "k"], ["a", "j", "e", "v", "a"]]]
[[["u", "z", "s", "t", "a"], ["s", "e", "m", "o", "c"], ["a", "h", "_", "w", "y"], ["s", "a", "e", "m", "k"], ["a", "j", "e", "v", "a"]], ["zeta", "sumac", "showy", "smeek", "ajava"]]
["[['u', 'z', 's', 't', 'a'], ['s', 'e', 'm', 'o', 'c'], ['a', 'h', '_', 'w', 'y'], ['s', 'a', 'e', 'm', 'k'], ['a', 'j', 'e', 'v', 'a']]", "['zeta', 'sumac', 'showy', 'smeek', 'ajava']"]
74
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
14
["M", "V", "Z", "E", "Z", "Q", "L", "K", "L"]
9
0.0362241268157959
9
14
17
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, ...
[[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, ...
["[[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1,...
74
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [5, 15, 15, 77, 12, 38, 41, 30, 31, 30, 13, 19, 9, 2, 23, 37, 14, 34, 29, 22, 22, 4, 16, 2, 12, 17, 9, 18, 19, 21, 4, 28, 40, 11, 30, 24, 19, 9, 10, 76, 34], such that the sum of the chosen coins adds up to 419. Each coin ...
coin_exchange
subset_sum
25
[15, 31, 28, 37, 77, 76, 40, 38, 10, 11, 21, 2, 19, 14]
74
0.058817148208618164
14
41
41
[[5, 15, 15, 77, 12, 38, 41, 30, 31, 30, 13, 19, 9, 2, 23, 37, 14, 34, 29, 22, 22, 4, 16, 2, 12, 17, 9, 18, 19, 21, 4, 28, 40, 11, 30, 24, 19, 9, 10, 76, 34]]
[[5, 15, 15, 77, 12, 38, 41, 30, 31, 30, 13, 19, 9, 2, 23, 37, 14, 34, 29, 22, 22, 4, 16, 2, 12, 17, 9, 18, 19, 21, 4, 28, 40, 11, 30, 24, 19, 9, 10, 76, 34], {"13": 8, "29": 10, "4": 4, "2": 2, "77": 17, "16": 10, "11": 2, "22": 18, "17": 10, "18": 18, "38": 7, "9": 6, "5": 2, "41": 14, "31": 3, "12": 10, "19": 5, "24...
["[5, 15, 15, 77, 12, 38, 41, 30, 31, 30, 13, 19, 9, 2, 23, 37, 14, 34, 29, 22, 22, 4, 16, 2, 12, 17, 9, 18, 19, 21, 4, 28, 40, 11, 30, 24, 19, 9, 10, 76, 34]", "{13: 8, 29: 10, 4: 4, 2: 2, 77: 17, 16: 10, 11: 2, 22: 18, 17: 10, 18: 18, 38: 7, 9: 6, 5: 2, 41: 14, 31: 3, 12: 10, 19: 5, 24: 16, 40: 6, 14: 4, 34: 13, 15: ...
74
The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
9
[[1, 0], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1]]
23
30.882342100143433
23
6
15
[[["Green", "Red", "Green", "Red", "Green"], ["Blue", "Red", "Green", "Blue", "Green"], ["Red", "Blue", "Red", "Blue", "Blue"]], 8]
[[["Green", "Red", "Green", "Red", "Green"], ["Blue", "Red", "Green", "Blue", "Green"], ["Red", "Blue", "Red", "Blue", "Blue"]], 8]
["[['Green', 'Red', 'Green', 'Red', 'Green'], ['Blue', 'Red', 'Green', 'Blue', 'Green'], ['Red', 'Blue', 'Red', 'Blue', 'Blue']]", "8"]
74
We have a 4x4 numerical grid, with numbers ranging from 44 to 89 (44 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 > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
15
[[0, 0, 24], [0, 1, 28], [1, 0, 23], [1, 2, 29], [1, 3, 51], [2, 2, 26], [3, 0, 14]]
495
83.38021159172058
7
45
16
["[['', '', '53', '62'], ['', '27', '', ''], ['21', '22', '', '50'], ['', '20', '25', '44']]", 14, 64]
["[['', '', '53', '62'], ['', '27', '', ''], ['21', '22', '', '50'], ['', '20', '25', '44']]", 14, 64]
["[['', '', '53', '62'], ['', '27', '', ''], ['21', '22', '', '50'], ['', '20', '25', '44']]", "14", "64"]
74
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 6 to 47. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 99, 126, None for columns 1 to 2 respectively, and the sums of rows must be None, 97, 107, None for rows 1 to 2 ...
magic_square
underdetermined_system
7
[[0, 2, 24], [0, 3, 14], [1, 1, 12], [1, 2, 39], [2, 0, 8], [2, 1, 25], [2, 3, 45], [3, 3, 7]]
406
1.2863490581512451
8
31
16
["[['15', '20', '', ''], ['6', '', '', '40'], ['', '', '29', ''], ['46', '42', '34', '']]", 4, 6, 47]
["[['15', '20', '', ''], ['6', '', '', '40'], ['', '', '29', ''], ['46', '42', '34', '']]", 6, 47, [1, 3], [1, 3], [99, 126], [97, 107], 124]
["[['15', '20', '', ''], ['6', '', '', '40'], ['', '', '29', ''], ['46', '42', '34', '']]", "6", "47", "[None, 99, 126, None]", "[None, 97, 107, None]", "124"]
74
In 'Restricted Sorting', there are 10 stacks each with a capacity of 6 blocks, with 5 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 5 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
3
[[0, 6], [0, 9], [2, 6], [5, 4], [7, 9], [7, 9], [7, 9], [7, 6], [7, 4], [1, 3], [2, 7], [2, 7], [2, 4], [2, 4], [2, 7], [0, 2], [0, 4], [0, 2], [1, 6], [1, 2], [1, 0], [1, 9], [5, 0], [5, 0], [5, 2], [5, 0], [3, 2], [5, 7], [1, 6]]
133
0.260591983795166
29
90
30
[[["Black", "Blue", "Red", "White", "Red", "Green"], ["Red", "Black", "Red", "Green", "Blue", "Black"], ["Black", "Yellow", "Yellow", "White", "White", "Yellow"], [], [], ["White", "Green", "Green", "Red", "Green", "Yellow"], [], ["Blue", "Blue", "Blue", "Black", "White", "Yellow"], [], []], 6, {"0": 3, "1": 8, "2": 5,...
[[["Black", "Blue", "Red", "White", "Red", "Green"], ["Red", "Black", "Red", "Green", "Blue", "Black"], ["Black", "Yellow", "Yellow", "White", "White", "Yellow"], [], [], ["White", "Green", "Green", "Red", "Green", "Yellow"], [], ["Blue", "Blue", "Blue", "Black", "White", "Yellow"], [], []], 6, {"0": 3, "1": 8, "2": 5,...
["[['Black', 'Blue', 'Red', 'White', 'Red', 'Green'], ['Red', 'Black', 'Red', 'Green', 'Blue', 'Black'], ['Black', 'Yellow', 'Yellow', 'White', 'White', 'Yellow'], [], [], ['White', 'Green', 'Green', 'Red', 'Green', 'Yellow'], [], ['Blue', 'Blue', 'Blue', 'Black', 'White', 'Yellow'], [], []]", "{0: 3, 1: 8, 2: 5, 3: 10...
74
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (3, 12) to his destination workshop at index (7, 3), indexing from 0. Ben's car can mov...
traffic
pathfinding
5
[[3, 12], [4, 12], [4, 11], [4, 10], [5, 10], [6, 10], [6, 9], [6, 8], [6, 7], [7, 7], [7, 6], [8, 6], [8, 5], [8, 4], [7, 4], [7, 3]]
102
0.02852487564086914
16
4
4
[[["10", "x", "x", "x", "16", "9", "x", "13", "12", "8", "x", "16", "17"], ["9", "2", "x", "x", "5", "x", "x", "x", "12", "x", "3", "x", "x"], ["x", "x", "7", "3", "12", "x", "11", "18", "10", "x", "x", "13", "x"], ["x", "6", "x", "19", "2", "x", "x", "11", "13", "13", "1", "x", "7"], ["x", "x", "11", "x", "16", "16", ...
[[["10", "x", "x", "x", "16", "9", "x", "13", "12", "8", "x", "16", "17"], ["9", "2", "x", "x", "5", "x", "x", "x", "12", "x", "3", "x", "x"], ["x", "x", "7", "3", "12", "x", "11", "18", "10", "x", "x", "13", "x"], ["x", "6", "x", "19", "2", "x", "x", "11", "13", "13", "1", "x", "7"], ["x", "x", "11", "x", "16", "16", ...
["[['10', 'x', 'x', 'x', '16', '9', 'x', '13', '12', '8', 'x', '16', '17'], ['9', '2', 'x', 'x', '5', 'x', 'x', 'x', '12', 'x', '3', 'x', 'x'], ['x', 'x', '7', '3', '12', 'x', '11', '18', '10', 'x', 'x', '13', 'x'], ['x', '6', 'x', '19', '2', 'x', 'x', '11', '13', '13', '1', 'x', '7'], ['x', 'x', '11', 'x', '16', '16',...
74
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
13
[[11, 3], [10, 3], [9, 3], [9, 4], [8, 5], [7, 5], [7, 6], [6, 7], [5, 7], [4, 8], [4, 9], [3, 10], [2, 10], [1, 10]]
14
0.024291276931762695
14
8
2
["[[1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1,...
["[[1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1,...
["[[1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1], [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0, 0, 0, 0, 1,...
74
Given 7 labeled water jugs with capacities 91, 141, 56, 65, 89, 40, 39, 92 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 294, 375, 459, 466 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo...
water_jug
subset_sum
6
[["+", 92, 4], ["+", 141, 4], ["+", 141, 4], ["+", 92, 4], ["+", 141, 3], ["+", 141, 3], ["+", 141, 3], ["-", 56, 3], ["+", 92, 3], ["+", 56, 2], ["+", 89, 2], ["+", 89, 2], ["+", 141, 2], ["+", 56, 1], ["+", 91, 1], ["+", 91, 1], ["+", 56, 1]]
17
0.0752251148223877
17
64
3
[[91, 141, 56, 65, 89, 40, 39, 92], [294, 375, 459, 466]]
[[91, 141, 56, 65, 89, 40, 39, 92], [294, 375, 459, 466]]
["[91, 141, 56, 65, 89, 40, 39, 92]", "[294, 375, 459, 466]"]
75
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
[61, 42, 41, 31, 55, 21, 97, 16, 21, 68, 31, 55, 83, 21, 73, 69, 16, 73, 68, 83, 55, 31, 42, 61, 67, 97, 83, 42, 61, 67, 97, 83, 73, 68, 69, 16, 68, 69, 42, 55, 21, 53, 16, 42, 53, 16]
46
68.0147922039032
46
4
15
[[["_", 67, 21, 97, 69], [61, 68, 55, 16, 73], [42, 41, 31, 83, 53]]]
[[["_", 67, 21, 97, 69], [61, 68, 55, 16, 73], [42, 41, 31, 83, 53]]]
["[['_', 67, 21, 97, 69], [61, 68, 55, 16, 73], [42, 41, 31, 83, 53]]"]
75
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-right", "up-right", "down-right", "down-left", "up-left", "up-left"]
6
0.19606399536132812
6
4
25
[[["_", "s", "s", "h", "o"], ["r", "i", "l", "o", "y"], ["j", "o", "l", "i", "p"], ["d", "r", "a", "i", "n"], ["n", "i", "v", "a", "l"]]]
[[["_", "s", "s", "h", "o"], ["r", "i", "l", "o", "y"], ["j", "o", "l", "i", "p"], ["d", "r", "a", "i", "n"], ["n", "i", "v", "a", "l"]], ["soho", "rilly", "josip", "drain", "nival"]]
["[['_', 's', 's', 'h', 'o'], ['r', 'i', 'l', 'o', 'y'], ['j', 'o', 'l', 'i', 'p'], ['d', 'r', 'a', 'i', 'n'], ['n', 'i', 'v', 'a', 'l']]", "['soho', 'rilly', 'josip', 'drain', 'nival']"]
75
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
14
["B", "E", "W", "F", "O", "K", "W", "F"]
8
0.03292369842529297
8
14
17
[[[0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, ...
[[[0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, ...
["[[0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0,...
75
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [8, 31, 28, 24, 19, 18, 26, 31, 43, 32, 3, 21, 21, 10, 36, 40, 19, 38, 3, 5, 24, 12, 11, 14, 40, 7, 19, 4, 22, 5, 33, 31, 40, 7, 5, 34, 33, 22, 14, 6, 14, 29], such that the sum of the chosen coins adds up to 408. Each coi...
coin_exchange
subset_sum
26
[36, 6, 29, 33, 33, 43, 40, 38, 24, 31, 31, 31, 12, 21]
125
0.06368541717529297
14
42
42
[[8, 31, 28, 24, 19, 18, 26, 31, 43, 32, 3, 21, 21, 10, 36, 40, 19, 38, 3, 5, 24, 12, 11, 14, 40, 7, 19, 4, 22, 5, 33, 31, 40, 7, 5, 34, 33, 22, 14, 6, 14, 29]]
[[8, 31, 28, 24, 19, 18, 26, 31, 43, 32, 3, 21, 21, 10, 36, 40, 19, 38, 3, 5, 24, 12, 11, 14, 40, 7, 19, 4, 22, 5, 33, 31, 40, 7, 5, 34, 33, 22, 14, 6, 14, 29], {"31": 12, "40": 17, "32": 19, "26": 14, "12": 1, "5": 3, "36": 1, "33": 5, "3": 2, "6": 1, "34": 19, "18": 18, "8": 7, "21": 11, "43": 20, "22": 20, "4": 4, "...
["[8, 31, 28, 24, 19, 18, 26, 31, 43, 32, 3, 21, 21, 10, 36, 40, 19, 38, 3, 5, 24, 12, 11, 14, 40, 7, 19, 4, 22, 5, 33, 31, 40, 7, 5, 34, 33, 22, 14, 6, 14, 29]", "{31: 12, 40: 17, 32: 19, 26: 14, 12: 1, 5: 3, 36: 1, 33: 5, 3: 2, 6: 1, 34: 19, 18: 18, 8: 7, 21: 11, 43: 20, 22: 20, 4: 4, 11: 6, 28: 20, 7: 3, 38: 13, 24:...
75
The game of 'Sort It' begins with 3 tubes, each filled with 5 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
9
[[0, 1], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 2], [0, 1]]
27
153.86922955513
27
6
15
[[["Red", "Red", "Blue", "Blue", "Red"], ["Green", "Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Blue", "Green"]], 8]
[[["Red", "Red", "Blue", "Blue", "Red"], ["Green", "Green", "Red", "Red", "Green"], ["Blue", "Blue", "Green", "Blue", "Green"]], 8]
["[['Red', 'Red', 'Blue', 'Blue', 'Red'], ['Green', 'Green', 'Red', 'Red', 'Green'], ['Blue', 'Blue', 'Green', 'Blue', 'Green']]", "8"]
75
We have a 4x4 numerical grid, with numbers ranging from 33 to 78 (33 included in the range but 78 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
15
[[0, 2, 51], [1, 0, 38], [1, 2, 47], [2, 2, 44], [3, 0, 42], [3, 2, 23], [3, 3, 22]]
563
0.643829345703125
7
45
16
["[['37', '50', '', '70'], ['', '46', '', '65'], ['41', '43', '', '49'], ['', '30', '', '']]", 22, 72]
["[['37', '50', '', '70'], ['', '46', '', '65'], ['41', '43', '', '49'], ['', '30', '', '']]", 22, 72]
["[['37', '50', '', '70'], ['', '46', '', '65'], ['41', '43', '', '49'], ['', '30', '', '']]", "22", "72"]
75
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 6 to 47. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 125, 51, None for columns 1 to 2 respectively, and the sums of rows must be None, 101, 108, None for rows 1 to 2...
magic_square
underdetermined_system
7
[[0, 0, 8], [0, 1, 40], [0, 2, 9], [0, 3, 6], [1, 2, 14], [1, 3, 26], [2, 1, 34], [2, 2, 21]]
356
132.15215873718262
8
31
16
["[['', '', '', ''], ['28', '33', '', ''], ['16', '', '', '37'], ['36', '18', '7', '23']]", 4, 6, 47]
["[['', '', '', ''], ['28', '33', '', ''], ['16', '', '', '37'], ['36', '18', '7', '23']]", 6, 47, [1, 3], [1, 3], [125, 51], [101, 108], 90]
["[['', '', '', ''], ['28', '33', '', ''], ['16', '', '', '37'], ['36', '18', '7', '23']]", "6", "47", "[None, 125, 51, None]", "[None, 101, 108, None]", "90"]
75
In 'Restricted Sorting', there are 10 stacks each with a capacity of 6 blocks, with 5 stacks filled with blocks of varying shades and the remaining are empty. The challenge is to sort the blocks by shade such that if a stack is not empty, it is stacked with 5 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
3
[[0, 6], [0, 5], [7, 5], [1, 3], [1, 3], [1, 6], [1, 4], [7, 9], [8, 9], [2, 6], [2, 4], [2, 6], [2, 9], [2, 3], [1, 5], [1, 5], [7, 1], [7, 6], [7, 4], [0, 1], [0, 4], [0, 1], [8, 1], [8, 4], [8, 1], [8, 3], [0, 9], [8, 9], [7, 3], [2, 5]]
190
0.2266242504119873
30
90
30
[[["White", "Green", "Red", "Blue", "Red", "Yellow"], ["Black", "Black", "White", "Blue", "Green", "Green"], ["White", "Blue", "White", "Yellow", "Black", "Green"], [], [], [], [], ["Green", "Yellow", "Red", "White", "Blue", "Black"], ["Yellow", "Red", "Blue", "Red", "Black", "Yellow"], []], 6, {"0": 8, "1": 8, "2": 10...
[[["White", "Green", "Red", "Blue", "Red", "Yellow"], ["Black", "Black", "White", "Blue", "Green", "Green"], ["White", "Blue", "White", "Yellow", "Black", "Green"], [], [], [], [], ["Green", "Yellow", "Red", "White", "Blue", "Black"], ["Yellow", "Red", "Blue", "Red", "Black", "Yellow"], []], 6, {"0": 8, "1": 8, "2": 10...
["[['White', 'Green', 'Red', 'Blue', 'Red', 'Yellow'], ['Black', 'Black', 'White', 'Blue', 'Green', 'Green'], ['White', 'Blue', 'White', 'Yellow', 'Black', 'Green'], [], [], [], [], ['Green', 'Yellow', 'Red', 'White', 'Blue', 'Black'], ['Yellow', 'Red', 'Blue', 'Red', 'Black', 'Yellow'], []]", "{0: 8, 1: 8, 2: 10, 3: 6...
75
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (7, 1) to his destination workshop at index (2, 10), indexing from 0. Ben's car can mov...
traffic
pathfinding
5
[[7, 1], [8, 1], [8, 2], [8, 3], [7, 3], [7, 4], [7, 5], [7, 6], [8, 6], [8, 7], [8, 8], [7, 8], [7, 9], [6, 9], [5, 9], [4, 9], [3, 9], [2, 9], [2, 10]]
145
0.027338504791259766
19
4
4
[[["x", "9", "4", "8", "x", "x", "4", "x", "8", "12", "x", "x", "14"], ["17", "x", "3", "x", "6", "x", "12", "2", "x", "x", "x", "5", "19"], ["x", "8", "8", "x", "5", "x", "15", "14", "14", "3", "10", "12", "3"], ["4", "x", "16", "x", "x", "11", "12", "x", "x", "6", "5", "18", "19"], ["x", "4", "9", "17", "x", "x", "x"...
[[["x", "9", "4", "8", "x", "x", "4", "x", "8", "12", "x", "x", "14"], ["17", "x", "3", "x", "6", "x", "12", "2", "x", "x", "x", "5", "19"], ["x", "8", "8", "x", "5", "x", "15", "14", "14", "3", "10", "12", "3"], ["4", "x", "16", "x", "x", "11", "12", "x", "x", "6", "5", "18", "19"], ["x", "4", "9", "17", "x", "x", "x"...
["[['x', '9', '4', '8', 'x', 'x', '4', 'x', '8', '12', 'x', 'x', '14'], ['17', 'x', '3', 'x', '6', 'x', '12', '2', 'x', 'x', 'x', '5', '19'], ['x', '8', '8', 'x', '5', 'x', '15', '14', '14', '3', '10', '12', '3'], ['4', 'x', '16', 'x', 'x', '11', '12', 'x', 'x', '6', '5', '18', '19'], ['x', '4', '9', '17', 'x', 'x', 'x...
75
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 13x13. Some trampolines are broken and unusable. A map of the park is provided below, with 1 indicating a broken trampoline and 0 indicating a functional one. Alex can jump to any of the eight adjacent trampolines, as long as they are...
trampoline_matrix
pathfinding
13
[[0, 7], [1, 6], [2, 5], [3, 4], [4, 4], [5, 3], [6, 3], [7, 3], [7, 2], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [11, 0], [12, 0]]
16
0.021950483322143555
16
8
2
["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1,...
["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1,...
["[[0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0], [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 0, 1,...
75
Given 7 labeled water jugs with capacities 98, 121, 131, 126, 141, 125, 20 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 309, 395, 407, 429 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo...
water_jug
subset_sum
6
[["+", 131, 4], ["+", 141, 4], ["+", 141, 4], ["-", 125, 4], ["+", 141, 4], ["+", 125, 3], ["+", 141, 3], ["+", 141, 3], ["+", 125, 2], ["+", 125, 2], ["+", 20, 2], ["+", 125, 2], ["+", 141, 1], ["+", 141, 1], ["-", 98, 1], ["+", 125, 1]]
16
0.04790830612182617
16
56
3
[[98, 121, 131, 126, 141, 125, 20], [309, 395, 407, 429]]
[[98, 121, 131, 126, 141, 125, 20], [309, 395, 407, 429]]
["[98, 121, 131, 126, 141, 125, 20]", "[309, 395, 407, 429]"]
76
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
[21, 59, 25, 43, 27, 25, 39, 76, 59, 39, 43, 45, 46, 27, 25, 21]
16
0.03995919227600098
16
4
15
[[[86, 78, 77, 39, 76], [54, 45, 25, 59, 21], [38, 46, 43, 27, "_"]]]
[[[86, 78, 77, 39, 76], [54, 45, 25, 59, 21], [38, 46, 43, 27, "_"]]]
["[[86, 78, 77, 39, 76], [54, 45, 25, 59, 21], [38, 46, 43, 27, '_']]"]
76
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-left", "down-left", "up-left", "up-right", "down-right", "down-left", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left"]
16
0.18000054359436035
16
4
25
[[["h", "q", "n", "a", "_"], ["b", "y", "a", "d", "g"], ["d", "e", "c", "a", "o"], ["h", "o", "n", "u", "r"], ["p", "i", "c", "k", "y"]]]
[[["h", "q", "n", "a", "_"], ["b", "y", "a", "d", "g"], ["d", "e", "c", "a", "o"], ["h", "o", "n", "u", "r"], ["p", "i", "c", "k", "y"]], ["quad", "bhang", "decay", "honor", "picky"]]
["[['h', 'q', 'n', 'a', '_'], ['b', 'y', 'a', 'd', 'g'], ['d', 'e', 'c', 'a', 'o'], ['h', 'o', 'n', 'u', 'r'], ['p', 'i', 'c', 'k', 'y']]", "['quad', 'bhang', 'decay', 'honor', 'picky']"]
76
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
14
["D", "Z", "A", "X", "K", "W", "L", "X", "K"]
9
0.0372929573059082
9
14
17
[[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, ...
[[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1, ...
["[[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 0, 1,...
76
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [8, 8, 6, 36, 7, 36, 33, 3, 31, 17, 21, 28, 41, 17, 23, 16, 39, 2, 3, 40, 23, 20, 5, 30, 8, 28, 17, 34, 38, 26, 16, 21, 15, 21, 11, 33, 5, 33, 2, 27, 26, 21, 14, 13, 7, 23], such that the sum of the chosen coins adds up to...
coin_exchange
subset_sum
27
[7, 41, 36, 8, 15, 21, 21, 8, 21, 8, 21, 20, 16, 39, 38, 36, 16, 31]
70
0.0619659423828125
18
46
46
[[8, 8, 6, 36, 7, 36, 33, 3, 31, 17, 21, 28, 41, 17, 23, 16, 39, 2, 3, 40, 23, 20, 5, 30, 8, 28, 17, 34, 38, 26, 16, 21, 15, 21, 11, 33, 5, 33, 2, 27, 26, 21, 14, 13, 7, 23]]
[[8, 8, 6, 36, 7, 36, 33, 3, 31, 17, 21, 28, 41, 17, 23, 16, 39, 2, 3, 40, 23, 20, 5, 30, 8, 28, 17, 34, 38, 26, 16, 21, 15, 21, 11, 33, 5, 33, 2, 27, 26, 21, 14, 13, 7, 23], {"28": 16, "5": 1, "3": 3, "40": 18, "33": 20, "34": 12, "20": 4, "39": 13, "2": 2, "31": 11, "36": 2, "17": 14, "7": 1, "14": 6, "23": 12, "8": ...
["[8, 8, 6, 36, 7, 36, 33, 3, 31, 17, 21, 28, 41, 17, 23, 16, 39, 2, 3, 40, 23, 20, 5, 30, 8, 28, 17, 34, 38, 26, 16, 21, 15, 21, 11, 33, 5, 33, 2, 27, 26, 21, 14, 13, 7, 23]", "{28: 16, 5: 1, 3: 3, 40: 18, 33: 20, 34: 12, 20: 4, 39: 13, 2: 2, 31: 11, 36: 2, 17: 14, 7: 1, 14: 6, 23: 12, 8: 1, 30: 15, 27: 13, 15: 2, 21:...
76
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[1, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1], [0, 2], [0, 1], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [1, 0], [1, 2], [1, 2], [1, 2], [1, 2], [0, 1], [0, 1]]
31
491.6853485107422
31
6
18
[[["Blue", "Green", "Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Blue", "Red", "Red"], ["Green", "Green", "Green", "Blue", "Red", "Red"]], 9]
[[["Blue", "Green", "Red", "Red", "Green", "Blue"], ["Green", "Blue", "Blue", "Blue", "Red", "Red"], ["Green", "Green", "Green", "Blue", "Red", "Red"]], 9]
["[['Blue', 'Green', 'Red', 'Red', 'Green', 'Blue'], ['Green', 'Blue', 'Blue', 'Blue', 'Red', 'Red'], ['Green', 'Green', 'Green', 'Blue', 'Red', 'Red']]", "9"]
76
We have a 4x4 numerical grid, with numbers ranging from 28 to 78 (28 included in the range but 78 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
11
[[0, 2, 52], [1, 2, 56], [1, 3, 65], [2, 0, 54], [3, 0, 57], [3, 1, 58], [3, 3, 75]]
735
44.25528311729431
7
50
16
["[['47', '51', '', '64'], ['50', '53', '', ''], ['', '55', '68', '74'], ['', '', '72', '']]", 37, 87]
["[['47', '51', '', '64'], ['50', '53', '', ''], ['', '55', '68', '74'], ['', '', '72', '']]", 37, 87]
["[['47', '51', '', '64'], ['50', '53', '', ''], ['', '55', '68', '74'], ['', '', '72', '']]", "37", "87"]
76
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 6 to 47. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 128, 80, None for columns 1 to 2 respectively, and the sums of rows must be None, 94, 109, None for rows 1 to 2 ...
magic_square
underdetermined_system
7
[[0, 3, 8], [1, 0, 29], [1, 1, 40], [1, 2, 6], [2, 0, 9], [2, 2, 13], [2, 3, 44], [3, 1, 7]]
405
1.2350444793701172
8
31
16
["[['26', '38', '27', ''], ['', '', '', '19'], ['', '43', '', ''], ['42', '', '34', '20']]", 4, 6, 47]
["[['26', '38', '27', ''], ['', '', '', '19'], ['', '43', '', ''], ['42', '', '34', '20']]", 6, 47, [1, 3], [1, 3], [128, 80], [94, 109], 99]
["[['26', '38', '27', ''], ['', '', '', '19'], ['', '43', '', ''], ['42', '', '34', '20']]", "6", "47", "[None, 128, 80, None]", "[None, 94, 109, None]", "99"]
76
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[0, 3], [0, 9], [2, 4], [6, 4], [6, 9], [7, 11], [10, 11], [5, 3], [5, 4], [0, 4], [0, 4], [0, 1], [0, 3], [0, 11], [7, 0], [10, 0], [7, 9], [7, 1], [7, 11], [7, 9], [10, 1], [10, 4], [10, 8], [10, 0], [2, 0], [2, 8], [2, 11], [2, 0], [2, 9], [5, 3], [5, 8], [5, 3], [5, 9], [5, 3], [6, 5], [6, 5], [6, 11], [6, 5], [2,...
246
1.6125590801239014
45
132
42
[[["Black", "Blue", "Green", "Green", "Pink", "Black", "Red"], [], ["Green", "White", "Yellow", "Red", "White", "Blue", "Pink"], [], [], ["Black", "Green", "Black", "Yellow", "Black", "Blue", "Black"], ["Green", "Blue", "Yellow", "Yellow", "Red", "Yellow", "Pink"], ["Red", "White", "Blue", "Pink", "Red", "Blue", "White...
[[["Black", "Blue", "Green", "Green", "Pink", "Black", "Red"], [], ["Green", "White", "Yellow", "Red", "White", "Blue", "Pink"], [], [], ["Black", "Green", "Black", "Yellow", "Black", "Blue", "Black"], ["Green", "Blue", "Yellow", "Yellow", "Red", "Yellow", "Pink"], ["Red", "White", "Blue", "Pink", "Red", "Blue", "White...
["[['Black', 'Blue', 'Green', 'Green', 'Pink', 'Black', 'Red'], [], ['Green', 'White', 'Yellow', 'Red', 'White', 'Blue', 'Pink'], [], [], ['Black', 'Green', 'Black', 'Yellow', 'Black', 'Blue', 'Black'], ['Green', 'Blue', 'Yellow', 'Yellow', 'Red', 'Yellow', 'Pink'], ['Red', 'White', 'Blue', 'Pink', 'Red', 'Blue', 'Whit...
76
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 3) to his destination workshop at index (8, 13), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[4, 3], [3, 3], [3, 4], [2, 4], [2, 5], [2, 6], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 10], [4, 11], [4, 12], [5, 12], [6, 12], [7, 12], [8, 12], [8, 13]]
151
0.02843952178955078
19
4
4
[[["x", "12", "8", "4", "4", "16", "8", "x", "x", "17", "18", "9", "x", "16"], ["2", "9", "x", "1", "4", "13", "20", "11", "2", "x", "11", "7", "14", "12"], ["x", "x", "x", "x", "17", "15", "8", "12", "x", "x", "7", "x", "x", "x"], ["2", "2", "x", "5", "14", "x", "1", "5", "4", "14", "7", "x", "x", "x"], ["19", "x", "1...
[[["x", "12", "8", "4", "4", "16", "8", "x", "x", "17", "18", "9", "x", "16"], ["2", "9", "x", "1", "4", "13", "20", "11", "2", "x", "11", "7", "14", "12"], ["x", "x", "x", "x", "17", "15", "8", "12", "x", "x", "7", "x", "x", "x"], ["2", "2", "x", "5", "14", "x", "1", "5", "4", "14", "7", "x", "x", "x"], ["19", "x", "1...
["[['x', '12', '8', '4', '4', '16', '8', 'x', 'x', '17', '18', '9', 'x', '16'], ['2', '9', 'x', '1', '4', '13', '20', '11', '2', 'x', '11', '7', '14', '12'], ['x', 'x', 'x', 'x', '17', '15', '8', '12', 'x', 'x', '7', 'x', 'x', 'x'], ['2', '2', 'x', '5', '14', 'x', '1', '5', '4', '14', '7', 'x', 'x', 'x'], ['19', 'x', '...
76
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[2, 12], [3, 11], [2, 10], [2, 9], [2, 8], [2, 7], [3, 7], [3, 6], [4, 6], [4, 5], [4, 4], [5, 4], [6, 4], [7, 4], [8, 3], [8, 2], [9, 1], [10, 1]]
18
0.029042482376098633
18
8
2
["[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1,...
["[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1,...
["[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1,...
76
Given 7 labeled water jugs with capacities 117, 118, 23, 86, 109, 128, 104, 61 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 367, 390, 400, 470 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the...
water_jug
subset_sum
6
[["+", 86, 4], ["+", 128, 4], ["+", 128, 4], ["+", 128, 4], ["+", 61, 3], ["+", 104, 3], ["+", 117, 3], ["+", 118, 3], ["+", 109, 2], ["+", 109, 2], ["+", 86, 2], ["+", 86, 2], ["+", 109, 1], ["+", 117, 1], ["+", 23, 1], ["+", 118, 1]]
16
0.038893938064575195
16
64
3
[[117, 118, 23, 86, 109, 128, 104, 61], [367, 390, 400, 470]]
[[117, 118, 23, 86, 109, 128, 104, 61], [367, 390, 400, 470]]
["[117, 118, 23, 86, 109, 128, 104, 61]", "[367, 390, 400, 470]"]
77
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
[88, 46, 66, 88, 81, 60, 88, 81, 46, 70, 8, 66, 70, 8, 24, 28, 62, 24, 28, 36, 66, 28, 36, 62, 24, 6, 8, 36, 28, 66, 62, 24]
32
1.3497884273529053
32
4
15
[[[60, 66, 46, 8, 36], [81, "_", 88, 70, 24], [20, 17, 6, 62, 28]]]
[[[60, 66, 46, 8, 36], [81, "_", 88, 70, 24], [20, 17, 6, 62, 28]]]
["[[60, 66, 46, 8, 36], [81, '_', 88, 70, 24], [20, 17, 6, 62, 28]]"]
77
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["up-left", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-left", "down-left", "up-left", "up-right", "up-right", "down-right", "down-left", "up-left", "down-left", "down-right", "up-right", "up-left", "up-left"]
22
0.6303999423980713
22
4
25
[[["l", "g", "a", "n", "g"], ["c", "o", "o", "e", "n"], ["e", "r", "_", "n", "t"], ["d", "b", "w", "o", "x"], ["t", "h", "w", "r", "p"]]]
[[["l", "g", "a", "n", "g"], ["c", "o", "o", "e", "n"], ["e", "r", "_", "n", "t"], ["d", "b", "w", "o", "x"], ["t", "h", "w", "r", "p"]], ["gong", "clown", "brent", "dewax", "thorp"]]
["[['l', 'g', 'a', 'n', 'g'], ['c', 'o', 'o', 'e', 'n'], ['e', 'r', '_', 'n', 't'], ['d', 'b', 'w', 'o', 'x'], ['t', 'h', 'w', 'r', 'p']]", "['gong', 'clown', 'brent', 'dewax', 'thorp']"]
77
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
14
["O", "S", "H", "F", "B", "D", "B", "U", "H"]
9
0.04355263710021973
9
14
17
[[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, ...
[[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, ...
["[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0,...
77
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [26, 32, 14, 36, 14, 8, 9, 3, 8, 18, 7, 23, 6, 20, 34, 8, 37, 19, 15, 6, 2, 13, 37, 7, 31, 2, 7, 4, 17, 9, 4, 22, 7, 16, 33, 14, 11, 30, 36, 14, 34, 37, 36, 37, 32, 38, 15, 17, 19, 14], such that the sum of the chosen coin...
coin_exchange
subset_sum
28
[34, 26, 8, 15, 8, 15, 33, 32, 8, 11, 31, 30, 37, 34, 32, 2, 19, 19, 2]
68
0.06271767616271973
19
50
50
[[26, 32, 14, 36, 14, 8, 9, 3, 8, 18, 7, 23, 6, 20, 34, 8, 37, 19, 15, 6, 2, 13, 37, 7, 31, 2, 7, 4, 17, 9, 4, 22, 7, 16, 33, 14, 11, 30, 36, 14, 34, 37, 36, 37, 32, 38, 15, 17, 19, 14]]
[[26, 32, 14, 36, 14, 8, 9, 3, 8, 18, 7, 23, 6, 20, 34, 8, 37, 19, 15, 6, 2, 13, 37, 7, 31, 2, 7, 4, 17, 9, 4, 22, 7, 16, 33, 14, 11, 30, 36, 14, 34, 37, 36, 37, 32, 38, 15, 17, 19, 14], {"17": 16, "4": 2, "15": 2, "8": 1, "19": 5, "9": 4, "23": 7, "3": 2, "16": 13, "2": 1, "38": 13, "11": 2, "31": 6, "7": 6, "36": 8, ...
["[26, 32, 14, 36, 14, 8, 9, 3, 8, 18, 7, 23, 6, 20, 34, 8, 37, 19, 15, 6, 2, 13, 37, 7, 31, 2, 7, 4, 17, 9, 4, 22, 7, 16, 33, 14, 11, 30, 36, 14, 34, 37, 36, 37, 32, 38, 15, 17, 19, 14]", "{17: 16, 4: 2, 15: 2, 8: 1, 19: 5, 9: 4, 23: 7, 3: 2, 16: 13, 2: 1, 38: 13, 11: 2, 31: 6, 7: 6, 36: 8, 14: 8, 37: 17, 32: 5, 6: 1,...
77
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[2, 1], [2, 0], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [1, 2], [0, 1], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1]]
29
413.2857873439789
29
6
18
[[["Red", "Blue", "Green", "Red", "Blue", "Green"], ["Blue", "Green", "Green", "Blue", "Red", "Blue"], ["Green", "Red", "Red", "Green", "Blue", "Red"]], 9]
[[["Red", "Blue", "Green", "Red", "Blue", "Green"], ["Blue", "Green", "Green", "Blue", "Red", "Blue"], ["Green", "Red", "Red", "Green", "Blue", "Red"]], 9]
["[['Red', 'Blue', 'Green', 'Red', 'Blue', 'Green'], ['Blue', 'Green', 'Green', 'Blue', 'Red', 'Blue'], ['Green', 'Red', 'Red', 'Green', 'Blue', 'Red']]", "9"]
77
We have a 4x4 numerical grid, with numbers ranging from 21 to 71 (21 included in the range but 71 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
11
[[1, 0, 22], [1, 1, 23], [1, 2, 34], [2, 0, 24], [2, 2, 39], [2, 3, 48], [3, 1, 40], [3, 3, 47]]
467
163.82063746452332
8
50
16
["[['20', '21', '33', '60'], ['', '', '', '49'], ['', '38', '', ''], ['36', '', '46', '']]", 14, 64]
["[['20', '21', '33', '60'], ['', '', '', '49'], ['', '38', '', ''], ['36', '', '46', '']]", 14, 64]
["[['20', '21', '33', '60'], ['', '', '', '49'], ['', '38', '', ''], ['36', '', '46', '']]", "14", "64"]
77
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 13 to 54. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 147, 128, None for columns 1 to 2 respectively, and the sums of rows must be None, 159, 114, None for rows 1 to...
magic_square
underdetermined_system
8
[[0, 0, 13], [0, 1, 14], [1, 0, 23], [1, 1, 53], [1, 2, 32], [2, 0, 17], [2, 1, 46], [2, 3, 35], [3, 1, 34]]
528
61.967140197753906
9
31
16
["[['', '', '37', '31'], ['', '', '', '51'], ['', '', '16', ''], ['41', '', '43', '42']]", 4, 13, 54]
["[['', '', '37', '31'], ['', '', '', '51'], ['', '', '16', ''], ['41', '', '43', '42']]", 13, 54, [1, 3], [1, 3], [147, 128], [159, 114], 150]
["[['', '', '37', '31'], ['', '', '', '51'], ['', '', '16', ''], ['41', '', '43', '42']]", "13", "54", "[None, 147, 128, None]", "[None, 159, 114, None]", "150"]
77
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[4, 8], [5, 8], [0, 1], [5, 1], [5, 8], [7, 6], [11, 6], [11, 1], [0, 3], [11, 3], [11, 9], [11, 8], [11, 8], [11, 1], [0, 11], [0, 6], [0, 11], [2, 11], [2, 8], [2, 11], [2, 11], [2, 1], [2, 6], [0, 10], [5, 10], [5, 10], [5, 0], [4, 3], [4, 3], [4, 11], [4, 3], [4, 1], [7, 10], [7, 10], [7, 10], [7, 4], [7, 5], [7, ...
309
44.145676374435425
44
132
42
[[["Green", "Black", "White", "Red", "White", "Yellow", "Blue"], [], ["White", "Pink", "White", "White", "Green", "Red", "Blue"], [], ["Pink", "Black", "Black", "White", "Black", "Green", "Blue"], ["Pink", "Green", "Pink", "Yellow", "Yellow", "Blue", "Red"], [], ["Red", "Yellow", "Yellow", "Yellow", "Blue", "Red", "Bla...
[[["Green", "Black", "White", "Red", "White", "Yellow", "Blue"], [], ["White", "Pink", "White", "White", "Green", "Red", "Blue"], [], ["Pink", "Black", "Black", "White", "Black", "Green", "Blue"], ["Pink", "Green", "Pink", "Yellow", "Yellow", "Blue", "Red"], [], ["Red", "Yellow", "Yellow", "Yellow", "Blue", "Red", "Bla...
["[['Green', 'Black', 'White', 'Red', 'White', 'Yellow', 'Blue'], [], ['White', 'Pink', 'White', 'White', 'Green', 'Red', 'Blue'], [], ['Pink', 'Black', 'Black', 'White', 'Black', 'Green', 'Blue'], ['Pink', 'Green', 'Pink', 'Yellow', 'Yellow', 'Blue', 'Red'], [], ['Red', 'Yellow', 'Yellow', 'Yellow', 'Blue', 'Red', 'Bl...
77
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, 1) to his destination workshop at index (3, 13), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[6, 1], [6, 2], [5, 2], [4, 2], [3, 2], [2, 2], [1, 2], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 11], [2, 12], [2, 13], [3, 13]]
168
0.022469043731689453
22
4
4
[[["x", "5", "9", "6", "13", "13", "8", "6", "13", "x", "13", "x", "x", "x"], ["3", "10", "16", "x", "x", "3", "13", "1", "11", "9", "7", "6", "x", "18"], ["9", "11", "3", "x", "x", "6", "13", "x", "14", "x", "12", "1", "2", "4"], ["x", "17", "13", "x", "14", "4", "6", "8", "x", "x", "1", "x", "6", "2"], ["7", "x", "11...
[[["x", "5", "9", "6", "13", "13", "8", "6", "13", "x", "13", "x", "x", "x"], ["3", "10", "16", "x", "x", "3", "13", "1", "11", "9", "7", "6", "x", "18"], ["9", "11", "3", "x", "x", "6", "13", "x", "14", "x", "12", "1", "2", "4"], ["x", "17", "13", "x", "14", "4", "6", "8", "x", "x", "1", "x", "6", "2"], ["7", "x", "11...
["[['x', '5', '9', '6', '13', '13', '8', '6', '13', 'x', '13', 'x', 'x', 'x'], ['3', '10', '16', 'x', 'x', '3', '13', '1', '11', '9', '7', '6', 'x', '18'], ['9', '11', '3', 'x', 'x', '6', '13', 'x', '14', 'x', '12', '1', '2', '4'], ['x', '17', '13', 'x', '14', '4', '6', '8', 'x', 'x', '1', 'x', '6', '2'], ['7', 'x', '1...
77
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[0, 13], [0, 12], [0, 11], [0, 10], [1, 10], [2, 10], [3, 9], [3, 8], [3, 7], [4, 7], [5, 7], [6, 6], [7, 5], [7, 4], [7, 3], [7, 2], [8, 1]]
17
0.03951430320739746
17
8
2
["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [1, 0, 0,...
["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [1, 0, 0,...
["[[0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], [1, 0, 0,...
77
Given 7 labeled water jugs with capacities 60, 59, 72, 93, 39, 74, 71, 84 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 166, 239, 286, 421 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amou...
water_jug
subset_sum
6
[["+", 71, 4], ["+", 71, 4], ["+", 93, 4], ["+", 93, 4], ["+", 93, 4], ["+", 71, 3], ["+", 84, 3], ["+", 60, 3], ["+", 71, 3], ["+", 71, 2], ["+", 84, 2], ["+", 84, 2], ["+", 39, 1], ["+", 93, 1], ["-", 59, 1], ["+", 93, 1]]
16
0.05889129638671875
16
64
3
[[60, 59, 72, 93, 39, 74, 71, 84], [166, 239, 286, 421]]
[[60, 59, 72, 93, 39, 74, 71, 84], [166, 239, 286, 421]]
["[60, 59, 72, 93, 39, 74, 71, 84]", "[166, 239, 286, 421]"]
78
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
[87, 85, 76, 17, 66, 24, 82, 43, 24, 66, 17, 24, 43, 82, 66, 17, 79, 76, 24, 79, 17, 43, 79, 24, 76, 17, 24, 77, 88, 87, 85, 75]
32
4.894534587860107
32
4
15
[[[94, 92, 77, 88, "_"], [82, 43, 76, 85, 87], [24, 66, 17, 79, 75]]]
[[[94, 92, 77, 88, "_"], [82, 43, 76, 85, 87], [24, 66, 17, 79, 75]]]
["[[94, 92, 77, 88, '_'], [82, 43, 76, 85, 87], [24, 66, 17, 79, 75]]"]
78
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-left", "down-right", "down-right", "down-left", "up-left", "up-right", "up-right", "up-left", "down-left", "up-left"]
10
0.18477082252502441
10
4
25
[[["a", "j", "_", "k", "e"], ["t", "s", "w", "y", "e"], ["t", "r", "a", "p", "a"], ["s", "e", "a", "m", "h"], ["c", "r", "s", "e", "p"]]]
[[["a", "j", "_", "k", "e"], ["t", "s", "w", "y", "e"], ["t", "r", "a", "p", "a"], ["s", "e", "a", "m", "h"], ["c", "r", "s", "e", "p"]], ["jake", "tawse", "trypa", "smash", "creep"]]
["[['a', 'j', '_', 'k', 'e'], ['t', 's', 'w', 'y', 'e'], ['t', 'r', 'a', 'p', 'a'], ['s', 'e', 'a', 'm', 'h'], ['c', 'r', 's', 'e', 'p']]", "['jake', 'tawse', 'trypa', 'smash', 'creep']"]
78
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
14
["A", "B", "C", "H", "J", "T", "W", "G", "W", "H"]
10
0.0448455810546875
10
14
17
[[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, ...
[[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, ...
["[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0,...
78
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [29, 32, 2, 34, 7, 25, 7, 14, 33, 1, 26, 18, 13, 11, 32, 31, 13, 2, 28, 21, 38, 8, 11, 28, 26, 9, 4, 28, 34, 23, 18, 31, 35, 2, 25, 20, 15, 5, 12, 10, 7, 14, 17, 4, 13, 24, 11, 16, 14, 27, 29], such that the sum of the cho...
coin_exchange
subset_sum
29
[28, 18, 12, 10, 8, 21, 33, 28, 24, 18, 35, 34, 32, 28, 26, 2, 5, 4, 13, 13]
99
0.0646202564239502
20
51
51
[[29, 32, 2, 34, 7, 25, 7, 14, 33, 1, 26, 18, 13, 11, 32, 31, 13, 2, 28, 21, 38, 8, 11, 28, 26, 9, 4, 28, 34, 23, 18, 31, 35, 2, 25, 20, 15, 5, 12, 10, 7, 14, 17, 4, 13, 24, 11, 16, 14, 27, 29]]
[[29, 32, 2, 34, 7, 25, 7, 14, 33, 1, 26, 18, 13, 11, 32, 31, 13, 2, 28, 21, 38, 8, 11, 28, 26, 9, 4, 28, 34, 23, 18, 31, 35, 2, 25, 20, 15, 5, 12, 10, 7, 14, 17, 4, 13, 24, 11, 16, 14, 27, 29], {"10": 1, "25": 18, "1": 1, "15": 7, "12": 1, "23": 16, "9": 7, "27": 15, "29": 16, "28": 2, "32": 12, "24": 6, "5": 1, "8": ...
["[29, 32, 2, 34, 7, 25, 7, 14, 33, 1, 26, 18, 13, 11, 32, 31, 13, 2, 28, 21, 38, 8, 11, 28, 26, 9, 4, 28, 34, 23, 18, 31, 35, 2, 25, 20, 15, 5, 12, 10, 7, 14, 17, 4, 13, 24, 11, 16, 14, 27, 29]", "{10: 1, 25: 18, 1: 1, 15: 7, 12: 1, 23: 16, 9: 7, 27: 15, 29: 16, 28: 2, 32: 12, 24: 6, 5: 1, 8: 1, 11: 8, 17: 13, 13: 6, ...
78
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[0, 1], [2, 0], [2, 1], [2, 0], [2, 1], [2, 0], [1, 0], [1, 2], [1, 2], [1, 2], [0, 2], [1, 2], [1, 2], [1, 2], [1, 0], [1, 2], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1], [0, 2], [0, 1], [0, 1], [2, 0], [2, 0], [2, 1], [2, 0], [2, 0], [2, 0], [1, 2], [1, 0], [1, 2], [1, 2], [0, 1]]
36
552.3669350147247
36
6
18
[[["Red", "Green", "Blue", "Red", "Green", "Blue"], ["Blue", "Blue", "Red", "Blue", "Green", "Red"], ["Green", "Red", "Green", "Blue", "Green", "Red"]], 9]
[[["Red", "Green", "Blue", "Red", "Green", "Blue"], ["Blue", "Blue", "Red", "Blue", "Green", "Red"], ["Green", "Red", "Green", "Blue", "Green", "Red"]], 9]
["[['Red', 'Green', 'Blue', 'Red', 'Green', 'Blue'], ['Blue', 'Blue', 'Red', 'Blue', 'Green', 'Red'], ['Green', 'Red', 'Green', 'Blue', 'Green', 'Red']]", "9"]
78
We have a 4x4 numerical grid, with numbers ranging from 17 to 67 (17 included in the range but 67 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
11
[[0, 0, 61], [0, 1, 60], [0, 3, 36], [1, 3, 62], [2, 1, 45], [3, 0, 37], [3, 1, 38], [3, 2, 64]]
734
0.4792149066925049
8
50
16
["[['', '', '58', ''], ['44', '54', '59', ''], ['43', '', '63', '75'], ['', '', '', '84']]", 36, 86]
["[['', '', '58', ''], ['44', '54', '59', ''], ['43', '', '63', '75'], ['', '', '', '84']]", 36, 86]
["[['', '', '58', ''], ['44', '54', '59', ''], ['43', '', '63', '75'], ['', '', '', '84']]", "36", "86"]
78
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 13 to 54. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 135, 153, None for columns 1 to 2 respectively, and the sums of rows must be None, 158, 87, None for rows 1 to ...
magic_square
underdetermined_system
8
[[0, 0, 13], [0, 2, 29], [0, 3, 31], [1, 3, 41], [2, 1, 17], [3, 0, 50], [3, 1, 49], [3, 2, 52], [3, 3, 14]]
505
17.9815993309021
9
31
16
["[['', '22', '', ''], ['28', '47', '42', ''], ['16', '', '30', '24'], ['', '', '', '']]", 4, 13, 54]
["[['', '22', '', ''], ['28', '47', '42', ''], ['16', '', '30', '24'], ['', '', '', '']]", 13, 54, [1, 3], [1, 3], [135, 153], [158, 87], 140]
["[['', '22', '', ''], ['28', '47', '42', ''], ['16', '', '30', '24'], ['', '', '', '']]", "13", "54", "[None, 135, 153, None]", "[None, 158, 87, None]", "140"]
78
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[5, 0], [10, 0], [6, 2], [6, 0], [4, 9], [4, 2], [1, 7], [4, 7], [8, 11], [8, 9], [8, 2], [8, 7], [8, 2], [8, 3], [8, 0], [1, 8], [10, 2], [10, 8], [10, 2], [10, 11], [10, 0], [1, 11], [1, 11], [10, 7], [1, 10], [1, 9], [4, 10], [4, 10], [4, 8], [6, 10], [6, 4], [6, 10], [6, 11], [5, 8], [5, 4], [5, 7], [5, 8], [5, 11...
275
30.320260763168335
45
132
42
[[[], ["Blue", "Pink", "Red", "Red", "Yellow", "White", "Green"], [], [], ["White", "Black", "Blue", "Yellow", "Yellow", "Pink", "White"], ["Green", "Pink", "White", "Blue", "Pink", "Red", "Pink"], ["Black", "Green", "Yellow", "White", "Yellow", "Red", "Blue"], [], ["Red", "White", "Black", "Blue", "Black", "Yellow", "...
[[[], ["Blue", "Pink", "Red", "Red", "Yellow", "White", "Green"], [], [], ["White", "Black", "Blue", "Yellow", "Yellow", "Pink", "White"], ["Green", "Pink", "White", "Blue", "Pink", "Red", "Pink"], ["Black", "Green", "Yellow", "White", "Yellow", "Red", "Blue"], [], ["Red", "White", "Black", "Blue", "Black", "Yellow", "...
["[[], ['Blue', 'Pink', 'Red', 'Red', 'Yellow', 'White', 'Green'], [], [], ['White', 'Black', 'Blue', 'Yellow', 'Yellow', 'Pink', 'White'], ['Green', 'Pink', 'White', 'Blue', 'Pink', 'Red', 'Pink'], ['Black', 'Green', 'Yellow', 'White', 'Yellow', 'Red', 'Blue'], [], ['Red', 'White', 'Black', 'Blue', 'Black', 'Yellow', ...
78
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (7, 12) to his destination workshop at index (2, 0), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[7, 12], [6, 12], [5, 12], [4, 12], [4, 11], [4, 10], [3, 10], [3, 9], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [2, 4], [2, 3], [3, 3], [3, 2], [3, 1], [3, 0], [2, 0]]
133
0.023016929626464844
20
4
4
[[["x", "x", "x", "16", "11", "12", "x", "x", "17", "3", "x", "x", "4", "6"], ["4", "17", "x", "x", "3", "x", "x", "1", "9", "11", "12", "4", "x", "x"], ["5", "x", "x", "7", "14", "4", "5", "7", "13", "4", "7", "x", "x", "x"], ["6", "6", "19", "3", "15", "x", "x", "x", "x", "4", "10", "19", "2", "4"], ["3", "16", "8", ...
[[["x", "x", "x", "16", "11", "12", "x", "x", "17", "3", "x", "x", "4", "6"], ["4", "17", "x", "x", "3", "x", "x", "1", "9", "11", "12", "4", "x", "x"], ["5", "x", "x", "7", "14", "4", "5", "7", "13", "4", "7", "x", "x", "x"], ["6", "6", "19", "3", "15", "x", "x", "x", "x", "4", "10", "19", "2", "4"], ["3", "16", "8", ...
["[['x', 'x', 'x', '16', '11', '12', 'x', 'x', '17', '3', 'x', 'x', '4', '6'], ['4', '17', 'x', 'x', '3', 'x', 'x', '1', '9', '11', '12', '4', 'x', 'x'], ['5', 'x', 'x', '7', '14', '4', '5', '7', '13', '4', '7', 'x', 'x', 'x'], ['6', '6', '19', '3', '15', 'x', 'x', 'x', 'x', '4', '10', '19', '2', '4'], ['3', '16', '8',...
78
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[10, 12], [9, 11], [8, 10], [7, 9], [6, 8], [5, 8], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [3, 4], [3, 3], [2, 3], [1, 3], [1, 2], [1, 1]]
17
0.030817031860351562
17
8
2
["[[1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1,...
["[[1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1,...
["[[1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0], [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1,...
78
Given 7 labeled water jugs with capacities 58, 18, 19, 47, 86, 75, 119, 34 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 234, 331, 343, 379 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the amo...
water_jug
subset_sum
6
[["+", 19, 4], ["+", 119, 4], ["+", 119, 4], ["+", 47, 4], ["+", 75, 4], ["+", 19, 3], ["+", 119, 3], ["+", 119, 3], ["+", 86, 3], ["+", 75, 2], ["+", 119, 2], ["+", 18, 2], ["+", 119, 2], ["+", 47, 1], ["+", 119, 1], ["-", 18, 1], ["+", 86, 1]]
17
0.05347609519958496
17
64
3
[[58, 18, 19, 47, 86, 75, 119, 34], [234, 331, 343, 379]]
[[58, 18, 19, 47, 86, 75, 119, 34], [234, 331, 343, 379]]
["[58, 18, 19, 47, 86, 75, 119, 34]", "[234, 331, 343, 379]"]
79
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
7
[99, 32, 89, 42, 54, 77, 33, 99, 32, 21, 42, 54, 77, 89, 99, 32, 21, 42, 58, 69, 42, 58, 54, 77, 89, 99, 58, 54, 77, 89, 99, 58, 54, 42, 39, 16]
36
5.105415344238281
36
4
15
[[[42, 89, 21, 58, 67], [54, 32, 99, 69, 38], [77, 33, "_", 39, 16]]]
[[[42, 89, 21, 58, 67], [54, 32, 99, 69, 38], [77, 33, "_", 39, 16]]]
["[[42, 89, 21, 58, 67], [54, 32, 99, 69, 38], [77, 33, '_', 39, 16]]"]
79
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-right", "down-left", "up-left", "up-left", "up-right", "up-right", "down-right", "down-right", "down-left", "up-left", "up-left", "up-right", "down-right", "down-left", "up-left", "up-left"]
16
0.3119840621948242
16
4
25
[[["r", "s", "c", "v", "a"], ["b", "b", "y", "r", "e"], ["u", "i", "_", "n", "i"], ["p", "n", "g", "i", "l"], ["l", "i", "y", "n", "e"]]]
[[["r", "s", "c", "v", "a"], ["b", "b", "y", "r", "e"], ["u", "i", "_", "n", "i"], ["p", "n", "g", "i", "l"], ["l", "i", "y", "n", "e"]], ["siva", "bryce", "birny", "pugil", "linne"]]
["[['r', 's', 'c', 'v', 'a'], ['b', 'b', 'y', 'r', 'e'], ['u', 'i', '_', 'n', 'i'], ['p', 'n', 'g', 'i', 'l'], ['l', 'i', 'y', 'n', 'e']]", "['siva', 'bryce', 'birny', 'pugil', 'linne']"]
79
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
14
["I", "V", "S", "E", "K", "W", "C", "W", "L", "F", "S"]
11
0.06302189826965332
11
14
17
[[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, ...
[[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, ...
["[[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0,...
79
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [33, 4, 5, 9, 31, 26, 25, 19, 31, 33, 24, 6, 13, 17, 15, 37, 7, 21, 3, 23, 22, 7, 3, 11, 19, 28, 24, 32, 27, 31, 24, 12, 23, 22, 16, 6, 33, 8, 19, 13, 5, 11, 10, 4, 8, 16, 14, 17, 13, 9, 25, 17], such that the sum of the c...
coin_exchange
subset_sum
30
[11, 19, 19, 16, 19, 37, 16, 17, 17, 17, 27, 33, 10, 11, 33, 14, 33, 28, 12]
84
0.06765866279602051
19
52
52
[[33, 4, 5, 9, 31, 26, 25, 19, 31, 33, 24, 6, 13, 17, 15, 37, 7, 21, 3, 23, 22, 7, 3, 11, 19, 28, 24, 32, 27, 31, 24, 12, 23, 22, 16, 6, 33, 8, 19, 13, 5, 11, 10, 4, 8, 16, 14, 17, 13, 9, 25, 17]]
[[33, 4, 5, 9, 31, 26, 25, 19, 31, 33, 24, 6, 13, 17, 15, 37, 7, 21, 3, 23, 22, 7, 3, 11, 19, 28, 24, 32, 27, 31, 24, 12, 23, 22, 16, 6, 33, 8, 19, 13, 5, 11, 10, 4, 8, 16, 14, 17, 13, 9, 25, 17], {"3": 3, "19": 1, "5": 2, "9": 4, "17": 4, "24": 11, "8": 5, "22": 10, "4": 2, "32": 10, "16": 1, "37": 5, "23": 12, "26": ...
["[33, 4, 5, 9, 31, 26, 25, 19, 31, 33, 24, 6, 13, 17, 15, 37, 7, 21, 3, 23, 22, 7, 3, 11, 19, 28, 24, 32, 27, 31, 24, 12, 23, 22, 16, 6, 33, 8, 19, 13, 5, 11, 10, 4, 8, 16, 14, 17, 13, 9, 25, 17]", "{3: 3, 19: 1, 5: 2, 9: 4, 17: 4, 24: 11, 8: 5, 22: 10, 4: 2, 32: 10, 16: 1, 37: 5, 23: 12, 26: 18, 12: 1, 27: 9, 14: 5, ...
79
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[2, 0], [1, 2], [1, 2], [0, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1]]
30
487.9078462123871
30
6
18
[[["Red", "Green", "Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Red", "Blue", "Blue"], ["Blue", "Red", "Green", "Blue", "Green", "Red"]], 9]
[[["Red", "Green", "Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Red", "Blue", "Blue"], ["Blue", "Red", "Green", "Blue", "Green", "Red"]], 9]
["[['Red', 'Green', 'Red', 'Blue', 'Blue', 'Green'], ['Green', 'Green', 'Red', 'Red', 'Blue', 'Blue'], ['Blue', 'Red', 'Green', 'Blue', 'Green', 'Red']]", "9"]
79
We have a 4x4 numerical grid, with numbers ranging from 14 to 64 (14 included in the range but 64 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
12
[[0, 0, 37], [0, 2, 24], [0, 3, 23], [1, 3, 39], [2, 1, 40], [2, 3, 44], [3, 0, 25], [3, 1, 41]]
447
2.1435494422912598
8
50
16
["[['', '35', '', ''], ['34', '36', '38', ''], ['29', '', '43', ''], ['', '', '49', '53']]", 23, 73]
["[['', '35', '', ''], ['34', '36', '38', ''], ['29', '', '43', ''], ['', '', '49', '53']]", 23, 73]
["[['', '35', '', ''], ['34', '36', '38', ''], ['29', '', '43', ''], ['', '', '49', '53']]", "23", "73"]
79
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 13 to 54. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 146, 168, None for columns 1 to 2 respectively, and the sums of rows must be None, 118, 120, None for rows 1 to...
magic_square
underdetermined_system
8
[[0, 0, 13], [0, 2, 50], [1, 0, 16], [1, 1, 51], [2, 1, 19], [2, 2, 29], [3, 0, 14], [3, 1, 30], [3, 3, 17]]
483
56.54647707939148
9
31
16
["[['', '46', '', '22'], ['', '', '36', '15'], ['47', '', '', '25'], ['', '', '53', '']]", 4, 13, 54]
["[['', '46', '', '22'], ['', '', '36', '15'], ['47', '', '', '25'], ['', '', '53', '']]", 13, 54, [1, 3], [1, 3], [146, 168], [118, 120], 91]
["[['', '46', '', '22'], ['', '', '36', '15'], ['47', '', '', '25'], ['', '', '53', '']]", "13", "54", "[None, 146, 168, None]", "[None, 118, 120, None]", "91"]
79
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[0, 11], [7, 11], [2, 9], [2, 9], [4, 9], [7, 9], [7, 1], [7, 3], [7, 9], [7, 11], [7, 1], [4, 7], [4, 3], [4, 11], [4, 7], [4, 1], [4, 11], [5, 4], [5, 3], [2, 7], [2, 3], [2, 8], [2, 7], [2, 7], [5, 2], [5, 1], [5, 2], [5, 9], [10, 2], [10, 3], [10, 2], [10, 7], [10, 1], [10, 2], [5, 3], [0, 5], [0, 5], [0, 5], [0, ...
172
1.1443188190460205
44
132
42
[[["Red", "Pink", "Pink", "Pink", "Red", "Black", "Pink"], [], ["Green", "Green", "Blue", "White", "Yellow", "Blue", "Blue"], [], ["Green", "Blue", "White", "Red", "Blue", "Black", "Red"], ["Pink", "White", "Yellow", "Black", "Yellow", "Green", "White"], [], ["Red", "Green", "Black", "White", "Green", "Red", "Black"], ...
[[["Red", "Pink", "Pink", "Pink", "Red", "Black", "Pink"], [], ["Green", "Green", "Blue", "White", "Yellow", "Blue", "Blue"], [], ["Green", "Blue", "White", "Red", "Blue", "Black", "Red"], ["Pink", "White", "Yellow", "Black", "Yellow", "Green", "White"], [], ["Red", "Green", "Black", "White", "Green", "Red", "Black"], ...
["[['Red', 'Pink', 'Pink', 'Pink', 'Red', 'Black', 'Pink'], [], ['Green', 'Green', 'Blue', 'White', 'Yellow', 'Blue', 'Blue'], [], ['Green', 'Blue', 'White', 'Red', 'Blue', 'Black', 'Red'], ['Pink', 'White', 'Yellow', 'Black', 'Yellow', 'Green', 'White'], [], ['Red', 'Green', 'Black', 'White', 'Green', 'Red', 'Black'],...
79
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (4, 12) to his destination workshop at index (7, 0), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[4, 12], [5, 12], [5, 11], [5, 10], [6, 10], [6, 9], [7, 9], [7, 8], [7, 7], [7, 6], [7, 5], [7, 4], [7, 3], [7, 2], [7, 1], [7, 0]]
142
0.02055048942565918
16
4
4
[[["x", "x", "17", "7", "x", "x", "11", "4", "5", "15", "17", "6", "6", "2"], ["17", "x", "x", "6", "x", "x", "x", "x", "1", "8", "x", "x", "x", "7"], ["x", "x", "x", "17", "4", "10", "6", "4", "x", "8", "16", "11", "x", "x"], ["x", "4", "x", "x", "10", "x", "8", "10", "x", "11", "x", "x", "1", "x"], ["x", "x", "11", "...
[[["x", "x", "17", "7", "x", "x", "11", "4", "5", "15", "17", "6", "6", "2"], ["17", "x", "x", "6", "x", "x", "x", "x", "1", "8", "x", "x", "x", "7"], ["x", "x", "x", "17", "4", "10", "6", "4", "x", "8", "16", "11", "x", "x"], ["x", "4", "x", "x", "10", "x", "8", "10", "x", "11", "x", "x", "1", "x"], ["x", "x", "11", "...
["[['x', 'x', '17', '7', 'x', 'x', '11', '4', '5', '15', '17', '6', '6', '2'], ['17', 'x', 'x', '6', 'x', 'x', 'x', 'x', '1', '8', 'x', 'x', 'x', '7'], ['x', 'x', 'x', '17', '4', '10', '6', '4', 'x', '8', '16', '11', 'x', 'x'], ['x', '4', 'x', 'x', '10', 'x', '8', '10', 'x', '11', 'x', 'x', '1', 'x'], ['x', 'x', '11', ...
79
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[10, 10], [9, 10], [8, 10], [7, 10], [6, 10], [5, 10], [4, 9], [3, 8], [2, 7], [2, 6], [2, 5], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]
16
0.03317451477050781
16
8
2
["[[0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1,...
["[[0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1,...
["[[0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1,...
79
Given 7 labeled water jugs with capacities 99, 47, 122, 123, 72, 136, 51, 71 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 274, 292, 361, 438 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed the a...
water_jug
subset_sum
6
[["+", 122, 4], ["+", 122, 4], ["+", 71, 4], ["+", 123, 4], ["+", 51, 3], ["+", 51, 3], ["+", 123, 3], ["+", 136, 3], ["+", 122, 2], ["+", 123, 2], ["+", 47, 2], ["+", 99, 1], ["+", 99, 1], ["-", 47, 1], ["+", 123, 1]]
15
0.051012516021728516
15
64
3
[[99, 47, 122, 123, 72, 136, 51, 71], [274, 292, 361, 438]]
[[99, 47, 122, 123, 72, 136, 51, 71], [274, 292, 361, 438]]
["[99, 47, 122, 123, 72, 136, 51, 71]", "[274, 292, 361, 438]"]
80
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
7
[9, 67, 66, 27, 14, 50, 92, 38, 18, 65, 52, 92, 38, 52, 92, 14, 50, 38, 14, 9, 78, 92, 52, 14, 9, 50, 38, 6]
28
0.24241900444030762
28
4
15
[[[97, 78, "_", 9, 67], [18, 65, 52, 27, 66], [38, 92, 50, 14, 6]]]
[[[97, 78, "_", 9, 67], [18, 65, 52, 27, 66], [38, 92, 50, 14, 6]]]
["[[97, 78, '_', 9, 67], [18, 65, 52, 27, 66], [38, 92, 50, 14, 6]]"]
80
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-right", "up-right", "down-right", "up-right", "up-left", "up-left", "down-left", "down-left", "down-right", "down-right", "up-right", "up-right", "up-left", "up-left", "down-left", "up-left"]
16
0.22876906394958496
16
4
25
[[["d", "w", "p", "l", "t"], ["e", "i", "d", "e", "c"], ["_", "q", "e", "i", "r"], ["m", "e", "c", "u", "r"], ["y", "u", "a", "t", "a"]]]
[[["d", "w", "p", "l", "t"], ["e", "i", "d", "e", "c"], ["_", "q", "e", "i", "r"], ["m", "e", "c", "u", "r"], ["y", "u", "a", "t", "a"]], ["welt", "eddic", "equip", "macer", "yurta"]]
["[['d', 'w', 'p', 'l', 't'], ['e', 'i', 'd', 'e', 'c'], ['_', 'q', 'e', 'i', 'r'], ['m', 'e', 'c', 'u', 'r'], ['y', 'u', 'a', 't', 'a']]", "['welt', 'eddic', 'equip', 'macer', 'yurta']"]
80
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
14
["Y", "P", "M", "T", "B", "S", "M", "W", "B"]
9
0.04214882850646973
9
14
17
[[[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, ...
[[[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, ...
["[[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0,...
80
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [8, 7, 5, 24, 3, 18, 36, 39, 36, 25, 25, 33, 16, 20, 34, 9, 1, 22, 25, 13, 8, 37, 35, 39, 11, 26, 36, 25, 25, 27, 2, 4, 35, 2, 16, 22, 12, 15, 19, 2, 17, 25, 28, 12, 26, 17, 33, 5, 30, 3, 21, 3], such that the sum of the c...
coin_exchange
subset_sum
31
[5, 33, 33, 39, 8, 39, 36, 8, 15, 35, 35, 37, 36, 34, 4]
58
0.06058311462402344
15
52
52
[[8, 7, 5, 24, 3, 18, 36, 39, 36, 25, 25, 33, 16, 20, 34, 9, 1, 22, 25, 13, 8, 37, 35, 39, 11, 26, 36, 25, 25, 27, 2, 4, 35, 2, 16, 22, 12, 15, 19, 2, 17, 25, 28, 12, 26, 17, 33, 5, 30, 3, 21, 3]]
[[8, 7, 5, 24, 3, 18, 36, 39, 36, 25, 25, 33, 16, 20, 34, 9, 1, 22, 25, 13, 8, 37, 35, 39, 11, 26, 36, 25, 25, 27, 2, 4, 35, 2, 16, 22, 12, 15, 19, 2, 17, 25, 28, 12, 26, 17, 33, 5, 30, 3, 21, 3], {"13": 7, "39": 4, "20": 18, "5": 1, "12": 7, "9": 5, "28": 20, "24": 11, "3": 3, "17": 3, "21": 9, "37": 6, "16": 8, "15":...
["[8, 7, 5, 24, 3, 18, 36, 39, 36, 25, 25, 33, 16, 20, 34, 9, 1, 22, 25, 13, 8, 37, 35, 39, 11, 26, 36, 25, 25, 27, 2, 4, 35, 2, 16, 22, 12, 15, 19, 2, 17, 25, 28, 12, 26, 17, 33, 5, 30, 3, 21, 3]", "{13: 7, 39: 4, 20: 18, 5: 1, 12: 7, 9: 5, 28: 20, 24: 11, 3: 3, 17: 3, 21: 9, 37: 6, 16: 8, 15: 1, 26: 10, 36: 6, 22: 9,...
80
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[0, 1], [2, 1], [2, 1], [0, 2], [0, 2], [1, 2], [0, 1], [0, 2], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 1], [0, 1]]
24
30.166829586029053
24
6
18
[[["Blue", "Red", "Blue", "Green", "Blue", "Green"], ["Green", "Green", "Green", "Blue", "Blue", "Red"], ["Green", "Blue", "Red", "Red", "Red", "Red"]], 9]
[[["Blue", "Red", "Blue", "Green", "Blue", "Green"], ["Green", "Green", "Green", "Blue", "Blue", "Red"], ["Green", "Blue", "Red", "Red", "Red", "Red"]], 9]
["[['Blue', 'Red', 'Blue', 'Green', 'Blue', 'Green'], ['Green', 'Green', 'Green', 'Blue', 'Blue', 'Red'], ['Green', 'Blue', 'Red', 'Red', 'Red', 'Red']]", "9"]
80
We have a 4x4 numerical grid, with numbers ranging from 22 to 72 (22 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 > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
12
[[0, 0, 10], [1, 0, 11], [1, 1, 16], [1, 2, 19], [2, 0, 12], [2, 1, 15], [2, 2, 18], [3, 0, 13], [3, 1, 14], [3, 2, 17]]
423
58.67084217071533
10
50
16
["[['', '33', '34', '47'], ['', '', '', '50'], ['', '', '', '52'], ['', '', '', '53']]", 10, 60]
["[['', '33', '34', '47'], ['', '', '', '50'], ['', '', '', '52'], ['', '', '', '53']]", 10, 60]
["[['', '33', '34', '47'], ['', '', '', '50'], ['', '', '', '52'], ['', '', '', '53']]", "10", "60"]
80
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 76. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 247, 236, None for columns 1 to 2 respectively, and the sums of rows must be None, 231, 259, None for rows 1 to...
magic_square
underdetermined_system
8
[[0, 0, 35], [0, 1, 36], [0, 2, 46], [1, 1, 66], [1, 2, 43], [1, 3, 50], [2, 2, 74], [2, 3, 52], [3, 2, 73], [3, 3, 37]]
913
48.18892478942871
10
31
16
["[['', '', '', '60'], ['72', '', '', ''], ['63', '70', '', ''], ['61', '75', '', '']]", 4, 35, 76]
["[['', '', '', '60'], ['72', '', '', ''], ['63', '70', '', ''], ['61', '75', '', '']]", 35, 76, [1, 3], [1, 3], [247, 236], [231, 259], 234]
["[['', '', '', '60'], ['72', '', '', ''], ['63', '70', '', ''], ['61', '75', '', '']]", "35", "76", "[None, 247, 236, None]", "[None, 231, 259, None]", "234"]
80
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[1, 8], [1, 2], [1, 6], [10, 7], [4, 8], [4, 7], [4, 8], [4, 8], [0, 2], [0, 2], [0, 8], [11, 6], [11, 6], [11, 7], [11, 2], [0, 9], [0, 7], [0, 7], [1, 3], [1, 9], [4, 1], [10, 1], [11, 1], [11, 6], [11, 8], [10, 11], [10, 11], [10, 7], [10, 6], [5, 10], [5, 10], [5, 10], [5, 1], [5, 2], [5, 11], [0, 2], [3, 11], [4,...
238
2.470271110534668
42
132
42
[[["Yellow", "Yellow", "Pink", "Black", "Green", "Green", "Yellow"], ["Pink", "Yellow", "White", "Red", "Black", "Blue", "Blue"], [], [], ["Pink", "Green", "Pink", "Pink", "Blue", "Red", "Red"], ["Black", "Black", "Black", "Blue", "Yellow", "Red", "White"], [], [], [], [], ["Green", "Blue", "Red", "Red", "Green", "Whit...
[[["Yellow", "Yellow", "Pink", "Black", "Green", "Green", "Yellow"], ["Pink", "Yellow", "White", "Red", "Black", "Blue", "Blue"], [], [], ["Pink", "Green", "Pink", "Pink", "Blue", "Red", "Red"], ["Black", "Black", "Black", "Blue", "Yellow", "Red", "White"], [], [], [], [], ["Green", "Blue", "Red", "Red", "Green", "Whit...
["[['Yellow', 'Yellow', 'Pink', 'Black', 'Green', 'Green', 'Yellow'], ['Pink', 'Yellow', 'White', 'Red', 'Black', 'Blue', 'Blue'], [], [], ['Pink', 'Green', 'Pink', 'Pink', 'Blue', 'Red', 'Red'], ['Black', 'Black', 'Black', 'Blue', 'Yellow', 'Red', 'White'], [], [], [], [], ['Green', 'Blue', 'Red', 'Red', 'Green', 'Whi...
80
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, 10) to his destination workshop at index (7, 2), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[1, 10], [1, 9], [2, 9], [3, 9], [4, 9], [4, 8], [4, 7], [3, 7], [3, 6], [3, 5], [3, 4], [4, 4], [5, 4], [5, 3], [6, 3], [6, 2], [7, 2]]
135
0.02765035629272461
17
4
4
[[["x", "x", "8", "16", "3", "x", "15", "17", "2", "x", "x", "5", "x", "x"], ["x", "x", "17", "x", "13", "x", "4", "x", "13", "3", "3", "6", "11", "x"], ["x", "x", "8", "x", "14", "1", "15", "11", "x", "18", "12", "x", "x", "x"], ["x", "13", "19", "4", "13", "2", "13", "3", "x", "1", "20", "18", "x", "15"], ["13", "x",...
[[["x", "x", "8", "16", "3", "x", "15", "17", "2", "x", "x", "5", "x", "x"], ["x", "x", "17", "x", "13", "x", "4", "x", "13", "3", "3", "6", "11", "x"], ["x", "x", "8", "x", "14", "1", "15", "11", "x", "18", "12", "x", "x", "x"], ["x", "13", "19", "4", "13", "2", "13", "3", "x", "1", "20", "18", "x", "15"], ["13", "x",...
["[['x', 'x', '8', '16', '3', 'x', '15', '17', '2', 'x', 'x', '5', 'x', 'x'], ['x', 'x', '17', 'x', '13', 'x', '4', 'x', '13', '3', '3', '6', '11', 'x'], ['x', 'x', '8', 'x', '14', '1', '15', '11', 'x', '18', '12', 'x', 'x', 'x'], ['x', '13', '19', '4', '13', '2', '13', '3', 'x', '1', '20', '18', 'x', '15'], ['13', 'x'...
80
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[7, 13], [8, 12], [9, 12], [10, 12], [11, 11], [12, 10], [12, 9], [13, 8], [13, 7], [13, 6], [13, 5], [13, 4], [13, 3], [13, 2], [13, 1], [13, 0]]
16
0.029587268829345703
16
8
2
["[[1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 1, 1,...
["[[1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 1, 1,...
["[[1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0], [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 1, 1,...
80
Given 7 labeled water jugs with capacities 110, 146, 117, 118, 148, 104, 79, 103 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 278, 378, 457, 462 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed t...
water_jug
subset_sum
6
[["+", 117, 4], ["+", 118, 4], ["+", 79, 4], ["+", 148, 4], ["+", 103, 3], ["+", 103, 3], ["+", 103, 3], ["+", 148, 3], ["+", 79, 2], ["+", 79, 2], ["+", 103, 2], ["+", 117, 2], ["+", 103, 1], ["+", 146, 1], ["-", 117, 1], ["+", 146, 1]]
16
0.0686345100402832
16
64
3
[[110, 146, 117, 118, 148, 104, 79, 103], [278, 378, 457, 462]]
[[110, 146, 117, 118, 148, 104, 79, 103], [278, 378, 457, 462]]
["[110, 146, 117, 118, 148, 104, 79, 103]", "[278, 378, 457, 462]"]
81
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
7
[72, 65, 49, 22, 26, 13, 52, 53, 65, 72, 76, 12, 61, 89, 64, 26, 22, 76, 12, 61, 89, 97, 61, 89, 97, 64, 26, 22, 13, 49, 53, 65, 72, 12, 76, 53, 12, 72, 65, 52, 49, 12, 52, 49]
44
85.10252380371094
44
4
15
[[[12, 76, "_", 72, 53], [61, 97, 49, 65, 52], [89, 64, 22, 26, 13]]]
[[[12, 76, "_", 72, 53], [61, 97, 49, 65, 52], [89, 64, 22, 26, 13]]]
["[[12, 76, '_', 72, 53], [61, 97, 49, 65, 52], [89, 64, 22, 26, 13]]"]
81
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["up-left", "up-right", "up-left", "down-left", "down-right", "down-left", "up-left", "up-right", "down-right", "up-right", "up-left", "down-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "up-left", "up-right", "up-left"]
24
1.593846082687378
24
4
25
[[["e", "c", "o", "r", "e"], ["r", "e", "u", "t", "l"], ["r", "i", "i", "c", "i"], ["k", "n", "z", "e", "l"], ["i", "z", "h", "l", "_"]]]
[[["e", "c", "o", "r", "e"], ["r", "e", "u", "t", "l"], ["r", "i", "i", "c", "i"], ["k", "n", "z", "e", "l"], ["i", "z", "h", "l", "_"]], ["core", "reuel", "rinch", "kizil", "iztle"]]
["[['e', 'c', 'o', 'r', 'e'], ['r', 'e', 'u', 't', 'l'], ['r', 'i', 'i', 'c', 'i'], ['k', 'n', 'z', 'e', 'l'], ['i', 'z', 'h', 'l', '_']]", "['core', 'reuel', 'rinch', 'kizil', 'iztle']"]
81
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
14
["U", "C", "J", "L", "G", "H", "T", "H", "D", "L"]
10
0.050522565841674805
10
14
17
[[[0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 1, 1, ...
[[[0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 1, 1, ...
["[[0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 1, 1,...
81
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [13, 30, 19, 13, 34, 12, 16, 21, 24, 39, 37, 32, 3, 5, 30, 37, 29, 20, 15, 23, 30, 24, 12, 21, 19, 10, 26, 29, 3, 23, 20, 40, 22, 13, 2, 36, 8, 40, 6, 24, 24, 11, 26, 37, 16, 57, 39, 21, 17], such that the sum of the chose...
coin_exchange
subset_sum
32
[17, 39, 26, 20, 39, 22, 20, 21, 37, 37, 37, 34, 32, 26, 2, 3]
59
0.06411933898925781
16
49
49
[[13, 30, 19, 13, 34, 12, 16, 21, 24, 39, 37, 32, 3, 5, 30, 37, 29, 20, 15, 23, 30, 24, 12, 21, 19, 10, 26, 29, 3, 23, 20, 40, 22, 13, 2, 36, 8, 40, 6, 24, 24, 11, 26, 37, 16, 57, 39, 21, 17]]
[[13, 30, 19, 13, 34, 12, 16, 21, 24, 39, 37, 32, 3, 5, 30, 37, 29, 20, 15, 23, 30, 24, 12, 21, 19, 10, 26, 29, 3, 23, 20, 40, 22, 13, 2, 36, 8, 40, 6, 24, 24, 11, 26, 37, 16, 57, 39, 21, 17], {"2": 2, "21": 6, "24": 9, "26": 2, "5": 3, "29": 10, "10": 7, "13": 13, "30": 17, "36": 15, "3": 1, "32": 7, "8": 5, "20": 2, ...
["[13, 30, 19, 13, 34, 12, 16, 21, 24, 39, 37, 32, 3, 5, 30, 37, 29, 20, 15, 23, 30, 24, 12, 21, 19, 10, 26, 29, 3, 23, 20, 40, 22, 13, 2, 36, 8, 40, 6, 24, 24, 11, 26, 37, 16, 57, 39, 21, 17]", "{2: 2, 21: 6, 24: 9, 26: 2, 5: 3, 29: 10, 10: 7, 13: 13, 30: 17, 36: 15, 3: 1, 32: 7, 8: 5, 20: 2, 22: 3, 57: 19, 40: 8, 6: ...
81
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[0, 1], [2, 0], [2, 0], [2, 0], [2, 1], [2, 0], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 2], [1, 0], [1, 2], [1, 0], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 1]]
31
517.1900751590729
31
6
18
[[["Green", "Red", "Red", "Red", "Green", "Green"], ["Green", "Red", "Red", "Blue", "Red", "Blue"], ["Blue", "Blue", "Blue", "Green", "Blue", "Green"]], 9]
[[["Green", "Red", "Red", "Red", "Green", "Green"], ["Green", "Red", "Red", "Blue", "Red", "Blue"], ["Blue", "Blue", "Blue", "Green", "Blue", "Green"]], 9]
["[['Green', 'Red', 'Red', 'Red', 'Green', 'Green'], ['Green', 'Red', 'Red', 'Blue', 'Red', 'Blue'], ['Blue', 'Blue', 'Blue', 'Green', 'Blue', 'Green']]", "9"]
81
We have a 4x4 numerical grid, with numbers ranging from 37 to 87 (37 included in the range but 87 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
12
[[0, 0, 10], [0, 2, 34], [0, 3, 52], [1, 2, 32], [2, 2, 30], [2, 3, 31]]
342
11.79056978225708
6
50
16
["[['', '21', '', ''], ['18', '27', '', '51'], ['24', '29', '', ''], ['54', '33', '25', '12']]", 10, 65]
["[['', '21', '', ''], ['18', '27', '', '51'], ['24', '29', '', ''], ['54', '33', '25', '12']]", 10, 65]
["[['', '21', '', ''], ['18', '27', '', '51'], ['24', '29', '', ''], ['54', '33', '25', '12']]", "10", "65"]
81
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 76. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 188, 234, None for columns 1 to 2 respectively, and the sums of rows must be None, 247, 238, None for rows 1 to...
magic_square
underdetermined_system
9
[[0, 1, 35], [0, 3, 37], [1, 0, 39], [1, 1, 71], [1, 2, 75], [1, 3, 62], [2, 3, 73], [3, 0, 63], [3, 2, 52], [3, 3, 36]]
861
137.55204916000366
10
31
16
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", 4, 35, 76]
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", 35, 76, [1, 3], [1, 3], [188, 234], [247, 238], 215]
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", "35", "76", "[None, 188, 234, None]", "[None, 247, 238, None]", "215"]
81
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[1, 0], [2, 8], [5, 0], [2, 7], [5, 7], [3, 11], [4, 10], [1, 8], [1, 11], [1, 8], [1, 6], [1, 10], [5, 1], [4, 1], [4, 7], [4, 1], [2, 11], [2, 0], [2, 11], [2, 8], [3, 0], [3, 2], [3, 0], [3, 0], [3, 8], [5, 3], [5, 3], [5, 1], [4, 5], [4, 11], [9, 7], [9, 1], [9, 7], [9, 3], [9, 7], [9, 2], [9, 11], [4, 8], [10, 3]...
260
34.757015228271484
43
132
42
[[[], ["White", "Black", "Yellow", "Black", "Green", "Blue", "Pink"], ["Black", "Red", "Yellow", "White", "Yellow", "Black", "Green"], ["Yellow", "White", "Green", "White", "White", "Black", "Blue"], ["Blue", "Pink", "Red", "Pink", "Green", "Yellow", "Black"], ["White", "Red", "Pink", "Blue", "Blue", "Pink", "Green"], ...
[[[], ["White", "Black", "Yellow", "Black", "Green", "Blue", "Pink"], ["Black", "Red", "Yellow", "White", "Yellow", "Black", "Green"], ["Yellow", "White", "Green", "White", "White", "Black", "Blue"], ["Blue", "Pink", "Red", "Pink", "Green", "Yellow", "Black"], ["White", "Red", "Pink", "Blue", "Blue", "Pink", "Green"], ...
["[[], ['White', 'Black', 'Yellow', 'Black', 'Green', 'Blue', 'Pink'], ['Black', 'Red', 'Yellow', 'White', 'Yellow', 'Black', 'Green'], ['Yellow', 'White', 'Green', 'White', 'White', 'Black', 'Blue'], ['Blue', 'Pink', 'Red', 'Pink', 'Green', 'Yellow', 'Black'], ['White', 'Red', 'Pink', 'Blue', 'Blue', 'Pink', 'Green'],...
81
Using the provided matrix map of a city, where numbers represent travel time in minutes (all numbers are positive integers) and 'x' marks closed workshops, find the quickest route for Ben to travel from his current workshop at index (2, 0) to his destination workshop at index (6, 11), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[2, 0], [1, 0], [0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [1, 5], [2, 5], [2, 6], [3, 6], [4, 6], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [6, 10], [6, 11]]
180
0.027744293212890625
20
4
4
[[["8", "15", "3", "10", "6", "15", "x", "4", "x", "x", "x", "x", "x", "4"], ["3", "x", "14", "8", "16", "19", "x", "18", "4", "x", "2", "x", "6", "x"], ["18", "18", "x", "4", "x", "17", "11", "10", "17", "9", "x", "4", "1", "5"], ["x", "2", "x", "12", "1", "x", "13", "17", "14", "15", "17", "x", "15", "x"], ["x", "x",...
[[["8", "15", "3", "10", "6", "15", "x", "4", "x", "x", "x", "x", "x", "4"], ["3", "x", "14", "8", "16", "19", "x", "18", "4", "x", "2", "x", "6", "x"], ["18", "18", "x", "4", "x", "17", "11", "10", "17", "9", "x", "4", "1", "5"], ["x", "2", "x", "12", "1", "x", "13", "17", "14", "15", "17", "x", "15", "x"], ["x", "x",...
["[['8', '15', '3', '10', '6', '15', 'x', '4', 'x', 'x', 'x', 'x', 'x', '4'], ['3', 'x', '14', '8', '16', '19', 'x', '18', '4', 'x', '2', 'x', '6', 'x'], ['18', '18', 'x', '4', 'x', '17', '11', '10', '17', '9', 'x', '4', '1', '5'], ['x', '2', 'x', '12', '1', 'x', '13', '17', '14', '15', '17', 'x', '15', 'x'], ['x', 'x'...
81
Alex is at a trampoline park with a grid of mini trampolines, arranged in a square of 14x14. 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
14
[[11, 12], [11, 11], [11, 10], [10, 9], [9, 8], [8, 7], [7, 6], [7, 5], [6, 5], [6, 4], [5, 4], [5, 3], [4, 3], [4, 2], [3, 2], [3, 1]]
16
0.025336027145385742
16
8
2
["[[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0,...
["[[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0,...
["[[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0], [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1], [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0,...
81
Given 7 labeled water jugs with capacities 127, 96, 108, 126, 132, 139, 146, 14 liters, we aim to fill 4 unlabeled buckets, numbered 1 to 4 and arranged in a line in ascending order, with 273, 349, 435, 503 liters of water respectively. The amount of water in each unlabeled bucket can not at any point in time exceed th...
water_jug
subset_sum
6
[["+", 96, 4], ["+", 108, 4], ["+", 139, 4], ["+", 146, 4], ["+", 14, 4], ["+", 139, 3], ["+", 146, 3], ["+", 126, 3], ["-", 108, 3], ["+", 132, 3], ["+", 96, 2], ["+", 126, 2], ["+", 127, 2], ["+", 127, 1], ["+", 146, 1]]
15
0.04054760932922363
15
64
3
[[127, 96, 108, 126, 132, 139, 146, 14], [273, 349, 435, 503]]
[[127, 96, 108, 126, 132, 139, 146, 14], [273, 349, 435, 503]]
["[127, 96, 108, 126, 132, 139, 146, 14]", "[273, 349, 435, 503]"]
82
In the 8-puzzle game, you are given a grid with numbered square tiles arranged randomly and one tile missing. The goal is to arrange the tiles in descending order by sliding them into the empty space. The tiles can move in 4 directions: left, right, up, and down. Given the initial state of the puzzle below, where the ...
8_puzzle
puzzle
7
[87, 60, 70, 88, 51, 85, 84, 27, 64, 43, 60, 87, 43, 64, 39, 51, 85, 84, 30, 47, 27, 30, 51, 60, 87, 70, 88, 87, 64, 39, 30, 27]
32
0.7831065654754639
32
4
15
[[[60, 70, 88, 51, 72], [87, 43, 39, 85, 30], ["_", 64, 27, 84, 47]]]
[[[60, 70, 88, 51, 72], [87, 43, 39, 85, 30], ["_", 64, 27, 84, 47]]]
["[[60, 70, 88, 51, 72], [87, 43, 39, 85, 30], ['_', 64, 27, 84, 47]]"]
82
In the game 'Sort the Chars', we are given a table of n by m dimensions. This table contains n words, each with m characters, except for the first word which has m - 1 characters. Each character is written on a separate tile. The objective of the game is to rearrange the characters such that row i spells the i-th word ...
8_puzzle_words
puzzle
3
["down-left", "down-right", "up-right", "up-left", "up-left", "down-left", "down-right", "down-right", "up-right", "up-right", "up-left", "down-left", "down-left", "down-right", "up-right", "up-left", "up-left", "up-left"]
18
0.7136387825012207
18
4
25
[[["i", "e", "k", "k", "a"], ["b", "e", "f", "a", "r"], ["g", "a", "_", "m", "e"], ["d", "i", "n", "k", "a"], ["b", "r", "m", "t", "t"]]]
[[["i", "e", "k", "k", "a"], ["b", "e", "f", "a", "r"], ["g", "a", "_", "m", "e"], ["d", "i", "n", "k", "a"], ["b", "r", "m", "t", "t"]], ["ekka", "bifer", "magma", "dinka", "brett"]]
["[['i', 'e', 'k', 'k', 'a'], ['b', 'e', 'f', 'a', 'r'], ['g', 'a', '_', 'm', 'e'], ['d', 'i', 'n', 'k', 'a'], ['b', 'r', 'm', 't', 't']]", "['ekka', 'bifer', 'magma', 'dinka', 'brett']"]
82
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
14
["J", "C", "L", "U", "L", "N", "F", "K", "F"]
9
0.11440420150756836
9
14
17
[[[0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, ...
[[[0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, ...
["[[0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1,...
82
In the 'taxed coin exchange' problem, you are required to choose a subset of coins from this list [7, 2, 20, 24, 9, 24, 29, 6, 32, 26, 17, 61, 33, 14, 12, 20, 15, 34, 60, 18, 18, 37, 25, 9, 9, 21, 24, 30, 28, 3, 21, 32, 13, 10, 4, 2, 33, 36, 13, 24, 27, 7, 21, 4, 8, 17, 22, 3, 21, 12], such that the sum of the chosen c...
coin_exchange
subset_sum
33
[24, 10, 21, 21, 21, 29, 24, 33, 24, 33, 24, 61, 60, 4]
69
0.05933260917663574
14
50
50
[[7, 2, 20, 24, 9, 24, 29, 6, 32, 26, 17, 61, 33, 14, 12, 20, 15, 34, 60, 18, 18, 37, 25, 9, 9, 21, 24, 30, 28, 3, 21, 32, 13, 10, 4, 2, 33, 36, 13, 24, 27, 7, 21, 4, 8, 17, 22, 3, 21, 12]]
[[7, 2, 20, 24, 9, 24, 29, 6, 32, 26, 17, 61, 33, 14, 12, 20, 15, 34, 60, 18, 18, 37, 25, 9, 9, 21, 24, 30, 28, 3, 21, 32, 13, 10, 4, 2, 33, 36, 13, 24, 27, 7, 21, 4, 8, 17, 22, 3, 21, 12], {"28": 10, "36": 13, "18": 13, "17": 8, "24": 3, "37": 19, "60": 16, "13": 5, "14": 8, "30": 18, "20": 5, "27": 16, "26": 11, "2":...
["[7, 2, 20, 24, 9, 24, 29, 6, 32, 26, 17, 61, 33, 14, 12, 20, 15, 34, 60, 18, 18, 37, 25, 9, 9, 21, 24, 30, 28, 3, 21, 32, 13, 10, 4, 2, 33, 36, 13, 24, 27, 7, 21, 4, 8, 17, 22, 3, 21, 12]", "{28: 10, 36: 13, 18: 13, 17: 8, 24: 3, 37: 19, 60: 16, 13: 5, 14: 8, 30: 18, 20: 5, 27: 16, 26: 11, 2: 2, 21: 3, 7: 7, 8: 6, 3:...
82
The game of 'Sort It' begins with 3 tubes, each filled with 6 balls of different colors. The goal is to sort the balls by color, with each tube containing balls of only one color. Only one ball can be moved at a time, taken from the top of one tube and placed on top of another. The capacity of each tube (maximum number...
color_sorting
sorting
10
[[2, 0], [1, 2], [1, 2], [0, 2], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1], [2, 0], [2, 1], [2, 1], [2, 1], [0, 2], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2], [0, 2], [1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0], [2, 1], [2, 1], [2, 1]]
30
488.8873255252838
30
6
18
[[["Red", "Green", "Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Red", "Blue", "Blue"], ["Blue", "Red", "Green", "Blue", "Green", "Red"]], 9]
[[["Red", "Green", "Red", "Blue", "Blue", "Green"], ["Green", "Green", "Red", "Red", "Blue", "Blue"], ["Blue", "Red", "Green", "Blue", "Green", "Red"]], 9]
["[['Red', 'Green', 'Red', 'Blue', 'Blue', 'Green'], ['Green', 'Green', 'Red', 'Red', 'Blue', 'Blue'], ['Blue', 'Red', 'Green', 'Blue', 'Green', 'Red']]", "9"]
82
We have a 4x4 numerical grid, with numbers ranging from 14 to 64 (14 included in the range but 64 is not included). The numbers in each row and column must be strictly increasing or decreasing. This means that either first > second > third > fourth or first < second < third < fourth in each row and column. If a grid ce...
consecutive_grid
underdetermined_system
13
[[0, 3, 31], [1, 0, 43], [1, 1, 60], [2, 0, 42], [2, 2, 67], [2, 3, 71]]
796
63.96863031387329
6
50
16
["[['85', '73', '59', ''], ['', '', '66', '70'], ['', '59', '', ''], ['40', '41', '79', '82']]", 31, 86]
["[['85', '73', '59', ''], ['', '', '66', '70'], ['', '59', '', ''], ['40', '41', '79', '82']]", 31, 86]
["[['85', '73', '59', ''], ['', '', '66', '70'], ['', '59', '', ''], ['40', '41', '79', '82']]", "31", "86"]
82
In the magic square problem, a 4x4 grid is filled with unique integers ranging from 35 to 76. Some numbers are already given, while others are unknown and represented as 'x'. The sums of columns must be None, 188, 234, None for columns 1 to 2 respectively, and the sums of rows must be None, 247, 238, None for rows 1 to...
magic_square
underdetermined_system
9
[[0, 1, 35], [0, 3, 37], [1, 0, 39], [1, 1, 71], [1, 2, 75], [1, 3, 62], [2, 3, 73], [3, 0, 63], [3, 2, 52], [3, 3, 36]]
861
137.55204916000366
10
31
16
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", 4, 35, 76]
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", 35, 76, [1, 3], [1, 3], [188, 234], [247, 238], 215]
["[['61', '', '50', ''], ['', '', '', ''], ['68', '40', '57', ''], ['', '42', '', '']]", "35", "76", "[None, 188, 234, None]", "[None, 247, 238, None]", "215"]
82
In 'Restricted Sorting', there are 12 stacks each with a capacity of 7 blocks, with 6 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 6 blocks of a single shade. The player can only transfer one b...
restricted_sorting
sorting
4
[[3, 4], [7, 4], [0, 10], [7, 10], [0, 11], [0, 4], [0, 11], [5, 9], [5, 10], [6, 9], [7, 9], [6, 8], [6, 8], [6, 11], [6, 10], [6, 9], [6, 11], [2, 6], [7, 6], [7, 6], [7, 4], [2, 8], [2, 7], [3, 10], [3, 9], [3, 7], [3, 11], [2, 4], [2, 8], [2, 4], [3, 1], [5, 7], [5, 7], [5, 7], [5, 11], [0, 6], [0, 8], [5, 8], [2, ...
332
7.222944021224976
42
132
42
[[["Red", "Black", "Yellow", "Black", "White", "Blue", "White"], [], ["White", "Blue", "Green", "Yellow", "Blue", "Yellow", "Pink"], ["Yellow", "Red", "Pink", "Green", "Black", "Red", "White"], [], ["Pink", "Red", "Green", "Green", "Green", "Black", "Blue"], ["Pink", "Blue", "Blue", "Black", "Red", "Pink", "Black"], ["...
[[["Red", "Black", "Yellow", "Black", "White", "Blue", "White"], [], ["White", "Blue", "Green", "Yellow", "Blue", "Yellow", "Pink"], ["Yellow", "Red", "Pink", "Green", "Black", "Red", "White"], [], ["Pink", "Red", "Green", "Green", "Green", "Black", "Blue"], ["Pink", "Blue", "Blue", "Black", "Red", "Pink", "Black"], ["...
["[['Red', 'Black', 'Yellow', 'Black', 'White', 'Blue', 'White'], [], ['White', 'Blue', 'Green', 'Yellow', 'Blue', 'Yellow', 'Pink'], ['Yellow', 'Red', 'Pink', 'Green', 'Black', 'Red', 'White'], [], ['Pink', 'Red', 'Green', 'Green', 'Green', 'Black', 'Blue'], ['Pink', 'Blue', 'Blue', 'Black', 'Red', 'Pink', 'Black'], [...
82
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, 13) to his destination workshop at index (7, 4), indexing from 0. Ben's car can mov...
traffic
pathfinding
6
[[1, 13], [2, 13], [3, 13], [4, 13], [5, 13], [5, 12], [5, 11], [5, 10], [5, 9], [5, 8], [5, 7], [5, 6], [6, 6], [6, 5], [6, 4], [7, 4]]
125
0.027818918228149414
16
4
4
[[["15", "19", "13", "4", "x", "x", "13", "7", "16", "6", "x", "x", "17", "x"], ["2", "2", "x", "7", "x", "12", "12", "x", "19", "x", "10", "4", "14", "2"], ["11", "x", "x", "3", "7", "x", "7", "x", "x", "6", "x", "19", "x", "1"], ["x", "x", "11", "x", "3", "x", "17", "x", "1", "20", "17", "8", "15", "1"], ["x", "x", "...
[[["15", "19", "13", "4", "x", "x", "13", "7", "16", "6", "x", "x", "17", "x"], ["2", "2", "x", "7", "x", "12", "12", "x", "19", "x", "10", "4", "14", "2"], ["11", "x", "x", "3", "7", "x", "7", "x", "x", "6", "x", "19", "x", "1"], ["x", "x", "11", "x", "3", "x", "17", "x", "1", "20", "17", "8", "15", "1"], ["x", "x", "...
["[['15', '19', '13', '4', 'x', 'x', '13', '7', '16', '6', 'x', 'x', '17', 'x'], ['2', '2', 'x', '7', 'x', '12', '12', 'x', '19', 'x', '10', '4', '14', '2'], ['11', 'x', 'x', '3', '7', 'x', '7', 'x', 'x', '6', 'x', '19', 'x', '1'], ['x', 'x', '11', 'x', '3', 'x', '17', 'x', '1', '20', '17', '8', '15', '1'], ['x', 'x', ...