messages listlengths 1 1 | ground_truth stringclasses 165
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"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, 1), (3, 3), (3, 1), (3, 4)?\n\nPresent the answer in LaTex format: \... | 6 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 3), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 13 | 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: (0, 6), (4, 3), (3, 1), (1, 1), (3, 4)?\n\nPresent the answer in LaTex f... | 37 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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), (2, 0), (4, 2), (0, 1)?\n\nPresent the answer in LaTex format: \... | 2 | MATH |
[
{
"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 1), (2, 1), (3, 3), (1, 0)?\n\nPresent the answer in LaTex format: \... | 9 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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), (0, 1), (4, 0), (3, 1), (1, 1)?\n\nPresent the answer in LaTex f... | 1 | 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, 3), (2, 4), (0, 2), (1, 2), (4, 2)?\n\nPresent the answer in LaTex f... | 28 | 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, 4), (5, 3), (1, 2), (3, 4)?\n\nPresent the answer in LaTex format: \... | 190 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 1 | 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: (1, 2), (3, 4), (5, 5), (3, 0), (2, 6)?\n\nPresent the answer in LaTex f... | 37 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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, 2), (2, 2), (3, 1)?\n\nPresent the answer in LaTex format: \... | 3 | 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, 3), (4, 3), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 67 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), 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, 2), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), 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), (1, 4), (0, 3), (0, 2)?\n\nPresent the answer in LaTex format: \... | 19 | MATH |
[
{
"content": "In a 7x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 2), 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, 1), (2, 2), (4, 0), (3, 0), (4, 2)?\n\nPresent the answer in... | 4 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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, 0), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 14 | 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), (2, 2), (1, 1), (0, 3)?\n\nPresent the answer in LaTex format: \... | 18 | MATH |
[
{
"content": "In a 7x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 2), 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), (2, 0), (1, 1), (5, 1), (4, 2)?\n\nPresent the answer in LaTex f... | 0 | 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, 0), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 91 | MATH |
[
{
"content": "In a 3x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 17 | 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: (0, 1), (3, 5), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 15 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 0), (2, 1), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 25 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 6), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 26 | 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: (1, 1), (4, 1), (3, 3), (2, 4), (4, 0)?\n\nPresent the answer in LaTex f... | 4 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 3), (2, 3), (0, 6)?\n\nPresent the answer in LaTex format: \... | 16 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 7 | MATH |
[
{
"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), 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), (2, 0), (2, 1), (0, 1), (4, 0)?\n\nPresent the answer in LaTex f... | 0 | 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: (3, 3), (2, 0), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 100 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 6 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), 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), (1, 4), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 16 | 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), (3, 1), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 62 | MATH |
[
{
"content": "In a 7x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 3), 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), (1, 0), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 25 | 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, 1), (0, 4), (2, 0), (1, 5), (1, 0)?\n\nPresent the answer in LaTex f... | 57 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 5 | 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: (4, 3), (4, 1), (2, 4), (1, 1), (1, 0), (4, 4)?\n\nPresent the answer in... | 3 | 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), (0, 5), (1, 1), (4, 2), (0, 4)?\n\nPresent the answer in LaTex f... | 77 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 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, 6), (2, 2), (1, 1), (0, 5)?\n\nPresent the answer in LaTex format: \... | 35 | 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: (6, 2), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 392 | 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: (1, 1), (3, 5), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 30 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 29 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3 | MATH |
[
{
"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), 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, 0), (1, 0), (3, 1), (2, 0)?\n\nPresent the answer in LaTex f... | 0 | 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, 0), (3, 3), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 114 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 2 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 5), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 48 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 8 | 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, 3), (1, 4), (2, 5), (0, 4), (0, 5)?\n\nPresent the answer in LaTex f... | 55 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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, 0), (2, 2), (5, 0), (1, 2)?\n\nPresent the answer in LaTex f... | 3 | MATH |
[
{
"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), 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), (3, 2), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 6 | MATH |
[
{
"content": "In a 7x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 3), 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, 3), (5, 1), (3, 1), (2, 1), (2, 3), (1, 0)?\n\nPresent the a... | 2 | 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: (4, 2), (1, 1), (3, 6), (3, 1), (5, 1), (5, 4), (2, 3)?\n\nPresent the a... | 60 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 3), (1, 6), (1, 1)?\n\nPresent the answer in LaTex format: \... | 9 | MATH |
[
{
"content": "In a 3x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 5), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 11 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), 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, 3), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 5 | 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: (1, 2), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 66 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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, 1), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | 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, 0), (3, 0), (0, 4), (0, 3), (2, 3)?\n\nPresent the answer in LaTex f... | 120 | MATH |
[
{
"content": "In a 7x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 3), 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, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 35 | 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, 5), (5, 5), (0, 6), (0, 2)?\n\nPresent the answer in LaTex format: \... | 107 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), 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), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 15 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 6 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (1, 0), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 11 | 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, 3), (3, 6), (1, 5), (5, 1), (1, 6), (3, 5)?\n\nPresent the answer in... | 244 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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), (1, 0), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 9 | 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: (4, 4), (6, 4), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 259 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 18 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 2), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 9 | MATH |
[
{
"content": "In a 3x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 18 | 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: (6, 3), (5, 1), (3, 4), (1, 3), (2, 2)?\n\nPresent the answer in LaTex f... | 86 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (2, 0), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 2 | MATH |
[
{
"content": "In a 7x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 3), 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, 3), (0, 1), (2, 3), (5, 3)?\n\nPresent the answer in LaTex f... | 11 | 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: (6, 3), (4, 4), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 357 | 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, 0), (5, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 117 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 3), (0, 3), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 21 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), 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), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 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: (4, 0), (0, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 208 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 2 | MATH |
[
{
"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), 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), (0, 2), (1, 1), (1, 0), (3, 1)?\n\nPresent the answer in LaTex f... | 0 | MATH |
[
{
"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), 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), (1, 1), (1, 0), (2, 1)?\n\nPresent the answer in LaTex format: \... | 1 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), 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), (2, 1), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 5 | 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: (1, 3), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 31 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 3), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 8 | 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), (0, 3), (2, 0), (2, 4)?\n\nPresent the answer in LaTex format: \... | 26 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 14 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), 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, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 5 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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), (3, 2), (0, 3), (3, 0), (3, 1)?\n\nPresent the answer in LaTex f... | 9 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 2), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 2 | MATH |
[
{
"content": "In a 3x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 1), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 10 | 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, 3), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 246 | MATH |
[
{
"content": "In a 3x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 5), (1, 5), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 14 | MATH |
[
{
"content": "In a 4x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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), (1, 2), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Y... | 13 | 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), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 140 | 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: (1, 6), (0, 6), (0, 1), (0, 3), (1, 5)?\n\nPresent the answer in LaTex f... | 205 | 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: (6, 1), (2, 1), (0, 2), (6, 0), (3, 4), (1, 3), (1, 1)?\n\nPresent the a... | 30 | MATH |
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