messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (2, 3), (0, 1), (2, 0), (1, 5), (5, 2), (3, 4), (0, 6), (5, 3), ... | 30 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 4), (0, 4), (4, 1), (0, 1), (4, 5), (2, 0)?\n\nPresent the a... | 15 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (1, 3), (2, 0), (4, 6), (0, 2), (3, 5), (5, 2), (4, 5)?\n\nPrese... | 50 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (3, 3), (3, 1), (3, 0), (2, 6), (4, 3), (4, 8)?\n\nPresent the a... | 290 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 7), (1, 5), (2, 1), (1, 3), (0, 1), (4, 2), (0, 2)?\n\nPrese... | 141 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 5), (6, 1), (0, 4), (6, 0), (2, 0), (6, 3), (1, 2), (3, 5)?\... | 182 | MATH |
[
{
"content": "In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (2, 8), (2, 0), (0, 2), (0, 7), (0, 6), (3, 5)?\n\nPresent the a... | 90 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (7, 0), (2, 4), (6, 1), (5, 2), (7, 2), (4, 0), (4, 4), (7, 1)?\... | 48 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (4, 4), (0, 4), (7, 0), (4, 5), (3, 0), (3, 2), (5, 2), (3, 1), ... | 111 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (6, 0), (0, 4), (0, 2), (3, 5), (2, 1), (4, 1), (5, 5), (7, 3), ... | 72 | MATH |
[
{
"content": "In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 3), (4, 7), (4, 2), (0, 6), (3, 0), (1, 7)?\n\nPresent the a... | 117 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (1, 4), (3, 3), (0, 5), (2, 6), (0, 2), (4, 3)?\n\nPresent the a... | 7 | MATH |
[
{
"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: (7, 1), (3, 4), (0, 8), (1, 6), (2, 8), (0, 2), (1, 2), (4, 0), (0, 1), ... | 1181 | MATH |
[
{
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (0, 6), (7, 5), (4, 1), (6, 1), (7, 4), (4, 0)?\n\nPresent the a... | 2210 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (3, 1), (0, 2), (0, 1), (2, 5), (1, 3), (1, 4), (3, 4), (3, 0)?\... | 12 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 1), (3, 0), (3, 2), (3, 6), (0, 6), (2, 4)?\n\nPresent the a... | 16 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (3, 3), (6, 3), (1, 0), (5, 5), (2, 0), (0, 5), (3, 4), (4, 5)?\... | 34 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (4, 5), (4, 3), (3, 4), (6, 2), (5, 5), (2, 5), (8, 3), (1, 3), ... | 180 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 5), (4, 0), (0, 1), (4, 1), (1, 3), (4, 5), (4, 4)?\n\nPrese... | 18 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (5, 1), (1, 4), (5, 0), (3, 1), (3, 0), (5, 2)?\n\nPresent the a... | 66 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 2), (3, 2), (4, 0), (3, 1), (1, 1), (2, 3)?\n\nPresent the a... | 2 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 1), (8, 1), (5, 7), (3, 1), (6, 4), (2, 5), (8, 4), (3, 7), ... | 249 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (2, 3), (0, 3), (3, 0), (3, 1), (2, 0), (4, 0)?\n\nPresent the a... | 8 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (1, 5), (0, 6), (4, 6), (5, 0), (2, 7), (6, 7), (3, 0), (8, 2), ... | 1285 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (7, 7), (1, 3), (8, 0), (0, 6), (3, 6), (3, 0), (8, 5), (2, 2), ... | 173 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (3, 6), (5, 5), (4, 3), (5, 7), (5, 1), (4, 5)?\n\nPresent the a... | 65 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (4, 8), (3, 8), (7, 0), (6, 5), (7, 2), (3, 6), (7, 7), (6, 4), ... | 1099 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (6, 1), (7, 4), (3, 4), (7, 1), (2, 1), (3, 1), (4, 4), (3, 0), ... | 232 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (3, 0), (2, 3), (5, 3), (1, 2), (7, 3), (5, 2), (7, 1)?\n\nPrese... | 23 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 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, 8), (3, 5), (3, 2), (0, 5), (0, 1), (2, 8), (4, 3), (1, 1)?\n\nPrese... | 91 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 3), (2, 2), (2, 0), (3, 3), (1, 1), (4, 4), (0, 6)?\n\nPrese... | 24 | MATH |
[
{
"content": "In a 7x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (0, 4), (1, 2), (1, 3), (2, 0), (0, 3), (6, 1)?\n\nPresent the a... | 62 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 0), (3, 5), (0, 3), (3, 3), (0, 4), (0, 6), (4, 5), (4, 4)?\... | 11 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (8, 2), (7, 3), (3, 6), (4, 6), (0, 4), (2, 5)?\n\nPresent the a... | 1116 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (4, 4), (3, 0), (4, 1), (1, 2), (1, 5), (1, 3)?\n\nPresent the a... | 17 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (5, 1), (1, 3), (3, 3), (3, 2), (0, 3), (2, 1), (2, 0), (0, 4)?\... | 3 | MATH |
[
{
"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: (5, 7), (3, 3), (0, 5), (4, 3), (6, 6), (1, 5), (3, 7)?\n\nPresent the a... | 441 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 7), (4, 7), (3, 4), (0, 7), (4, 2), (1, 3)?\n\nPresent the a... | 73 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 0), (5, 3), (2, 3), (4, 1), (1, 1), (3, 0), (1, 4), (1, 3)?\... | 3 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (5, 1), (3, 3), (5, 4), (1, 4), (5, 2), (2, 3), (1, 3), (3, 1)?\... | 7 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 2), (0, 2), (2, 0), (5, 4), (2, 4), (4, 4)?\n\nPresent the a... | 6 | MATH |
[
{
"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\nPrese... | 1870 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (3, 7), (6, 3), (2, 8), (5, 0), (8, 1), (3, 2), (5, 1)?\n\nPrese... | 6225 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (4, 0), (4, 4), (3, 3), (1, 0), (0, 2), (3, 2)?\n\nPresent the a... | 9 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (5, 4), (5, 3), (5, 7), (6, 3), (2, 3), (0, 4)?\n\nPresent the a... | 310 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (6, 5), (0, 1), (2, 0), (4, 5), (1, 7), (6, 1)?\n\nPresent the a... | 136 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (5, 3), (1, 0), (5, 0), (4, 3), (2, 3), (5, 1), (2, 7)?\n\nPrese... | 179 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (0, 5), (7, 6), (1, 4), (6, 0), (2, 5), (8, 4), (8, 5), (2, 3), ... | 526 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 2), (5, 1), (7, 0), (4, 1), (6, 2), (2, 0), (7, 2), (5, 4)?\... | 20 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 0), (3, 3), (5, 1), (3, 2), (1, 0), (4, 4), (0, 4)?\n\nPrese... | 2 | MATH |
[
{
"content": "In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (4, 1), (4, 2), (1, 0), (3, 3), (2, 4), (3, 6)?\n\nPresent the a... | 62 | MATH |
[
{
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (7, 2), (6, 5), (5, 7), (0, 3), (2, 6), (5, 3), (6, 3), (2, 7), ... | 461 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (6, 6), (1, 0), (2, 7), (8, 1), (4, 5), (5, 2), (5, 7), (0, 2), ... | 197 | MATH |
[
{
"content": "In a 7x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (3, 4), (5, 5), (0, 2), (5, 1), (3, 0), (3, 3), (2, 5)?\n\nPrese... | 66 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 5), (0, 5), (1, 4), (3, 4), (5, 2), (0, 4), (1, 6), (5, 1)?\... | 175 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (2, 0), (6, 0), (5, 5), (2, 3), (1, 2), (4, 7), (3, 5)?\n\nPrese... | 118 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (1, 0), (1, 6), (2, 2), (0, 5), (3, 2), (1, 3)?\n\nPresent the a... | 4 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 4), (3, 4), (3, 1), (2, 2), (1, 1), (1, 3), (1, 2), (4, 4)?\... | 1 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 3), (4, 4), (0, 3), (5, 1), (1, 1), (2, 4)?\n\nPresent the a... | 26 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (5, 1), (0, 8), (6, 0), (2, 2), (2, 7), (0, 7), (1, 7), (0, 1), ... | 298 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 5), (4, 0), (2, 3), (1, 0), (5, 3), (5, 2), (1, 6)?\n\nPrese... | 44 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (4, 5), (4, 2), (0, 4), (0, 1), (0, 2), (0, 5), (4, 0), (3, 1)?\... | 19 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 3), (0, 1), (1, 4), (2, 0), (2, 2), (4, 0), (2, 4)?\n\nPrese... | 4 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (1, 5), (3, 1), (0, 1), (1, 3), (6, 0), (2, 4), (4, 5), (0, 2), ... | 152 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (8, 0), (8, 2), (7, 2), (7, 0), (5, 1), (5, 5)?\n\nPresent the a... | 750 | MATH |
[
{
"content": "In a 7x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (4, 4), (5, 3), (1, 2), (3, 2), (0, 4), (6, 0), (5, 4)?\n\nPrese... | 6 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (3, 2), (5, 0), (5, 6), (6, 6), (7, 0), (4, 2)?\n\nPresent the a... | 1375 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 3), (2, 5), (4, 0), (3, 2), (1, 2), (3, 6), (3, 5), (0, 4), ... | 87 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (5, 0), (5, 3), (1, 4), (0, 3), (4, 2), (3, 4)?\n\nPresent the a... | 9 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 6), (6, 3), (2, 0), (0, 5), (1, 1), (1, 6)?\n\nPresent the a... | 364 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (5, 5), (6, 3), (1, 8), (4, 7), (1, 7), (2, 2), (3, 6), (4, 2), ... | 144 | MATH |
[
{
"content": "In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (4, 5), (1, 8), (1, 3), (2, 6), (2, 8), (3, 6)?\n\nPresent the a... | 6 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (0, 2), (3, 5), (1, 2), (4, 1), (1, 0), (2, 4)?\n\nPresent the a... | 5 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 2), (0, 2), (1, 4), (3, 4), (0, 5), (4, 2)?\n\nPresent the a... | 4 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 0), (0, 6), (1, 3), (4, 2), (5, 3), (3, 4), (5, 2)?\n\nPrese... | 56 | MATH |
[
{
"content": "In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (4, 3), (2, 2), (3, 6), (4, 0), (3, 4), (2, 4)?\n\nPresent the a... | 21 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (4, 7), (3, 0), (3, 6), (5, 4), (1, 8), (4, 6), (3, 3), (2, 6)?\... | 71 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (3, 5), (4, 3), (1, 5), (6, 0), (2, 4), (2, 3), (4, 2)?\n\nPrese... | 236 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (2, 3), (0, 4), (2, 0), (2, 4), (1, 4), (5, 2)?\n\nPresent the a... | 7 | MATH |
[
{
"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, 8), (5, 1), (5, 6), (2, 1), (6, 2), (6, 6), (3, 6), (2, 3), (2, 0), ... | 187 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (4, 1), (5, 4), (0, 2), (0, 1), (7, 0), (4, 2), (6, 0), (7, 3), ... | 6 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (0, 2), (3, 1), (2, 5), (3, 0), (2, 6), (2, 1)?\n\nPresent the a... | 20 | MATH |
[
{
"content": "In a 5x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 0), (2, 6), (4, 0), (1, 1), (2, 1), (1, 4)?\n\nPresent the a... | 19 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (1, 7), (2, 6), (0, 3), (6, 5), (0, 7), (3, 2), (5, 7), (3, 8), ... | 315 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (3, 1), (1, 6), (4, 5), (1, 1), (1, 2), (5, 5), (0, 4), (5, 6), ... | 40 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (2, 1), (5, 4), (6, 3), (6, 0), (5, 0), (0, 2), (5, 3)?\n\nPrese... | 2 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (6, 5), (6, 3), (4, 5), (2, 1), (6, 2), (4, 2), (0, 6), (3, 0), ... | 114 | MATH |
[
{
"content": "In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (1, 4), (3, 0), (4, 0), (1, 3), (5, 4), (0, 3), (2, 2), (4, 3), ... | 30 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (4, 2), (2, 0), (2, 2), (2, 1), (4, 0), (5, 3), (5, 2), (5, 1)?\... | 8 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (4, 4), (2, 8), (4, 2), (4, 5), (3, 6), (1, 8), (0, 7)?\n\nPrese... | 308 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 6), (2, 1), (2, 7), (3, 5), (4, 4), (4, 1)?\n\nPresent the a... | 8 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 1), (4, 1), (2, 1), (0, 2), (3, 2), (0, 5)?\n\nPresent the a... | 32 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 3), (3, 0), (1, 3), (4, 2), (1, 4), (4, 0), (5, 3), (3, 2)?\... | 10 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (5, 2), (3, 5), (2, 1), (1, 0), (0, 4), (4, 3), (4, 2), (1, 3)?\... | 10 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (0, 1), (0, 4), (1, 4), (1, 3), (7, 4), (4, 1), (2, 0), (3, 4), ... | 167 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (7, 4), (1, 0), (8, 3), (5, 3), (8, 5), (2, 2)?\n\nPresent the a... | 2385 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1), (3, 3), (4, 2), (0, 5), (8, 0), (5, 6), (0, 4), (4, 3), ... | 159 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 3), (3, 2), (0, 6), (2, 7), (1, 2), (5, 2), (0, 2), (3, 7), ... | 70 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 3), (8, 1), (0, 8), (5, 5), (2, 8), (6, 0), (3, 2), (4, 0), ... | 1420 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (7, 1), (8, 0), (7, 5), (3, 0), (1, 3), (5, 0), (6, 1), (8, 3), ... | 148 | MATH |
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