messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
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[
{
"content": "There is a collection of 6 indistinguishable white chips and 6 indistinguishable black chips. Find the number of ways to place some of these chips in the 6 unit cells of a 1 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 64 | MATH |
[
{
"content": "There is a collection of 28 indistinguishable white chips and 28 indistinguishable black chips. Find the number of ways to place some of these chips in the 28 unit cells of a 7 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 1766 | MATH |
[
{
"content": "There is a collection of 35 indistinguishable white chips and 35 indistinguishable black chips. Find the number of ways to place some of these chips in the 35 unit cells of a 5 x 7 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 3782 | MATH |
[
{
"content": "There is a collection of 52 indistinguishable white chips and 52 indistinguishable black chips. Find the number of ways to place some of these chips in the 52 unit cells of a 4 x 13 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 114662 | MATH |
[
{
"content": "There is a collection of 16 indistinguishable white chips and 16 indistinguishable black chips. Find the number of ways to place some of these chips in the 16 unit cells of a 2 x 8 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 510 | MATH |
[
{
"content": "There is a collection of 30 indistinguishable white chips and 30 indistinguishable black chips. Find the number of ways to place some of these chips in the 30 unit cells of a 3 x 10 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 6134 | MATH |
[
{
"content": "There is a collection of 77 indistinguishable white chips and 77 indistinguishable black chips. Find the number of ways to place some of these chips in the 77 unit cells of a 11 x 7 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 257798 | MATH |
[
{
"content": "There is a collection of 72 indistinguishable white chips and 72 indistinguishable black chips. Find the number of ways to place some of these chips in the 72 unit cells of a 8 x 9 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 129542 | MATH |
[
{
"content": "There is a collection of 48 indistinguishable white chips and 48 indistinguishable black chips. Find the number of ways to place some of these chips in the 48 unit cells of a 12 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 57318 | MATH |
[
{
"content": "There is a collection of 35 indistinguishable white chips and 35 indistinguishable black chips. Find the number of ways to place some of these chips in the 35 unit cells of a 7 x 5 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 3782 | MATH |
[
{
"content": "There is a collection of 28 indistinguishable white chips and 28 indistinguishable black chips. Find the number of ways to place some of these chips in the 28 unit cells of a 4 x 7 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 1766 | MATH |
[
{
"content": "There is a collection of 11 indistinguishable white chips and 11 indistinguishable black chips. Find the number of ways to place some of these chips in the 11 unit cells of a 1 x 11 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 2048 | MATH |
[
{
"content": "There is a collection of 52 indistinguishable white chips and 52 indistinguishable black chips. Find the number of ways to place some of these chips in the 52 unit cells of a 13 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 114662 | MATH |
[
{
"content": "There is a collection of 8 indistinguishable white chips and 8 indistinguishable black chips. Find the number of ways to place some of these chips in the 8 unit cells of a 4 x 2 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 30 | MATH |
[
{
"content": "There is a collection of 4 indistinguishable white chips and 4 indistinguishable black chips. Find the number of ways to place some of these chips in the 4 unit cells of a 2 x 2 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 6 | MATH |
[
{
"content": "There is a collection of 72 indistinguishable white chips and 72 indistinguishable black chips. Find the number of ways to place some of these chips in the 72 unit cells of a 12 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 253830 | MATH |
[
{
"content": "There is a collection of 22 indistinguishable white chips and 22 indistinguishable black chips. Find the number of ways to place some of these chips in the 22 unit cells of a 2 x 11 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 4094 | MATH |
[
{
"content": "There is a collection of 42 indistinguishable white chips and 42 indistinguishable black chips. Find the number of ways to place some of these chips in the 42 unit cells of a 7 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 7814 | MATH |
[
{
"content": "There is a collection of 12 indistinguishable white chips and 12 indistinguishable black chips. Find the number of ways to place some of these chips in the 12 unit cells of a 1 x 12 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 4096 | MATH |
[
{
"content": "There is a collection of 60 indistinguishable white chips and 60 indistinguishable black chips. Find the number of ways to place some of these chips in the 60 unit cells of a 15 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 458726 | MATH |
[
{
"content": "There is a collection of 30 indistinguishable white chips and 30 indistinguishable black chips. Find the number of ways to place some of these chips in the 30 unit cells of a 10 x 3 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 6134 | MATH |
[
{
"content": "There is a collection of 14 indistinguishable white chips and 14 indistinguishable black chips. Find the number of ways to place some of these chips in the 14 unit cells of a 2 x 7 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 254 | MATH |
[
{
"content": "There is a collection of 2 indistinguishable white chips and 2 indistinguishable black chips. Find the number of ways to place some of these chips in the 2 unit cells of a 1 x 2 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 4 | MATH |
[
{
"content": "There is a collection of 48 indistinguishable white chips and 48 indistinguishable black chips. Find the number of ways to place some of these chips in the 48 unit cells of a 8 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 15750 | MATH |
[
{
"content": "There is a collection of 8 indistinguishable white chips and 8 indistinguishable black chips. Find the number of ways to place some of these chips in the 8 unit cells of a 2 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 30 | MATH |
[
{
"content": "There is a collection of 40 indistinguishable white chips and 40 indistinguishable black chips. Find the number of ways to place some of these chips in the 40 unit cells of a 5 x 8 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 7622 | MATH |
[
{
"content": "There is a collection of 42 indistinguishable white chips and 42 indistinguishable black chips. Find the number of ways to place some of these chips in the 42 unit cells of a 6 x 7 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 7814 | MATH |
[
{
"content": "There is a collection of 78 indistinguishable white chips and 78 indistinguishable black chips. Find the number of ways to place some of these chips in the 78 unit cells of a 6 x 13 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 507782 | MATH |
[
{
"content": "There is a collection of 45 indistinguishable white chips and 45 indistinguishable black chips. Find the number of ways to place some of these chips in the 45 unit cells of a 9 x 5 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 15302 | MATH |
[
{
"content": "There is a collection of 16 indistinguishable white chips and 16 indistinguishable black chips. Find the number of ways to place some of these chips in the 16 unit cells of a 8 x 2 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 510 | MATH |
[
{
"content": "There is a collection of 66 indistinguishable white chips and 66 indistinguishable black chips. Find the number of ways to place some of these chips in the 66 unit cells of a 11 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 126854 | MATH |
[
{
"content": "There is a collection of 8 indistinguishable white chips and 8 indistinguishable black chips. Find the number of ways to place some of these chips in the 8 unit cells of a 1 x 8 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 256 | MATH |
[
{
"content": "There is a collection of 27 indistinguishable white chips and 27 indistinguishable black chips. Find the number of ways to place some of these chips in the 27 unit cells of a 3 x 9 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 3062 | MATH |
[
{
"content": "There is a collection of 26 indistinguishable white chips and 26 indistinguishable black chips. Find the number of ways to place some of these chips in the 26 unit cells of a 2 x 13 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 16382 | MATH |
[
{
"content": "There is a collection of 24 indistinguishable white chips and 24 indistinguishable black chips. Find the number of ways to place some of these chips in the 24 unit cells of a 6 x 4 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 870 | MATH |
[
{
"content": "There is a collection of 20 indistinguishable white chips and 20 indistinguishable black chips. Find the number of ways to place some of these chips in the 20 unit cells of a 2 x 10 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 2046 | MATH |
[
{
"content": "There is a collection of 33 indistinguishable white chips and 33 indistinguishable black chips. Find the number of ways to place some of these chips in the 33 unit cells of a 3 x 11 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 12278 | MATH |
[
{
"content": "There is a collection of 18 indistinguishable white chips and 18 indistinguishable black chips. Find the number of ways to place some of these chips in the 18 unit cells of a 3 x 6 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 374 | MATH |
[
{
"content": "There is a collection of 70 indistinguishable white chips and 70 indistinguishable black chips. Find the number of ways to place some of these chips in the 70 unit cells of a 5 x 14 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 491462 | MATH |
[
{
"content": "There is a collection of 2 indistinguishable white chips and 2 indistinguishable black chips. Find the number of ways to place some of these chips in the 2 unit cells of a 2 x 1 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 4 | MATH |
[
{
"content": "There is a collection of 54 indistinguishable white chips and 54 indistinguishable black chips. Find the number of ways to place some of these chips in the 54 unit cells of a 6 x 9 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 31622 | MATH |
[
{
"content": "There is a collection of 64 indistinguishable white chips and 64 indistinguishable black chips. Find the number of ways to place some of these chips in the 64 unit cells of a 8 x 8 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 64518 | MATH |
[
{
"content": "There is a collection of 72 indistinguishable white chips and 72 indistinguishable black chips. Find the number of ways to place some of these chips in the 72 unit cells of a 6 x 12 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 253830 | MATH |
[
{
"content": "There is a collection of 77 indistinguishable white chips and 77 indistinguishable black chips. Find the number of ways to place some of these chips in the 77 unit cells of a 7 x 11 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 257798 | MATH |
[
{
"content": "There is a collection of 88 indistinguishable white chips and 88 indistinguishable black chips. Find the number of ways to place some of these chips in the 88 unit cells of a 11 x 8 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 519686 | MATH |
[
{
"content": "There is a collection of 11 indistinguishable white chips and 11 indistinguishable black chips. Find the number of ways to place some of these chips in the 11 unit cells of a 11 x 1 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 2048 | MATH |
[
{
"content": "There is a collection of 5 indistinguishable white chips and 5 indistinguishable black chips. Find the number of ways to place some of these chips in the 5 unit cells of a 5 x 1 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 32 | MATH |
[
{
"content": "There is a collection of 3 indistinguishable white chips and 3 indistinguishable black chips. Find the number of ways to place some of these chips in the 3 unit cells of a 3 x 1 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column ha... | 8 | MATH |
[
{
"content": "There is a collection of 30 indistinguishable white chips and 30 indistinguishable black chips. Find the number of ways to place some of these chips in the 30 unit cells of a 2 x 15 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same colum... | 65534 | MATH |
[
{
"content": "There is a collection of 40 indistinguishable white chips and 40 indistinguishable black chips. Find the number of ways to place some of these chips in the 40 unit cells of a 8 x 5 grid such that: 1) Each cell contains at most one chip, 2) All chips in the same row and all chips in the same column... | 7622 | MATH |
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