Dataset Viewer
id
string | original_id
string | family
string | difficulty_level
int64 | source_family
string | source_level
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|---|---|---|---|
omega_500_000
|
arithmetic_matrix_power_level_7_0038
|
arithmetic_matrix_power
| 7 |
arithmetic_matrix_power
|
7
|
[
{
"role": "user",
"content": "For the matrix power A^9 where A =\n[[12, -8, -13, 7, -3, -12, 1, 2, -5, 1, 0, 13],\n [7, -6, 6, 0, -16, -2, 15, -8, -2, 11, 7, 5],\n [10, 2, -5, 3, -16, 4, -16, -7, 15, 5, 1, 15],\n [10, 11, 1, 12, 1, -9, 14, -10, 1, -8, -8, -9],\n [1, -12, -3, 11, 13, -13, 3, 8, 11, -5, -15, -3],\n [5, 14, 6, 3, -13, -2, 7, 8, -16, -10, 14, -5],\n [-12, -5, 1, -15, -7, -2, 13, 0, -13, -10, 14, -11],\n [-2, -3, -11, 15, -14, -14, 5, 5, -7, -14, -5, 12],\n [0, -10, -4, -15, -13, -7, 7, 0, -11, 2, -12, 15],\n [-7, -8, 10, -4, 2, 4, 7, -13, 7, -14, -13, 14],\n [8, -4, -13, -3, -4, 10, -11, 0, 0, -15, -4, -15],\n [11, 9, 5, -14, -5, 7, -12, 3, -4, -5, -4, -7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
441018063982865
|
OMEGA_500_SAMPLE
|
omega_500_001
|
combinatory_probability_exactly_n_specific_fixed_level_3_0009
|
combinatory_probability_exactly_n_specific_fixed
| 3 |
combinatory_probability_exactly_n_specific_fixed
|
3
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, j: 1, v: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
OMEGA_500_SAMPLE
|
omega_500_002
|
logic_puzzles_grid_knight_level_5_0002
|
logic_puzzles_grid_knight
| 5 |
logic_puzzles_grid_knight
|
5
|
[
{
"role": "user",
"content": "Supposing you start in the bottom left (0, 0) cell of a 47x47 grid, what is minimum number of steps you can take to get to (44, 46), if your only valid moves are to move over 5 squares in one direction and over 1 squares in a perpendicular direction (at once)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
OMEGA_500_SAMPLE
|
omega_500_003
|
algebra_func_derivative_sign_level_1_0014
|
algebra_func_derivative_sign
| 1 |
algebra_func_derivative_sign
|
1
|
[
{
"role": "user",
"content": "For the function f(x) = 2sin(1π(-2x + 1) + 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
OMEGA_500_SAMPLE
|
omega_500_004
|
algebra_func_area_level_5_0004
|
algebra_func_area
| 5 |
algebra_func_area
|
5
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|((3((-3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) + 1)))/(1((-3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) + 1)) + 2)) + 2| + 3 and g(x) = 2(-3sin(2π((-1((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) - 2)/(3((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) + 2)) + 3) - 3)^2 - 2(-3sin(2π((-1((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) - 2)/(3((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) + 2)) + 3) - 3) - 2 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.5
|
OMEGA_500_SAMPLE
|
omega_500_005
|
arithmetic_matrix_rank_level_2_0062
|
arithmetic_matrix_rank
| 2 |
arithmetic_matrix_rank
|
2
|
[
{
"role": "user",
"content": "Calculate the rank of matrix A where A =\n[[-4, 26, -43, -1, 6],\n [16, -14, 54, -4, 22],\n [22, 19, 15, -4, 19],\n [-31, -22, -14, -2, 21],\n [-20, -29, 3, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
OMEGA_500_SAMPLE
|
omega_500_006
|
arithmetic_matrix_power_level_2_0048
|
arithmetic_matrix_power
| 2 |
arithmetic_matrix_power
|
2
|
[
{
"role": "user",
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 0, 1],\n [1, -1, -2, -1],\n [-4, -1, -4, -4],\n [1, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
643
|
OMEGA_500_SAMPLE
|
omega_500_007
|
logic_puzzles_blocked_grid_level_4_0050
|
logic_puzzles_blocked_grid
| 4 |
logic_puzzles_blocked_grid
|
4
|
[
{
"role": "user",
"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 20), (23, 22), (12, 15), (21, 24), (29, 20), (22, 35), (22, 17), (30, 11), (14, 10), (27, 17), (28, 16), (21, 7), (24, 28), (3, 25), (27, 30), (13, 13), (1, 27), (15, 8), (18, 17), (8, 14), (15, 33), (8, 8), (24, 9), (13, 3), (24, 5), (8, 27), (18, 10), (0, 20), (8, 26), (1, 2), (15, 35), (0, 13), (7, 2), (29, 34), (30, 35), (22, 11), (14, 36), (23, 4), (18, 9), (13, 6), (5, 0), (13, 23), (26, 21), (7, 14), (17, 26), (26, 16), (5, 27), (21, 0), (18, 30), (30, 27), (3, 9), (27, 1), (16, 3), (28, 28), (0, 9), (2, 29), (8, 29), (2, 3), (26, 24), (20, 29), (8, 10), (29, 28), (16, 29), (5, 5), (17, 0), (0, 11), (13, 36), (2, 36), (27, 4), (23, 33), (16, 37), (30, 13), (21, 8), (2, 17), (25, 21), (10, 23), (18, 23), (18, 16), (23, 19), (9, 0), (27, 37), (17, 14), (19, 33), (20, 28), (8, 17), (6, 12), (6, 17), (0, 19), (11, 2), (10, 9), (10, 16), (6, 8), (29, 2), (12, 4), (14, 34), (20, 24), (25, 4), (27, 8), (7, 36), (2, 20), (16, 23), (1, 30), (28, 32), (17, 21), (14, 0), (7, 0), (13, 5), (17, 36), (29, 29), (0, 17), (15, 27), (25, 8), (1, 16), (9, 20), (12, 17), (9, 29), (21, 6), (7, 32), (4, 35), (0, 35), (30, 28), (15, 21), (18, 33), (20, 13), (15, 31), (10, 30), (28, 27), (19, 36), (4, 3), (20, 2), (28, 12), (24, 30), (7, 8), (17, 20), (26, 0), (21, 28), (5, 12), (7, 20), (26, 27), (0, 36), (12, 0), (8, 9), (27, 33), (25, 30), (9, 19), (19, 5), (21, 3), (20, 18), (0, 33), (23, 29), (6, 30), (25, 27), (14, 12), (6, 1), (20, 3), (6, 9), (10, 8), (4, 36), (8, 7), (1, 14), (18, 7), (12, 33), (12, 21), (19, 30), (28, 25), (23, 25), (28, 7), (6, 31), (25, 5), (24, 15), (5, 15), (20, 21), (12, 13), (6, 37), (15, 20), (12, 23), (13, 20), (2, 33), (5, 13), (5, 3), (3, 21), (4, 4), (9, 3), (14, 30), (3, 5), (27, 29), (23, 20), (21, 12), (19, 21), (20, 16), (11, 12), (14, 5), (11, 24), (20, 23), (11, 26), (18, 34), (30, 19), (3, 20), (3, 35), (30, 22), (16, 15), (4, 6), (8, 4), (11, 31), (19, 4), (10, 36), (30, 9), (3, 37), (21, 13), (18, 15), (4, 20), (1, 31), (21, 17), (9, 6), (2, 14), (13, 35), (29, 4), (12, 11), (1, 9), (14, 33), (19, 18), (30, 10), (3, 7), (8, 30), (5, 30), (26, 5), (6, 24), (20, 10), (25, 20), (16, 22), (5, 19), (12, 2), (5, 33), (26, 20), (15, 0), (2, 0), (19, 37), (13, 26), (17, 27), (8, 33), (9, 5), (14, 29), (30, 4), (14, 15), (26, 9), (5, 16), (20, 36), (14, 28), (16, 13), (18, 5), (10, 32), (20, 31), (5, 24), (25, 25), (5, 22), (29, 33), (1, 17), (21, 4), (24, 32), (30, 24), (13, 2), (11, 16), (22, 26), (1, 25), (27, 20), (27, 9), (28, 21), (20, 25), (9, 30), (5, 34), (23, 6), (26, 37), (3, 34), (11, 20), (28, 10), (12, 37), (29, 13), (16, 9), (7, 5), (9, 28), (30, 21), (2, 18), (19, 7), (10, 13), (6, 21), (19, 1), (28, 24), (29, 23), (10, 22), (27, 36), (19, 12), (7, 35), (18, 2), (22, 21), (4, 8), (4, 19), (23, 1), (29, 32), (21, 30), (12, 19), (30, 25), (25, 16), (16, 1), (6, 35), (22, 20), (24, 14), (3, 8), (24, 35), (1, 5), (15, 16), (12, 24), (16, 35), (10, 20), (28, 0), (12, 28), (16, 11), (2, 2), (26, 12), (11, 30), (23, 27), (30, 14), (3, 23), (6, 26), (1, 37), (7, 24), (23, 23), (3, 24), (25, 3), (9, 17), (23, 10), (13, 32), (1, 23), (2, 7), (14, 27), (0, 10), (15, 5), (2, 34), (17, 16), (10, 6), (20, 1), (8, 12), (14, 18), (10, 29), (11, 5), (0, 22), (23, 12), (13, 22), (10, 4), (8, 5), (2, 5), (0, 18), (12, 16), (24, 20), (9, 25), (21, 5), (2, 22), (4, 11), (24, 6), (28, 20), (28, 37), (14, 6), (10, 31), (7, 34), (27, 22), (29, 21), (27, 14), (3, 14), (29, 12), (24, 12), (2, 30), (28, 1), (2, 27), (17, 22), (21, 37), (18, 12), (3, 1), (1, 4), (18, 24), (6, 33), (26, 28), (20, 27), (4, 15), (15, 7), (14, 16), (22, 19), (5, 25), (2, 1), (25, 18), (29, 31), (12, 5), (26, 25), (9, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
535248
|
OMEGA_500_SAMPLE
|
omega_500_008
|
logic_puzzles_grid_rook_level_2_0038
|
logic_puzzles_grid_rook
| 2 |
logic_puzzles_grid_rook
|
2
|
[
{
"role": "user",
"content": "In a 15x11 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (14, 10), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 0), (13, 2), (10, 0), (10, 1), (11, 6), (12, 2), (4, 4), (13, 0), (9, 5), (2, 5), (13, 6), (4, 8), (0, 6), (2, 9), (9, 7), (0, 8), (9, 3), (5, 4), (13, 4), (11, 2), (13, 1), (12, 4), (1, 0), (2, 2), (7, 5), (6, 8), (2, 10), (4, 7), (7, 10), (7, 3), (12, 5), (10, 2), (6, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
OMEGA_500_SAMPLE
|
omega_500_009
|
arithmetic_list_prime_factors_level_2_0015
|
arithmetic_list_prime_factors
| 2 |
arithmetic_list_prime_factors
|
2
|
[
{
"role": "user",
"content": "What is the second-largest prime factor of 529908601?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21851
|
OMEGA_500_SAMPLE
|
omega_500_010
|
combinatory_probability_no_fixed_points_level_5_0031
|
combinatory_probability_no_fixed_points
| 5 |
combinatory_probability_no_fixed_points
|
5
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 2, i: 2, j: 4, b: 2, w: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4006
|
OMEGA_500_SAMPLE
|
omega_500_011
|
combinatory_probability_exactly_n_specific_fixed_level_4_0066
|
combinatory_probability_exactly_n_specific_fixed
| 4 |
combinatory_probability_exactly_n_specific_fixed
|
4
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 1, y: 1, f: 4, j: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'y' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
OMEGA_500_SAMPLE
|
omega_500_012
|
logic_puzzles_grid_rook_level_3_0060
|
logic_puzzles_grid_rook
| 3 |
logic_puzzles_grid_rook
|
3
|
[
{
"role": "user",
"content": "In a 20x24 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (19, 23), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 13), (9, 21), (1, 21), (13, 19), (19, 9), (0, 11), (19, 11), (6, 8), (13, 10), (13, 22), (15, 17), (14, 20), (3, 0), (9, 19), (6, 1), (17, 7), (16, 5), (8, 22), (7, 23), (1, 13), (8, 20), (0, 4), (17, 22), (0, 8), (15, 10), (3, 4), (2, 0), (11, 17), (5, 11), (2, 3), (0, 2), (12, 21), (18, 2), (7, 1), (3, 20), (18, 17), (0, 10), (15, 8), (8, 0), (5, 3), (4, 11), (7, 20), (19, 13), (17, 12), (14, 7), (13, 12), (6, 22), (5, 4), (11, 11), (3, 9), (12, 17), (3, 11), (19, 14), (1, 11), (15, 23), (7, 3), (9, 10), (16, 20), (0, 22), (7, 17), (13, 13), (18, 16), (11, 12), (14, 5), (10, 16), (16, 8), (11, 7), (2, 1), (8, 19), (16, 17), (8, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6
|
OMEGA_500_SAMPLE
|
omega_500_013
|
logic_puzzles_grid_chip_level_3_0054
|
logic_puzzles_grid_chip
| 3 |
logic_puzzles_grid_chip
|
3
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in the cells of a 6x6 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (5, 1) is white, cell (3, 3) is black, cell (5, 0) is white, cell (2, 5) is black, cell (4, 2) is black, cell (1, 5) is black, cell (0, 2) is black, cell (5, 4) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18
|
OMEGA_500_SAMPLE
|
omega_500_014
|
algebra_func_area_level_3_0013
|
algebra_func_area
| 3 |
algebra_func_area
|
3
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-3(-1|(-3x^2 - 4x - 1) - 2|)^2 - 2(-1|(-3x^2 - 4x - 1) - 2|) - 3) + 1)/(-1(-3(-1|(-3x^2 - 4x - 1) - 2|)^2 - 2(-1|(-3x^2 - 4x - 1) - 2|) - 3) + 2), g(x) = (-1(-1|(3|x| + 3) - 2| + 3) + 3)/(-3(-1|(3|x| + 3) - 2| + 3)), x = -0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.2
|
OMEGA_500_SAMPLE
|
omega_500_015
|
combinatory_probability_at_least_n_specific_fixed_level_2_0039
|
combinatory_probability_at_least_n_specific_fixed
| 2 |
combinatory_probability_at_least_n_specific_fixed
|
2
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, r: 4, b: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
OMEGA_500_SAMPLE
|
omega_500_016
|
combinatory_probability_exactly_n_specific_fixed_level_3_0059
|
combinatory_probability_exactly_n_specific_fixed
| 3 |
combinatory_probability_exactly_n_specific_fixed
|
3
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 2, u: 4, l: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'l' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
OMEGA_500_SAMPLE
|
omega_500_017
|
number_theory_prime_mod_level_4_0070
|
number_theory_prime_mod
| 4 |
number_theory_prime_mod
|
4
|
[
{
"role": "user",
"content": "Let p be the minimum prime where n^6+1=0 (mod p^4) has a solution for some integer n, then find the minimum n for this p.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
182
|
OMEGA_500_SAMPLE
|
omega_500_018
|
arithmetic_mixed_level_1_0005
|
arithmetic_mixed
| 1 |
arithmetic_mixed
|
1
|
[
{
"role": "user",
"content": "28*1 + 28 + -162 + 156 Express your answer as an integer or in the form p/q where p and q are coprime.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
50
|
OMEGA_500_SAMPLE
|
omega_500_019
|
logic_puzzles_blocked_grid_level_4_0036
|
logic_puzzles_blocked_grid
| 4 |
logic_puzzles_blocked_grid
|
4
|
[
{
"role": "user",
"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 36), (25, 28), (19, 14), (0, 27), (5, 10), (3, 0), (6, 30), (7, 22), (22, 31), (22, 36), (26, 34), (1, 1), (23, 22), (25, 15), (17, 9), (18, 9), (0, 30), (21, 34), (28, 9), (10, 26), (4, 27), (20, 24), (2, 27), (3, 36), (9, 7), (17, 10), (12, 32), (28, 37), (21, 0), (6, 19), (14, 9), (29, 32), (11, 17), (26, 16), (20, 2), (11, 10), (17, 23), (10, 0), (3, 16), (21, 21), (28, 11), (11, 1), (15, 20), (23, 14), (27, 15), (1, 38), (1, 2), (12, 4), (17, 7), (3, 27), (11, 25), (1, 27), (9, 5), (1, 13), (15, 10), (14, 28), (8, 13), (5, 27), (7, 26), (16, 6), (5, 19), (20, 38), (16, 13), (8, 26), (6, 23), (4, 37), (24, 13), (14, 20), (23, 7), (24, 30), (27, 35), (5, 18), (12, 2), (3, 25), (8, 34), (14, 29), (1, 18), (20, 20), (7, 7), (5, 3), (9, 10), (0, 19), (9, 38), (17, 1), (25, 14), (4, 0), (23, 32), (19, 35), (12, 30), (20, 35), (6, 8), (22, 0), (2, 12), (9, 33), (24, 31), (2, 22), (5, 9), (19, 24), (21, 19), (0, 21), (13, 14), (4, 22), (8, 37), (16, 15), (12, 16), (29, 16), (26, 18), (2, 14), (13, 17), (12, 26), (29, 29), (11, 4), (19, 17), (29, 21), (2, 9), (26, 12), (5, 25), (15, 0), (22, 23), (4, 10), (27, 11), (22, 9), (27, 22), (20, 29), (1, 19), (6, 27), (22, 8), (29, 31), (20, 30), (8, 27), (1, 24), (7, 14), (17, 5), (6, 38), (15, 23), (26, 4), (21, 10), (26, 25), (16, 2), (27, 18), (21, 4), (6, 18), (7, 2), (5, 30), (13, 35), (25, 31), (23, 21), (23, 4), (5, 7), (24, 0), (12, 8), (13, 13), (4, 3), (5, 12), (5, 4), (20, 11), (23, 33), (2, 33), (19, 10), (9, 26), (18, 13), (4, 1), (4, 24), (8, 7), (29, 35), (11, 16), (8, 2), (7, 4), (15, 4), (27, 38), (23, 10), (17, 38), (23, 25), (21, 18), (13, 36), (5, 5), (25, 11), (7, 21), (17, 22), (6, 4), (4, 34), (14, 37), (19, 32), (20, 13), (15, 28), (3, 7), (20, 37), (14, 25), (26, 31), (17, 16), (16, 8), (20, 21), (14, 23), (17, 4), (20, 15), (14, 27), (24, 35), (0, 18), (11, 31), (9, 24), (28, 28), (29, 9), (17, 2), (25, 5), (27, 16), (17, 20), (27, 14), (15, 34), (18, 3), (12, 10), (14, 34), (16, 38), (5, 37), (8, 9), (3, 23), (27, 29), (14, 32), (0, 11), (19, 15), (28, 25), (3, 21), (0, 36), (10, 9), (5, 26), (29, 24), (12, 24), (26, 26), (15, 3), (5, 15), (8, 4), (27, 32), (13, 16), (5, 13), (20, 9), (22, 3), (8, 32), (22, 17), (5, 1), (24, 7), (15, 24), (8, 3), (25, 7), (4, 7), (27, 25), (11, 11), (21, 5), (9, 31), (29, 27), (29, 17), (18, 33), (25, 17), (25, 12), (17, 31), (12, 12), (27, 5), (10, 12), (1, 9), (13, 28), (25, 13), (10, 21), (23, 5), (1, 30), (21, 15), (28, 26), (3, 37), (0, 14), (4, 32), (0, 4), (26, 27), (4, 31), (24, 11), (22, 5), (25, 9), (20, 28), (25, 10), (3, 28), (22, 10), (2, 15), (11, 37), (7, 20), (12, 31), (29, 1), (23, 36), (2, 21), (11, 32), (3, 11), (17, 15), (1, 8), (11, 27), (17, 33), (13, 15), (2, 3), (18, 27), (23, 6), (2, 1), (8, 17), (0, 33), (28, 15), (17, 35), (28, 29), (25, 18), (10, 35), (22, 1), (14, 7), (8, 28), (22, 29), (6, 7), (8, 0), (28, 14), (8, 11), (5, 31), (29, 14), (14, 10), (16, 3), (29, 3), (29, 7), (28, 7), (27, 27), (19, 21), (5, 23), (23, 19), (25, 21), (7, 38), (27, 33), (28, 35), (22, 18), (9, 19), (13, 20), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
823680
|
OMEGA_500_SAMPLE
|
omega_500_020
|
arithmetic_list_prime_factors_level_5_0036
|
arithmetic_list_prime_factors
| 5 |
arithmetic_list_prime_factors
|
5
|
[
{
"role": "user",
"content": "Suppose -12503*t + 45972428259648 + 727262558155388 = -368676002301465. What is the second-largest prime factor of t?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2441
|
OMEGA_500_SAMPLE
|
omega_500_021
|
logic_puzzles_grid_chip_level_4_0013
|
logic_puzzles_grid_chip
| 4 |
logic_puzzles_grid_chip
|
4
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in a 7x7 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (4, 0) is white, cell (6, 4) is white, cell (5, 3) is white, cell (1, 5) is white, cell (2, 6) is white, cell (0, 2) is white, cell (5, 3) is white, cell (3, 4) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
OMEGA_500_SAMPLE
|
omega_500_022
|
arithmetic_matrix_inverse_level_5_0009
|
arithmetic_matrix_inverse
| 5 |
arithmetic_matrix_inverse
|
5
|
[
{
"role": "user",
"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, -6, -1, 8, -2, 4, 12, 12, -6],\n [-6, -7, -11, -12, -16, -11, 22, -9, 2],\n [-1, -11, -22, -6, 14, 1, 7, 3, -7],\n [8, -12, -6, 0, 6, -24, 8, -12, -17],\n [-2, -16, 14, 6, -9, 4, 12, 0, -14],\n [4, -11, 1, -24, 4, 25, 1, 14, 0],\n [12, 22, 7, 8, 12, 1, 1, 25, 1],\n [12, -9, 3, -12, 0, 14, 25, -9, -12],\n [-6, 2, -7, -17, -14, 0, 1, -12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
818
|
OMEGA_500_SAMPLE
|
omega_500_023
|
logic_puzzles_grid_knight_level_2_0005
|
logic_puzzles_grid_knight
| 2 |
logic_puzzles_grid_knight
|
2
|
[
{
"role": "user",
"content": "Supposing you start in the bottom left (0, 0) cell of a 14x14 grid, what is minimum number of steps you can take to get to (10, 12), if your only valid moves are to move over 1 squares in one direction and over 3 squares in a perpendicular direction (at once)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6
|
OMEGA_500_SAMPLE
|
omega_500_024
|
geometry_rotation_level_1_0012
|
geometry_rotation
| 1 |
geometry_rotation
|
1
|
[
{
"role": "user",
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 3 and from vertex 3 to vertex 6. Then, rotate the entire setup, including the constructed diagonals, 1 vertices counterclockwise (so that vertex 1 ends up where vertex 2 was), and superimpose it on the original (so that the resulting diagram contains both the original diagonals and the rotated versions of the diagonals). The original 6-gon will be partitioned into a collection of smaller polygons. (Only count the \"smallest\" polygons, i.e, those that do not have any of the diagonals running through them; this is not a combinatorics problem.) How many such polygons will there be?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
OMEGA_500_SAMPLE
|
omega_500_025
|
arithmetic_matrix_determinant_level_2_0021
|
arithmetic_matrix_determinant
| 2 |
arithmetic_matrix_determinant
|
2
|
[
{
"role": "user",
"content": "Determine the value of det(A) where A =\n[[6, -2, -8, 8],\n [-2, -1, -4, 6],\n [-8, -4, -4, -4],\n [8, 6, -4, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
752
|
OMEGA_500_SAMPLE
|
omega_500_026
|
arithmetic_list_prime_factors_level_2_0038
|
arithmetic_list_prime_factors
| 2 |
arithmetic_list_prime_factors
|
2
|
[
{
"role": "user",
"content": "What is the second-largest prime factor of 132494139303?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
677
|
OMEGA_500_SAMPLE
|
omega_500_027
|
algebra_func_intersection_coords_level_2_0039
|
algebra_func_intersection_coords
| 2 |
algebra_func_intersection_coords
|
2
|
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = -2((-1(2e^(-2x)) + 3)/(-3(2e^(-2x)) + 2))^2 + 4((-1(2e^(-2x)) + 3)/(-3(2e^(-2x)) + 2)) - 4 and g(x) = -4(2cos(1πx + 1) - 3)^2 + 2(2cos(1πx + 1) - 3) - 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
OMEGA_500_SAMPLE
|
omega_500_028
|
logic_puzzles_grid_knight_level_5_0095
|
logic_puzzles_grid_knight
| 5 |
logic_puzzles_grid_knight
|
5
|
[
{
"role": "user",
"content": "Supposing you start in the bottom left (0, 0) cell of a 48x49 grid, what is minimum number of steps you can take to get to (44, 45), if your only valid moves are to move over 4 squares in one direction and over 3 squares in a perpendicular direction (at once)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
OMEGA_500_SAMPLE
|
omega_500_029
|
arithmetic_matrix_rank_level_4_0084
|
arithmetic_matrix_rank
| 4 |
arithmetic_matrix_rank
|
4
|
[
{
"role": "user",
"content": "Find the rank of the matrix:\n[[131, -53, -37, 56, 64, -179, -108],\n [-25, 111, 48, 74, 55, 165, 216],\n [-203, 15, -63, -21, -130, 64, 152],\n [-10, 25, -109, -79, -68, -25, 153],\n [34, -151, -23, -15, 42, 78, -147],\n [90, -103, 79, 61, 100, -22, -259],\n [-73, -5, -112, -190, -177, -114, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
OMEGA_500_SAMPLE
|
omega_500_030
|
logic_puzzles_grid_chip_level_1_0045
|
logic_puzzles_grid_chip
| 1 |
logic_puzzles_grid_chip
|
1
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 3) is white, cell (0, 1) is black, cell (2, 1) is black, cell (3, 2) is black, cell (3, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
OMEGA_500_SAMPLE
|
omega_500_031
|
algebra_func_intersection_coords_level_5_0019
|
algebra_func_intersection_coords
| 5 |
algebra_func_intersection_coords
|
5
|
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1((-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1))/(-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1) - 3)) + 2)/(-1((-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1))/(-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1) - 3)) - 1) and g(x) = (-2(1(-2|(3(1x - 5) - 1) + 2| - 1) + 5) - 3)/(2(1(-2|(3(1x - 5) - 1) + 2| - 1) + 5)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
OMEGA_500_SAMPLE
|
omega_500_032
|
arithmetic_matrix_power_level_2_0039
|
arithmetic_matrix_power
| 2 |
arithmetic_matrix_power
|
2
|
[
{
"role": "user",
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, -1, -3, -2],\n [-1, -3, -2, 0],\n [-3, -2, 4, 2],\n [-2, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-120
|
OMEGA_500_SAMPLE
|
omega_500_033
|
logic_puzzles_grid_rook_level_3_0029
|
logic_puzzles_grid_rook
| 3 |
logic_puzzles_grid_rook
|
3
|
[
{
"role": "user",
"content": "In a 21x27 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (20, 26), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 9), (19, 15), (7, 8), (4, 21), (13, 13), (12, 25), (12, 21), (17, 2), (17, 18), (20, 11), (16, 14), (11, 4), (1, 26), (17, 0), (9, 20), (4, 7), (9, 10), (8, 6), (14, 17), (12, 5), (11, 10), (8, 26), (20, 17), (18, 2), (17, 1), (8, 9), (17, 11), (19, 16), (16, 21), (9, 16), (2, 17), (12, 9), (20, 13), (17, 4), (4, 3), (16, 24), (16, 0), (9, 25), (20, 9), (19, 1), (3, 16), (12, 12), (18, 16), (10, 25), (3, 26), (6, 21), (13, 19), (16, 1), (14, 2), (15, 4), (14, 15), (2, 0), (13, 0), (10, 13), (15, 7), (12, 20), (10, 7), (4, 18), (4, 5), (20, 14), (19, 11), (6, 14), (2, 6), (19, 21), (6, 9), (17, 20), (18, 5), (8, 13), (5, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
OMEGA_500_SAMPLE
|
omega_500_034
|
arithmetic_matrix_svd_level_7_0039
|
arithmetic_matrix_svd
| 7 |
arithmetic_matrix_svd
|
7
|
[
{
"role": "user",
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -13, -3, 23, 22, 5, 9, 5, -12, 16, 8, -24],\n [-11, -22, -6, -17, -8, -2, -23, 2, -8, 16, -25, -17],\n [16, -2, -7, 21, -8, -4, -3, -16, 19, 7, 1, -22],\n [-22, 24, -6, -15, 23, -23, 22, 15, -7, 11, -2, -13],\n [-16, 5, -16, -9, 0, -9, -4, -16, -6, 17, -22, -4],\n [14, -2, 14, -17, -5, -8, -26, -20, -23, -26, -12, 13],\n [-15, -5, -5, 23, 20, -10, 2, 19, -13, 23, -7, 23],\n [21, 6, 16, -12, -15, 13, -7, 3, 11, -24, 1, -1],\n [3, -14, -14, -25, 10, 22, 11, -25, 9, -1, -16, -19],\n [17, 13, 16, -5, -7, -19, 2, 13, -1, 3, -10, -7],\n [25, -11, 19, 16, -20, -11, 18, 20, 21, 0, 26, -4],\n [-3, -18, 8, 24, -7, 10, 15, -10, 20, 4, -19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
90
|
OMEGA_500_SAMPLE
|
omega_500_035
|
logic_puzzles_grid_rook_level_4_0059
|
logic_puzzles_grid_rook
| 4 |
logic_puzzles_grid_rook
|
4
|
[
{
"role": "user",
"content": "In a 37x30 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (36, 29), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (10, 12), (36, 13), (3, 15), (16, 1), (6, 21), (16, 21), (26, 13), (10, 23), (5, 7), (2, 29), (14, 7), (7, 14), (21, 2), (0, 7), (7, 2), (17, 16), (18, 8), (20, 29), (29, 10), (8, 21), (16, 0), (35, 9), (9, 24), (23, 1), (14, 1), (13, 16), (13, 0), (15, 6), (32, 28), (25, 10), (21, 1), (9, 14), (8, 28), (22, 12), (36, 3), (28, 9), (6, 24), (6, 23), (4, 28), (7, 23), (24, 26), (14, 29), (18, 24), (35, 5), (16, 23), (31, 19), (26, 26), (16, 27), (1, 25), (2, 6), (20, 0), (13, 26), (30, 4), (6, 10), (35, 17), (23, 26), (27, 16), (12, 13), (0, 13), (25, 25), (30, 19), (24, 2), (32, 9), (33, 16), (36, 24), (24, 7), (11, 26), (24, 12), (29, 4), (14, 15), (27, 1), (6, 27), (14, 5), (15, 11), (17, 17), (27, 15), (32, 8), (25, 9), (24, 17), (8, 19), (4, 14), (24, 19), (5, 25), (30, 10), (27, 6), (1, 20), (2, 3), (9, 3), (20, 22), (3, 4), (17, 14), (18, 11), (18, 10), (31, 12), (3, 29), (10, 21), (36, 15), (32, 21), (24, 5), (29, 16), (28, 2), (3, 5), (5, 16), (27, 19), (15, 23), (3, 23), (4, 11), (15, 8), (25, 18), (1, 27), (20, 15), (9, 18), (6, 19), (13, 6), (29, 11), (28, 29), (10, 5), (12, 4), (22, 20), (22, 16), (15, 21), (2, 12), (4, 4), (19, 27), (29, 20), (36, 18), (23, 20), (14, 8), (18, 3), (33, 27), (3, 28), (4, 5), (1, 5), (13, 27), (8, 22), (19, 14), (28, 17), (29, 21), (36, 8), (7, 21), (7, 12), (3, 11), (14, 12), (21, 10), (35, 19), (12, 8), (35, 11), (28, 19), (3, 10), (6, 26), (10, 1), (36, 9), (12, 1), (5, 3), (15, 9), (12, 23), (4, 25), (12, 11), (17, 18), (32, 6), (17, 23), (15, 0), (35, 23), (17, 9), (11, 20), (12, 0), (20, 1), (17, 15), (7, 17), (1, 21), (6, 3), (26, 4), (3, 8), (13, 24), (32, 18), (11, 28), (9, 13), (1, 15), (14, 16), (10, 20), (26, 8), (0, 2), (24, 29), (15, 26), (26, 16), (25, 4), (33, 8), (8, 26), (20, 9), (1, 7), (4, 12), (14, 25), (22, 21), (28, 18), (29, 29), (22, 11), (5, 12), (34, 1), (7, 0), (8, 25), (10, 0), (9, 23), (32, 25), (15, 20), (19, 20), (6, 2), (17, 24), (25, 15), (30, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
OMEGA_500_SAMPLE
|
omega_500_036
|
algebra_func_zeros_level_1_0053
|
algebra_func_zeros
| 1 |
algebra_func_zeros
|
1
|
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1cos(2π((2x + 1)/(-2x)) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
OMEGA_500_SAMPLE
|
omega_500_037
|
algebra_func_intersection_coords_level_1_0060
|
algebra_func_intersection_coords
| 1 |
algebra_func_intersection_coords
|
1
|
[
{
"role": "user",
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (3(1x^2 - 5x - 3) - 2)/(1(1x^2 - 5x - 3) + 2) and g(x) = -4x - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
OMEGA_500_SAMPLE
|
omega_500_038
|
arithmetic_matrix_multiplication_level_6_0057
|
arithmetic_matrix_multiplication
| 6 |
arithmetic_matrix_multiplication
|
6
|
[
{
"role": "user",
"content": "Find the sum of absolute values of all entries of the product of the following matrices:\nA =\n[[-10, -11, 22, -18, -13, 17, -19, -9, 24, 6],\n [-4, 25, -13, 21, -3, 3, -4, -25, 3, 22],\n [-21, 9, -16, -7, 11, -19, 20, 9, 19, -13],\n [-16, -24, -20, -18, 10, -1, 18, 21, 14, -19],\n [20, -3, -7, 20, -4, -13, -5, -25, -7, 7],\n [-22, 16, -23, 1, 15, 9, 2, -20, -20, 18],\n [-3, 7, -10, -2, -21, 15, 16, -13, 21, -14],\n [-21, 11, 5, 2, 2, 4, -8, 18, 1, 9],\n [0, 13, 23, 25, -8, 7, -1, 5, 11, -24],\n [7, 13, 17, 17, 6, -8, -9, 8, 13, -19]]\nB =\n[[16, 9, 4, -14, 9, -15, 18, -22, -1, 22, 6],\n [-6, 24, 5, -22, 12, 21, -25, -23, 11, -4, -9],\n [-12, 15, 9, -13, 9, 17, -24, 21, -13, 25, -10],\n [-8, -19, 19, 10, 15, 4, 16, 15, -19, -11, 14],\n [-7, 17, 11, -24, 16, 22, -13, 14, 15, 17, 17],\n [5, -10, 16, 18, -20, 2, 6, 18, -16, 24, -8],\n [-22, -17, -19, 24, -18, 17, -19, 15, 14, -23, -9],\n [-24, -11, 20, 3, 24, 22, -4, -22, -20, 12, 0],\n [-15, 0, -9, -2, 2, 9, 5, -13, 9, -10, -11],\n [17, -8, 21, 11, 22, 22, 23, 15, 1, 9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60032
|
OMEGA_500_SAMPLE
|
omega_500_039
|
combinatory_probability_no_fixed_points_level_4_0013
|
combinatory_probability_no_fixed_points
| 4 |
combinatory_probability_no_fixed_points
|
4
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, z: 1, v: 2, o: 6}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
139
|
OMEGA_500_SAMPLE
|
omega_500_040
|
arithmetic_matrix_inverse_level_6_0044
|
arithmetic_matrix_inverse
| 6 |
arithmetic_matrix_inverse
|
6
|
[
{
"role": "user",
"content": "Calculate the inverse matrix of 1/600 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[24, -21, 16, -8, -10, -10, 12, -18, 6, 2],\n [-7, 13, -20, -14, -27, 16, -6, -1, -22, -10],\n [-11, -12, -12, -19, 6, 11, -14, 6, 23, 17],\n [8, -3, 10, 4, 16, 17, -13, -17, 4, 13],\n [10, 29, -24, 10, -18, -13, 6, -18, 5, 0],\n [-29, -15, -22, -22, 7, -20, 23, 25, -9, 2],\n [5, 14, -8, 14, 14, 3, -22, -7, -23, -24],\n [5, -13, -28, -3, -25, 13, 13, -10, -3, 9],\n [23, 23, -30, 5, -10, 29, 12, 4, -18, 26],\n [18, 23, 23, -21, 22, 13, 16, 22, -21, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-77
|
OMEGA_500_SAMPLE
|
omega_500_041
|
logic_puzzles_blocked_grid_level_2_0051
|
logic_puzzles_blocked_grid
| 2 |
logic_puzzles_blocked_grid
|
2
|
[
{
"role": "user",
"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 15), (8, 14), (1, 10), (7, 1), (14, 14), (5, 5), (9, 0), (11, 1), (9, 2), (14, 9), (5, 10), (13, 2), (4, 7), (2, 3), (5, 11), (2, 16), (12, 17), (4, 9), (11, 6), (0, 12), (0, 13), (6, 17), (4, 11), (4, 8), (4, 2), (14, 2), (14, 7), (13, 4), (8, 16), (13, 6), (9, 10), (1, 5), (14, 12), (11, 4), (3, 3), (2, 1), (10, 6), (11, 9), (4, 3), (2, 15), (9, 12), (6, 11), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
953188
|
OMEGA_500_SAMPLE
|
omega_500_042
|
algebra_func_extrema_coords_level_2_0080
|
algebra_func_extrema_coords
| 2 |
algebra_func_extrema_coords
|
2
|
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3))^2 - 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
OMEGA_500_SAMPLE
|
omega_500_043
|
arithmetic_matrix_svd_level_6_0093
|
arithmetic_matrix_svd
| 6 |
arithmetic_matrix_svd
|
6
|
[
{
"role": "user",
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, -20, -12, -8, 22, 5, -13, 15, -16, -8],\n [-5, -5, 18, 1, -21, 17, -3, 11, 20, 3],\n [-16, 15, 7, 19, -18, -12, -22, 11, -22, -4],\n [-21, -2, -3, 0, -2, 1, -19, -11, -1, -3],\n [-5, -22, 7, 10, 1, -9, 13, -18, -12, 1],\n [8, -10, -7, 1, -10, 1, 3, -21, -7, 15],\n [-22, -12, 12, 20, 6, 14, -6, 16, 19, 5],\n [6, 20, -20, -13, 19, -9, -11, 19, 7, 9],\n [9, 19, 9, 3, -22, 19, -21, -6, 7, 16],\n [-16, 4, -14, -1, 11, -22, -14, -3, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
348
|
OMEGA_500_SAMPLE
|
omega_500_044
|
arithmetic_matrix_eigenvalues_level_3_0072
|
arithmetic_matrix_eigenvalues
| 3 |
arithmetic_matrix_eigenvalues
|
3
|
[
{
"role": "user",
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 7, 5, 3, 0, 0],\n [7, 8, 9, -4, -12, 2],\n [5, 9, 4, 2, -3, -2],\n [3, -4, 2, -12, 4, 4],\n [0, -12, -3, 4, -14, -4],\n [0, 2, -2, 4, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
OMEGA_500_SAMPLE
|
omega_500_045
|
number_theory_prime_mod_level_2_0069
|
number_theory_prime_mod
| 2 |
number_theory_prime_mod
|
2
|
[
{
"role": "user",
"content": "Let p be the least prime number for which there exists a positive integer n such that n^4+(0) is divisible by p^3. Find the least positive integer m such that m^4+(0) is divisible by p^3.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
OMEGA_500_SAMPLE
|
omega_500_046
|
geometry_polygon_color_level_5_0096
|
geometry_polygon_color
| 5 |
geometry_polygon_color
|
5
|
[
{
"role": "user",
"content": "A 14-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue, vertex 10 is blue, vertex 11 is red, vertex 12 is red, vertex 13 is blue. The 14-gon is then rotated clockwise by 3 positions, so that the vertex that was originally in position 0 is now in position 3. How many blue vertices are now in positions where there were originally red vertices?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
OMEGA_500_SAMPLE
|
omega_500_047
|
algebra_func_zeros_level_3_0040
|
algebra_func_zeros
| 3 |
algebra_func_zeros
|
3
|
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3cos(1π(4(2|(4x^2 + 4)| - 2) - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1194
|
OMEGA_500_SAMPLE
|
omega_500_048
|
number_theory_digit_sum_level_4_0090
|
number_theory_digit_sum
| 4 |
number_theory_digit_sum
|
4
|
[
{
"role": "user",
"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9996
|
OMEGA_500_SAMPLE
|
omega_500_049
|
arithmetic_matrix_eigenvalues_level_1_0069
|
arithmetic_matrix_eigenvalues
| 1 |
arithmetic_matrix_eigenvalues
|
1
|
[
{
"role": "user",
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[2, 4, 4],\n [4, -8, 2],\n [4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
OMEGA_500_SAMPLE
|
omega_500_050
|
combinatory_probability_no_fixed_points_level_4_0091
|
combinatory_probability_no_fixed_points
| 4 |
combinatory_probability_no_fixed_points
|
4
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 3, y: 4, t: 1, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
367
|
OMEGA_500_SAMPLE
|
omega_500_051
|
algebra_func_area_level_2_0057
|
algebra_func_area
| 2 |
algebra_func_area
|
2
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(-5x^2 + 4x - 2) - 5) + 1)/(1(-3(-5x^2 + 4x - 2) - 5) + 1) and g(x) = -2(-3x^2 - 2x) + 1 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23.3
|
OMEGA_500_SAMPLE
|
omega_500_052
|
logic_puzzles_grid_knight_level_4_0072
|
logic_puzzles_grid_knight
| 4 |
logic_puzzles_grid_knight
|
4
|
[
{
"role": "user",
"content": "Supposing you start in the bottom left (0, 0) cell of a 37x37 grid, what is minimum number of steps you can take to get to (33, 35), if your only valid moves are like a chess knight, i.e, over two squares in one direction and over one square in a perpendicular direction in one move?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24
|
OMEGA_500_SAMPLE
|
omega_500_053
|
arithmetic_matrix_eigenvalues_level_4_0004
|
arithmetic_matrix_eigenvalues
| 4 |
arithmetic_matrix_eigenvalues
|
4
|
[
{
"role": "user",
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-12, 9, -9, -1, -2, 12, 2],\n [9, 12, -4, 8, -10, 2, 12],\n [-9, -4, -7, -8, 4, 12, 2],\n [-1, 8, -8, -16, 9, 2, 0],\n [-2, -10, 4, 9, 1, 8, 10],\n [12, 2, 12, 2, 8, -17, 6],\n [2, 12, 2, 0, 10, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
37
|
OMEGA_500_SAMPLE
|
omega_500_054
|
algebra_func_area_level_3_0018
|
algebra_func_area
| 3 |
algebra_func_area
|
3
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|((-2((-1x - 3)/(1x + 2)) - 1)/(-1((-1x - 3)/(1x + 2)) + 2)) - 2|) + 4 and g(x) = (2(2|(2cos(2πx + 3) - 2) - 2| + 3) + 2)/(1(2|(2cos(2πx + 3) - 2) - 2| + 3) - 3) between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
OMEGA_500_SAMPLE
|
omega_500_055
|
arithmetic_matrix_power_level_5_0099
|
arithmetic_matrix_power
| 5 |
arithmetic_matrix_power
|
5
|
[
{
"role": "user",
"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[9, 12, 10, -2, -2, -2, 7, -10],\n [12, -11, -6, 3, -6, -4, -6, 4],\n [10, -6, 3, 8, 0, -3, -10, 9],\n [-2, 3, 8, -11, 3, 6, -6, -5],\n [-2, -6, 0, 3, 11, 4, -6, 0],\n [-2, -4, -3, 6, 4, -11, 4, 0],\n [7, -6, -10, -6, -6, 4, 1, 5],\n [-10, 4, 9, -5, 0, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-11427783176
|
OMEGA_500_SAMPLE
|
omega_500_056
|
arithmetic_matrix_svd_level_7_0045
|
arithmetic_matrix_svd
| 7 |
arithmetic_matrix_svd
|
7
|
[
{
"role": "user",
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 8, 26, -1, -11, -21, 17, 16, 20, 20, 21, 15],\n [-15, -14, -23, 12, -25, -1, 0, 0, -12, -19, -20, 20],\n [19, 13, -15, -14, 16, -10, -10, 9, -6, -19, -22, -1],\n [-11, 9, 1, 2, 20, -15, 10, 3, -4, -11, -13, -17],\n [-20, 18, 25, 10, 2, -24, -12, 9, 20, 19, 25, -8],\n [-14, 15, -6, 10, 0, 25, 2, -7, -2, -21, 9, -25],\n [-5, 5, -11, -9, -22, 9, 3, 18, -8, -4, 7, -14],\n [16, 2, 9, -5, 25, 25, 20, 9, -18, 12, 24, -8],\n [11, -21, 25, 20, -12, -7, -18, 5, -23, 23, -9, -22],\n [-7, -4, -16, 10, -5, -23, 2, 17, 7, -14, 15, -18],\n [15, 4, -20, -23, -8, 15, 3, 4, 8, -6, 4, -8],\n [4, 26, 5, -25, 25, -17, -25, -25, -3, -10, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
526
|
OMEGA_500_SAMPLE
|
omega_500_057
|
logic_puzzles_grid_knight_level_5_0098
|
logic_puzzles_grid_knight
| 5 |
logic_puzzles_grid_knight
|
5
|
[
{
"role": "user",
"content": "Supposing you start in the bottom left (0, 0) cell of a 42x40 grid, what is minimum number of steps you can take to get to (38, 36), if your only valid moves are to move over 3 squares in one direction and over 1 squares in a perpendicular direction (at once)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
OMEGA_500_SAMPLE
|
omega_500_058
|
arithmetic_matrix_inverse_level_2_0047
|
arithmetic_matrix_inverse
| 2 |
arithmetic_matrix_inverse
|
2
|
[
{
"role": "user",
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-7, -12, 11, 2],\n [10, -3, 6, 4],\n [-8, -9, -3, 11],\n [4, -3, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-22
|
OMEGA_500_SAMPLE
|
omega_500_059
|
algebra_func_zeros_level_4_0044
|
algebra_func_zeros
| 4 |
algebra_func_zeros
|
4
|
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3|(3((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3))^2 + 5((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3)) - 1) - 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
OMEGA_500_SAMPLE
|
omega_500_060
|
arithmetic_matrix_determinant_level_1_0019
|
arithmetic_matrix_determinant
| 1 |
arithmetic_matrix_determinant
|
1
|
[
{
"role": "user",
"content": "What is the determinant of the matrix:\n[[1, -5, -7],\n [0, 6, -5],\n [-6, 9, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
589
|
OMEGA_500_SAMPLE
|
omega_500_061
|
arithmetic_matrix_svd_level_2_0020
|
arithmetic_matrix_svd
| 2 |
arithmetic_matrix_svd
|
2
|
[
{
"role": "user",
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -2, 0, 2, 5],\n [-2, -6, 3, 3, -6],\n [-5, -1, 2, 1, 6],\n [-2, -6, 6, 0, -2],\n [-1, 6, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
35
|
OMEGA_500_SAMPLE
|
omega_500_062
|
algebra_func_zeros_level_2_0031
|
algebra_func_zeros
| 2 |
algebra_func_zeros
|
2
|
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2(-2|(1x^2 - 5x) - 3| + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
OMEGA_500_SAMPLE
|
omega_500_063
|
logic_puzzles_grid_chip_level_5_0055
|
logic_puzzles_grid_chip
| 5 |
logic_puzzles_grid_chip
|
5
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 4) is white, cell (0, 4) is white, cell (4, 4) is white, cell (6, 6) is white, cell (1, 2) is black, cell (7, 3) is black, cell (5, 7) is white, cell (3, 1) is black, cell (6, 0) is white, cell (3, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
32
|
OMEGA_500_SAMPLE
|
omega_500_064
|
arithmetic_matrix_multiplication_level_7_0038
|
arithmetic_matrix_multiplication
| 7 |
arithmetic_matrix_multiplication
|
7
|
[
{
"role": "user",
"content": "Find the trace (sum of diagonal elements) of the product of the following matrices:\nA =\n[[-27, -22, 10, -9, -13, -19, 11, 12, 8, -22, -25, -12, 17, 16],\n [-24, -15, -26, -15, -30, 20, 6, 8, -12, 23, 6, 30, -14, -5],\n [-9, -23, 30, 30, 2, -29, -1, 16, -11, 29, -13, 12, 26, -21],\n [-7, 25, -27, 6, -27, -18, -6, -18, -13, 30, 28, -7, -29, 17],\n [2, 27, -12, -22, -3, 4, 26, 8, 30, -21, -30, 11, -10, -22],\n [29, 16, -16, 4, 26, -26, 10, 27, -9, 10, -8, -24, 25, -8],\n [13, -6, -4, 10, -25, 24, 3, -22, 29, 30, 18, 2, 20, 29],\n [-25, 6, 0, 3, 10, -2, 27, -17, 5, 5, 22, -16, -23, -5],\n [5, 17, -10, -3, -27, -15, -9, -19, -15, 20, 9, 7, 11, 6],\n [-2, -13, -21, 11, 8, -13, -30, 8, -10, -30, -16, -27, 29, 30],\n [-11, -21, -8, 10, 3, 29, 15, 17, 2, 3, 8, 30, -21, 23],\n [-11, -30, -18, -30, -26, -15, -16, 18, -3, 0, -8, 17, 14, 12],\n [-14, 18, 3, -18, -17, -20, -3, 11, 1, 4, 30, 28, 0, -14]]\nB =\n[[16, -22, -21, -23, -10, -18, 28, 19, -26, -25, -1, 0, -14],\n [-20, -11, 17, -22, -29, 6, -30, -27, 5, 23, 27, -6, -28],\n [-22, -9, -8, -19, -21, 3, 12, -21, -1, -9, -25, 19, -29],\n [-1, -29, 1, 11, -15, -19, -30, 22, -23, 17, 19, -18, -16],\n [22, 13, -23, -21, 15, -26, 19, -12, 16, 7, 28, -20, 22],\n [12, -11, -11, -10, -13, 26, 19, -21, 3, -5, -1, -22, 15],\n [20, 0, 11, 24, -27, 30, 30, -25, -17, -27, -5, 16, 17],\n [8, -14, -12, 30, 20, 18, -25, -2, -20, -15, -1, -6, 9],\n [-20, -24, -5, 25, -9, -6, -12, 0, -5, 11, 10, 5, -8],\n [16, -18, -6, -29, -29, -15, -22, -3, -18, 4, 10, -18, 0],\n [-10, 1, 23, 3, -23, 28, 10, 17, -29, 7, 1, 23, 9],\n [27, -3, 6, 10, -30, 10, -21, 24, -27, 4, -21, 16, -20],\n [-17, 7, -19, 14, -14, -15, 4, -29, -20, 30, 10, -28, -2],\n [-13, -11, 16, -17, 3, 18, 23, 0, 27, 9, 11, 27, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-6261
|
OMEGA_500_SAMPLE
|
omega_500_065
|
arithmetic_matrix_eigenvalues_level_6_0029
|
arithmetic_matrix_eigenvalues
| 6 |
arithmetic_matrix_eigenvalues
|
6
|
[
{
"role": "user",
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, -6, 5, 8, 1, -12, 20, 12, 2, -5],\n [-6, 18, -20, -1, 4, -4, 5, -14, -22, 1],\n [5, -20, 8, -6, 6, -23, 1, 3, 6, 27],\n [8, -1, -6, -11, -6, 9, -16, 14, -3, 2],\n [1, 4, 6, -6, 28, -20, 4, 10, 21, -12],\n [-12, -4, -23, 9, -20, -16, -2, 0, 0, 8],\n [20, 5, 1, -16, 4, -2, -5, -12, 11, -5],\n [12, -14, 3, 14, 10, 0, -12, -6, 2, -3],\n [2, -22, 6, -3, 21, 0, 11, 2, 4, -2],\n [-5, 1, 27, 2, -12, 8, -5, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
313
|
OMEGA_500_SAMPLE
|
omega_500_066
|
arithmetic_matrix_determinant_level_7_0097
|
arithmetic_matrix_determinant
| 7 |
arithmetic_matrix_determinant
|
7
|
[
{
"role": "user",
"content": "What is the determinant of the matrix:\n[[-19, -29, 24, 12, -26, 5, -17, 26, 30, -28, -6, 0],\n [0, -34, -31, 10, 4, 21, -25, 2, -19, -10, 3, 31],\n [0, 0, 10, 5, 14, 8, -26, -34, -15, -11, 33, -14],\n [0, 0, 0, -31, -30, -20, 10, -12, -22, -12, -13, 3],\n [0, 0, 0, 0, 23, 33, 6, 23, -1, 5, 31, 29],\n [0, 0, 0, 0, 0, 4, -24, -6, 34, 6, -22, -31],\n [0, 0, 0, 0, 0, 0, 29, 16, -27, -20, -1, -20],\n [0, 0, 0, 0, 0, 0, 0, 22, 26, -11, 35, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 7, -32, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 11, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
999
|
OMEGA_500_SAMPLE
|
omega_500_067
|
logic_puzzles_blocked_grid_level_5_0082
|
logic_puzzles_blocked_grid
| 5 |
logic_puzzles_blocked_grid
|
5
|
[
{
"role": "user",
"content": "In a 43x41 grid, how many different paths are there from the bottom left (0, 0) to the top right (42, 40), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (4, 25), (5, 18), (23, 12), (17, 36), (10, 15), (40, 33), (8, 10), (32, 32), (34, 15), (10, 16), (37, 40), (16, 8), (37, 30), (3, 16), (22, 23), (0, 12), (20, 39), (7, 14), (24, 14), (17, 8), (40, 8), (9, 22), (19, 33), (12, 34), (28, 0), (11, 36), (16, 11), (7, 40), (30, 37), (4, 0), (14, 25), (23, 34), (31, 4), (17, 12), (23, 40), (28, 37), (35, 6), (15, 3), (33, 34), (9, 27), (29, 3), (29, 33), (34, 40), (22, 22), (34, 2), (20, 2), (38, 14), (13, 3), (6, 35), (31, 14), (39, 22), (15, 11), (41, 35), (27, 22), (26, 2), (0, 3), (40, 26), (18, 13), (31, 27), (42, 23), (16, 30), (0, 19), (34, 18), (33, 31), (17, 7), (21, 33), (21, 11), (8, 21), (12, 36), (9, 25), (29, 32), (9, 32), (42, 7), (30, 3), (20, 21), (24, 26), (2, 26), (17, 16), (35, 9), (29, 28), (1, 7), (13, 18), (34, 39), (1, 6), (24, 3), (21, 9), (42, 30), (30, 25), (41, 12), (18, 25), (12, 8), (0, 8), (33, 24), (15, 28), (21, 29), (28, 4), (2, 36), (6, 9), (3, 24), (12, 1), (15, 33), (20, 12), (17, 9), (12, 23), (42, 17), (26, 22), (17, 5), (34, 34), (4, 8), (4, 6), (6, 40), (23, 0), (36, 6), (39, 5), (22, 39), (7, 35), (2, 17), (4, 16), (6, 33), (30, 4), (40, 2), (11, 34), (35, 20), (34, 38), (28, 15), (24, 37), (34, 22), (1, 17), (6, 24), (1, 35), (3, 4), (11, 30), (36, 16), (26, 14), (28, 16), (42, 8), (41, 10), (26, 25), (32, 18), (5, 35), (11, 10), (29, 23), (27, 3), (15, 27), (28, 39), (15, 34), (25, 12), (42, 9), (38, 8), (40, 9), (3, 36), (33, 5), (34, 11), (24, 17), (34, 7), (22, 35), (40, 7), (4, 7), (15, 38), (7, 18), (27, 24), (32, 21), (14, 1), (29, 5), (22, 14), (21, 17), (5, 8), (13, 39), (20, 24), (18, 21), (39, 21), (29, 19), (40, 25), (10, 5), (25, 27), (38, 27), (41, 25), (14, 32), (15, 36), (21, 20), (14, 38), (7, 21), (13, 15), (12, 10), (40, 13), (41, 27), (42, 1), (39, 20), (12, 39), (21, 18), (32, 16), (1, 1), (28, 5), (40, 3), (13, 14), (40, 12), (8, 22), (7, 15), (41, 15), (4, 30), (34, 5), (13, 19), (42, 10), (26, 5), (25, 5), (8, 5), (27, 30), (26, 38), (31, 12), (4, 21), (16, 15), (41, 34), (20, 20), (20, 7), (42, 33), (2, 12), (11, 35), (35, 24), (5, 32), (37, 2), (23, 36), (42, 28), (13, 26), (29, 7), (26, 31), (15, 1), (20, 1), (2, 19), (26, 7), (23, 29), (20, 16), (4, 38), (13, 36), (11, 15), (4, 22), (14, 15), (29, 13), (38, 6), (29, 22), (22, 25), (11, 9), (17, 40), (7, 30), (32, 3), (24, 20), (19, 25), (28, 24), (23, 23), (27, 16), (16, 35), (10, 9), (42, 31), (3, 22), (17, 23), (36, 10), (11, 12), (17, 21), (2, 18), (0, 39), (21, 26), (21, 1), (33, 10), (32, 22), (27, 11), (9, 23), (24, 40), (32, 30), (25, 34), (14, 40), (27, 10), (6, 15), (31, 39), (38, 32), (39, 1), (34, 21), (32, 14), (0, 1), (8, 18), (19, 14), (8, 8), (41, 31), (35, 22), (8, 35), (23, 18), (15, 9), (31, 18), (29, 39), (36, 36), (27, 4), (18, 1), (19, 26), (15, 26), (32, 29), (15, 12), (18, 26), (26, 24), (24, 1), (24, 12), (39, 27), (11, 21), (6, 10), (18, 31), (35, 0), (33, 3), (36, 11), (8, 14), (25, 33), (39, 32), (18, 39), (13, 6), (29, 18), (33, 15), (6, 36), (35, 3), (6, 29), (2, 1), (3, 12), (20, 17), (25, 1), (18, 35), (10, 36), (6, 26), (37, 33), (9, 0), (16, 24), (18, 37), (18, 40), (5, 22), (40, 35), (40, 23), (16, 31), (41, 11), (34, 12), (6, 38), (12, 24), (9, 1), (2, 10), (8, 1), (39, 17), (32, 20), (13, 13), (22, 5), (39, 11), (39, 33), (38, 5), (32, 39), (5, 2), (7, 31), (24, 9), (29, 24), (10, 25), (1, 11), (22, 18), (39, 34), (34, 10), (17, 30), (32, 35), (22, 33), (18, 5), (36, 21), (16, 22), (6, 22), (39, 12), (6, 6), (35, 39), (25, 26), (19, 21), (14, 2), (22, 8), (13, 29), (11, 37), (0, 2), (24, 32), (33, 2), (3, 6), (14, 4), (37, 17), (38, 38), (16, 20), (21, 8), (1, 9), (38, 9), (25, 6), (26, 23), (7, 5), (16, 4), (20, 8), (15, 17), (31, 22), (18, 18), (34, 33), (3, 40), (1, 40), (17, 26), (25, 10), (24, 21), (2, 15), (30, 40), (0, 38), (4, 17), (14, 31), (42, 24), (2, 25), (21, 30), (38, 7), (35, 19), (14, 12), (13, 37), (33, 38), (0, 40), (7, 11), (15, 22), (26, 27), (12, 14), (33, 1), (13, 40), (33, 37), (29, 20), (26, 20), (15, 25), (7, 12), (2, 22), (34, 8), (9, 40), (29, 26), (35, 7), (37, 15), (31, 33), (6, 11), (5, 7), (31, 16), (15, 10), (23, 39), (24, 28), (4, 24), (40, 6), (16, 12), (34, 16), (23, 6), (28, 18), (19, 35), (41, 19), (38, 21), (28, 3), (29, 12), (35, 8), (34, 25), (15, 2), (7, 28), (5, 34), (37, 31), (22, 10), (31, 1), (37, 34), (36, 30), (13, 30), (2, 34), (0, 14), (38, 0), (12, 5), (7, 10), (1, 16), (31, 2), (27, 31), (2, 9), (31, 0), (24, 8), (36, 22), (25, 30), (25, 22), (31, 21), (1, 22), (19, 17), (6, 2), (2, 2), (31, 26), (19, 0), (10, 0), (23, 9), (16, 39), (23, 13), (7, 39), (32, 1), (36, 28), (24, 2), (26, 10), (39, 39), (35, 18), (8, 28), (36, 29), (5, 6), (41, 18), (19, 27), (25, 32), (10, 1), (1, 15), (33, 4), (11, 23), (1, 32), (11, 3), (19, 13), (14, 16), (5, 38), (2, 29), (31, 20), (20, 11), (25, 40), (35, 28), (20, 19), (12, 15), (13, 10), (2, 5), (21, 27), (33, 21), (21, 38), (3, 29), (8, 13), (8, 9), (4, 14), (10, 19), (11, 16), (11, 5), (17, 15), (25, 4), (35, 5), (23, 5), (25, 2), (22, 40), (37, 38), (4, 27), (17, 34), (24, 4), (23, 16), (32, 2), (9, 19), (30, 26), (25, 11), (11, 22), (30, 38), (0, 9), (5, 30), (13, 17), (22, 32), (19, 37), (11, 24), (40, 10), (19, 4), (1, 13), (18, 7), (4, 20), (7, 25), (37, 36), (42, 19), (26, 39), (14, 10), (33, 19), (31, 29), (5, 25), (10, 6), (12, 33), (2, 8), (9, 4), (26, 18), (7, 20), (30, 9), (3, 14), (0, 21), (22, 30), (11, 31), (28, 13), (37, 23), (26, 8), (9, 14), (39, 13), (17, 39), (24, 18), (3, 17), (14, 37), (17, 1), (10, 39), (21, 10), (18, 16), (6, 30), (7, 24), (8, 4), (18, 11), (14, 7), (17, 38), (36, 35), (4, 35), (27, 13), (14, 30), (22, 9), (40, 14), (31, 15), (32, 23), (22, 15), (35, 26), (40, 4), (2, 39), (2, 14), (37, 7), (17, 2), (9, 21), (13, 21), (42, 26), (40, 30), (16, 33), (21, 2), (26, 40), (26, 13), (31, 17), (41, 39)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
491520
|
OMEGA_500_SAMPLE
|
omega_500_068
|
algebra_func_derivative_sign_level_1_0011
|
algebra_func_derivative_sign
| 1 |
algebra_func_derivative_sign
|
1
|
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π((3x)/(-2x - 2)) - 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
OMEGA_500_SAMPLE
|
omega_500_069
|
arithmetic_matrix_determinant_level_1_0044
|
arithmetic_matrix_determinant
| 1 |
arithmetic_matrix_determinant
|
1
|
[
{
"role": "user",
"content": "Compute |A| for the matrix A =\n[[-10, -6, 2],\n [-7, 5, 5],\n [-9, 6, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
748
|
OMEGA_500_SAMPLE
|
omega_500_070
|
arithmetic_matrix_inverse_level_7_0037
|
arithmetic_matrix_inverse
| 7 |
arithmetic_matrix_inverse
|
7
|
[
{
"role": "user",
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[2, 5, 9, 4, -19, 21, -34, 26, -27, 32, -19, 14],\n [0, 22, -15, -18, 19, -7, -12, -19, -18, 6, 9, -19],\n [0, 0, -7, -32, -16, 11, -27, -9, -21, -17, 16, -10],\n [0, 0, 0, 13, 17, -33, 30, 6, -17, -19, -3, 13],\n [0, 0, 0, 0, 19, -10, 16, -29, 10, 10, -20, -12],\n [0, 0, 0, 0, 0, -11, -26, -20, 22, -7, -30, -20],\n [0, 0, 0, 0, 0, 0, -10, 9, 27, 31, 16, 32],\n [0, 0, 0, 0, 0, 0, 0, -3, -23, -10, -15, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, -33, 19, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 16, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-338783
|
OMEGA_500_SAMPLE
|
omega_500_071
|
arithmetic_matrix_svd_level_7_0023
|
arithmetic_matrix_svd
| 7 |
arithmetic_matrix_svd
|
7
|
[
{
"role": "user",
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 9, 16, -7, -9, 16, -6, -23, 23, 6, 0, -20],\n [-21, -12, -9, 5, -16, -7, -3, -12, 21, -20, -6, 15],\n [-1, 17, -13, 10, -6, -9, -22, -24, -4, -1, 10, -3],\n [22, -8, 24, -2, -6, -15, 14, 6, 23, 26, -23, 15],\n [-20, -5, 6, -10, -3, 7, 1, 16, 14, 12, -5, 22],\n [-10, 7, -21, 19, -21, 7, -26, -17, -6, -22, -25, -5],\n [21, -25, -17, 7, -11, 21, 24, 12, -5, -15, -3, 20],\n [13, 11, -17, 8, 24, 22, 5, -20, -6, -7, -1, -23],\n [19, 25, -5, -12, 13, -6, -12, -5, 25, 1, -13, 0],\n [14, 13, 1, -1, 22, -25, -2, -24, -19, 17, 6, 15],\n [25, 8, -21, 12, 25, -4, -2, 23, 16, -8, -22, 24],\n [-16, -15, -17, -19, -3, 1, 14, 9, 10, -6, -19, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
538
|
OMEGA_500_SAMPLE
|
omega_500_072
|
arithmetic_matrix_multiplication_level_3_0035
|
arithmetic_matrix_multiplication
| 3 |
arithmetic_matrix_multiplication
|
3
|
[
{
"role": "user",
"content": "Find the sum of all entries of the product of the following matrices:\nA =\n[[7, 7, 8, -1, 6, 1, 4],\n [11, 8, -10, 10, -6, 4, -1],\n [-4, 2, 5, 8, 0, 8, -5],\n [1, -5, 1, -6, 10, -1, -2],\n [9, 9, -2, 12, 9, 0, 5],\n [-11, 8, 2, 7, 5, 2, 6]]\nB =\n[[10, 11, -1, 0, 9, -2, -8],\n [-12, 11, -10, 9, 6, 10, -6],\n [-1, 2, 12, -8, 2, -5, -3],\n [3, -5, -12, -1, -8, -10, -12],\n [-9, -5, -10, -3, -11, -2, 12],\n [-3, 8, 1, -6, -11, -4, 3],\n [0, -4, 7, -9, 9, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1652
|
OMEGA_500_SAMPLE
|
omega_500_073
|
number_theory_prime_mod_level_3_0030
|
number_theory_prime_mod
| 3 |
number_theory_prime_mod
|
3
|
[
{
"role": "user",
"content": "Let p be the smallest prime number for which there exists a positive integer n where n^1+(1) is a multiple of p^5, and n^1+(1) is also a multiple of p^5. Find the largest positive integer m such that m^1+(1) is a multiple of p^5.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
31
|
OMEGA_500_SAMPLE
|
omega_500_074
|
logic_puzzles_grid_chip_level_3_0086
|
logic_puzzles_grid_chip
| 3 |
logic_puzzles_grid_chip
|
3
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in a 6x6 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (5, 4) is black, cell (4, 5) is black, cell (2, 0) is black, cell (4, 1) is black, cell (1, 2) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
OMEGA_500_SAMPLE
|
omega_500_075
|
arithmetic_gcd_level_2_0016
|
arithmetic_gcd
| 2 |
arithmetic_gcd
|
2
|
[
{
"role": "user",
"content": "Calculate the greatest common divisor of 381 and 28031777439.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
381
|
OMEGA_500_SAMPLE
|
omega_500_076
|
algebra_func_intersection_level_3_0022
|
algebra_func_intersection
| 3 |
algebra_func_intersection
|
3
|
[
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (1((-1((-2(3sin(2πx + 1)) + 1)/(1(3sin(2πx + 1)) - 2)) + 1)/(-1((-2(3sin(2πx + 1)) + 1)/(1(3sin(2πx + 1)) - 2)) - 2)) + 1)/(-1((-1((-2(3sin(2πx + 1)) + 1)/(1(3sin(2πx + 1)) - 2)) + 1)/(-1((-2(3sin(2πx + 1)) + 1)/(1(3sin(2πx + 1)) - 2)) - 2)) + 2) and g(x) = (1(-1(2x^2 - 5x) + 1) - 1)/(3(-1(2x^2 - 5x) + 1) + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
OMEGA_500_SAMPLE
|
omega_500_077
|
algebra_func_area_level_2_0095
|
algebra_func_area
| 2 |
algebra_func_area
|
2
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-5(3cos(3πx - 1) + 1) - 5)^2 - 2(-5(3cos(3πx - 1) + 1) - 5) + 4 and g(x) = (-1((2x + 2)/(2x + 2)) + 3)/(1((2x + 2)/(2x + 2)) + 1) between the vertical lines x = 3.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
OMEGA_500_SAMPLE
|
omega_500_078
|
combinatory_probability_no_fixed_points_level_5_0041
|
combinatory_probability_no_fixed_points
| 5 |
combinatory_probability_no_fixed_points
|
5
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 5, b: 2, a: 1, l: 2, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3868
|
OMEGA_500_SAMPLE
|
omega_500_079
|
combinatory_pattern_matching_level_3_0026
|
combinatory_pattern_matching
| 3 |
combinatory_pattern_matching
|
3
|
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {l: 1, e: 2, i: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
OMEGA_500_SAMPLE
|
omega_500_080
|
combinatory_probability_no_specific_letter_fixed_level_4_0035
|
combinatory_probability_no_specific_letter_fixed
| 4 |
combinatory_probability_no_specific_letter_fixed
|
4
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 2, m: 3, i: 2, b: 3}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
191
|
OMEGA_500_SAMPLE
|
omega_500_081
|
arithmetic_matrix_multiplication_level_7_0063
|
arithmetic_matrix_multiplication
| 7 |
arithmetic_matrix_multiplication
|
7
|
[
{
"role": "user",
"content": "Find the sum of all entries of the product of the following matrices:\nA =\n[[-16, 15, 13, -28, 1, -21, 9, 7, -9, -17, -14, -10, 20, 17],\n [-16, 27, -16, -30, -7, 24, 24, -19, -21, 15, 11, 11, 21, 30],\n [0, -20, 23, -15, 30, -22, 16, -17, -12, 0, -22, 5, 22, 8],\n [23, -5, -23, -7, -23, -12, 16, 17, -1, 27, -9, 24, -22, 27],\n [27, 13, 17, -27, 6, -23, -30, -3, -25, 16, 5, 22, -20, -26],\n [19, -7, 16, -13, -11, -3, -18, -26, -1, -30, -9, -13, 15, -26],\n [0, -25, -4, 25, -6, -2, -3, -15, 23, 22, -19, -11, -13, 3],\n [24, 22, -8, 14, -4, 18, -14, 17, -10, 19, 9, 0, -28, -14],\n [30, 19, 27, -5, -8, -25, -3, -23, 24, 27, 14, -23, -12, 7],\n [-2, -8, 16, 1, -21, -4, 18, -30, 8, -2, 28, 14, -28, 20],\n [16, 6, 0, -20, -9, -13, 4, -25, -28, -26, -22, -3, -12, -3],\n [-4, -18, 30, 7, 12, 22, -10, -4, 15, -25, 7, 18, -20, 16],\n [10, 22, -14, 25, 8, -24, -1, -10, -30, -6, 1, 28, 26, -23],\n [-26, -1, 20, -23, 18, -12, 13, 28, 24, -1, -16, 5, 24, 13]]\nB =\n[[-4, -18, -17, 6, 23, 17, -1, 8, 16, -18, 27, -15, 13],\n [-24, 17, 24, 24, -4, 14, 30, 24, 4, -16, -3, 4, -24],\n [19, 15, 19, 20, 15, -11, 1, 7, 30, 9, 1, -5, 27],\n [8, -11, -13, 19, -16, 21, -9, 20, -9, 22, -10, -29, 9],\n [22, 12, -13, -8, -18, 10, -22, 18, -24, 10, 23, -30, -29],\n [-27, -17, 1, 5, -29, 9, 19, 20, -17, -11, -6, 11, 18],\n [-23, -3, 15, -10, -8, 1, -23, 0, 6, -15, 9, 11, -4],\n [9, 10, -13, 4, 18, 21, -16, 22, -4, -14, 9, -29, 18],\n [19, 0, 30, 6, 10, 10, 3, 3, 20, 24, 28, -28, -14],\n [-17, -17, 15, 7, 4, -30, 17, -2, -27, 30, 2, -14, -3],\n [19, -5, -23, 3, 28, -13, 0, 28, -4, -15, 27, -21, 9],\n [-19, -9, -15, -19, -20, -11, 20, -30, -4, -28, -19, -1, -22],\n [22, 30, 23, 6, -30, 11, 18, -27, -16, 20, -4, -23, 29],\n [29, -8, -16, -4, 0, 8, 16, -23, -1, 27, 24, 11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
869
|
OMEGA_500_SAMPLE
|
omega_500_082
|
arithmetic_matrix_eigenvalues_level_2_0058
|
arithmetic_matrix_eigenvalues
| 2 |
arithmetic_matrix_eigenvalues
|
2
|
[
{
"role": "user",
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[2, 10, 4, -2],\n [10, 1, 6, -10],\n [4, 6, 11, 4],\n [-2, -10, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
OMEGA_500_SAMPLE
|
omega_500_083
|
logic_puzzles_grid_chip_level_2_0003
|
logic_puzzles_grid_chip
| 2 |
logic_puzzles_grid_chip
|
2
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in a 5x5 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is white, cell (2, 4) is white, cell (0, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
OMEGA_500_SAMPLE
|
omega_500_084
|
logic_puzzles_zebralogic_level_2_0065
|
logic_puzzles_zebralogic
| 2 |
logic_puzzles_zebralogic
|
2
|
[
{
"role": "user",
"content": "There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Arnold`, `Eric`\n - Everyone has a unique favorite cigar: `pall mall`, `prince`\n\n## Clues:\n1. The person partial to Pall Mall is Arnold.\n2. Arnold is in the first house.\n\n\nChoices:\n0. prince\n1. pall mall\n\nWhen answering, please specify the number corresponding to the correct choice, instead of the choice itself.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
OMEGA_500_SAMPLE
|
omega_500_085
|
combinatory_pattern_matching_level_3_0001
|
combinatory_pattern_matching
| 3 |
combinatory_pattern_matching
|
3
|
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {x: 6, u: 3} to form a word, what is the expected number of matches of the pattern 'u*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.57
|
OMEGA_500_SAMPLE
|
omega_500_086
|
logic_puzzles_grid_chip_level_2_0057
|
logic_puzzles_grid_chip
| 2 |
logic_puzzles_grid_chip
|
2
|
[
{
"role": "user",
"content": "Chips, colored either black or white, are placed in a 5x5 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is white, cell (1, 2) is white, cell (3, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
OMEGA_500_SAMPLE
|
omega_500_087
|
combinatory_distribution_level_4_0038
|
combinatory_distribution
| 4 |
combinatory_distribution
|
4
|
[
{
"role": "user",
"content": "Arrange the letters {'d': 2, 'b': 3, 'e': 3, 'f': 3} into 4 uniquely identified boxes that can hold [4, 4, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
567
|
OMEGA_500_SAMPLE
|
omega_500_088
|
combinatory_probability_no_specific_letter_fixed_level_1_0054
|
combinatory_probability_no_specific_letter_fixed
| 1 |
combinatory_probability_no_specific_letter_fixed
|
1
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, z: 1, y: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
OMEGA_500_SAMPLE
|
omega_500_089
|
arithmetic_matrix_inverse_level_6_0025
|
arithmetic_matrix_inverse
| 6 |
arithmetic_matrix_inverse
|
6
|
[
{
"role": "user",
"content": "Find the inverse of 1/600 times the matrix and calculate the value at position (4, 6) of the inverse. Round your answer to the nearest integer:\n[[-3, -15, 4, -12, -10, -24, -14, -23, 16, 4],\n [-15, -29, 7, -8, -2, -16, -26, 1, 8, 14],\n [4, 7, 18, -4, -10, 6, 18, -5, -6, -14],\n [-12, -8, -4, 1, -7, 22, -4, -12, 15, 11],\n [-10, -2, -10, -7, -23, -14, 24, -16, -6, 17],\n [-24, -16, 6, 22, -14, 29, -27, 13, -6, 12],\n [-14, -26, 18, -4, 24, -27, 23, -8, 22, 6],\n [-23, 1, -5, -12, -16, 13, -8, 7, 6, 8],\n [16, 8, -6, 15, -6, -6, 22, 6, 5, -14],\n [4, 14, -14, 11, 17, 12, 6, 8, -14, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
OMEGA_500_SAMPLE
|
omega_500_090
|
arithmetic_matrix_rank_level_1_0071
|
arithmetic_matrix_rank
| 1 |
arithmetic_matrix_rank
|
1
|
[
{
"role": "user",
"content": "Compute the rank of the given 4x4 matrix:\n[[-28, -20, 20, 17],\n [-4, -4, -4, -2],\n [-12, -12, -4, -1],\n [-28, -34, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
OMEGA_500_SAMPLE
|
omega_500_091
|
arithmetic_matrix_multiplication_level_6_0069
|
arithmetic_matrix_multiplication
| 6 |
arithmetic_matrix_multiplication
|
6
|
[
{
"role": "user",
"content": "Find the trace (sum of diagonal elements) of the product of the following matrices:\nA =\n[[-15, -9, 22, 19, -4, 11, -6, 22, 22, 22, 20],\n [-20, 8, -12, 22, -3, -6, -13, 21, 18, 15, 6],\n [0, 24, -12, 10, -18, 14, -4, -4, -10, 1, -16],\n [-1, 5, -5, 1, -9, 7, 5, 24, 16, 0, -5],\n [10, -25, -22, -22, 0, -22, 23, -17, 4, 25, 19],\n [-22, -21, 19, -3, -10, -4, 11, -18, 22, 7, 12],\n [17, -10, -21, -10, -19, 25, -25, -17, -8, 19, 21],\n [-23, -2, 2, -16, -17, -13, 22, 9, -3, 21, -9],\n [20, -19, -10, 14, 10, -6, -2, 21, -21, 19, -20],\n [2, -21, 23, 13, 12, -24, 17, 13, -5, 14, 11],\n [-8, 22, 20, -14, -9, 11, 20, 12, -11, -19, -12]]\nB =\n[[24, -25, 12, -23, 11, 18, 5, 17, -13, 22, -8],\n [-9, -9, -15, -6, -16, 3, 22, 8, -9, 16, -13],\n [18, 21, 13, 1, 0, 2, -13, -14, 18, 2, -24],\n [11, 8, -3, 19, 3, 9, -15, 22, 7, 25, -15],\n [-17, -12, -17, 13, 22, -23, 3, -7, 10, 6, -19],\n [2, 18, -8, -21, -3, -4, 0, 16, -14, 14, -7],\n [21, -25, -23, 1, -8, 24, 4, -24, -21, 3, 7],\n [16, -6, 4, 16, -21, 24, -5, -11, -6, -18, 23],\n [5, -14, -5, 4, 1, 18, 0, 7, 0, 0, 10],\n [14, -25, -11, 24, -25, -15, -24, -25, 5, 18, -10],\n [-4, 16, -8, 21, -9, 4, -16, 9, -5, -10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1700
|
OMEGA_500_SAMPLE
|
omega_500_092
|
arithmetic_matrix_rank_level_2_0065
|
arithmetic_matrix_rank
| 2 |
arithmetic_matrix_rank
|
2
|
[
{
"role": "user",
"content": "Find the rank of the matrix:\n[[17, -9, -5, -9, 30],\n [-2, 6, -18, 10, 12],\n [7, 3, 11, -9, -12],\n [-3, 8, 40, -15, -56],\n [17, 10, -18, -9, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
OMEGA_500_SAMPLE
|
omega_500_093
|
algebra_func_derivative_sign_level_1_0071
|
algebra_func_derivative_sign
| 1 |
algebra_func_derivative_sign
|
1
|
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(2π(-4x^2 - 4x + 4) + 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
OMEGA_500_SAMPLE
|
omega_500_094
|
number_theory_prime_mod_level_4_0074
|
number_theory_prime_mod
| 4 |
number_theory_prime_mod
|
4
|
[
{
"role": "user",
"content": "Let p be the minimum prime where n^2+-2=0 (mod p^4) has a solution for some integer n, then find the minimum n for this p.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
235
|
OMEGA_500_SAMPLE
|
omega_500_095
|
logic_puzzles_blocked_grid_level_1_0041
|
logic_puzzles_blocked_grid
| 1 |
logic_puzzles_blocked_grid
|
1
|
[
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (6, 3), (2, 8), (6, 1), (6, 2), (7, 3), (1, 3), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1870
|
OMEGA_500_SAMPLE
|
omega_500_096
|
arithmetic_matrix_multiplication_level_1_0099
|
arithmetic_matrix_multiplication
| 1 |
arithmetic_matrix_multiplication
|
1
|
[
{
"role": "user",
"content": "Compute the sum of absolute values of all entries of the product matrix AB given:\nA =\n[[6, -2, -3, -8],\n [6, -2, 8, -7],\n [0, 0, 4, -3],\n [-3, -6, 8, 8],\n [3, 7, 6, 4]]\nB =\n[[-8, 8, -6],\n [6, -5, -5],\n [8, 2, -6],\n [-1, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
628
|
OMEGA_500_SAMPLE
|
omega_500_097
|
arithmetic_list_prime_factors_level_3_0028
|
arithmetic_list_prime_factors
| 3 |
arithmetic_list_prime_factors
|
3
|
[
{
"role": "user",
"content": "What is the second-largest prime factor of 694529888368?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13007
|
OMEGA_500_SAMPLE
|
omega_500_098
|
combinatory_probability_no_specific_letter_fixed_level_3_0077
|
combinatory_probability_no_specific_letter_fixed
| 3 |
combinatory_probability_no_specific_letter_fixed
|
3
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, n: 3, s: 4}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
OMEGA_500_SAMPLE
|
omega_500_099
|
algebra_func_zeros_level_3_0051
|
algebra_func_zeros
| 3 |
algebra_func_zeros
|
3
|
[
{
"role": "user",
"content": "How many solutions does the equation 1(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5)^2 + 4(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
OMEGA_500_SAMPLE
|
End of preview. Expand
in Data Studio
Omega-500: Random Sample of Mathematical Problems
This dataset contains a random sample of 500 mathematical problems selected from the comprehensive OMEGA problem families dataset. It provides a diverse, manageable subset for quick evaluation and experimentation across multiple mathematical domains and difficulty levels.
Overview
Omega-500 is designed for:
- Quick Evaluation: Fast assessment of model capabilities across math domains
- Prototyping: Testing new approaches before scaling to larger datasets
- Benchmarking: Standardized subset for fair model comparisons
- Research: Focused analysis on a balanced mathematical problem set
The sample maintains diversity across mathematical domains and difficulty levels while keeping the dataset size manageable for rapid iteration.
Quick Start
from datasets import load_dataset
# Load the Omega-500 sample
dataset = load_dataset("sunyiyou/omega-500")
problems = dataset["train"]
# Access individual problems
first_problem = problems[0]
print("Problem:", first_problem["messages"][0]["content"])
print("Answer:", first_problem["ground_truth"])
print("Family:", first_problem["family"])
print("Difficulty:", first_problem["difficulty_level"])
Dataset Composition
Total Problems: 500
Domain Distribution:
- Algebra: 106 problems (21.2%)
- Arithmetic: 171 problems (34.2%)
- Combinatorics: 70 problems (14.0%)
- Geometry: 37 problems (7.4%)
- Logic: 76 problems (15.2%)
- Number Theory: 40 problems (8.0%)
### Problem Families Included: 35
- algebra_func_area: 15 problems
- algebra_func_derivative_sign: 19 problems
- algebra_func_extrema: 9 problems
- algebra_func_extrema_coords: 15 problems
- algebra_func_intersection: 16 problems
- algebra_func_intersection_coords: 11 problems
- algebra_func_zeros: 11 problems
- algebra_linear_equation: 10 problems
- arithmetic_gcd: 11 problems
- arithmetic_list_prime_factors: 17 problems
- arithmetic_matrix_determinant: 19 problems
- arithmetic_matrix_eigenvalues: 24 problems
- arithmetic_matrix_inverse: 19 problems
- arithmetic_matrix_multiplication: 20 problems
- arithmetic_matrix_power: 21 problems
- arithmetic_matrix_rank: 14 problems
- arithmetic_matrix_svd: 16 problems
- arithmetic_mixed: 10 problems
- combinatory_distribution: 9 problems
- combinatory_pattern_matching: 14 problems
- combinatory_probability_at_least_n_specific_fixed: 13 problems
- combinatory_probability_exactly_n_specific_fixed: 9 problems
- combinatory_probability_no_fixed_points: 13 problems
- combinatory_probability_no_specific_letter_fixed: 12 problems
- geometry_polygon_chords: 11 problems
- geometry_polygon_color: 12 problems
- geometry_rotation: 14 problems
- logic_puzzles_blocked_grid: 18 problems
- logic_puzzles_grid_chip: 21 problems
- logic_puzzles_grid_knight: 15 problems
- logic_puzzles_grid_rook: 13 problems
- logic_puzzles_zebralogic: 9 problems
- number_theory_digit_sum: 12 problems
- number_theory_prime_mod: 18 problems
- number_theory_triple_count: 10 problems
Sampling Method
- Source: Randomly sampled from the complete OMEGA problem families dataset
- Seed: Fixed random seed (42) for reproducibility
- Strategy: Simple random sampling across all families and difficulty levels
- Balance: Natural distribution reflecting the diversity of the source dataset
Use Cases
- Model Evaluation: Quick assessment of mathematical reasoning capabilities
- Method Development: Testing new prompting or fine-tuning approaches
- Comparative Studies: Standardized benchmark for fair model comparison
- Educational: Learning about mathematical problem types and difficulties
- Debugging: Smaller dataset for faster debugging and iteration
Data Fields
Each problem contains:
id: Unique identifier for this sampleoriginal_id: Original identifier from source datasetfamily: Problem family (e.g., "algebra_func_area")difficulty_level: Numeric difficulty level from sourcesource_family: Source family directory namesource_level: Source difficulty level namemessages: Problem statement in chat formatground_truth: Correct answerdataset: Dataset identifier ("OMEGA_500_SAMPLE")
Citation
If you use this dataset, please cite the original OMEGA work:
@article{sun2024omega,
title = {OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization},
author = {Yiyou Sun and Shawn Hu and Georgia Zhou and Ken Zheng and Hannaneh Hajishirzi and Nouha Dziri and Dawn Song},
journal = {arXiv preprint arXiv:2506.18880},
year = {2024},
}
Related Resources
- Full Problem Families: See omega-prob-families for the complete dataset
- Explorative Dataset: See omega-explorative for explorative reasoning challenges
- Compositional Dataset: See omega-compositional for compositional reasoning challenges
- Transformative Dataset: See omega-transformative for transformative reasoning challenges
- Paper: See the full details in paper
- Code Repository: See generation code on github
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