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

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, 2), (3, 0), (2, 2), (1, 4), (5, 4), (2, 1), (2, 3)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 7), (3, 1), (4, 3), (0, 6), (1, 5), (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: (6, 0), (6, 1), (2, 3), (4, 3), (1, 5), (0, 1), (3, 0), (5, 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, 0), (3, 2), (1, 3), (3, 4), (1, 1), (4, 2), (2, 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, 5), (5, 6), (0, 4), (3, 0), (2, 3), (4, 4), (2, 4), (6, 2), (6, 0), (4, 1)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (3, 3), (0, 4), (2, 1), (1, 1), (7, 4), (6, 4), (4, 2), (7, 3), (2, 3)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (5, 3), (8, 0), (6, 7), (7, 7), (8, 5), (7, 5)?

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

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

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (3, 6), (2, 5), (1, 3), (5, 1), (6, 1), (2, 2), (3, 4), (5, 0)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 8), (6, 1), (2, 6), (5, 7), (2, 5), (6, 8), (7, 2), (0, 7), (0, 3), (0, 2), (3, 5), (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: (3, 2), (3, 4), (0, 3), (3, 3), (0, 1), (0, 4), (2, 4)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (5, 5), (5, 1), (2, 3), (3, 0), (3, 1), (2, 2)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (2, 3), (3, 1), (4, 3), (5, 4), (2, 1), (5, 0), (1, 3), (7, 4), (5, 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: (1, 0), (6, 0), (5, 6), (1, 1), (5, 2), (3, 2), (1, 3), (2, 4)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (4, 6), (2, 3), (7, 7), (6, 5), (3, 6), (0, 1), (3, 8)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 0), (4, 5), (4, 4), (6, 5), (4, 6), (4, 1)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (2, 5), (5, 5), (5, 3), (3, 3), (5, 0), (3, 5)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (0, 1), (3, 1), (0, 3), (4, 1), (2, 6), (0, 6)?

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

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (6, 4), (5, 0), (5, 4), (2, 0), (4, 2), (0, 4), (6, 2), (7, 1), (2, 1), (7, 0)?

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


[User]
In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 4), (2, 8), (2, 4), (1, 7), (3, 8), (3, 0)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 1), (3, 6), (0, 2), (1, 6), (2, 4), (1, 4)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (3, 0), (4, 7), (2, 1), (6, 6), (3, 2), (1, 0), (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, 2), (5, 2), (0, 4), (4, 0), (1, 1), (0, 1), (2, 3)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 3), (4, 2), (4, 6), (0, 2), (4, 1), (5, 3), (5, 8)?

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: (5, 1), (2, 3), (1, 1), (4, 2), (4, 1), (3, 4), (0, 4)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 6), (0, 7), (4, 7), (5, 2), (4, 3), (4, 4), (3, 2)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (7, 5), (5, 4), (6, 4), (1, 2), (6, 8), (2, 1), (0, 8), (6, 2), (7, 8)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (1, 2), (2, 3), (5, 2), (6, 5), (5, 3), (4, 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, 1), (6, 1), (6, 2), (1, 3), (6, 3), (5, 3), (2, 1), (4, 2), (5, 0), (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: (2, 5), (5, 1), (2, 1), (2, 4), (2, 0), (1, 1), (4, 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: (0, 1), (4, 0), (5, 0), (5, 2), (3, 2), (2, 3), (1, 1), (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: (5, 3), (6, 2), (6, 1), (4, 1), (3, 5), (0, 4), (1, 5), (2, 3), (6, 4)?

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


[User]
In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (5, 5), (1, 2), (4, 0), (0, 5), (1, 5), (5, 1), (3, 3)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (5, 5), (4, 0), (2, 1), (3, 6), (0, 5), (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: (1, 4), (1, 3), (2, 4), (0, 3), (2, 0), (2, 2), (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: (5, 0), (3, 2), (1, 2), (5, 2), (2, 0), (2, 5), (0, 5)?

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


[User]
In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (0, 1), (5, 6), (4, 1), (1, 2), (3, 6), (2, 0), (7, 3), (0, 5), (5, 3), (7, 4), (2, 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: (5, 0), (2, 1), (3, 3), (3, 0), (5, 1), (3, 5), (0, 5), (4, 2)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (6, 8), (2, 0), (4, 3), (3, 8), (4, 8), (2, 5)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (7, 6), (7, 5), (0, 6), (8, 1), (3, 3), (5, 1), (5, 0), (1, 2), (3, 5), (4, 4), (0, 5)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (4, 6), (1, 7), (3, 2), (5, 3), (0, 4), (0, 1), (1, 6)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (2, 7), (3, 7), (3, 4), (1, 2), (3, 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: (5, 0), (0, 1), (1, 3), (5, 1), (3, 1), (2, 0), (3, 4)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (0, 4), (5, 2), (6, 3), (0, 5), (4, 2), (3, 2), (1, 3), (5, 3)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (8, 0), (0, 4), (6, 5), (4, 5), (1, 5), (0, 6)?

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, 1), (3, 1), (1, 4), (1, 3), (3, 4), (3, 3)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (5, 6), (0, 7), (2, 7), (1, 2), (0, 1), (5, 0), (4, 2), (5, 3)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 4), (0, 1), (6, 0), (8, 0), (6, 3), (0, 4), (3, 1), (8, 1), (6, 2), (5, 0), (2, 1), (7, 3)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (1, 4), (0, 7), (5, 8), (5, 6), (7, 4), (7, 3), (6, 4), (0, 1)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 1), (6, 4), (3, 4), (4, 1), (3, 1), (7, 1)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 2), (5, 1), (3, 5), (3, 3), (2, 0), (7, 2), (4, 0), (1, 4)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 5), (4, 0), (3, 3), (6, 1), (6, 5), (5, 7), (5, 3), (3, 6)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 0), (3, 6), (7, 0), (3, 4), (1, 7), (5, 3)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (7, 2), (3, 2), (3, 5), (3, 0), (1, 3), (4, 4), (6, 5), (2, 5), (0, 5), (7, 3), (7, 1)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 0), (5, 7), (6, 4), (7, 0), (2, 5), (3, 6)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (6, 1), (2, 1), (6, 2), (2, 6), (1, 0), (8, 1), (5, 1), (4, 0)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (0, 3), (3, 4), (3, 5), (0, 2), (3, 6), (1, 5)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (1, 7), (3, 5), (1, 0), (1, 1), (4, 0), (0, 3)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (2, 0), (4, 2), (3, 5), (3, 0), (6, 5), (4, 8), (6, 1), (3, 2), (6, 4), (2, 3), (7, 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, 5), (1, 3), (2, 1), (5, 0), (1, 1), (2, 4), (4, 3), (4, 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, 0), (4, 2), (5, 2), (1, 2), (3, 2), (2, 1), (2, 4), (0, 4), (0, 2)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (7, 2), (1, 0), (4, 3), (3, 7), (7, 3), (6, 7), (1, 1), (6, 6), (0, 5)?

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


[User]
In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (2, 6), (1, 0), (6, 6), (3, 4), (5, 0), (5, 4), (3, 2)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (3, 2), (4, 2), (5, 4), (5, 5), (2, 6), (4, 6), (0, 6)?

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), (3, 3), (5, 1), (0, 2), (1, 6), (0, 6), (3, 6), (1, 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), (1, 0), (4, 0), (3, 2), (1, 4), (2, 4), (4, 3)?

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, 1), (5, 3), (4, 0), (1, 4), (0, 2), (2, 6), (3, 2), (5, 1), (1, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (7, 5), (8, 0), (0, 1), (2, 5), (4, 4), (5, 4), (6, 1), (1, 4), (6, 5), (7, 3), (6, 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: (6, 3), (0, 5), (2, 2), (0, 4), (3, 0), (0, 3), (1, 2), (1, 3), (1, 1)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (8, 1), (4, 2), (7, 3), (6, 4), (1, 2), (1, 1), (7, 4), (3, 1), (2, 1), (6, 1)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (0, 4), (0, 2), (6, 2), (1, 2), (4, 1), (3, 2), (5, 4), (5, 0), (7, 3), (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: (5, 1), (3, 0), (1, 0), (0, 2), (2, 6), (3, 5), (0, 6)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 1), (1, 4), (4, 0), (2, 6), (3, 4), (5, 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: (2, 0), (6, 0), (3, 4), (4, 5), (0, 4), (1, 5), (5, 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), (6, 3), (3, 0), (3, 1), (5, 1), (4, 2), (2, 2), (1, 4), (2, 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: (4, 1), (3, 2), (2, 5), (1, 3), (1, 0), (3, 0), (4, 2)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (8, 1), (1, 6), (4, 1), (5, 3), (5, 1), (7, 5), (1, 4)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (1, 2), (3, 5), (6, 0), (0, 5), (0, 6), (6, 6)?

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), (5, 1), (1, 0), (2, 6), (5, 0), (3, 4), (4, 3), (5, 3), (0, 5)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (7, 1), (6, 3), (3, 2), (0, 1), (3, 4), (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: (4, 4), (1, 3), (0, 2), (2, 1), (2, 2), (6, 1), (6, 0), (0, 4)?

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


[User]
In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 2), (2, 7), (2, 0), (0, 5), (2, 6), (4, 1)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 0), (2, 2), (4, 2), (4, 3), (5, 2), (5, 4), (3, 4)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 4), (5, 2), (4, 3), (5, 6), (3, 3), (1, 4)?

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), (1, 2), (1, 5), (0, 1), (4, 0), (3, 1), (0, 3), (5, 0), (6, 1), (3, 5)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 0), (6, 1), (5, 3), (1, 0), (2, 1), (4, 4), (2, 4), (4, 1), (1, 3)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (2, 4), (5, 3), (5, 1), (5, 2), (8, 0), (1, 3), (7, 2), (0, 4), (0, 3), (4, 1), (2, 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: (2, 3), (0, 2), (4, 4), (3, 1), (1, 4), (2, 2), (4, 3)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (6, 3), (0, 3), (3, 2), (5, 1), (0, 6), (2, 1)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 3), (2, 2), (2, 3), (1, 1), (8, 2), (5, 4), (0, 3), (8, 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: (4, 2), (4, 1), (0, 6), (3, 3), (2, 0), (4, 5), (0, 2)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (7, 3), (0, 1), (2, 4), (4, 2), (5, 0), (4, 4), (0, 4), (2, 3), (6, 2), (3, 1), (1, 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: (4, 3), (0, 2), (2, 2), (0, 4), (1, 6), (0, 3), (1, 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: (4, 1), (1, 1), (2, 3), (4, 5), (0, 1), (1, 5), (3, 5), (3, 6), (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: (3, 3), (4, 0), (6, 3), (1, 1), (5, 0), (1, 3), (4, 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, 1), (4, 0), (1, 3), (1, 4), (1, 1), (3, 2), (4, 1)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (4, 4), (1, 0), (5, 0), (2, 4), (0, 3), (5, 1), (7, 2), (3, 1), (5, 3)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (6, 2), (0, 3), (3, 7), (4, 0), (4, 1), (4, 6), (2, 3), (6, 5), (5, 5)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 4), (3, 1), (3, 3), (4, 6), (1, 5), (2, 3)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (7, 0), (2, 2), (5, 4), (4, 1), (5, 2), (5, 0), (0, 4), (0, 2)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (4, 3), (0, 6), (7, 2), (5, 1), (4, 4), (2, 1), (5, 6), (0, 2), (6, 0), (7, 4)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (2, 0), (3, 4), (4, 5), (4, 7), (1, 5), (4, 3)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (0, 6), (0, 5), (5, 1), (1, 6), (5, 6), (4, 4), (3, 4), (1, 5)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (6, 0), (2, 3), (2, 2), (5, 2), (5, 0), (4, 2), (6, 1), (6, 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: (2, 3), (1, 3), (4, 4), (1, 5), (3, 0), (2, 2), (2, 4)?

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), (1, 2), (2, 0), (0, 2), (5, 3), (0, 5), (4, 2), (6, 4)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (4, 5), (3, 2), (1, 7), (3, 1), (3, 3), (2, 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), (2, 0), (2, 5), (1, 3), (1, 2), (1, 5), (4, 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: (3, 4), (2, 3), (3, 3), (0, 2), (1, 3), (1, 0), (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: (2, 1), (0, 4), (3, 1), (4, 2), (2, 0), (3, 2), (3, 4)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 2), (3, 5), (2, 0), (3, 1), (1, 5), (2, 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, 1), (2, 3), (1, 4), (0, 4), (3, 1), (1, 1), (5, 1)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (2, 1), (6, 8), (6, 3), (1, 1), (4, 3), (6, 7), (1, 7), (5, 0), (7, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 1), (5, 3), (3, 5), (3, 1), (4, 2), (4, 3), (2, 5)?

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), (1, 4), (4, 1), (0, 2), (3, 0), (4, 2), (1, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (4, 4), (3, 1), (8, 0), (5, 0), (4, 3), (2, 4), (1, 0), (0, 5)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (7, 6), (4, 0), (2, 7), (4, 5), (2, 2), (7, 4), (1, 1), (0, 7), (5, 4), (7, 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: (0, 1), (0, 5), (4, 1), (5, 1), (2, 1), (1, 4), (1, 2)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 4), (2, 3), (0, 2), (6, 0), (8, 0), (8, 1), (1, 0), (7, 2), (5, 0), (8, 2), (3, 0), (0, 4)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 4), (5, 2), (3, 1), (1, 5), (5, 3), (3, 5), (7, 2), (8, 1), (4, 1), (0, 4), (5, 5)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (5, 2), (5, 1), (3, 1), (4, 1), (8, 4), (4, 4)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 3), (1, 5), (6, 3), (8, 0), (7, 2), (1, 0), (7, 5), (5, 5), (3, 5), (0, 4), (7, 3), (2, 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, 1), (1, 1), (3, 3), (3, 2), (0, 1), (2, 3), (2, 2), (0, 2)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 2), (1, 3), (4, 0), (0, 2), (6, 1), (4, 1), (2, 2), (7, 0), (2, 3), (3, 0), (5, 1)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 1), (4, 4), (2, 4), (3, 0), (7, 3), (2, 3), (6, 0), (3, 1), (2, 0), (6, 2), (3, 3)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 0), (0, 6), (1, 1), (4, 5), (1, 6), (2, 7)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (4, 2), (3, 2), (4, 4), (0, 3), (4, 1), (1, 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, 3), (1, 4), (4, 3), (2, 1), (4, 0), (3, 5), (1, 1)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (7, 3), (3, 4), (1, 2), (2, 6), (2, 4), (8, 3), (4, 4), (5, 1), (3, 3), (3, 1), (2, 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: (5, 1), (3, 0), (3, 1), (3, 5), (1, 0), (5, 3), (4, 0), (5, 5)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (1, 6), (1, 3), (6, 3), (1, 1), (6, 7), (0, 3), (0, 7), (7, 2), (5, 3), (1, 7), (5, 2)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 4), (1, 2), (6, 0), (4, 3), (4, 1), (0, 3), (3, 1), (8, 2), (1, 3), (0, 2), (3, 2), (5, 3), (6, 1)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (0, 6), (3, 5), (2, 5), (6, 1), (1, 3), (4, 6), (6, 8), (1, 6), (3, 1), (3, 6), (6, 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, 2), (6, 5), (0, 5), (6, 0), (1, 0), (5, 0), (0, 4), (6, 1), (4, 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: (2, 4), (4, 1), (2, 2), (0, 4), (3, 3), (5, 1), (1, 2)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 1), (3, 4), (8, 0), (2, 2), (0, 3), (5, 0), (7, 1), (6, 2), (7, 2), (3, 5), (7, 5), (7, 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: (5, 3), (5, 0), (1, 4), (1, 1), (5, 5), (2, 3), (0, 3)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 1), (1, 2), (7, 0), (3, 0), (4, 0), (1, 3), (0, 3), (7, 1), (5, 4)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (7, 2), (7, 3), (0, 2), (3, 4), (7, 5), (4, 1), (6, 1), (1, 1)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (3, 4), (5, 2), (6, 1), (4, 1), (5, 3), (4, 0), (2, 1), (6, 0), (7, 2), (0, 2)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 4), (0, 5), (1, 1), (3, 1), (6, 6), (0, 3)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (7, 2), (0, 2), (4, 0), (2, 6), (5, 0), (1, 4), (0, 4), (3, 2), (4, 3), (7, 5), (5, 1), (7, 3)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 3), (2, 4), (4, 1), (8, 2), (5, 0), (6, 1)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 3), (2, 2), (1, 3), (0, 1), (5, 6), (1, 4), (0, 3)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (4, 2), (1, 1), (1, 4), (3, 6), (0, 7), (0, 5)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (4, 0), (4, 8), (7, 2), (8, 0), (1, 3), (1, 2), (2, 1), (8, 7), (4, 5), (3, 5), (6, 8), (2, 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: (3, 5), (2, 3), (1, 0), (0, 4), (0, 5), (4, 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: (4, 1), (3, 4), (1, 1), (4, 2), (3, 0), (1, 2), (0, 1)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (0, 5), (3, 3), (4, 4), (1, 5), (0, 6), (4, 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: (2, 3), (5, 6), (4, 6), (1, 1), (5, 3), (0, 4), (4, 1), (0, 2)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (1, 3), (2, 4), (5, 4), (1, 0), (0, 4), (2, 1), (1, 1), (0, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (8, 3), (3, 5), (1, 0), (4, 3), (0, 4), (3, 4), (3, 1), (7, 1), (4, 4), (1, 5), (0, 3), (8, 0)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (0, 2), (1, 2), (6, 2), (5, 1), (1, 4), (8, 2), (3, 4), (4, 1), (3, 3), (5, 2), (5, 3)?

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


[User]
In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 1), (2, 7), (2, 3), (0, 8), (1, 6), (0, 6)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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, 5), (6, 1), (0, 5), (1, 2), (3, 0), (0, 1), (0, 3), (0, 2), (1, 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, 2), (3, 4), (3, 2), (3, 1), (0, 3), (4, 0), (1, 4)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (6, 6), (4, 0), (6, 1), (2, 0), (6, 5), (4, 6), (8, 0), (6, 2), (7, 5), (1, 3), (7, 1), (7, 3)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (4, 2), (0, 4), (2, 3), (5, 0), (1, 2), (2, 1), (6, 3), (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: (4, 0), (4, 2), (2, 4), (3, 3), (1, 4), (0, 2), (0, 4), (2, 1)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (0, 2), (2, 2), (1, 4), (5, 2), (3, 2), (7, 2), (7, 3), (1, 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: (2, 0), (5, 2), (4, 0), (1, 0), (5, 3), (4, 2), (5, 0), (2, 1), (2, 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, 4), (1, 4), (4, 5), (1, 5), (1, 1), (0, 3), (2, 0)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 1), (5, 0), (3, 0), (1, 4), (8, 4), (2, 2), (2, 1), (8, 2), (3, 4), (6, 5), (7, 3)?

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), (2, 0), (3, 4), (4, 0), (2, 1), (4, 4), (3, 0)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (1, 1), (2, 8), (0, 4), (3, 7), (4, 3), (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: (3, 0), (5, 0), (1, 3), (2, 2), (4, 4), (0, 4), (4, 1), (0, 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: (4, 1), (4, 3), (1, 1), (4, 4), (3, 3), (0, 3), (4, 2)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (0, 1), (5, 6), (5, 2), (4, 0), (0, 7), (4, 5), (4, 6)?

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

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 5), (3, 5), (0, 7), (1, 5), (2, 1), (4, 5), (4, 2), (5, 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, 2), (4, 1), (2, 4), (0, 3), (2, 1), (3, 2), (1, 4)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (4, 0), (6, 0), (5, 0), (4, 4), (0, 4), (3, 0), (6, 3), (2, 4)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (1, 3), (0, 8), (2, 1), (1, 7), (4, 5), (2, 7)?

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, 0), (1, 2), (3, 4), (1, 4), (5, 1), (1, 5), (0, 1), (5, 2)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (0, 5), (6, 1), (2, 1), (5, 7), (1, 2), (3, 6), (1, 7), (0, 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: (4, 2), (2, 5), (5, 2), (2, 2), (1, 0), (5, 3), (5, 4), (3, 3)?

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, 5), (1, 2), (1, 3), (4, 5), (5, 2), (4, 0), (1, 1), (3, 1)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (5, 5), (5, 0), (2, 3), (3, 4), (2, 7), (4, 8), (2, 0)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (3, 0), (0, 1), (5, 1), (0, 3), (6, 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, 0), (2, 2), (6, 0), (2, 0), (2, 4), (1, 4), (4, 0), (5, 3)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (3, 0), (0, 1), (4, 2), (0, 3), (5, 3), (6, 4), (4, 5), (6, 2), (1, 3), (5, 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: (1, 4), (2, 3), (2, 2), (3, 2), (1, 3), (3, 1), (0, 2), (5, 0)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (4, 5), (0, 3), (2, 3), (3, 1), (4, 6), (4, 2)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (4, 6), (2, 5), (2, 7), (2, 1), (3, 6), (6, 6), (1, 1), (6, 4)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (0, 7), (2, 0), (2, 3), (1, 0), (1, 3), (3, 4)?

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, 2), (3, 0), (2, 0), (3, 2), (2, 5), (0, 4), (1, 0)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (4, 2), (1, 4), (5, 1), (5, 5), (5, 2), (3, 3)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (4, 1), (6, 0), (5, 2), (1, 1), (0, 3), (6, 3), (1, 4), (4, 2), (2, 3), (6, 2)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 4), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 1), (6, 3), (4, 1), (7, 1), (1, 3), (1, 2), (0, 4), (2, 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: (4, 0), (3, 0), (2, 3), (2, 4), (3, 2), (1, 2), (1, 3)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (5, 1), (2, 5), (1, 5), (5, 3), (4, 0), (5, 4)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 6), (3, 0), (3, 6), (6, 3), (6, 0), (4, 6), (6, 5), (1, 7), (0, 6), (5, 8), (4, 5)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (8, 0), (7, 1), (7, 6), (3, 6), (0, 6), (0, 4), (4, 0), (3, 4), (5, 4), (3, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (8, 0), (6, 3), (3, 1), (5, 1), (0, 2), (4, 1), (8, 1)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (4, 1), (4, 3), (5, 2), (1, 2), (6, 1), (0, 1), (7, 2), (0, 3), (3, 2), (5, 0), (8, 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: (0, 6), (5, 5), (1, 5), (3, 2), (3, 0), (5, 4), (2, 2), (5, 0), (4, 5)?

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), (3, 3), (0, 1), (1, 5), (4, 1), (3, 4), (0, 4)?

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, 1), (2, 1), (3, 2), (3, 1), (2, 0), (2, 5), (1, 3)?

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


[User]
In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (6, 1), (2, 2), (0, 3), (7, 5), (2, 6), (3, 6), (2, 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: (4, 3), (1, 4), (2, 1), (6, 0), (5, 1), (4, 2), (2, 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: (5, 2), (1, 4), (5, 4), (3, 1), (1, 6), (6, 1), (5, 0), (5, 5), (1, 1)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 3), (6, 2), (1, 1), (4, 7), (2, 0), (0, 4), (1, 5), (2, 7), (4, 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, 5), (6, 4), (3, 2), (3, 3), (1, 2), (2, 3), (1, 5), (1, 0), (2, 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), (6, 3), (1, 2), (1, 1), (6, 1), (4, 1), (1, 3), (5, 2), (6, 0), (1, 4)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (4, 5), (3, 4), (3, 0), (7, 3), (5, 0), (5, 3), (0, 3), (2, 3), (5, 2), (0, 1), (5, 5)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (3, 2), (3, 4), (1, 5), (3, 0), (2, 6), (3, 1)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (5, 0), (3, 7), (1, 3), (1, 6), (3, 6), (3, 4), (7, 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: (1, 4), (6, 2), (4, 5), (2, 4), (3, 6), (3, 4), (5, 0), (6, 0), (2, 3), (5, 1)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (2, 1), (6, 3), (3, 2), (7, 0), (2, 2), (6, 2), (0, 2), (1, 2), (4, 0)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (1, 6), (3, 4), (7, 1), (3, 0), (1, 5), (5, 6), (1, 7), (1, 0), (3, 3), (5, 7), (5, 1), (6, 2)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 7), (3, 8), (4, 5), (4, 8), (1, 3), (4, 6)?

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, 2), (3, 0), (5, 3), (2, 2), (5, 0), (2, 3), (3, 5), (2, 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, 1), (0, 1), (5, 4), (4, 2), (3, 2), (3, 0), (4, 1)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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, 2), (5, 0), (7, 0), (0, 3), (2, 4), (0, 2), (5, 2), (3, 4), (3, 3)?

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, 5), (3, 0), (0, 4), (4, 0), (2, 4), (0, 3), (5, 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: (0, 2), (1, 2), (4, 0), (4, 1), (2, 0), (1, 4), (3, 0), (5, 3), (3, 3)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (4, 4), (4, 1), (1, 5), (2, 1), (5, 6), (1, 4), (0, 8)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (2, 4), (7, 4), (7, 3), (2, 7), (3, 2), (4, 0)?

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


[User]
In a 9x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (7, 3), (0, 1), (8, 3), (2, 2), (6, 2), (4, 1), (4, 0)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 5), (3, 0), (1, 2), (1, 7), (3, 5), (5, 4), (3, 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: (2, 0), (5, 5), (3, 4), (6, 0), (2, 3), (4, 0), (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: (4, 4), (1, 4), (4, 2), (2, 1), (3, 2), (2, 2), (1, 3), (6, 2)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (6, 4), (7, 0), (4, 3), (2, 0), (7, 2), (4, 5), (0, 3), (2, 1), (0, 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: (2, 3), (2, 2), (4, 1), (1, 3), (1, 2), (1, 1), (2, 1)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (2, 3), (1, 1), (1, 7), (2, 5), (6, 3), (6, 7), (4, 2), (0, 2), (7, 1), (1, 4), (2, 2), (5, 7)?

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, 2), (0, 4), (2, 0), (1, 4), (3, 0), (1, 0), (1, 2), (0, 2)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 2), (4, 4), (0, 7), (5, 5), (1, 1), (4, 7), (1, 6)?

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

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (1, 4), (2, 4), (7, 2), (2, 2), (7, 0), (4, 5), (3, 6), (7, 3), (1, 3), (2, 7), (2, 1)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (3, 3), (2, 3), (3, 6), (0, 5), (1, 7), (5, 0), (5, 3), (1, 0)?

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


[User]
In a 5x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 5), (2, 1), (1, 0), (2, 7), (2, 0), (3, 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: (4, 2), (5, 0), (1, 0), (4, 0), (0, 4), (0, 5), (0, 3)?

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


[User]
In a 6x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 6), (4, 2), (1, 0), (5, 0), (0, 3), (5, 2), (2, 0), (2, 7)?

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

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (6, 3), (1, 2), (3, 0), (7, 4), (5, 4), (8, 4), (5, 0), (2, 4), (3, 6)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (3, 5), (4, 5), (5, 2), (1, 3), (0, 5), (7, 5), (8, 2), (8, 1), (2, 1), (3, 1), (0, 3), (3, 2)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (0, 8), (5, 4), (4, 2), (6, 1), (6, 6), (1, 8), (7, 1), (1, 4), (0, 3), (1, 6), (7, 2)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 5), (3, 1), (5, 5), (5, 3), (1, 0), (1, 5)?

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


[User]
In a 8x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (4, 3), (7, 2), (5, 1), (1, 3), (5, 0), (2, 4), (4, 4), (2, 2)?

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


[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (3, 4), (4, 8), (7, 3), (3, 1), (0, 5), (5, 4), (5, 3)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 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), (5, 2), (8, 2), (2, 0), (4, 0), (5, 3), (8, 1), (3, 5), (6, 4), (0, 3), (3, 3), (0, 4), (7, 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: (0, 1), (2, 1), (1, 6), (5, 5), (0, 4), (3, 6), (2, 4), (0, 6), (1, 4)?

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: (4, 1), (5, 3), (3, 1), (3, 0), (2, 1), (2, 2), (5, 0)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (3, 8), (6, 1), (4, 6), (6, 2), (4, 7), (0, 4), (1, 8), (5, 6)?

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, 2), (3, 3), (1, 1), (4, 3), (4, 4), (2, 3), (0, 3)?

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


[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (2, 2), (3, 4), (4, 2), (6, 0), (7, 0), (2, 5), (6, 6), (3, 1), (7, 4), (7, 5), (6, 5)?

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


[User]
In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (6, 2), (3, 0), (6, 3), (4, 1), (8, 5), (1, 4), (5, 2), (7, 7), (8, 0)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (1, 4), (3, 2), (4, 7), (2, 7), (1, 2), (4, 0)?

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


[User]
In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 2), (3, 1), (3, 3), (2, 7), (4, 7), (1, 0)?

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


[User]
In a 8x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 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), (6, 2), (2, 0), (2, 2), (6, 0), (4, 3), (1, 0), (5, 1), (3, 2), (1, 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, 3), (1, 5), (0, 2), (1, 4), (3, 1), (1, 3), (1, 2), (3, 4)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (7, 1), (6, 5), (5, 2), (2, 4), (8, 2), (5, 1), (1, 3), (1, 4), (8, 0), (6, 0), (6, 2), (5, 0)?

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[User]
In a 5x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (3, 2), (1, 8), (1, 5), (1, 1), (3, 1), (1, 2)?

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

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[User]
In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (0, 1), (5, 2), (2, 4), (1, 7), (7, 0), (2, 6), (5, 0), (1, 5), (7, 6)?

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[User]
In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (2, 2), (3, 3), (0, 6), (6, 5), (1, 0), (4, 1)?

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


[User]
In a 9x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 5), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (1, 5), (7, 3), (4, 4), (7, 4), (2, 4), (8, 2), (4, 1), (4, 3), (7, 0), (8, 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: (6, 1), (2, 0), (4, 5), (5, 3), (0, 5), (2, 3), (3, 5), (5, 1)?

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


[User]
In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (5, 1), (0, 4), (3, 1), (5, 0), (1, 5), (1, 0), (3, 6), (5, 6)?

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


[User]
In a 6x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 7), (2, 6), (2, 2), (1, 5), (0, 4), (3, 7), (4, 6)?

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


[User]
In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 6), (6, 7), (0, 7), (2, 1), (1, 4), (6, 2), (3, 7), (3, 0), (4, 5), (3, 5), (4, 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: (2, 0), (5, 2), (3, 0), (0, 1), (2, 1), (3, 3), (6, 3), (5, 1), (3, 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, 4), (5, 0), (4, 2), (2, 2), (4, 3), (4, 0), (1, 0), (0, 3)?

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


[User]
In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 8), (6, 7), (3, 8), (6, 5), (4, 1), (4, 5), (6, 4), (0, 5)?

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