messages listlengths 1 1 | ground_truth stringclasses 7 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (6, 5), (6, 7), (3, ... | 4 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (2, 0), (2, 7), (5, ... | 3 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (2, 8), (0, 5), (2, ... | 4 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (0, 6), (0, 2), (0, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (6, 3), (1, 5), (5, ... | 3 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (8, 0), (0, 3), (7, ... | 3 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (7, 1), (5, 3), (8, ... | 4 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 0), (3, 0), (2, ... | 3 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 1), (4, 6), (5, ... | 2 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (3, 3), (5, 4), (2, ... | 3 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (7, 2), (4, 4), (7, ... | 5 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (3, 6), (2, 2), (2, ... | -1 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (1, 5), (4, 4), (8, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (0, 2), (5, 5), (1, ... | 3 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (6, 2), (5, 4), (2, ... | 2 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (3, 0), (2, 5), (3, ... | 4 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 6), (3, 5), (4, ... | 4 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (4, 1), (5, 5), (6, ... | 4 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (5, 4), (6, 6), (5, ... | 3 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (5, 0), (1, 4), (4, ... | 5 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 5), (5, 2), (0, ... | 3 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (8, 3), (3, 5), (1, ... | 6 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (4, 6), (1, 2), (8, ... | 4 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (4, 0), (1, 1), (5, ... | 6 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (2, 4), (2, 2), (7, ... | -1 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (5, 0), (0, 1), (1, ... | 3 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (5, 5), (0, 2), (5, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (3, 3), (0, 2), (0, ... | 4 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 6), (5, 6), (2, ... | 4 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 3), (6, 5), (6, ... | 5 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 3), (1, 1), (1, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (5, 3), (4, 5), (0, ... | 3 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 3), (6, 2), (2, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 4), (3, 3), (3, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 5), (0, 5), (1, ... | -1 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (7, 1), (0, 4), (7, ... | 4 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (5, 2), (7, 4), (3, ... | 4 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (6, 5), (6, 1), (1, ... | 5 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (8, 0), (6, 6), (8, ... | 4 | MATH |
[
{
"content": "In a 7x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (5, 5), (0, 2), (1, ... | -1 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (4, 5), (1, 5), (7, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (2, 0), (4, 0), (4, ... | 3 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (8, 1), (5, 2), (7, ... | -1 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (4, 0), (2, 6), (3, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 3), (4, 7), (6, ... | 5 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (6, 6), (0, 6), (5, ... | 4 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 2), (3, 3), (4, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (5, 1), (5, 4), (4, ... | 2 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (7, 2), (5, 3), (7, ... | 3 | MATH |
[
{
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 6), (4, 2), (2, ... | 5 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (4, 3), (0, 2), (7, ... | 5 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (7, 2), (6, 8), (6, ... | 3 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (8, 0), (6, 5), (0, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (3, 4), (1, 2), (0, ... | 5 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 4), (1, 2), (1, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (5, 1), (3, 4), (2, ... | 2 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 6), (0, 4), (0, ... | 3 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 6), (1, 3), (7, ... | 3 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (5, 1), (2, 5), (8, ... | 4 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (4, 0), (3, 5), (2, ... | 4 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (4, 5), (2, 3), (5, ... | 3 | MATH |
[
{
"content": "In a 7x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (2, 3), (2, 1), (4, ... | 2 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (7, 2), (3, 3), (6, ... | -1 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 4), (6, 2), (0, ... | 3 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (1, 2), (1, 1), (2, ... | -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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 2), (3, 0), (1, ... | 5 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (0, 3), (1, 0), (7, ... | -1 | MATH |
[
{
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (3, 6), (2, 5), (5, ... | 2 | MATH |
[
{
"content": "In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (3, 7), (5, 1), (1, ... | 3 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 0), (3, 2), (1, ... | 4 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (6, 0), (4, 1), (6, ... | -1 | MATH |
[
{
"content": "In a 7x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (1, 5), (5, 1), (0, ... | 2 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (2, 2), (0, 2), (2, ... | 6 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (5, 1), (3, 4), (7, ... | 2 | MATH |
[
{
"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 4), (2, 0), (3, ... | 4 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (4, 6), (4, 1), (3, ... | 3 | MATH |
[
{
"content": "In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 1), (2, 2), (0, ... | 2 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 5), (0, 6), (1, ... | 4 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 2), (1, 3), (4, ... | -1 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (8, 3), (7, 1), (4, ... | 3 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (2, 1), (1, 1), (1, ... | 2 | MATH |
[
{
"content": "In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (6, 1), (5, 4), (4, ... | 2 | MATH |
[
{
"content": "In a 7x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 2), (5, 1), (2, ... | 2 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (6, 0), (0, 6), (5, ... | 5 | MATH |
[
{
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (2, 1), (5, 2), (4, ... | -1 | MATH |
[
{
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (6, 0), (2, 6), (5, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (1, 4), (0, 1), (4, ... | -1 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (6, 1), (1, 8), (5, ... | -1 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (0, 3), (4, 3), (1, ... | 3 | MATH |
[
{
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (8, 4), (5, 1), (5, ... | 5 | MATH |
[
{
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (7, 7), (7, 6), (3, ... | -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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (5, 2), (0, 5), (3, ... | 3 | MATH |
[
{
"content": "In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (7, 1), (3, 1), (4, ... | -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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 4), (1, 6), (5, ... | 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), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (7, 6), (7, 5), (7, ... | -1 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 0), (1, 2), (1, ... | 3 | MATH |
[
{
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 4), (6, 0), (0, ... | 3 | MATH |
[
{
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 0), (3, 2), (1, 0), (3, ... | -1 | MATH |
[
{
"content": "In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (0, 1), (1, 5), (4, ... | -1 | MATH |
[
{
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 1), (5, 4), (7, ... | 7 | MATH |
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