[User]
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: (0, 2), (4, 5), (5, 0), (0, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 2), (5, 0), (4, 2), (6, 3), (6, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (3, 1), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (3, 5), (0, 2), (4, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (2, 5), (4, 6), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (1, 0), (0, 3), (0, 4), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (1, 3), (0, 2), (5, 3), (1, 4), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (0, 1), (1, 0), (4, 2), (5, 1), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (0, 3), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 0), (1, 6)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 2), (0, 3), (5, 0), (3, 1), (4, 2), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 1), (1, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 2), (1, 0), (3, 1), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 0), (0, 1), (3, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (6, 0), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 0), (1, 2), (4, 0), (4, 1), (2, 1), (6, 0), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (0, 4), (3, 1), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 6), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (0, 1), (2, 4), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 6), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 4), (1, 0), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 0), (4, 4), (0, 2), (4, 3), (2, 0), (4, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (0, 3), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 1), (2, 4), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (6, 2), (2, 4), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 3), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (5, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 2), (1, 2), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 4), (1, 4), (1, 0), (1, 6)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 2), (3, 0), (0, 1), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (3, 0), (5, 0), (4, 1), (1, 0), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 0), (3, 1), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 3), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 1), (3, 0), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 1), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (4, 2), (4, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (1, 1), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 0), (2, 0), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (1, 4), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 4), (0, 2), (4, 1), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 6), (2, 5), (5, 4), (4, 4), (1, 6), (5, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 5), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (1, 1), (1, 4), (4, 3), (0, 4), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (3, 0), (1, 3), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 3), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (6, 0), (5, 2), (0, 2), (1, 0), (4, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (2, 0), (4, 0), (3, 0), (0, 2), (4, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (0, 1), (5, 1), (2, 4), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (1, 1), (1, 3), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 1), (5, 0), (3, 2), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (1, 3), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (2, 1), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (3, 1), (1, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 4), (1, 2), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (0, 4), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (0, 4), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (2, 0), (3, 1), (4, 1), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 1), (0, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 1), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (0, 1), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 1), (2, 1), (3, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (0, 2), (5, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 2), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (3, 5), (2, 5), (0, 2), (1, 5), (4, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 0), (2, 2), (1, 1), (4, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (2, 3), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (0, 2), (4, 0), (2, 1), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 3), (6, 3), (0, 1), (3, 0), (4, 2), (5, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 3), (1, 0), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 5), (0, 1), (1, 1), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (5, 3), (2, 5), (4, 2), (2, 2), (4, 0), (3, 6)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (4, 1), (2, 4), (4, 4), (5, 0), (6, 3), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (1, 4), (4, 3), (0, 1), (6, 2), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 4), (0, 4), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 3), (0, 3), (5, 0), (4, 3), (5, 3), (5, 2), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (5, 0), (5, 1), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (1, 0), (1, 3), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (4, 0), (1, 1), (1, 0), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (3, 0), (1, 1), (6, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (3, 1), (5, 0), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 4), (1, 2), (0, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (4, 3), (1, 2), (2, 0), (2, 2), (0, 3), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (2, 0), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 5), (0, 6), (3, 4), (5, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (1, 2), (2, 2), (1, 0), (4, 0), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 2), (1, 1), (2, 0), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 5), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 4), (4, 1), (5, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (4, 3), (0, 1), (5, 2), (2, 0), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 2), (5, 0), (1, 0), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (1, 5), (6, 3), (6, 4), (3, 2), (6, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 5), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 1), (2, 2), (2, 0), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 6), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (4, 0), (3, 1), (4, 1), (0, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 3), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 3), (2, 0), (3, 4), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (5, 6), (4, 4), (1, 6), (2, 5), (4, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (1, 4), (0, 1), (1, 0), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (0, 6), (1, 1), (3, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (3, 0), (4, 5), (0, 4), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (4, 4), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 3), (4, 0), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (5, 0), (0, 2), (3, 1), (4, 3), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (1, 0), (0, 1), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (2, 4), (3, 1), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (1, 4), (6, 1), (6, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (0, 5), (1, 3), (0, 3), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (0, 3), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (4, 3), (3, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (0, 4), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (2, 1), (4, 1), (1, 2), (1, 0), (1, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 0), (4, 1), (1, 0), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (3, 4), (1, 0), (3, 1), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 1), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (3, 1), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 4), (6, 3), (1, 3), (3, 3), (5, 2), (6, 2), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 2), (3, 0), (4, 2), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (3, 1), (4, 1), (4, 0), (4, 3), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 4), (3, 2), (4, 0), (1, 3), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (0, 2), (4, 0), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (1, 2), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 1), (2, 4), (0, 1), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 3), (0, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (4, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (4, 2), (3, 3), (3, 2), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 5), (2, 3), (0, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (3, 2), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (0, 2), (1, 0), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 0), (4, 2), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (2, 1), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 0), (1, 2), (3, 2), (1, 3), (3, 0), (6, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 1), (0, 5), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 0), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 3), (5, 1), (2, 4), (2, 0), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (2, 5), (2, 1), (2, 0), (1, 5), (5, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (3, 0), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (4, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (4, 1), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 3), (2, 2), (2, 0), (4, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 4), (3, 3), (3, 0), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 3), (1, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 5), (0, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (1, 5), (0, 3), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (6, 1), (4, 0), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (4, 4), (5, 1), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (4, 0), (2, 2), (3, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 4), (3, 3), (2, 0), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 1), (1, 3), (0, 3), (4, 0), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 3), (6, 0), (5, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 4), (2, 4), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 1), (5, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 5), (0, 2), (0, 4), (2, 4), (5, 1), (4, 2), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 4), (2, 2), (2, 3), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (2, 2), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (3, 1), (4, 0), (4, 5), (5, 2), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (1, 1), (6, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (6, 1), (5, 2), (2, 4), (2, 1), (4, 0), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (3, 2), (2, 0), (2, 1), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 2), (4, 4), (3, 0), (2, 2), (3, 4), (0, 2), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 0), (0, 2), (5, 0), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 2), (5, 4), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 3), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (3, 3), (1, 0), (4, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (3, 2), (3, 1), (5, 1), (0, 1), (3, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (3, 0), (1, 3), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 0), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (2, 0), (3, 1), (1, 2), (6, 0), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (4, 4), (6, 4), (5, 2), (3, 6), (6, 0), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (5, 0), (4, 0), (3, 2), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 3), (3, 2), (4, 2), (5, 1), (3, 4), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (1, 0), (0, 1), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (2, 3), (0, 3), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 0), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 2), (3, 0), (1, 0), (5, 1), (3, 1), (2, 1), (6, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (5, 3), (0, 4), (5, 4), (5, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (5, 0), (0, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 3), (1, 1), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (0, 1), (2, 1), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (3, 1), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (3, 0), (2, 0), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (2, 0), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 0), (2, 3), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (1, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (3, 1), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 5), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (4, 1), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (4, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (1, 6), (4, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (2, 5), (1, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (1, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 4), (1, 3), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 1), (1, 4), (4, 5), (3, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (1, 0), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (1, 5), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (3, 3), (2, 0), (4, 2), (2, 2), (5, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (2, 1), (6, 5), (0, 1), (1, 4), (3, 1), (0, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (0, 1), (4, 0), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 2), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (4, 2), (5, 0), (3, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (1, 2), (0, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (5, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (0, 5), (2, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 2), (0, 1), (4, 1), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 6), (3, 0), (5, 0), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 1), (3, 3), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 3), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (0, 2), (1, 2), (1, 0), (3, 0), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (3, 2), (5, 1), (4, 6), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (4, 4), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 3), (1, 4), (5, 3), (5, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 2), (1, 3), (1, 5), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 2), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (1, 1), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 3), (1, 1), (2, 4), (0, 1), (4, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (2, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (3, 2), (2, 5), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 1), (4, 1), (2, 3), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (0, 1), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (3, 6), (0, 3), (1, 5), (2, 3), (2, 1), (3, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (0, 3), (2, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (6, 0), (5, 0), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (2, 0), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 2), (4, 1), (2, 0), (4, 0), (0, 1), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 3), (2, 1), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (2, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (4, 0), (0, 1), (0, 2), (5, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 1), (1, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (0, 4), (0, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (0, 1), (1, 2), (3, 3), (1, 4)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 3), (0, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (1, 0), (6, 1), (3, 3), (6, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 0), (2, 0), (0, 1)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 3), (2, 2), (1, 2)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 0), (1, 5), (0, 3), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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: (1, 3), (0, 1), (2, 0)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 5), (0, 4), (4, 3), (2, 2), (2, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 4), (0, 2), (1, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 1), (4, 1), (4, 4), (0, 5)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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), (1, 3), (0, 1), (4, 2), (3, 3)?

Present the answer in LaTex format: \boxed{Your answer}


[User]
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, 2), (1, 1)?

Present the answer in LaTex format: \boxed{Your answer}