messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 0), (5, 8), (2, 8), (1, 2), (9, 6), (6, 8), (8, 0), (8, 1), (9, 7),... | 876 | 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: (6, 1), (3, 5), (0, 3), (3, 4), (2, 1), (7, 0)?\n\nPresent the answer in... | 470 | 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, 4), (7, 3), (6, 2), (0, 3), (1, 1)?\n\nPresent the answer in LaTex f... | 486 | MATH |
[
{
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 0), (2, 3), (1, 6), (0, 3), (6, 0), (2, 2), (1, 4), (5, 1),... | 288 | MATH |
[
{
"content": "In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), 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, 8), (6, 8), (5, 1), (1, 8), (0, 9), (6, 6), (3, 1), (5, 6)?... | 1612 | 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, 4), (2, 3), (1, 3), (4, 5), (6, 5), (5, 4), (1, 1), (4, 6)?\n\nPrese... | 0 | 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: (5, 6), (1, 1), (5, 0), (4, 2), (3, 6)?\n\nPresent the answer in LaTex f... | 134 | MATH |
[
{
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (6, 3), (2, 6), (2, 1), (0, 5), (1, 4), (0, 3), (2, 0), (8, 7),... | 0 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 2), (9, 5), (5, 2), (7, 2), (6, 0), (5, 4), (4, 4), (6, 4)?\n\nPres... | 5232 | 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, 6), (1, 5), (0, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 12105 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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), (5, 4), (4, 3), (2, 0), (8, 5), (8, 0), (6, 6), (4, 4), (5, 3),... | 21 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 3), (3, 6), (0, 5), (7, 4), (6, 1), (6, 6), (1, 1), (0, 4), (6, 3),... | 210 | MATH |
[
{
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (7, 3), (6, 7), (3, 0), (7, 1), (7, 4), (6, 3), (6, 8), (2, 0),... | 1622 | 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: (7, 0), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3312 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 3), (4, 4), (4, 7), (9, 0), (7, 3), (8, 5), (3, 1), (1, 7), (0, 7),... | 2560 | 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: (3, 7), (3, 0), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 1681 | 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: (4, 1), (7, 1), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 1083 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 2), (6, 1), (1, 8), (5, 6), (3, 2), (9, 2)?\n\nPresent the answer i... | 7390 | 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), (3, 4), (2, 5), (3, 7), (2, 3), (3, 3)?\n\nPresent the answer in... | 183 | 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: (2, 3), (6, 5), (2, 1), (7, 2), (4, 1), (4, 5), (3, 2), (2, 8), (4, 4), ... | 380 | 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: (5, 7), (5, 6), (3, 4), (1, 4), (5, 5)?\n\nPresent the answer in LaTex f... | 175 | MATH |
[
{
"content": "In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), 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), (5, 9), (6, 3), (6, 0), (3, 0), (1, 7), (6, 5)?\n\nPresent the ... | 6309 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 6), (7, 0), (9, 2), (5, 2), (8, 3), (2, 5), (8, 6)?\n\nPresent the ... | 966 | 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: (0, 3), (0, 6), (4, 5), (1, 5), (4, 2), (5, 5), (6, 2), (2, 1), (3, 5), ... | 90 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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), (6, 0), (8, 3), (3, 7), (5, 6), (2, 5), (7, 6), (8, 7), (3, 3),... | 414 | 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: (4, 8), (8, 7), (6, 3), (0, 7), (5, 8), (7, 3), (1, 4), (8, 6), (1, 1), ... | 581 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 2), (5, 3), (4, 0), (8, 2), (8, 3), (4, 3), (3, 5)?\n\nPresent the ... | 1119 | 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: (1, 1), (5, 6), (3, 4), (0, 5), (2, 6)?\n\nPresent the answer in LaTex f... | 149 | 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, 4), (0, 8), (7, 2), (4, 4), (4, 7), (6, 6), (1, 5), (6, 2), (0, 7), ... | 649 | 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: (2, 0), (0, 7), (6, 7), (2, 6), (0, 5), (2, 7), (7, 3), (8, 4), (3, 7), ... | 1236 | 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: (3, 2), (8, 5), (1, 4), (7, 8), (7, 0), (6, 1), (2, 5), (5, 5), (2, 8), ... | 976 | 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: (2, 4), (5, 1), (3, 3), (1, 3), (4, 2), (2, 0), (7, 5), (7, 7), (3, 2), ... | 0 | 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: (4, 3), (6, 2), (0, 4), (6, 1), (5, 2), (2, 4)?\n\nPresent the answer in... | 3009 | 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, 6), (5, 6), (6, 2), (3, 1), (5, 2), (2, 3), (1, 7), (1, 8), (1, 4), ... | 230 | 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: (0, 4), (8, 3), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 2793 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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), (3, 8), (6, 2), (8, 0), (7, 3), (1, 1)?\n\nPresent the answer i... | 6556 | 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: (3, 5), (2, 1), (5, 6), (0, 1)?\n\nPresent the answer in LaTex format: \... | 212 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 8), (5, 8), (6, 0), (3, 6), (3, 3), (6, 4), (5, 4), (3, 4), (8, 8)?... | 2472 | 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, 2), (3, 0), (7, 3), (4, 0), (2, 5), (2, 0), (3, 4), (1, 4), (3, 3), ... | 222 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 4), (0, 3), (0, 1), (7, 6), (9, 2)?\n\nPresent the answer i... | 1153 | 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: (3, 7), (3, 4), (3, 2), (5, 1)?\n\nPresent the answer in LaTex format: \... | 900 | MATH |
[
{
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), 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), (4, 9), (2, 7), (3, 3), (2, 4), (0, 9), (3, 7), (5, 4), (3, 1),... | 1188 | 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, 1), (3, 8), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 2378 | 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, 2), (2, 3), (6, 2), (1, 2)?\n\nPresent the answer in LaTex format: \... | 2472 | 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: (7, 4), (2, 4), (6, 2), (3, 6)?\n\nPresent the answer in LaTex format: \... | 1431 | 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, 5), (0, 2), (3, 5), (4, 3), (6, 1), (7, 3), (0, 3)?\n\nPresent the a... | 1162 | 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, 3), (6, 2), (3, 1), (7, 6), (3, 2)?\n\nPresent the answer in LaTex f... | 828 | 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, 3), (4, 5), (6, 6), (3, 6), (3, 1), (5, 2), (1, 2)?\n\nPresent the a... | 122 | 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), (4, 3), (5, 5), (0, 2), (4, 0), (3, 6)?\n\nPresent the answer in... | 108 | 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: (3, 6), (4, 6), (5, 3), (1, 5), (4, 0), (6, 2), (4, 2)?\n\nPresent the a... | 649 | 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: (5, 5), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3327 | 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: (3, 6), (0, 2), (6, 1), (0, 8), (3, 8), (1, 0), (8, 1), (1, 6)?\n\nPrese... | 2930 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 4), (7, 8), (5, 3), (5, 1), (0, 7), (3, 0), (7, 1), (8, 0), (4, 5)?... | 3336 | MATH |
[
{
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (8, 3), (2, 4), (9, 3), (5, 2)?\n\nPresent the answer in LaTex ... | 6555 | 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, 0), (5, 4), (6, 2), (2, 5), (2, 7)?\n\nPresent the answer in LaTex f... | 854 | 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, 0), (0, 1), (4, 3), (2, 3), (4, 0), (5, 3), (2, 0), (5, 5), (5, 1)?\... | 27 | MATH |
[
{
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), 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), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4445 | 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, 2), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 783 | MATH |
[
{
"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), 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), (5, 3), (1, 7), (9, 7), (2, 0), (7, 8), (3, 6), (1, 0), (0, 9)... | 427 | MATH |
[
{
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), 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), (6, 4), (2, 6), (3, 1), (0, 2), (4, 4)?\n\nPresent the answer i... | 522 | 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: (4, 0), (2, 2), (7, 1), (2, 5), (5, 2), (7, 5), (2, 4), (3, 0), (1, 0), ... | 259 | MATH |
[
{
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 4), (6, 1), (7, 2), (0, 2), (9, 4), (1, 1), (9, 5), (6, 5), (3, 6),... | 192 | 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: (2, 4), (1, 4), (0, 3), (0, 7), (4, 1), (1, 3), (5, 5)?\n\nPresent the a... | 367 | 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, 1), (1, 0), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 937 | 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, 3), (5, 5), (3, 2), (3, 5), (3, 4), (5, 1), (7, 1), (4, 3), (4, 2), ... | 8 | 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, 2), (0, 2), (4, 3), (5, 7), (6, 2), (5, 3)?\n\nPresent the answer in... | 709 | 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: (3, 1), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 1506 | 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, 2), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 516 | MATH |
[
{
"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), 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), (9, 5), (1, 8), (9, 1), (7, 8), (6, 5), (6, 0), (3, 9), (4, 7)... | 1799 | 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: (1, 1), (0, 3), (3, 5), (6, 6), (3, 0), (5, 6), (2, 3), (7, 2), (7, 1), ... | 134 | MATH |
[
{
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (2, 4), (6, 2), (0, 6), (3, 9), (5, 9), (1, 4), (0, 7), (6, 5)?... | 1262 | 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: (5, 3), (4, 3), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 490 | 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, 1), (8, 0), (4, 6), (7, 8), (8, 4), (6, 2), (2, 0)?\n\nPresent the a... | 3323 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 2), (7, 8), (7, 6), (5, 8), (5, 4), (2, 0), (6, 5), (5, 2), (4, 1),... | 838 | 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: (2, 1), (2, 4), (1, 7), (1, 5), (2, 5), (6, 6)?\n\nPresent the answer in... | 208 | 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, 2), (2, 5), (1, 0), (8, 6), (3, 1), (3, 7), (4, 3), (3, 4), (7, 3)?\... | 34 | 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: (1, 2), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 252 | 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: (8, 2), (3, 2), (5, 6), (0, 2), (2, 3), (6, 8), (3, 6), (8, 0), (2, 0), ... | 366 | 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: (8, 4), (7, 3), (7, 4), (7, 5)?\n\nPresent the answer in LaTex format: \... | 9207 | MATH |
[
{
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), 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), (8, 4), (7, 3), (7, 8), (1, 0), (3, 8), (7, 9), (2, 9), (4, 2),... | 1268 | MATH |
[
{
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), 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), (3, 8), (2, 4), (0, 9)?\n\nPresent the answer in LaTex format: ... | 1794 | 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, 4), (2, 7), (6, 5), (2, 2), (1, 2), (0, 6)?\n\nPresent the answer in... | 282 | MATH |
[
{
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), 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), (6, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 11110 | 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: (4, 3), (6, 2), (5, 1), (7, 4), (2, 4), (4, 0), (0, 1), (2, 5)?\n\nPrese... | 455 | 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: (0, 1), (8, 5), (0, 2), (8, 2), (2, 2), (6, 0), (4, 3), (2, 6), (2, 4), ... | 170 | MATH |
[
{
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), 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, 0), (8, 3), (3, 5), (6, 7)?\n\nPresent the answer in LaTex ... | 5867 | 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: (2, 0), (6, 3), (3, 4), (2, 5), (0, 1), (5, 3), (0, 5)?\n\nPresent the a... | 106 | 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: (3, 5), (5, 0), (4, 8), (6, 6), (2, 1), (0, 4), (3, 0)?\n\nPresent the a... | 940 | 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: (2, 1), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 1413 | MATH |
[
{
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (8, 1), (4, 4), (7, 3), (2, 7), (1, 4), (8, 5), (8, 4), (5, 4),... | 236 | 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, 2), (0, 5), (0, 1), (1, 0), (6, 6)?\n\nPresent the answer in LaTex f... | 0 | MATH |
[
{
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 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, 0), (9, 3), (4, 4), (6, 2), (5, 1), (0, 4), (5, 6), (7, 4), (8, 8),... | 200 | 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, 0), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 11025 | 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, 6), (1, 2), (1, 6)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 1974 | 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: (2, 6), (6, 8), (5, 4), (6, 6), (2, 2), (3, 8), (7, 6), (7, 2)?\n\nPrese... | 302 | 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: (0, 3), (1, 2), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 444 | 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, 2), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 700 | 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, 6), (6, 6), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 4446 | 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: (6, 8), (7, 1), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 2584 | 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, 7), (6, 7), (0, 1), (3, 3), (6, 4)?\n\nPresent the answer in LaTex f... | 280 | MATH |
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