{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 2), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (2, 0), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (1, 1), (3, 0), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 3), (0, 3), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (0, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (4, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (3, 1), (3, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 4), (3, 1), (3, 3), (2, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 3), (4, 1), (2, 1), (3, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (5, 1), (5, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (2, 3), (4, 1), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (4, 3), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 0), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 1), (2, 3), (0, 3), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 3), (3, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 2), (5, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (5, 1), (0, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 3), (1, 4), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 1), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 5), (1, 0), (3, 4), (2, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (0, 5), (2, 0), (4, 3), (1, 0), (2, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (4, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 1), (0, 4), (5, 0), (2, 3), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (2, 3), (3, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (0, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (5, 2), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (0, 2), (2, 2), (2, 3), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (4, 1), (3, 0), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (4, 4), (4, 1), (2, 2), (3, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 5), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (5, 3), (3, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (5, 1), (2, 5), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 1), (2, 5), (3, 2), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 0), (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 1), (4, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 5), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 2), (2, 0), (1, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 5), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 1), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (2, 3), (1, 5), (5, 1), (2, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1), (2, 2), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 4), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 4), (0, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (5, 3), (1, 3), (4, 0), (3, 4), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 0), (1, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (0, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 0), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (3, 0), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 1), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 4), (1, 1), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 3), (1, 2), (0, 4), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 5), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 3), (1, 2), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 2), (4, 1), (4, 5), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 2), (1, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 4), (0, 3), (2, 3), (3, 4), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 3), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 4), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 2), (4, 2), (1, 3), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (3, 0), (4, 1), (3, 3), (2, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (0, 5), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 2), (1, 0), (2, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 4), (0, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 4), (2, 2), (0, 1), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (1, 1), (0, 2), (0, 5), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 0), (1, 4), (1, 0), (3, 3), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 5), (1, 4), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (4, 1), (0, 4), (1, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 5), (1, 1), (1, 4), (3, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 1), (1, 4), (5, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2), (0, 4), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 3), (3, 4), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (5, 3), (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 3), (0, 3), (5, 0), (0, 1), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (5, 1), (0, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (2, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 3), (2, 0), (3, 0), (0, 4), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 1), (0, 4), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 5), (0, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 4), (0, 1), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (3, 4), (1, 2), (0, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 3), (2, 1), (0, 5), (0, 2), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 1), (4, 3), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (5, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2), (4, 1), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 0), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 0), (2, 0), (2, 1), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (1, 2), (1, 0), (5, 1), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 4), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (0, 1), (3, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 5), (1, 5), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 4), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (2, 5), (0, 1), (4, 4), (1, 1), (1, 4), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 1), (5, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (4, 0), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 2), (2, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 0), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (0, 3), (3, 5), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (3, 2), (2, 5), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (1, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 0), (0, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 1), (3, 4), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 2), (4, 1), (1, 3), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 5), (4, 4), (0, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 0), (5, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 0), (0, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 1), (2, 0), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 4), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 2), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (5, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (4, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (1, 3), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 5), (2, 0), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (3, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 4), (2, 4), (1, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (3, 4), (5, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 1), (2, 0), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 3), (3, 4), (2, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (4, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (5, 4), (5, 1), (1, 1), (4, 2), (1, 3), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 0), (2, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (0, 4), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 3), (3, 4), (1, 0), (2, 4), (5, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0), (0, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (5, 2), (0, 1), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 1), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (0, 3), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 4), (2, 3), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (4, 3), (4, 2), (4, 4), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (5, 1), (0, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (4, 2), (0, 3), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1), (0, 4), (5, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (5, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (0, 5), (4, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (5, 2), (1, 0), (1, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 3), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 0), (4, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (0, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 0), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 3), (2, 5), (1, 4), (2, 4), (2, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 3), (1, 4), (1, 0), (3, 3), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (1, 5), (1, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (3, 3), (2, 4), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 0), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 0), (0, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 0), (3, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 1), (1, 1), (0, 3), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (0, 4), (3, 3), (4, 3), (2, 2), (3, 1), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 2), (2, 3), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 4), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 3), (5, 1), (4, 3), (3, 2), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (4, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 1), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (0, 3), (2, 4), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (1, 4), (2, 3), (2, 0), (5, 1), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 0), (1, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 3), (3, 0), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 4), (2, 4), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 1), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 5), (3, 4), (4, 0), (0, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (3, 5), (2, 5), (1, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 1), (0, 2), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (4, 1), (4, 0), (0, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 0), (0, 3), (2, 4), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 1), (2, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (2, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 3), (2, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0), (3, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 2), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 4), (3, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 3), (0, 4), (4, 3), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (5, 1), (4, 0), (3, 1), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (4, 1), (0, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 4), (5, 1), (5, 2), (2, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (5, 1), (3, 4), (1, 0), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 2), (5, 4), (2, 4), (4, 3), (3, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (4, 1), (2, 2), (4, 3), (2, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 1), (0, 4), (3, 4), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 0), (0, 5), (0, 1), (2, 3), (5, 4), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 0), (3, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 0), (4, 4), (4, 3), (0, 5), (3, 2), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 5), (2, 5), (0, 2), (1, 1), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (1, 4), (5, 4), (2, 5), (4, 4), (4, 5), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 1), (1, 4), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 1), (2, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 4), (1, 5), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1), (0, 4), (3, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 4), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 0), (5, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 3), (4, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (3, 5), (3, 3), (5, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (4, 1), (2, 3), (1, 5), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 1), (2, 0), (1, 0), (4, 4), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (4, 1), (3, 1), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 1), (0, 2), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 0), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 4), (2, 2), (3, 0), (2, 5), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (4, 2), (3, 2), (3, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0), (3, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 0), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 3), (3, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (0, 2), (2, 3), (1, 2), (1, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 4), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 3), (3, 0), (4, 4), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 3), (5, 0), (0, 5), (1, 3), (1, 5), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (5, 0), (1, 1), (3, 1), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 3), (3, 3), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (2, 3), (1, 2), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (2, 0), (2, 1), (1, 4), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 4), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 2), (2, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 2), (5, 1), (4, 4), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 2), (2, 4), (0, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 3), (1, 4), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 1), (2, 0), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 4), (2, 4), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 5), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (5, 2), (0, 3), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 4), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 1), (3, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1), (1, 0), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 0), (2, 0), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 2), (1, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 2), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 2), (0, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 3), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (5, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 4), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 4), (4, 1), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (4, 4), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 5), (1, 4), (5, 3), (5, 2), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 0), (0, 1), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (4, 3), (4, 0), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (4, 2), (0, 4), (5, 1), (2, 4), (5, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (2, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 5), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 2), (4, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 2), (2, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 3), (1, 1), (1, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 0), (0, 1), (4, 0), (4, 4), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 1), (4, 3), (2, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 3), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 2), (2, 5), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 1), (1, 2), (5, 3), (1, 4), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 3), (3, 1), (5, 0), (0, 4), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 3), (1, 4), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (0, 2), (2, 1), (1, 2), (1, 5), (4, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 3), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (2, 0), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 2), (3, 4), (5, 1), (3, 1), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (0, 2), (2, 2), (1, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (1, 3), (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 1), (3, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 2), (2, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 2), (4, 3), (4, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (4, 2), (4, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (0, 2), (4, 3), (0, 3), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 0), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 3), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 4), (2, 1), (0, 3), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 3), (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (2, 0), (0, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 4), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 0), (0, 5), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 2), (2, 5), (4, 4), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (0, 1), (2, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 1), (0, 3), (1, 1), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2), (1, 5), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (2, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 4), (2, 5), (1, 5), (4, 0), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 2), (2, 4), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 1), (0, 1), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 1), (1, 4), (1, 5), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 1), (0, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (4, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (2, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (5, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (4, 2), (4, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 0), (0, 4), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 0), (3, 1), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 1), (1, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (0, 5), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 2), (3, 0), (0, 4), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 3), (1, 1), (1, 4), (5, 3), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 2), (0, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 5), (5, 1), (4, 1), (5, 0), (1, 1), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (4, 1), (0, 2), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 2), (2, 4), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (4, 3), (5, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 1), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (3, 4), (3, 1), (3, 0), (3, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (3, 2), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 1), (4, 3), (3, 2), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (2, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 0), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 5), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 2), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 1), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (1, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (5, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 0), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (3, 1), (5, 0), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (5, 4), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 4), (1, 0), (4, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (1, 3), (4, 4), (2, 4), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 3), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 4), (2, 2), (2, 1), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 3), (5, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 2), (3, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 1), (4, 0), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 3), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 2), (4, 4), (1, 3), (3, 4), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 4), (4, 2), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 3), (0, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 3), (1, 1), (5, 1), (1, 3), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (4, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (0, 3), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 5), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (0, 1), (0, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (5, 1), (4, 0), (0, 4), (4, 3), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (1, 0), (4, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (4, 2), (4, 0), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (5, 0), (5, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (0, 1), (4, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 1), (2, 4), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 1), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 2), (0, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 0), (4, 0), (1, 2), (4, 2), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (3, 0), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 2), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 2), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 0), (0, 2), (1, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 3), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 2), (0, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 1), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (1, 1), (0, 3), (2, 3), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (3, 0), (1, 1), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 4), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (0, 3), (1, 4), (4, 4), (4, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (1, 4), (3, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (2, 3), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 4), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (2, 3), (0, 4), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 2), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 1), (5, 1), (2, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 1), (4, 1), (4, 2), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 1), (4, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (0, 3), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (2, 1), (2, 2), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (0, 4), (4, 4), (1, 5), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 1), (2, 3), (5, 1), (1, 0), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 1), (3, 3), (0, 1), (0, 3), (4, 4), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 2), (0, 3), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 2), (3, 2), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 2), (3, 0), (2, 3), (2, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (2, 2), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (2, 5), (0, 5), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (2, 4), (5, 4), (1, 5), (4, 3), (3, 2), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (0, 1), (0, 2), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 0), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 4), (2, 4), (5, 4), (4, 3), (5, 3), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 1), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (0, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (2, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 0), (4, 3), (2, 1), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 4), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (0, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (0, 5), (3, 2), (4, 0), (0, 4), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 3), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (4, 1), (0, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (0, 2), (3, 1), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 1), (5, 1), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 2), (5, 2), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (5, 0), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (4, 0), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (2, 1), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 3), (3, 0), (3, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (1, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (3, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 4), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (4, 2), (1, 5), (1, 2), (2, 1), (5, 2), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (3, 1), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 2), (0, 1), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 3), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (2, 1), (1, 2), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 2), (3, 4), (2, 0), (4, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (3, 3), (3, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 1), (5, 3), (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 3), (2, 0), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (1, 1), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 5), (1, 2), (3, 1), (2, 0), (5, 3), (4, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 4x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 2), (4, 3), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 2), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 4x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 0), (1, 1), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (4, 4), (5, 3), (0, 1), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (5, 3), (3, 1), (1, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (5, 2), (0, 2), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (5, 0), (0, 1), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 6x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 3), (1, 3), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (4, 0), (3, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 3), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (3, 0), (2, 1), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: ? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 5x5 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 4), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (1, 3), (2, 2), (3, 3), (0, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 4), (2, 5), (3, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "In a 4x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (3, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 2), (3, 2), (2, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "In a 5x6 grid, how many different paths are there from the bottom left (0, 0) to the top right (4, 5), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (0, 5), (1, 4), (3, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "In a 3x3 grid, how many different paths are there from the bottom left (0, 0) to the top right (2, 2), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}