messages listlengths 1 1 | ground_truth stringclasses 5 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 2), (3, 0), (2, 1)? If i... | 2 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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)? If it's impossible, ... | 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: (5, 3), (4, 2), (3, 0), (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: (0, 4), (0, 2), (1, 5), (1, ... | 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: (4, 1), (1, 4), (0, 3), (1, ... | 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: (4, 2), (0, 1), (1, 5), (3, ... | 3 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (1, 1)? If i... | 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), 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), (1, 0)? If it's impo... | -1 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (2, 0)? If it's impo... | 2 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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), (0, 3), (1, 3), (4, ... | 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, 4), (3, 5), (1, 1), (4, ... | 3 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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, 0), (4, 2)? If i... | 3 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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), (4, 2), (2, 2), (3, ... | 2 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (3, 0), (1, 0)? If i... | 3 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (3, 1), (4, 2), (4, ... | 2 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), 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)? If it's impossible, ... | 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), 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), (2, 1), (0, 1)? If i... | 2 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (1, 1)? If i... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (4, 0), (3, 1), (3, ... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (2, 3), (1, 3)? If i... | 2 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 2)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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, 3), (5, 2), (0, 3), (4, ... | -1 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 4)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (5, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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, 2)? If it's impo... | 3 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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), (1, 3), (2, 2), (1, ... | -1 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (1, 0), (1, 4)? If i... | 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), 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), (1, 0), (0, 1)? If i... | -1 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), 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), (1, 2), (2, 0), (1, ... | 3 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (5, 1), (1, 3), (2, ... | 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), 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), (2, 1), (0, 1)? If i... | 3 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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), (1, 0)? If it's impo... | 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), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 3), (2, 4), (2, 5)? If i... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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), (4, 1), (0, 3), (3, ... | 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), 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), (3, 2), (2, 2)? If i... | 3 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), 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), (1, 3), (0, 4)? If i... | 3 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (1, 3)? If it's impo... | 2 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 2), (0, 2), (1, ... | 2 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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), (4, 0), (1, 0), (4, ... | 2 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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, 0), (0, 3), (4, 0)? If i... | 3 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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, 0), (3, 2), (0, 1)? If i... | 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), 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, 0)? If it's impo... | 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), 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, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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), (2, 2)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (5, 0), (4, 1), (2, ... | 2 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 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, 3), (1, 1), (0, 1)? If i... | 2 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), 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, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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, 2)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (0, 2), (1, 3)? If i... | 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), 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), (1, 3), (0, 1)? If i... | -1 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), 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), (0, 1), (1, 4)? If i... | 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), 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, 4), (2, 3), (2, ... | 3 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 2), (4, 0)? If i... | 2 | MATH |
[
{
"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), 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, 1)? If it's impo... | 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), 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), (1, 1)? If it's impo... | 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), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 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, 1), (3, 3), (1, 4), (2, ... | 5 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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: ? If it's impossible, answer... | 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), 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), (1, 0), (3, 2), (2, ... | 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), 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), (4, 0), (2, 3), (4, ... | 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), 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), (2, 0)? If it's impo... | 3 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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), (1, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), 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, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 1)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (1, 3)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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, 1), (2, 3), (0, 4)? If i... | 3 | MATH |
[
{
"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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), (1, 3)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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), (4, 2), (2, 4)? If i... | 2 | MATH |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), 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), (4, 3), (0, 1), (1, ... | -1 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), 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: ? If it's impossible, answer... | 2 | MATH |
[
{
"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 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), (0, 3), (2, 1)? If i... | 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: (3, 1), (1, 1), (0, 4), (5, ... | 3 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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)? If it's impossible, ... | 2 | MATH |
[
{
"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), 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, 0), (0, 2), (5, 1)? If i... | 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), 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, 4), (1, 3), (0, ... | 2 | MATH |
[
{
"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), 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), (0, 2), (2, 0), (0, ... | 3 | MATH |
[
{
"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), 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, 3), (2, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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, 3), (3, 1), (2, 1)? If i... | 2 | MATH |
[
{
"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), 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), (2, 0), (5, 3), (4, ... | -1 | MATH |
[
{
"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), 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, 1)? If it's impo... | 2 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 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), (3, 2), (4, 1), (1, ... | -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, 0), (5, 1), (2, 4), (2, ... | 2 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 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, 1), (4, 4), (4, 2), (2, ... | 3 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 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), (2, 1), (2, 4), (2, ... | 2 | MATH |
[
{
"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 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), (0, 4), (3, 1), (1, ... | 3 | MATH |
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