{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (11, 3), (1, 15), (2, 13), (14, 0), (14, 9), (5, 10), (1, 8), (10, 15), (8, 12), (5, 3), (5, 7), (8, 14), (6, 4), (7, 11), (5, 15), (5, 6), (9, 14), (9, 10), (4, 1), (7, 3), (10, 2), (12, 13), (0, 5), (4, 2), (6, 13), (3, 10), (12, 10), (5, 1), (11, 4), (6, 8), (9, 15), (7, 2), (7, 13), (0, 4), (11, 2), (5, 9), (0, 10), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "665101", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (9, 14), (1, 13), (9, 9), (1, 14), (2, 3), (10, 5), (5, 10), (8, 10), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305223", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (13, 0), (2, 9), (9, 1), (12, 4), (8, 5), (5, 4), (5, 1), (0, 7), (0, 4), (12, 6), (10, 9), (10, 1), (12, 1), (0, 9), (9, 0), (9, 3), (6, 5), (12, 0), (3, 1), (11, 4), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85175", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 12), (10, 1), (2, 14), (11, 10), (3, 5), (6, 10), (1, 10), (9, 1), (6, 15), (2, 4), (5, 14), (14, 5), (1, 14), (16, 6), (16, 3), (2, 13), (3, 10), (1, 0), (8, 0), (11, 11), (13, 2), (15, 5), (8, 15), (1, 15), (15, 10), (5, 1), (16, 4), (13, 3), (0, 11), (14, 12), (8, 7), (12, 7), (11, 6), (9, 2), (0, 4), (3, 3), (17, 12), (13, 10), (4, 12), (0, 13), (15, 6), (1, 7), (17, 0), (15, 12), (17, 3), (2, 12), (6, 2), (8, 9), (14, 14), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591491", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (2, 0), (9, 11), (10, 5), (1, 0), (4, 2), (6, 0), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45812", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (7, 5), (7, 8), (10, 10), (3, 7), (11, 4), (8, 8), (4, 4), (12, 8), (14, 10), (13, 9), (2, 2), (2, 6), (12, 7), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219976", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 10), (2, 14), (10, 9), (7, 6), (9, 13), (3, 10), (15, 1), (4, 4), (7, 14), (12, 3), (7, 5), (11, 3), (3, 2), (9, 8), (8, 2), (13, 5), (0, 8), (2, 4), (4, 11), (12, 12), (7, 8), (5, 14), (14, 10), (10, 5), (5, 10), (7, 9), (13, 8), (2, 11), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "935397", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 2), (9, 12), (2, 1), (7, 7), (1, 7), (13, 3), (7, 0), (0, 7), (10, 12), (12, 8), (11, 2), (0, 9), (12, 1), (5, 3), (2, 5), (13, 2), (11, 1), (5, 12), (12, 6), (15, 9), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925708", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 9), (4, 0), (0, 10), (4, 2), (0, 4), (4, 3), (3, 4), (6, 8), (6, 9), (10, 2), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755432", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 12), (9, 4), (10, 6), (10, 7), (2, 9), (1, 13), (0, 3), (5, 6), (10, 5), (3, 10), (6, 12), (4, 14), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844334", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (5, 0), (11, 8), (15, 3), (10, 8), (8, 2), (11, 5), (4, 6), (10, 0), (6, 7), (5, 9), (0, 2), (11, 7), (16, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515709", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 5), (9, 8), (1, 4), (2, 10), (7, 4), (5, 7), (2, 0), (8, 4), (3, 1), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7589", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (9, 3), (7, 10), (3, 3), (0, 6), (6, 11), (7, 8), (11, 2), (5, 0), (9, 7), (2, 1), (5, 8), (0, 2), (5, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26787", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (9, 4), (2, 10), (6, 10), (9, 6), (9, 2), (11, 7), (9, 9), (3, 8), (4, 9), (4, 4), (2, 3), (2, 4), (12, 7), (3, 11), (5, 4), (14, 4), (15, 8), (15, 6), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888550", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 0), (9, 4), (2, 0), (1, 5), (7, 5), (5, 5), (8, 1), (10, 2), (10, 4), (9, 5), (3, 5), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7386", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 8), (1, 0), (6, 11), (2, 10), (3, 9), (2, 6), (1, 2), (2, 1), (10, 10), (2, 4), (10, 2), (10, 0), (10, 1), (10, 3), (4, 2), (1, 3), (12, 4), (5, 11), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2709", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (7, 11), (11, 11), (5, 1), (11, 0), (11, 16), (3, 3), (4, 5), (8, 18), (13, 11), (10, 7), (8, 16), (8, 10), (9, 2), (1, 14), (14, 0), (13, 16), (5, 12), (7, 8), (5, 5), (9, 16), (4, 1), (4, 6), (14, 5), (0, 6), (14, 15), (8, 8), (6, 14), (7, 14), (10, 1), (10, 5), (11, 18), (13, 14), (7, 12), (14, 14), (3, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947358", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 0), (4, 9), (8, 8), (6, 1), (3, 8), (8, 5), (6, 7), (8, 1), (10, 2), (2, 3), (1, 4), (14, 0), (15, 4), (8, 7), (7, 10), (15, 0), (0, 1), (0, 8), (12, 3), (11, 9), (3, 2), (15, 1), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205893", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (8, 5), (5, 18), (1, 14), (7, 14), (0, 5), (9, 16), (2, 14), (1, 11), (4, 15), (0, 17), (7, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638152", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 12), (10, 12), (12, 2), (4, 16), (4, 6), (3, 14), (8, 5), (3, 5), (16, 1), (10, 15), (5, 6), (7, 5), (5, 11), (10, 14), (6, 6), (4, 4), (11, 5), (13, 7), (6, 13), (17, 15), (5, 8), (14, 6), (13, 10), (16, 0), (1, 0), (0, 4), (12, 1), (8, 8), (15, 9), (16, 9), (9, 1), (4, 3), (10, 5), (9, 13), (11, 8), (15, 11), (11, 4), (1, 2), (16, 8), (17, 9), (16, 11), (8, 9), (9, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530841", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (10, 5), (7, 6), (3, 9), (10, 1), (5, 9), (1, 2), (3, 3), (6, 5), (12, 6), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63863", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 15), (9, 8), (14, 0), (13, 2), (1, 6), (0, 15), (8, 0), (13, 13), (4, 15), (5, 3), (11, 13), (7, 7), (4, 6), (4, 12), (7, 10), (4, 1), (6, 6), (10, 7), (13, 1), (13, 12), (9, 15), (9, 13), (1, 2), (7, 12), (11, 0), (16, 11), (4, 11), (8, 14), (0, 13), (4, 10), (15, 14), (1, 10), (9, 9), (12, 3), (9, 5), (6, 9), (11, 14), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706381", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 2), (4, 2), (4, 8), (7, 14), (2, 15), (4, 5), (0, 6), (14, 4), (5, 11), (11, 7), (11, 4), (10, 2), (14, 12), (11, 12), (3, 6), (12, 11), (0, 11), (4, 15), (4, 13), (4, 9), (6, 4), (8, 4), (13, 14), (12, 10), (12, 5), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920569", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 5), (7, 7), (15, 0), (11, 2), (6, 8), (10, 12), (15, 11), (14, 9), (11, 7), (11, 9), (15, 6), (4, 12), (3, 7), (13, 9), (8, 2), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984460", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (6, 2), (3, 1), (0, 16), (1, 17), (0, 5), (9, 6), (9, 12), (9, 4), (8, 0), (2, 14), (5, 0), (5, 4), (2, 11), (2, 4), (6, 1), (9, 8), (3, 14), (9, 9), (0, 12), (8, 11), (0, 13), (9, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874318", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (17, 9), (9, 9), (17, 6), (7, 12), (1, 6), (5, 5), (17, 13), (4, 15), (7, 5), (12, 1), (8, 10), (1, 16), (5, 12), (12, 15), (5, 13), (1, 11), (14, 4), (14, 0), (1, 17), (6, 3), (5, 11), (16, 2), (4, 7), (5, 17), (12, 12), (15, 0), (12, 6), (0, 8), (16, 4), (13, 13), (2, 0), (10, 1), (16, 9), (8, 1), (1, 0), (16, 14), (4, 5), (9, 6), (4, 2), (3, 4), (8, 5), (12, 9), (16, 1), (9, 8), (7, 0), (13, 9), (0, 6), (1, 8), (13, 16), (9, 5), (10, 15), (7, 6), (15, 3), (13, 2), (0, 14), (11, 17), (10, 13), (9, 2), (12, 16), (16, 13), (17, 2), (9, 17), (3, 12), (2, 17), (3, 1), (2, 9), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991236", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 0), (4, 9), (2, 11), (11, 8), (10, 9), (9, 6), (8, 2), (8, 11), (6, 5), (6, 15), (9, 7), (12, 15), (10, 3), (6, 12), (5, 13), (9, 10), (10, 6), (4, 10), (6, 7), (13, 2), (0, 3), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980717", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (13, 15), (2, 4), (8, 2), (7, 0), (10, 14), (12, 4), (15, 11), (8, 9), (6, 13), (11, 5), (0, 2), (3, 11), (14, 4), (5, 1), (7, 2), (3, 13), (13, 14), (15, 2), (14, 11), (5, 11), (6, 4), (10, 11), (4, 10), (9, 0), (14, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933950", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (0, 3), (3, 6), (10, 9), (1, 0), (3, 10), (8, 9), (2, 2), (1, 4), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4701", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (9, 5), (3, 8), (13, 4), (0, 9), (9, 3), (12, 15), (2, 4), (3, 15), (10, 5), (8, 8), (11, 4), (6, 5), (13, 10), (3, 4), (13, 1), (1, 2), (1, 5), (2, 2), (7, 8), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707999", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (6, 3), (0, 5), (5, 2), (2, 11), (9, 0), (2, 8), (3, 0), (0, 11), (3, 13), (5, 3), (8, 14), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "666835", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 16), (13, 4), (16, 13), (14, 9), (0, 1), (0, 10), (13, 15), (9, 5), (5, 18), (2, 15), (11, 7), (5, 16), (12, 12), (2, 1), (11, 14), (14, 5), (9, 14), (2, 8), (7, 11), (2, 18), (5, 14), (15, 1), (8, 8), (14, 7), (8, 13), (1, 6), (9, 0), (15, 7), (6, 9), (0, 11), (15, 3), (2, 9), (14, 14), (0, 17), (0, 14), (6, 4), (7, 3), (2, 4), (6, 16), (3, 12), (10, 4), (2, 3), (7, 13), (4, 2), (6, 14), (11, 5), (16, 0), (13, 14), (14, 18), (7, 9), (7, 16), (9, 4), (2, 16), (16, 14), (6, 2), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923351", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (16, 2), (14, 7), (3, 10), (6, 2), (11, 8), (10, 9), (1, 2), (2, 3), (13, 3), (14, 6), (7, 3), (11, 3), (4, 11), (3, 1), (3, 5), (8, 10), (7, 10), (4, 8), (0, 8), (3, 9), (9, 10), (17, 10), (11, 4), (9, 9), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354362", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 13), (5, 17), (3, 8), (8, 14), (2, 2), (1, 10), (0, 10), (11, 3), (1, 7), (8, 9), (11, 2), (4, 2), (8, 12), (10, 18), (8, 17), (8, 13), (6, 11), (11, 10), (5, 7), (0, 17), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779008", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (4, 4), (5, 6), (3, 6), (10, 8), (1, 9), (5, 3), (1, 6), (4, 9), (13, 6), (8, 2), (7, 8), (1, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "473541", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (9, 11), (8, 4), (8, 5), (4, 10), (3, 1), (9, 10), (7, 4), (2, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80683", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (16, 6), (14, 9), (4, 7), (0, 6), (10, 9), (3, 1), (7, 8), (2, 2), (17, 5), (17, 8), (2, 4), (6, 4), (12, 8), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64716", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 16), (8, 11), (8, 5), (6, 8), (9, 7), (5, 6), (9, 13), (5, 4), (6, 11), (7, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690975", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 7), (2, 2), (11, 0), (14, 3), (6, 3), (2, 5), (10, 0), (11, 5), (14, 6), (0, 3), (7, 10), (7, 8), (10, 3), (5, 16), (12, 15), (1, 5), (9, 1), (15, 3), (4, 5), (12, 8), (0, 2), (3, 2), (3, 6), (5, 8), (6, 16), (2, 15), (14, 15), (12, 0), (9, 12), (12, 14), (0, 15), (0, 1), (2, 4), (14, 16), (2, 12), (5, 5), (13, 12), (13, 8), (2, 13), (0, 4), (3, 16), (7, 9), (10, 13), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602318", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (13, 6), (1, 3), (15, 11), (10, 8), (8, 15), (15, 3), (6, 2), (13, 1), (9, 2), (11, 6), (2, 9), (12, 6), (12, 3), (14, 4), (4, 1), (12, 11), (15, 4), (3, 12), (13, 0), (6, 15), (9, 7), (6, 4), (4, 10), (12, 2), (1, 8), (14, 12), (0, 4), (13, 7), (4, 4), (5, 10), (9, 9), (3, 10), (5, 9), (14, 2), (4, 15), (7, 3), (1, 11), (1, 14), (10, 5), (14, 13), (9, 3), (3, 3), (1, 13), (15, 0), (7, 0), (0, 2), (1, 10), (6, 13), (8, 3), (7, 4), (10, 7), (15, 2), (7, 8), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917394", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (5, 6), (8, 0), (11, 8), (13, 0), (4, 9), (10, 0), (8, 5), (1, 8), (11, 7), (0, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204845", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (2, 8), (5, 7), (2, 0), (4, 6), (9, 5), (8, 4), (1, 7), (3, 1), (11, 1), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56302", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (10, 12), (5, 7), (3, 7), (14, 3), (7, 6), (16, 15), (10, 2), (1, 2), (12, 16), (12, 2), (10, 6), (12, 8), (7, 0), (0, 14), (2, 10), (9, 2), (4, 18), (16, 11), (9, 13), (8, 11), (8, 18), (13, 8), (3, 17), (16, 2), (16, 9), (14, 8), (14, 15), (10, 17), (3, 3), (8, 14), (16, 5), (10, 15), (5, 4), (5, 6), (10, 1), (3, 6), (3, 10), (14, 1), (15, 7), (2, 5), (11, 12), (15, 8), (11, 5), (2, 2), (3, 15), (2, 4), (0, 4), (9, 15), (7, 13), (11, 9), (14, 18), (4, 1), (15, 11), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459197", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (8, 8), (0, 10), (12, 3), (2, 4), (5, 2), (13, 0), (11, 7), (10, 9), (12, 12), (10, 2), (12, 2), (11, 0), (7, 9), (12, 13), (8, 9), (12, 10), (7, 5), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970713", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (0, 10), (6, 4), (0, 3), (0, 2), (4, 0), (8, 9), (9, 9), (4, 10), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59487", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (5, 13), (2, 8), (6, 18), (7, 3), (0, 13), (5, 11), (4, 1), (4, 7), (4, 8), (11, 5), (5, 10), (10, 4), (9, 14), (1, 1), (10, 16), (0, 6), (7, 7), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950567", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 10), (0, 1), (5, 0), (15, 7), (10, 8), (18, 4), (5, 2), (8, 9), (6, 7), (15, 0), (7, 7), (0, 4), (11, 4), (10, 4), (9, 11), (16, 0), (12, 9), (12, 10), (12, 3), (7, 5), (3, 11), (1, 10), (10, 3), (16, 10), (5, 1), (12, 0), (8, 2), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225890", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (4, 7), (2, 7), (4, 2), (9, 4), (2, 9), (3, 4), (2, 14), (7, 0), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244324", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (9, 4), (14, 5), (4, 1), (10, 4), (5, 1), (6, 3), (5, 5), (4, 7), (8, 3), (8, 4), (7, 1), (5, 3), (1, 6), (3, 8), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63949", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (2, 9), (1, 8), (4, 9), (6, 3), (0, 5), (4, 10), (4, 4), (6, 6), (5, 11), (9, 0), (9, 11), (7, 8), (1, 6), (8, 10), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25247", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (11, 4), (8, 14), (9, 11), (7, 11), (4, 3), (2, 13), (13, 9), (12, 7), (4, 7), (10, 3), (3, 1), (12, 10), (3, 8), (11, 8), (2, 11), (7, 12), (14, 0), (13, 1), (2, 12), (10, 15), (1, 3), (10, 10), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640918", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 15), (8, 14), (1, 10), (7, 1), (14, 14), (5, 5), (9, 0), (11, 1), (9, 2), (14, 9), (5, 10), (13, 2), (4, 7), (2, 3), (5, 11), (2, 16), (12, 17), (4, 9), (11, 6), (0, 12), (0, 13), (6, 17), (4, 11), (4, 8), (4, 2), (14, 2), (14, 7), (13, 4), (8, 16), (13, 6), (9, 10), (1, 5), (14, 12), (11, 4), (3, 3), (2, 1), (10, 6), (11, 9), (4, 3), (2, 15), (9, 12), (6, 11), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953188", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (7, 14), (12, 18), (10, 12), (11, 0), (2, 11), (11, 7), (9, 9), (14, 6), (4, 18), (15, 15), (4, 6), (9, 15), (6, 0), (2, 18), (13, 9), (13, 5), (2, 4), (9, 7), (15, 9), (13, 11), (9, 4), (0, 18), (7, 5), (5, 11), (10, 11), (7, 16), (9, 10), (1, 3), (11, 1), (8, 11), (5, 3), (4, 3), (9, 1), (12, 13), (13, 18), (14, 7), (13, 8), (12, 6), (14, 9), (15, 8), (3, 3), (2, 10), (2, 14), (3, 16), (15, 3), (11, 8), (12, 17), (7, 0), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766154", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 9), (3, 7), (2, 3), (2, 10), (4, 0), (5, 2), (1, 3), (8, 11), (0, 4), (7, 8), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636418", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 14), (0, 13), (13, 2), (1, 9), (7, 11), (14, 4), (8, 11), (11, 15), (10, 8), (11, 9), (11, 14), (8, 10), (7, 5), (4, 6), (4, 8), (9, 5), (7, 6), (5, 8), (0, 8), (5, 14), (11, 5), (4, 4), (14, 11), (2, 0), (4, 1), (0, 4), (9, 8), (13, 1), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799192", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (5, 1), (9, 0), (13, 5), (13, 0), (16, 10), (4, 1), (9, 12), (0, 3), (12, 4), (15, 3), (16, 4), (4, 5), (6, 4), (18, 9), (7, 11), (2, 9), (10, 0), (17, 4), (14, 11), (15, 1), (10, 10), (14, 6), (16, 3), (0, 7), (1, 4), (5, 2), (2, 3), (12, 8), (6, 7), (8, 9), (8, 12), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "871945", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (11, 0), (0, 2), (2, 10), (12, 3), (3, 1), (8, 9), (6, 11), (3, 14), (9, 3), (10, 9), (10, 10), (10, 5), (2, 1), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682270", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 11), (7, 11), (3, 11), (14, 15), (9, 5), (6, 3), (14, 9), (5, 16), (0, 16), (13, 3), (3, 10), (1, 0), (1, 8), (3, 13), (4, 12), (10, 2), (4, 14), (4, 2), (1, 1), (4, 9), (1, 3), (4, 3), (13, 7), (8, 9), (13, 8), (5, 2), (1, 12), (6, 16), (12, 2), (12, 3), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942376", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 7), (6, 17), (7, 4), (15, 0), (0, 8), (4, 15), (8, 1), (7, 1), (3, 6), (11, 8), (2, 2), (16, 14), (4, 16), (1, 7), (3, 18), (2, 5), (1, 11), (10, 12), (5, 5), (9, 4), (3, 12), (3, 16), (10, 6), (10, 1), (10, 3), (15, 13), (11, 5), (14, 12), (8, 4), (6, 7), (6, 13), (9, 7), (13, 3), (9, 6), (14, 4), (16, 2), (13, 10), (6, 8), (10, 15), (1, 6), (3, 13), (13, 15), (11, 17), (16, 17), (13, 11), (7, 14), (2, 1), (3, 4), (2, 11), (9, 8), (4, 18), (12, 3), (11, 10), (2, 15), (14, 13), (3, 5), (16, 9), (13, 1), (6, 11), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763656", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (10, 2), (7, 8), (7, 6), (2, 10), (2, 7), (8, 10), (0, 10), (6, 8), (8, 9), (6, 2), (9, 8), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21420", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (6, 7), (1, 13), (11, 5), (6, 11), (5, 2), (5, 13), (8, 10), (8, 2), (8, 14), (4, 3), (3, 7), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717450", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (0, 1), (1, 3), (2, 1), (8, 0), (12, 5), (13, 5), (5, 5), (11, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88427", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 9), (15, 4), (9, 9), (3, 1), (4, 8), (16, 2), (15, 7), (9, 4), (0, 7), (10, 3), (16, 11), (16, 5), (7, 8), (4, 0), (9, 5), (16, 10), (5, 11), (10, 0), (16, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72071", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 10), (16, 4), (18, 5), (1, 4), (14, 1), (18, 2), (12, 0), (16, 2), (3, 10), (0, 8), (8, 2), (12, 4), (4, 2), (15, 7), (15, 9), (8, 5), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890721", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 4), (9, 6), (10, 9), (1, 13), (2, 4), (4, 1), (8, 3), (3, 12), (0, 4), (9, 5), (7, 10), (5, 9), (12, 0), (10, 11), (11, 5), (4, 10), (2, 13), (7, 12), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959345", "dataset": "MATH"}
{"messages": [{"content": "In a 11x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (0, 13), (1, 7), (4, 1), (10, 7), (6, 2), (7, 10), (1, 1), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168809", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 6), (1, 14), (8, 11), (2, 12), (4, 1), (6, 10), (4, 13), (9, 14), (2, 15), (8, 16), (8, 18), (2, 4), (2, 9), (5, 4), (1, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183747", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 14), (9, 7), (2, 14), (4, 15), (2, 1), (12, 4), (9, 1), (10, 15), (3, 2), (12, 16), (6, 14), (7, 16), (12, 2), (1, 7), (5, 16), (6, 17), (6, 7), (0, 10), (9, 8), (11, 2), (12, 5), (11, 6), (5, 10), (2, 17), (9, 10), (0, 6), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557840", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (2, 4), (6, 4), (8, 6), (2, 5), (1, 0), (0, 9), (3, 5), (6, 10), (10, 8), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38536", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 7), (10, 10), (10, 1), (12, 3), (5, 8), (15, 8), (12, 12), (0, 12), (15, 7), (8, 10), (3, 0), (6, 11), (4, 5), (0, 2), (14, 7), (2, 10), (11, 12), (6, 6), (0, 11), (9, 3), (6, 1), (10, 6), (11, 9), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977820", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (9, 2), (11, 4), (6, 9), (0, 2), (11, 7), (10, 0), (11, 2), (14, 4), (1, 9), (9, 4), (3, 5), (10, 10), (0, 10), (3, 9), (10, 4), (0, 7), (15, 5), (2, 11), (10, 7), (14, 8), (9, 3), (3, 8), (14, 9), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "826660", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (4, 0), (8, 2), (5, 1), (4, 5), (2, 3), (5, 5), (9, 4), (12, 3), (2, 6), (10, 1), (4, 2), (9, 0), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18166", "dataset": "MATH"}
{"messages": [{"content": "In a 19x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 13), (11, 5), (14, 12), (1, 15), (6, 4), (6, 13), (18, 14), (3, 12), (12, 0), (0, 12), (11, 7), (1, 5), (4, 9), (0, 6), (5, 15), (16, 11), (15, 3), (10, 12), (14, 6), (10, 5), (6, 0), (12, 10), (10, 15), (10, 10), (4, 5), (18, 10), (15, 8), (6, 5), (16, 10), (13, 6), (5, 13), (10, 7), (8, 2), (1, 1), (14, 9), (5, 0), (3, 14), (1, 11), (2, 7), (2, 11), (7, 14), (15, 5), (3, 0), (15, 12), (16, 8), (15, 1), (15, 14), (7, 5), (3, 10), (8, 11), (1, 12), (6, 6), (8, 16), (2, 3), (1, 0), (13, 3), (10, 2), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355428", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (5, 1), (7, 1), (1, 7), (7, 4), (0, 3), (9, 0), (4, 6), (7, 2), (8, 4), (1, 8), (6, 9), (9, 3), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49488", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (9, 0), (17, 7), (15, 2), (9, 1), (12, 4), (17, 8), (6, 7), (18, 10), (13, 5), (11, 8), (1, 9), (0, 5), (12, 13), (6, 9), (18, 11), (8, 9), (16, 2), (1, 8), (1, 2), (2, 8), (5, 5), (17, 5), (14, 12), (11, 13), (5, 3), (12, 6), (3, 6), (1, 4), (17, 6), (18, 8), (13, 0), (14, 8), (18, 9), (12, 10), (0, 4), (12, 2), (9, 2), (8, 8), (1, 7), (17, 11), (6, 1), (14, 11), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887697", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (10, 10), (4, 4), (13, 3), (15, 7), (2, 5), (15, 14), (9, 3), (8, 4), (11, 0), (17, 4), (14, 5), (8, 9), (13, 1), (7, 3), (15, 3), (6, 9), (4, 12), (2, 3), (5, 12), (14, 10), (4, 1), (8, 3), (3, 14), (6, 6), (5, 2), (8, 8), (3, 9), (2, 12), (3, 3), (12, 7), (4, 14), (10, 9), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915333", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (13, 0), (11, 13), (9, 1), (3, 10), (11, 9), (14, 2), (8, 8), (9, 8), (13, 6), (2, 16), (3, 12), (6, 12), (2, 8), (3, 16), (5, 3), (4, 2), (12, 15), (5, 15), (10, 2), (11, 0), (7, 7), (13, 15), (9, 9), (8, 4), (14, 16), (7, 17), (13, 1), (6, 15), (11, 17), (1, 14), (6, 8), (0, 5), (13, 3), (5, 16), (3, 5), (11, 11), (9, 12), (11, 8), (14, 15), (5, 7), (12, 9), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "756469", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (13, 7), (4, 13), (0, 13), (10, 0), (10, 4), (1, 1), (0, 9), (0, 3), (5, 8), (3, 6), (11, 5), (1, 0), (7, 10), (12, 16), (6, 14), (5, 14), (13, 1), (2, 5), (5, 16), (7, 1), (5, 11), (5, 10), (13, 5), (7, 0), (12, 4), (8, 14), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854750", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (2, 11), (4, 2), (9, 12), (2, 5), (5, 12), (10, 11), (12, 5), (1, 10), (6, 2), (3, 6), (6, 6), (11, 15), (4, 6), (4, 12), (7, 1), (5, 0), (11, 10), (2, 7), (7, 3), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971503", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (3, 6), (8, 1), (7, 8), (8, 4), (4, 4), (2, 0), (7, 10), (1, 10), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71273", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 10), (1, 12), (5, 4), (6, 6), (8, 5), (10, 15), (8, 8), (8, 16), (0, 3), (11, 13), (8, 6), (8, 9), (3, 8), (11, 1), (3, 15), (3, 11), (7, 17), (7, 1), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906098", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (12, 10), (13, 3), (7, 4), (0, 11), (3, 14), (5, 7), (1, 0), (11, 12), (4, 15), (8, 10), (8, 18), (8, 13), (7, 10), (6, 7), (11, 11), (8, 5), (0, 15), (4, 10), (13, 10), (9, 9), (6, 11), (7, 11), (6, 9), (11, 9), (0, 3), (12, 12), (13, 11), (4, 7), (9, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875139", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (12, 10), (7, 7), (4, 9), (12, 18), (11, 0), (5, 16), (10, 4), (8, 8), (7, 3), (5, 6), (9, 17), (2, 18), (1, 7), (2, 8), (4, 4), (7, 18), (8, 2), (13, 13), (2, 2), (4, 18), (13, 6), (13, 14), (9, 15), (2, 3), (7, 6), (5, 14), (1, 12), (10, 6), (13, 2), (6, 5), (3, 11), (0, 10), (7, 5), (10, 15), (3, 17), (4, 16), (4, 8), (6, 18), (6, 0), (0, 12), (1, 11), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485080", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (9, 3), (16, 2), (1, 4), (7, 2), (6, 11), (15, 10), (0, 7), (15, 9), (17, 11), (5, 9), (15, 7), (13, 4), (13, 5), (1, 7), (10, 3), (18, 2), (7, 8), (11, 4), (12, 4), (11, 3), (11, 2), (15, 2), (9, 2), (16, 1), (0, 4), (13, 3), (1, 0), (14, 8), (14, 6), (7, 4), (4, 11), (3, 2), (16, 8), (3, 12), (6, 1), (9, 9), (6, 8), (2, 5), (8, 11), (3, 8), (9, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677706", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (7, 7), (11, 3), (5, 11), (3, 10), (8, 9), (9, 13), (6, 13), (10, 16), (2, 3), (4, 4), (2, 5), (3, 16), (1, 9), (5, 9), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377500", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (9, 11), (1, 9), (7, 4), (14, 1), (13, 2), (12, 4), (12, 0), (0, 9), (14, 4), (2, 9), (8, 0), (10, 11), (5, 11), (0, 3), (5, 4), (7, 7), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980020", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (2, 13), (8, 0), (13, 7), (17, 10), (6, 14), (4, 14), (16, 9), (4, 6), (8, 1), (9, 13), (6, 11), (7, 3), (4, 10), (10, 14), (13, 4), (4, 4), (2, 4), (9, 1), (11, 12), (16, 0), (4, 11), (1, 11), (6, 2), (11, 4), (14, 11), (2, 0), (2, 14), (1, 1), (3, 7), (5, 9), (7, 8), (1, 7), (16, 14), (13, 3), (5, 14), (11, 8), (0, 11), (3, 3), (6, 1), (6, 7), (7, 10), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685011", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 5), (7, 11), (4, 12), (1, 7), (3, 5), (14, 4), (9, 10), (9, 7), (0, 8), (13, 6), (5, 5), (7, 12), (1, 3), (12, 11), (5, 10), (2, 8), (9, 0), (11, 2), (6, 11), (4, 7), (2, 3), (8, 4), (4, 11), (11, 1), (6, 1), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605204", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (1, 6), (10, 9), (8, 1), (2, 10), (3, 4), (4, 5), (4, 10), (6, 0), (9, 2), (9, 7), (14, 9), (9, 3), (2, 4), (8, 5), (0, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124371", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (12, 5), (4, 5), (0, 1), (12, 0), (11, 1), (10, 5), (0, 3), (3, 5), (5, 9), (0, 4), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103627", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 2), (4, 1), (1, 4), (11, 10), (9, 5), (4, 2), (11, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213952", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 4), (1, 2), (3, 3), (8, 6), (0, 1), (14, 2), (11, 4), (12, 3), (9, 4), (3, 0), (6, 0), (6, 4), (3, 1), (12, 5), (14, 6), (6, 1), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16350", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (2, 2), (2, 8), (1, 8), (0, 4), (3, 13), (3, 10), (6, 11), (1, 11), (1, 0), (4, 5), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32028", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (9, 2), (8, 6), (1, 6), (7, 6), (10, 6), (9, 7), (10, 7), (4, 0), (5, 5), (10, 1), (3, 2), (0, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10955", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (3, 7), (3, 11), (3, 0), (7, 4), (2, 2), (7, 6), (8, 11), (11, 7), (6, 4), (8, 5), (4, 5), (3, 4), (5, 5), (13, 12), (1, 12), (2, 3), (11, 1), (11, 9), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172886", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (0, 6), (8, 12), (7, 2), (11, 1), (5, 12), (4, 3), (14, 12), (15, 11), (15, 6), (1, 10), (3, 1), (11, 0), (16, 1), (0, 11), (13, 1), (4, 13), (1, 14), (1, 13), (13, 3), (13, 2), (14, 4), (17, 13), (15, 12), (2, 6), (12, 1), (11, 6), (14, 2), (5, 1), (15, 3), (9, 10), (0, 12), (8, 16), (16, 6), (1, 6), (9, 6), (2, 8), (7, 10), (14, 9), (3, 7), (6, 16), (5, 16), (12, 14), (15, 16), (5, 14), (7, 13), (4, 14), (7, 9), (10, 11), (1, 1), (3, 4), (6, 7), (13, 15), (4, 0), (13, 9), (4, 10), (17, 11), (8, 13), (4, 7), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605898", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 14), (10, 2), (6, 14), (3, 2), (0, 3), (4, 11), (1, 5), (2, 2), (9, 2), (12, 13), (8, 3), (7, 4), (14, 2), (5, 2), (2, 8), (4, 6), (13, 9), (9, 15), (9, 5), (8, 8), (14, 8), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "756692", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 5), (5, 3), (2, 6), (3, 6), (1, 10), (1, 4), (9, 0), (5, 10), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38852", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (1, 5), (5, 3), (2, 1), (9, 7), (7, 10), (6, 0), (0, 2), (2, 2), (2, 10), (5, 8), (1, 1), (8, 9), (8, 10), (2, 5), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2700", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (2, 6), (5, 3), (4, 7), (4, 0), (17, 8), (9, 7), (15, 6), (15, 0), (14, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600666", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (5, 6), (0, 5), (7, 9), (6, 0), (8, 8), (2, 5), (8, 5), (0, 3), (9, 4), (6, 7), (2, 12), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26258", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (8, 4), (13, 12), (9, 4), (4, 0), (0, 8), (1, 9), (4, 7), (0, 3), (3, 12), (8, 13), (10, 17), (9, 15), (10, 7), (8, 1), (5, 17), (5, 8), (4, 14), (3, 7), (2, 11), (0, 13), (3, 4), (11, 14), (1, 2), (1, 14), (6, 10), (11, 0), (9, 14), (11, 7), (7, 16), (10, 14), (1, 7), (5, 9), (7, 0), (2, 13), (11, 8), (10, 4), (1, 4), (9, 9), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730865", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 3), (2, 1), (7, 13), (2, 13), (12, 3), (13, 2), (11, 4), (6, 11), (15, 2), (11, 10), (17, 2), (8, 5), (11, 5), (11, 13), (2, 2), (10, 10), (3, 5), (2, 10), (4, 8), (12, 12), (11, 11), (3, 6), (5, 13), (0, 2), (0, 5), (12, 7), (16, 11), (7, 0), (12, 8), (4, 10), (4, 0), (6, 3), (0, 11), (14, 5), (5, 10), (8, 7), (15, 6), (8, 10), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726265", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (3, 2), (6, 5), (1, 3), (4, 6), (8, 0), (4, 1), (0, 8), (3, 10), (9, 1), (6, 7), (10, 6), (6, 4), (7, 1), (2, 10), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3668", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 10), (0, 1), (0, 7), (3, 3), (3, 2), (4, 8), (10, 3), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34065", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (4, 10), (0, 4), (5, 14), (3, 10), (3, 5), (3, 0), (2, 12), (3, 11), (2, 4), (4, 2), (6, 1), (2, 10), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127462", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (8, 7), (9, 3), (14, 0), (9, 4), (5, 8), (13, 2), (14, 2), (4, 0), (7, 2), (8, 1), (3, 5), (5, 2), (0, 5), (2, 9), (8, 3), (7, 1), (7, 6), (9, 1), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17227", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 9), (6, 9), (17, 6), (7, 8), (4, 6), (16, 8), (1, 8), (15, 9), (8, 5), (4, 0), (10, 3), (9, 7), (10, 11), (5, 5), (5, 7), (1, 0), (6, 1), (15, 4), (16, 4), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896169", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (1, 14), (12, 6), (0, 15), (11, 12), (12, 15), (3, 10), (4, 11), (10, 9), (0, 3), (2, 1), (0, 13), (2, 11), (8, 2), (7, 11), (0, 14), (5, 10), (9, 10), (5, 4), (7, 15), (13, 7), (5, 2), (1, 11), (9, 7), (8, 8), (6, 2), (12, 9), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "733490", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 13), (9, 4), (10, 14), (14, 1), (5, 17), (2, 13), (6, 3), (9, 7), (8, 16), (11, 9), (2, 5), (9, 15), (3, 6), (4, 15), (2, 6), (7, 10), (14, 10), (7, 14), (6, 14), (14, 4), (6, 16), (11, 0), (2, 9), (3, 2), (12, 0), (8, 7), (3, 17), (10, 7), (7, 13), (7, 1), (13, 6), (12, 1), (1, 16), (9, 11), (7, 5), (4, 1), (7, 3), (9, 17), (9, 10), (8, 11), (7, 4), (11, 13), (4, 14), (13, 0), (10, 13), (3, 5), (6, 13), (9, 16), (12, 8), (14, 5), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704786", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 10), (2, 6), (2, 2), (9, 2), (0, 2), (0, 4), (10, 7), (7, 1), (1, 2), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214787", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (5, 4), (2, 9), (0, 8), (1, 9), (8, 0), (6, 7), (7, 6), (10, 7), (6, 2), (3, 9), (3, 8), (0, 6), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10717", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (16, 6), (13, 4), (4, 3), (12, 5), (5, 9), (8, 0), (0, 4), (10, 9), (10, 4), (3, 2), (15, 0), (9, 7), (12, 2), (2, 0), (4, 0), (17, 7), (8, 5), (7, 8), (4, 7), (10, 7), (2, 1), (11, 7), (13, 6), (16, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16473", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 16), (11, 9), (9, 5), (6, 4), (7, 2), (14, 6), (1, 13), (4, 6), (10, 16), (11, 0), (13, 12), (5, 13), (0, 14), (3, 14), (9, 0), (7, 4), (14, 16), (3, 15), (7, 3), (10, 7), (13, 9), (10, 6), (0, 2), (11, 4), (1, 7), (12, 4), (11, 12), (1, 4), (1, 11), (8, 3), (2, 1), (4, 5), (1, 9), (4, 13), (6, 3), (2, 6), (9, 3), (8, 7), (6, 10), (0, 17), (1, 14), (2, 8), (11, 7), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606988", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (9, 15), (2, 9), (4, 10), (0, 16), (12, 9), (4, 4), (2, 14), (15, 13), (9, 13), (15, 3), (11, 16), (3, 0), (5, 6), (10, 7), (0, 8), (9, 5), (1, 5), (0, 4), (0, 11), (2, 2), (9, 9), (7, 1), (1, 12), (13, 10), (10, 12), (3, 15), (5, 5), (11, 5), (3, 5), (11, 4), (4, 5), (15, 9), (15, 2), (9, 3), (4, 1), (9, 2), (1, 14), (7, 5), (9, 1), (7, 13), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844428", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (8, 1), (8, 3), (4, 5), (7, 0), (8, 8), (4, 7), (1, 6), (2, 0), (2, 7), (4, 3), (4, 4), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1491", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (10, 2), (10, 3), (10, 9), (8, 12), (7, 5), (12, 7), (12, 3), (6, 3), (6, 4), (12, 1), (3, 4), (8, 8), (13, 2), (6, 12), (7, 2), (8, 5), (0, 12), (4, 8), (11, 10), (8, 14), (4, 1), (9, 7), (5, 3), (5, 0), (1, 8), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934426", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 4), (8, 0), (11, 3), (3, 4), (11, 13), (2, 7), (16, 0), (15, 8), (4, 15), (14, 6), (6, 9), (7, 10), (10, 5), (2, 4), (2, 11), (4, 6), (14, 8), (3, 0), (5, 2), (0, 1), (2, 9), (2, 12), (1, 2), (8, 1), (14, 3), (8, 14), (12, 0), (4, 12), (1, 9), (13, 7), (11, 4), (5, 5), (10, 3), (7, 9), (5, 8), (11, 15), (15, 2), (3, 9), (15, 15), (0, 3), (14, 11), (0, 11), (1, 5), (4, 0), (13, 9), (9, 10), (5, 0), (12, 8), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "843164", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (9, 5), (7, 6), (7, 5), (8, 5), (7, 0), (4, 8), (0, 3), (1, 0), (6, 2), (10, 3), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10289", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 13), (2, 0), (1, 0), (7, 12), (11, 5), (2, 1), (8, 6), (14, 12), (15, 1), (15, 4), (14, 3), (15, 11), (8, 2), (10, 0), (11, 12), (9, 0), (13, 9), (11, 7), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872080", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 6), (9, 1), (9, 8), (8, 7), (3, 2), (6, 4), (5, 1), (5, 8), (7, 9), (10, 0), (6, 1), (3, 3), (1, 8), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1669", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 9), (10, 1), (2, 4), (9, 11), (9, 7), (10, 9), (11, 13), (10, 7), (2, 6), (9, 4), (6, 2), (2, 0), (9, 5), (4, 14), (8, 14), (2, 1), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822432", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (7, 9), (2, 12), (2, 0), (8, 4), (6, 1), (10, 12), (4, 11), (5, 5), (7, 4), (1, 2), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690400", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (3, 3), (9, 4), (11, 5), (8, 10), (11, 6), (8, 7), (6, 4), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270347", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 5), (10, 2), (11, 7), (1, 11), (5, 5), (5, 6), (0, 11), (0, 5), (15, 5), (6, 0), (1, 6), (4, 3), (13, 1), (12, 2), (6, 4), (7, 12), (0, 15), (13, 6), (11, 15), (0, 14), (0, 12), (3, 6), (9, 0), (8, 14), (5, 0), (3, 12), (10, 12), (0, 13), (0, 10), (5, 9), (14, 5), (11, 3), (7, 6), (13, 5), (11, 8), (6, 11), (12, 7), (10, 0), (9, 6), (15, 11), (3, 13), (4, 10), (1, 4), (13, 7), (13, 15), (2, 6), (15, 15), (5, 13), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447600", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 16), (13, 9), (13, 0), (13, 3), (11, 11), (7, 10), (14, 12), (8, 14), (7, 12), (6, 16), (3, 1), (3, 9), (6, 2), (13, 13), (1, 2), (12, 1), (11, 4), (12, 8), (10, 0), (11, 13), (10, 16), (2, 10), (2, 11), (3, 15), (5, 12), (4, 5), (1, 7), (14, 10), (9, 13), (4, 11), (2, 5), (13, 2), (11, 7), (11, 12), (13, 12), (13, 4), (13, 6), (8, 6), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987672", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (8, 17), (8, 11), (1, 16), (9, 8), (1, 3), (4, 9), (6, 16), (4, 1), (8, 5), (15, 0), (2, 7), (14, 14), (0, 7), (9, 18), (2, 6), (12, 12), (3, 7), (9, 5), (14, 1), (3, 14), (8, 12), (5, 16), (10, 11), (2, 1), (9, 12), (5, 3), (6, 2), (11, 0), (7, 17), (3, 15), (2, 18), (2, 4), (11, 9), (13, 6), (13, 11), (14, 13), (15, 17), (9, 2), (3, 16), (12, 16), (1, 10), (15, 15), (7, 8), (12, 2), (3, 1), (2, 12), (3, 12), (10, 15), (2, 0), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436368", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (14, 10), (7, 14), (8, 15), (8, 4), (2, 4), (13, 6), (10, 13), (2, 11), (12, 8), (13, 13), (9, 6), (0, 2), (2, 12), (3, 15), (8, 5), (10, 4), (1, 10), (1, 14), (8, 2), (8, 0), (12, 7), (9, 5), (4, 1), (6, 0), (2, 5), (9, 10), (11, 15), (0, 7), (10, 12), (14, 4), (12, 4), (12, 10), (11, 11), (5, 7), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964850", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 9), (10, 9), (8, 2), (6, 8), (6, 2), (10, 5), (10, 0), (3, 3), (11, 5), (7, 10), (10, 6), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334417", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (0, 7), (5, 1), (5, 3), (6, 3), (2, 9), (8, 0), (4, 10), (9, 7), (4, 3), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47565", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (16, 5), (4, 11), (3, 8), (18, 2), (11, 6), (4, 0), (9, 6), (15, 11), (5, 3), (7, 9), (15, 5), (14, 14), (3, 1), (9, 15), (14, 12), (2, 5), (3, 2), (9, 3), (14, 11), (4, 16), (14, 7), (0, 14), (7, 17), (0, 4), (4, 8), (12, 13), (15, 0), (8, 6), (16, 17), (12, 1), (17, 14), (2, 14), (13, 16), (12, 11), (18, 11), (14, 15), (7, 0), (1, 3), (6, 17), (10, 5), (6, 11), (13, 2), (1, 16), (0, 12), (6, 14), (7, 5), (11, 3), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839700", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (10, 9), (10, 4), (7, 7), (12, 2), (2, 2), (12, 7), (1, 12), (5, 1), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "826299", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (12, 5), (1, 0), (0, 9), (11, 7), (4, 1), (12, 1), (8, 5), (1, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276214", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 9), (0, 12), (8, 3), (0, 11), (1, 9), (10, 12), (6, 6), (6, 12), (2, 5), (13, 3), (11, 4), (12, 6), (3, 0), (7, 10), (8, 10), (12, 9), (14, 0), (12, 5), (8, 12), (6, 5), (10, 3), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963034", "dataset": "MATH"}
{"messages": [{"content": "In a 19x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (4, 15), (0, 3), (16, 9), (15, 3), (0, 5), (5, 11), (13, 1), (6, 0), (4, 10), (17, 9), (10, 10), (4, 5), (17, 0), (3, 8), (3, 1), (7, 2), (17, 3), (4, 1), (5, 5), (11, 5), (2, 9), (14, 13), (7, 13), (9, 5), (4, 11), (13, 7), (7, 9), (2, 12), (0, 13), (9, 2), (0, 8), (5, 7), (1, 11), (16, 4), (9, 0), (14, 16), (14, 11), (11, 8), (17, 16), (4, 7), (11, 11), (10, 15), (11, 7), (6, 1), (11, 9), (16, 6), (2, 10), (8, 3), (7, 5), (11, 10), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523607", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 5), (16, 6), (2, 11), (0, 12), (5, 14), (4, 3), (17, 2), (16, 14), (6, 9), (11, 3), (12, 1), (3, 9), (17, 7), (13, 14), (12, 8), (5, 5), (11, 7), (9, 6), (0, 2), (5, 10), (16, 11), (15, 6), (13, 8), (11, 2), (8, 9), (16, 1), (7, 11), (17, 8), (12, 12), (10, 14), (10, 5), (5, 1), (15, 3), (5, 8), (4, 4), (5, 11), (13, 7), (9, 12), (13, 0), (4, 5), (5, 3), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605307", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (1, 8), (4, 2), (1, 4), (8, 8), (10, 0), (8, 9), (13, 1), (0, 5), (8, 1), (6, 6), (1, 5), (3, 3), (4, 10), (12, 5), (2, 0), (3, 0), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41971", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (3, 3), (2, 9), (8, 6), (5, 3), (7, 9), (6, 5), (1, 5), (1, 6), (10, 0), (2, 8), (7, 1), (2, 0), (5, 8), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7910", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (9, 5), (13, 4), (4, 0), (0, 7), (8, 6), (12, 3), (6, 16), (7, 0), (0, 3), (8, 15), (11, 1), (8, 12), (3, 6), (9, 16), (11, 13), (5, 1), (10, 5), (1, 11), (0, 13), (3, 11), (7, 11), (8, 1), (9, 12), (9, 2), (7, 6), (13, 6), (9, 1), (10, 13), (5, 7), (6, 14), (13, 8), (1, 8), (11, 10), (3, 13), (6, 10), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478254", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (14, 9), (5, 11), (14, 5), (6, 11), (13, 5), (5, 4), (10, 0), (0, 10), (2, 3), (4, 6), (6, 0), (1, 12), (11, 1), (1, 7), (6, 12), (0, 8), (4, 3), (0, 1), (13, 10), (10, 8), (3, 6), (10, 11), (12, 8), (13, 12), (1, 8), (0, 5), (2, 10), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897723", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 5), (3, 8), (8, 1), (3, 1), (0, 5), (14, 2), (17, 4), (9, 3), (15, 8), (0, 3), (6, 4), (17, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504479", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (9, 7), (6, 9), (10, 12), (1, 1), (13, 5), (7, 11), (4, 7), (9, 12), (8, 13), (3, 2), (12, 1), (14, 10), (1, 2), (1, 8), (7, 7), (9, 0), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986279", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (8, 8), (3, 13), (5, 10), (8, 3), (1, 14), (11, 11), (0, 12), (4, 12), (8, 12), (4, 14), (6, 3), (5, 8), (7, 7), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925183", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (0, 2), (13, 6), (14, 1), (0, 7), (4, 5), (14, 4), (5, 0), (9, 0), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953403", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (7, 1), (8, 7), (2, 5), (4, 8), (1, 3), (6, 5), (7, 6), (3, 2), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4592", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (14, 3), (9, 7), (0, 2), (8, 6), (10, 9), (13, 7), (12, 6), (6, 0), (4, 2), (1, 9), (14, 0), (8, 3), (4, 4), (11, 2), (11, 4), (4, 7), (3, 0), (12, 0), (12, 7), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4927", "dataset": "MATH"}
{"messages": [{"content": "In a 17x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 7), (11, 4), (13, 12), (5, 15), (3, 11), (3, 15), (4, 11), (12, 15), (8, 7), (13, 5), (1, 10), (16, 6), (8, 16), (5, 9), (8, 17), (4, 4), (6, 16), (3, 0), (7, 9), (8, 5), (0, 6), (3, 8), (15, 5), (9, 7), (14, 1), (16, 5), (6, 15), (15, 12), (3, 2), (9, 1), (14, 6), (13, 0), (8, 0), (1, 4), (8, 9), (9, 14), (4, 6), (10, 10), (16, 0), (1, 15), (12, 0), (15, 0), (3, 6), (6, 9), (6, 2), (13, 14), (1, 0), (13, 8), (12, 12), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "714336", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (7, 1), (3, 5), (0, 4), (1, 5), (1, 4), (7, 8), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81689", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (9, 8), (10, 1), (4, 2), (4, 1), (5, 9), (2, 1), (1, 5), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29053", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 15), (7, 17), (7, 16), (4, 10), (10, 15), (4, 7), (8, 17), (1, 5), (8, 6), (3, 9), (7, 12), (1, 18), (0, 6), (5, 16), (8, 3), (9, 17), (2, 13), (6, 13), (9, 14), (10, 11), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840161", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 4), (11, 4), (5, 2), (1, 3), (15, 4), (1, 4), (6, 6), (6, 2), (7, 8), (7, 7), (12, 3), (14, 8), (7, 3), (13, 11), (13, 6), (2, 4), (13, 3), (5, 12), (9, 10), (6, 1), (11, 11), (7, 5), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324458", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (6, 7), (9, 9), (3, 5), (8, 4), (7, 4), (9, 4), (8, 10), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7584", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (2, 1), (1, 8), (9, 4), (6, 8), (3, 14), (6, 12), (10, 11), (12, 10), (0, 7), (2, 7), (6, 14), (11, 7), (4, 13), (8, 13), (11, 9), (4, 11), (11, 13), (5, 14), (12, 2), (10, 8), (4, 2), (16, 11), (1, 2), (2, 16), (10, 17), (10, 15), (12, 1), (5, 8), (13, 9), (12, 5), (4, 0), (12, 13), (3, 6), (14, 7), (18, 14), (4, 7), (3, 7), (5, 11), (6, 3), (8, 6), (11, 4), (2, 11), (18, 2), (14, 13), (8, 7), (1, 6), (6, 2), (3, 10), (14, 17), (18, 0), (17, 14), (17, 2), (1, 10), (18, 10), (9, 6), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289188", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (10, 17), (4, 8), (7, 17), (3, 16), (7, 14), (9, 17), (0, 15), (3, 18), (0, 18), (5, 12), (6, 12), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141837", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (14, 3), (10, 2), (16, 1), (1, 2), (9, 11), (2, 7), (16, 2), (12, 9), (10, 9), (0, 11), (10, 1), (2, 5), (5, 1), (6, 11), (7, 10), (11, 6), (5, 7), (3, 6), (1, 5), (11, 1), (5, 10), (6, 6), (10, 10), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577792", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (6, 9), (9, 12), (9, 11), (9, 4), (9, 9), (2, 2), (1, 8), (8, 9), (5, 5), (1, 12), (0, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210395", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (7, 3), (13, 5), (0, 9), (1, 2), (1, 4), (13, 8), (9, 6), (5, 4), (2, 9), (8, 6), (10, 3), (6, 2), (6, 1), (11, 8), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14347", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (12, 10), (7, 4), (2, 8), (9, 2), (3, 12), (13, 10), (12, 1), (12, 7), (7, 12), (9, 0), (5, 0), (12, 2), (11, 11), (13, 8), (3, 9), (6, 11), (8, 12), (11, 9), (14, 12), (8, 6), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914468", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 12), (11, 2), (6, 13), (9, 12), (12, 9), (8, 5), (1, 8), (4, 8), (8, 11), (8, 2), (11, 5), (4, 13), (5, 12), (15, 3), (0, 11), (0, 9), (4, 11), (6, 9), (10, 6), (11, 7), (15, 11), (10, 1), (3, 9), (1, 7), (2, 4), (12, 5), (6, 6), (6, 8), (13, 2), (15, 2), (8, 9), (15, 1), (12, 2), (13, 5), (8, 13), (15, 6), (3, 5), (1, 3), (10, 4), (5, 11), (11, 0), (2, 7), (1, 10), (4, 9), (3, 13), (10, 7), (5, 7), (5, 6), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44488", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (3, 1), (7, 0), (5, 0), (0, 9), (9, 6), (8, 16), (10, 10), (11, 12), (6, 9), (8, 14), (4, 12), (1, 7), (5, 3), (14, 9), (1, 8), (11, 8), (9, 2), (10, 13), (6, 16), (8, 2), (1, 5), (0, 14), (1, 0), (10, 0), (2, 8), (7, 9), (15, 1), (9, 15), (10, 4), (2, 9), (5, 8), (14, 13), (0, 4), (5, 9), (3, 7), (3, 16), (3, 11), (2, 14), (5, 16), (10, 12), (3, 10), (2, 15), (12, 2), (9, 12), (14, 8), (14, 2), (10, 1), (13, 1), (9, 1), (14, 11), (6, 5), (8, 10), (2, 0), (13, 10), (0, 12), (7, 10), (13, 8), (0, 16), (7, 13), (3, 13), (0, 7), (7, 11), (12, 16), (12, 1), (3, 12), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11205", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (5, 1), (3, 8), (13, 6), (0, 3), (6, 1), (13, 1), (0, 6), (12, 9), (4, 6), (2, 3), (9, 3), (14, 5), (12, 6), (8, 6), (14, 7), (7, 2), (5, 8), (10, 9), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37004", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (16, 2), (10, 4), (15, 1), (12, 9), (11, 3), (15, 2), (12, 4), (9, 8), (9, 1), (7, 2), (8, 7), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706602", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (0, 12), (4, 5), (4, 3), (15, 11), (12, 0), (8, 9), (9, 4), (8, 2), (1, 9), (3, 0), (5, 12), (11, 0), (1, 1), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641640", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (7, 11), (3, 0), (6, 12), (1, 11), (9, 12), (0, 6), (2, 2), (9, 8), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "885950", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (9, 3), (2, 5), (9, 9), (2, 8), (7, 9), (7, 3), (1, 9), (7, 0), (9, 2), (8, 0), (1, 1), (2, 3), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2607", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 11), (9, 13), (11, 0), (11, 2), (3, 4), (15, 10), (2, 0), (7, 5), (4, 0), (13, 12), (12, 2), (1, 6), (14, 8), (14, 3), (12, 1), (8, 7), (12, 5), (11, 8), (7, 6), (7, 8), (8, 4), (0, 13), (14, 13), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239708", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (10, 1), (3, 5), (8, 5), (6, 12), (6, 4), (11, 4), (9, 11), (1, 4), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "673496", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (5, 7), (11, 8), (14, 2), (15, 1), (12, 0), (12, 6), (8, 4), (3, 10), (2, 1), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257242", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (1, 5), (2, 9), (9, 8), (7, 2), (9, 7), (5, 0), (6, 0), (11, 1), (9, 3), (8, 4), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18294", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (8, 0), (7, 1), (0, 2), (0, 6), (2, 3), (4, 3), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67949", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (1, 6), (8, 2), (10, 6), (14, 10), (12, 14), (15, 4), (11, 2), (1, 0), (14, 12), (6, 7), (13, 6), (15, 0), (6, 10), (9, 9), (2, 10), (2, 0), (14, 4), (7, 2), (13, 0), (2, 13), (1, 10), (8, 13), (2, 3), (4, 3), (2, 9), (7, 1), (15, 1), (2, 7), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954979", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (10, 9), (2, 4), (16, 4), (9, 2), (2, 5), (0, 12), (0, 6), (4, 15), (13, 7), (7, 7), (10, 11), (11, 14), (1, 7), (13, 15), (14, 3), (2, 14), (5, 9), (3, 0), (9, 7), (14, 12), (7, 13), (3, 13), (14, 6), (8, 9), (10, 15), (14, 4), (10, 4), (5, 18), (8, 14), (8, 4), (4, 17), (6, 18), (10, 1), (7, 4), (12, 5), (1, 11), (7, 3), (4, 16), (11, 17), (2, 3), (11, 15), (1, 12), (7, 0), (5, 5), (2, 9), (8, 6), (5, 10), (6, 15), (16, 3), (8, 2), (16, 6), (13, 9), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768596", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (6, 5), (5, 4), (3, 7), (5, 3), (3, 12), (4, 8), (3, 1), (3, 3), (5, 8), (6, 7), (1, 10), (8, 1), (10, 11), (2, 10), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36273", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (1, 9), (11, 1), (11, 9), (6, 1), (2, 4), (10, 6), (3, 3), (9, 6), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24915", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 13), (6, 4), (8, 10), (1, 11), (1, 1), (5, 4), (0, 2), (0, 9), (13, 8), (4, 11), (7, 6), (13, 1), (12, 12), (2, 2), (4, 10), (4, 9), (2, 11), (4, 15), (12, 4), (8, 13), (9, 16), (1, 9), (0, 8), (4, 14), (8, 12), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845287", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 11), (3, 5), (2, 6), (10, 6), (3, 8), (13, 3), (2, 10), (7, 2), (3, 11), (7, 4), (2, 5), (9, 1), (14, 1), (11, 11), (1, 1), (3, 4), (4, 11), (11, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114206", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (4, 10), (9, 4), (11, 6), (4, 0), (5, 4), (0, 2), (0, 1), (8, 13), (11, 12), (12, 6), (8, 8), (12, 2), (1, 9), (13, 1), (7, 12), (1, 10), (11, 8), (2, 13), (0, 12), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "815457", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 14), (4, 4), (6, 7), (9, 15), (2, 2), (9, 1), (3, 9), (10, 15), (11, 5), (8, 4), (9, 11), (1, 16), (3, 1), (9, 0), (4, 10), (8, 5), (3, 6), (0, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289926", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (3, 5), (5, 12), (3, 6), (10, 1), (4, 4), (7, 2), (5, 7), (15, 6), (9, 9), (18, 8), (17, 3), (7, 4), (18, 1), (4, 7), (0, 7), (14, 10), (8, 6), (15, 7), (3, 12), (0, 10), (16, 11), (9, 10), (6, 9), (8, 2), (15, 1), (10, 2), (4, 1), (8, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766771", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 16), (3, 1), (2, 14), (11, 15), (13, 6), (3, 12), (0, 12), (13, 15), (11, 9), (2, 11), (8, 17), (1, 3), (7, 15), (2, 2), (3, 16), (3, 13), (6, 3), (10, 12), (3, 11), (3, 14), (0, 16), (5, 12), (12, 4), (5, 0), (10, 18), (6, 12), (9, 7), (1, 4), (4, 11), (4, 13), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966024", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 8), (1, 6), (5, 10), (1, 10), (2, 3), (7, 7), (5, 5), (10, 10), (8, 14), (7, 14), (5, 6), (9, 1), (2, 13), (10, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140893", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (6, 15), (8, 3), (14, 12), (4, 16), (4, 8), (8, 16), (4, 6), (1, 9), (13, 5), (7, 13), (9, 13), (10, 1), (7, 7), (6, 3), (3, 6), (11, 6), (11, 12), (5, 15), (1, 17), (4, 9), (1, 12), (0, 2), (12, 9), (3, 9), (9, 4), (13, 2), (3, 2), (5, 3), (4, 10), (13, 0), (2, 4), (2, 7), (9, 5), (11, 8), (0, 17), (13, 4), (14, 4), (5, 4), (12, 3), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667786", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 17), (2, 12), (5, 12), (1, 15), (6, 13), (9, 10), (8, 7), (7, 10), (2, 6), (2, 14), (7, 1), (8, 1), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "668774", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (6, 14), (8, 14), (11, 4), (6, 15), (5, 9), (1, 1), (4, 16), (5, 11), (4, 10), (4, 8), (0, 8), (10, 2), (1, 11), (5, 7), (4, 0), (0, 7), (8, 7), (1, 6), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626606", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (6, 5), (6, 1), (3, 5), (16, 5), (2, 0), (5, 10), (14, 10), (2, 10), (4, 5), (8, 2), (9, 7), (14, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "782732", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (3, 5), (6, 11), (8, 10), (4, 9), (5, 15), (6, 16), (4, 11), (5, 5), (8, 3), (8, 7), (2, 12), (5, 17), (7, 5), (10, 15), (3, 2), (8, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923949", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (2, 4), (13, 7), (12, 10), (2, 3), (10, 1), (10, 8), (3, 8), (8, 0), (10, 9), (0, 10), (7, 11), (12, 5), (1, 13), (5, 17), (7, 2), (7, 5), (4, 10), (7, 8), (10, 0), (0, 2), (9, 2), (4, 4), (3, 9), (2, 7), (0, 17), (11, 3), (12, 3), (11, 15), (9, 3), (1, 14), (5, 8), (3, 14), (0, 15), (7, 14), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774696", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (10, 5), (0, 2), (1, 6), (9, 3), (3, 9), (2, 5), (8, 3), (10, 0), (0, 1), (10, 6), (0, 5), (2, 9), (11, 1), (9, 5), (2, 8), (7, 6), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16148", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (6, 4), (17, 12), (11, 6), (17, 7), (0, 5), (4, 7), (8, 15), (10, 15), (9, 15), (3, 4), (2, 2), (15, 1), (13, 15), (14, 14), (1, 7), (1, 2), (2, 1), (14, 16), (3, 8), (3, 0), (5, 2), (16, 6), (3, 16), (1, 15), (12, 3), (10, 12), (7, 2), (9, 13), (3, 1), (8, 11), (11, 10), (17, 1), (2, 0), (11, 7), (6, 10), (4, 9), (5, 5), (6, 0), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993735", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 11), (4, 8), (8, 13), (6, 13), (2, 3), (4, 3), (6, 2), (12, 11), (11, 5), (0, 1), (7, 3), (7, 11), (4, 7), (6, 14), (2, 1), (10, 2), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "873437", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (10, 15), (13, 13), (2, 3), (4, 6), (8, 12), (9, 13), (1, 14), (0, 10), (8, 6), (2, 11), (3, 6), (11, 9), (13, 2), (5, 8), (7, 11), (10, 8), (1, 5), (13, 0), (2, 9), (0, 9), (6, 1), (9, 1), (1, 0), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "905308", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (1, 0), (0, 6), (1, 12), (2, 0), (4, 0), (2, 1), (5, 1), (2, 2), (0, 4), (1, 11), (7, 10), (5, 8), (6, 11), (9, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56751", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (7, 9), (1, 3), (9, 4), (5, 2), (6, 6), (2, 8), (4, 1), (0, 7), (8, 5), (1, 0), (10, 1), (7, 3), (8, 2), (2, 2), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (1, 4), (6, 5), (11, 6), (6, 2), (10, 12), (8, 14), (6, 11), (3, 10), (10, 1), (5, 6), (11, 4), (3, 5), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180385", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 9), (3, 0), (4, 4), (8, 11), (11, 3), (6, 8), (10, 5), (1, 2), (1, 8), (8, 12), (11, 1), (7, 2), (0, 3), (2, 4), (8, 5), (8, 8), (3, 10), (9, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60510", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (16, 11), (8, 8), (6, 1), (10, 11), (1, 5), (17, 9), (5, 8), (13, 5), (12, 5), (18, 4), (2, 10), (9, 8), (7, 4), (13, 6), (16, 5), (10, 8), (12, 2), (3, 10), (9, 11), (7, 8), (15, 7), (10, 7), (14, 10), (16, 12), (5, 12), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "868784", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (7, 3), (7, 0), (6, 0), (1, 3), (3, 7), (4, 8), (11, 11), (4, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509021", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (7, 3), (4, 4), (11, 4), (11, 1), (2, 4), (11, 8), (5, 14), (2, 9), (7, 0), (0, 7), (2, 0), (10, 1), (7, 8), (6, 0), (11, 13), (3, 6), (10, 2), (7, 9), (6, 8), (2, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999949", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (3, 10), (3, 2), (1, 11), (6, 1), (3, 11), (2, 0), (9, 6), (11, 11), (2, 9), (2, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294093", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 12), (10, 1), (6, 12), (7, 8), (8, 8), (0, 8), (8, 4), (9, 7), (4, 2), (2, 5), (1, 13), (4, 6), (8, 11), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151039", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (6, 0), (6, 3), (5, 1), (1, 2), (2, 9), (0, 1), (11, 0), (1, 3), (10, 5), (5, 2), (3, 6), (3, 2), (10, 8), (5, 10), (1, 8), (10, 1), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8432", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (3, 14), (4, 15), (12, 0), (7, 10), (3, 0), (12, 2), (5, 6), (10, 5), (10, 10), (5, 14), (9, 16), (4, 8), (2, 1), (10, 15), (10, 8), (2, 9), (6, 15), (7, 16), (8, 15), (8, 3), (13, 2), (7, 12), (2, 16), (8, 5), (1, 2), (13, 1), (10, 9), (2, 2), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886835", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (4, 4), (4, 7), (3, 3), (4, 0), (4, 9), (0, 9), (5, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44471", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (8, 7), (10, 2), (5, 11), (6, 6), (7, 5), (8, 10), (9, 7), (4, 0), (3, 2), (4, 5), (7, 2), (10, 5), (12, 13), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977751", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (11, 8), (12, 3), (11, 0), (0, 8), (12, 2), (3, 4), (8, 11), (9, 6), (8, 1), (3, 2), (3, 6), (5, 9), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778929", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (2, 6), (10, 0), (2, 4), (6, 5), (9, 6), (1, 6), (5, 3), (0, 9), (3, 8), (5, 8), (10, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14309", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (11, 6), (0, 2), (3, 11), (7, 10), (2, 7), (1, 9), (2, 5), (1, 2), (11, 0), (0, 10), (2, 8), (4, 3), (9, 5), (7, 2), (7, 9), (4, 1), (3, 8), (13, 7), (13, 9), (9, 12), (13, 8), (8, 2), (9, 6), (4, 0), (0, 3), (11, 3), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875894", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (12, 4), (2, 11), (13, 7), (7, 11), (0, 9), (10, 13), (13, 12), (10, 10), (6, 13), (5, 1), (10, 4), (3, 7), (11, 6), (11, 8), (4, 13), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950785", "dataset": "MATH"}
{"messages": [{"content": "In a 15x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 9), (4, 7), (14, 1), (4, 0), (8, 13), (5, 13), (3, 3), (5, 4), (7, 11), (7, 7), (0, 1), (10, 6), (1, 14), (6, 2), (8, 5), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "782180", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (7, 0), (5, 6), (2, 4), (1, 7), (0, 2), (3, 2), (3, 3), (0, 9), (0, 5), (5, 1), (1, 2), (7, 4), (10, 8), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10504", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (10, 4), (6, 4), (1, 2), (2, 12), (10, 11), (5, 17), (9, 5), (3, 2), (9, 3), (3, 16), (0, 16), (5, 18), (8, 7), (9, 0), (10, 3), (4, 8), (9, 10), (7, 13), (1, 18), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901130", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (11, 0), (9, 8), (11, 1), (2, 3), (9, 6), (12, 4), (2, 8), (5, 8), (9, 4), (0, 1), (6, 7), (4, 2), (9, 5), (13, 7), (3, 4), (3, 3), (10, 2), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10261", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (4, 13), (4, 7), (3, 6), (9, 6), (3, 8), (3, 11), (7, 15), (0, 4), (4, 10), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266816", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (7, 6), (5, 7), (9, 1), (5, 2), (2, 3), (7, 8), (5, 4), (9, 7), (5, 8), (2, 0), (8, 9), (0, 7), (6, 2), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2411", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (10, 5), (7, 9), (14, 7), (1, 0), (16, 0), (5, 7), (8, 10), (4, 4), (15, 10), (4, 2), (4, 8), (9, 0), (15, 9), (10, 7), (15, 12), (1, 11), (4, 11), (12, 12), (14, 11), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554338", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (7, 3), (2, 8), (0, 11), (3, 14), (4, 5), (7, 15), (3, 15), (1, 15), (10, 16), (7, 1), (0, 4), (8, 2), (1, 13), (9, 2), (5, 6), (6, 12), (10, 0), (7, 14), (7, 4), (4, 13), (10, 17), (3, 11), (2, 5), (0, 2), (9, 0), (0, 9), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405697", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 6), (1, 8), (14, 8), (2, 9), (4, 3), (7, 5), (0, 9), (0, 11), (0, 7), (5, 5), (3, 2), (8, 4), (5, 11), (4, 4), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "589902", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (3, 7), (9, 5), (1, 9), (8, 5), (10, 13), (4, 5), (6, 7), (3, 4), (14, 0), (4, 0), (8, 1), (4, 12), (14, 7), (4, 13), (14, 9), (1, 12), (9, 11), (9, 2), (6, 0), (0, 7), (14, 1), (0, 6), (1, 4), (15, 4), (5, 13), (3, 13), (0, 8), (12, 8), (12, 4), (3, 3), (3, 6), (13, 5), (1, 2), (15, 2), (2, 3), (7, 1), (4, 8), (8, 9), (8, 2), (6, 12), (14, 6), (8, 3), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757163", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 15), (13, 10), (14, 10), (9, 4), (5, 7), (11, 14), (5, 10), (9, 8), (6, 14), (4, 7), (6, 8), (9, 5), (11, 10), (10, 0), (14, 12), (3, 14), (7, 4), (14, 5), (0, 2), (2, 14), (14, 9), (4, 2), (10, 1), (8, 12), (13, 0), (3, 4), (4, 13), (3, 8), (1, 13), (9, 7), (1, 12), (14, 4), (14, 11), (13, 3), (5, 1), (2, 7), (9, 14), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839121", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (15, 6), (12, 4), (15, 10), (6, 1), (5, 1), (17, 11), (11, 0), (5, 6), (7, 15), (16, 15), (4, 7), (9, 4), (6, 9), (8, 1), (16, 11), (6, 2), (13, 11), (16, 10), (15, 2), (12, 11), (13, 10), (12, 2), (4, 8), (3, 10), (18, 14), (4, 5), (11, 13), (9, 2), (13, 14), (10, 13), (0, 14), (6, 11), (10, 2), (2, 13), (2, 10), (18, 11), (10, 0), (16, 4), (0, 12), (14, 9), (4, 1), (2, 12), (15, 9), (7, 9), (14, 4), (7, 11), (3, 3), (9, 9), (13, 1), (16, 3), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959256", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 1), (4, 2), (15, 14), (12, 5), (0, 4), (10, 8), (12, 2), (11, 9), (15, 15), (13, 12), (2, 4), (11, 14), (7, 8), (9, 13), (11, 7), (12, 7), (10, 16), (3, 11), (0, 6), (14, 1), (0, 5), (14, 15), (8, 1), (4, 9), (8, 4), (6, 2), (5, 10), (3, 4), (13, 11), (5, 4), (13, 3), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751990", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (4, 2), (3, 6), (8, 2), (4, 8), (5, 10), (1, 0), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21662", "dataset": "MATH"}
{"messages": [{"content": "In a 19x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 8), (9, 8), (9, 5), (9, 9), (8, 4), (16, 2), (13, 5), (18, 1), (0, 4), (18, 2), (6, 3), (1, 7), (8, 5), (6, 6), (7, 7), (2, 14), (18, 6), (3, 2), (7, 6), (1, 11), (18, 12), (8, 10), (10, 7), (14, 0), (15, 9), (10, 2), (9, 7), (17, 7), (11, 1), (4, 5), (15, 0), (5, 13), (12, 7), (9, 16), (2, 8), (3, 12), (14, 11), (15, 6), (13, 4), (18, 13), (17, 11), (10, 8), (5, 14), (5, 9), (16, 7), (11, 9), (10, 16), (10, 3), (7, 13), (2, 6), (12, 2), (17, 1), (15, 10), (5, 11), (17, 5), (16, 3), (6, 16), (0, 1), (8, 12), (13, 9), (9, 12), (15, 8), (11, 15), (1, 14), (4, 13), (7, 15), (14, 10), (1, 10), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739390", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (0, 4), (1, 0), (9, 7), (10, 1), (6, 3), (9, 10), (4, 2), (6, 4), (5, 9), (11, 3), (11, 1), (8, 2), (8, 6), (10, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33144", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (9, 10), (4, 9), (4, 2), (5, 12), (8, 5), (7, 5), (10, 12), (12, 5), (17, 4), (10, 6), (3, 3), (12, 12), (0, 1), (6, 13), (11, 6), (6, 0), (0, 6), (4, 5), (7, 8), (8, 9), (4, 7), (10, 8), (6, 11), (13, 1), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877379", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 5), (11, 11), (2, 7), (13, 8), (8, 8), (8, 11), (11, 10), (11, 2), (8, 0), (0, 8), (16, 1), (10, 2), (16, 11), (0, 1), (7, 0), (8, 10), (17, 6), (7, 2), (4, 10), (12, 6), (0, 11), (16, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "689532", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (10, 13), (11, 2), (5, 10), (5, 7), (9, 7), (12, 9), (4, 0), (8, 3), (2, 2), (3, 3), (3, 6), (11, 11), (14, 7), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920996", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (0, 10), (7, 6), (1, 2), (4, 4), (11, 1), (2, 0), (6, 10), (6, 4), (6, 9), (8, 10), (3, 2), (4, 3), (10, 3), (5, 0), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14227", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (3, 2), (7, 7), (0, 13), (6, 14), (1, 7), (10, 7), (8, 10), (9, 2), (2, 13), (1, 13), (3, 4), (4, 4), (5, 10), (3, 0), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170754", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (0, 8), (3, 8), (11, 12), (8, 12), (4, 6), (0, 12), (1, 12), (2, 11), (2, 8), (10, 14), (10, 11), (0, 1), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "433911", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (10, 9), (11, 0), (4, 1), (8, 6), (5, 10), (3, 12), (1, 10), (6, 10), (5, 0), (8, 12), (1, 3), (2, 7), (4, 8), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149661", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (9, 9), (9, 0), (0, 4), (11, 11), (10, 4), (3, 8), (10, 6), (4, 0), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383692", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 15), (7, 13), (6, 10), (12, 10), (11, 12), (2, 11), (1, 17), (4, 17), (11, 17), (8, 17), (8, 2), (10, 9), (12, 12), (8, 16), (2, 7), (5, 2), (1, 4), (12, 1), (9, 11), (2, 2), (11, 3), (8, 3), (8, 9), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "955918", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (6, 14), (5, 12), (8, 15), (7, 13), (10, 8), (3, 12), (7, 10), (0, 11), (4, 6), (4, 9), (2, 5), (1, 5), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "309817", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (0, 7), (12, 11), (4, 4), (7, 5), (2, 12), (3, 4), (11, 11), (5, 7), (8, 2), (6, 4), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348333", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (1, 6), (4, 9), (5, 2), (6, 14), (9, 13), (4, 10), (7, 13), (4, 7), (5, 5), (3, 2), (4, 15), (4, 5), (12, 13), (12, 6), (4, 12), (5, 15), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575627", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (16, 5), (8, 15), (4, 0), (6, 9), (5, 5), (10, 6), (2, 12), (16, 7), (1, 4), (5, 1), (9, 12), (4, 12), (9, 9), (7, 10), (10, 13), (3, 15), (9, 13), (10, 11), (3, 13), (8, 9), (13, 1), (7, 14), (10, 7), (13, 4), (5, 14), (11, 7), (0, 7), (1, 10), (10, 8), (3, 0), (2, 3), (12, 14), (14, 13), (3, 4), (16, 12), (6, 0), (11, 12), (7, 5), (7, 13), (8, 10), (4, 5), (1, 3), (1, 9), (8, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619836", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 5), (7, 11), (11, 4), (2, 8), (9, 9), (11, 13), (4, 0), (3, 3), (0, 5), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847944", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (11, 10), (1, 10), (5, 1), (4, 0), (2, 2), (11, 0), (6, 9), (7, 0), (8, 13), (11, 3), (10, 2), (12, 11), (5, 12), (8, 15), (9, 16), (12, 12), (3, 11), (3, 6), (8, 4), (9, 2), (10, 5), (3, 3), (8, 6), (4, 8), (5, 2), (1, 13), (0, 14), (4, 3), (2, 13), (5, 8), (0, 16), (3, 9), (6, 3), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657157", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 2), (12, 10), (9, 1), (8, 4), (8, 5), (15, 6), (9, 10), (6, 5), (8, 10), (9, 4), (11, 8), (6, 3), (14, 3), (7, 8), (2, 2), (14, 0), (9, 2), (5, 9), (15, 0), (7, 6), (17, 2), (16, 7), (3, 0), (8, 11), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "293593", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 12), (8, 14), (0, 8), (1, 14), (3, 12), (11, 6), (13, 0), (15, 0), (9, 1), (8, 2), (4, 7), (13, 6), (1, 7), (6, 14), (14, 3), (13, 1), (4, 12), (10, 5), (4, 13), (13, 11), (2, 2), (1, 11), (5, 9), (9, 4), (10, 12), (15, 11), (1, 0), (12, 7), (11, 9), (9, 12), (8, 7), (5, 13), (2, 14), (3, 9), (1, 9), (3, 4), (5, 7), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899116", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 5), (11, 2), (11, 1), (13, 2), (17, 3), (4, 12), (11, 9), (4, 5), (0, 13), (8, 9), (16, 7), (16, 8), (2, 2), (13, 8), (10, 9), (12, 10), (6, 10), (15, 1), (2, 14), (9, 3), (12, 1), (3, 9), (11, 14), (8, 0), (15, 13), (16, 2), (17, 4), (15, 9), (6, 7), (13, 0), (15, 6), (2, 7), (8, 12), (9, 0), (15, 12), (4, 9), (9, 6), (4, 3), (5, 7), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848238", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (1, 1), (0, 12), (3, 12), (4, 2), (3, 2), (5, 0), (7, 0), (6, 8), (5, 2), (11, 4), (4, 3), (1, 11), (5, 4), (6, 1), (8, 8), (5, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155530", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 6), (1, 7), (7, 1), (11, 6), (5, 0), (12, 6), (12, 3), (7, 6), (5, 9), (17, 6), (2, 4), (12, 8), (12, 5), (15, 3), (13, 1), (5, 4), (12, 9), (4, 0), (0, 2), (14, 9), (10, 3), (11, 3), (16, 5), (10, 10), (14, 10), (15, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163720", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 10), (9, 4), (3, 8), (9, 9), (11, 6), (2, 10), (8, 12), (7, 4), (2, 7), (10, 3), (8, 7), (0, 5), (11, 1), (4, 9), (5, 15), (11, 2), (11, 13), (10, 9), (0, 15), (7, 15), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832291", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 2), (0, 3), (4, 9), (10, 7), (4, 8), (9, 10), (8, 4), (2, 8), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99437", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (15, 7), (12, 1), (6, 4), (11, 4), (4, 4), (0, 7), (13, 7), (7, 7), (13, 3), (11, 1), (12, 3), (2, 6), (0, 6), (6, 10), (11, 0), (13, 6), (12, 5), (0, 4), (12, 2), (5, 8), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "444619", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (10, 12), (9, 2), (13, 3), (4, 10), (2, 2), (4, 12), (14, 11), (3, 2), (13, 0), (7, 4), (9, 10), (2, 9), (15, 9), (16, 9), (15, 5), (6, 5), (9, 8), (0, 10), (1, 3), (13, 9), (2, 4), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270297", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (13, 4), (12, 0), (11, 7), (1, 1), (0, 3), (5, 0), (9, 2), (8, 5), (10, 0), (13, 2), (1, 7), (4, 0), (13, 3), (7, 7), (6, 7), (3, 5), (12, 4), (12, 8), (1, 8), (2, 8), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28794", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (4, 6), (9, 11), (3, 3), (15, 5), (8, 7), (6, 6), (8, 3), (7, 2), (4, 10), (1, 11), (12, 4), (11, 1), (15, 8), (15, 1), (7, 0), (1, 9), (3, 8), (6, 2), (14, 8), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562720", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 15), (7, 16), (5, 7), (7, 3), (7, 2), (3, 5), (4, 10), (5, 9), (1, 0), (8, 0), (0, 13), (0, 4), (4, 13), (8, 8), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643939", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (9, 3), (1, 2), (4, 6), (4, 8), (8, 4), (1, 7), (3, 8), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19128", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 4), (12, 3), (10, 5), (3, 9), (2, 5), (0, 11), (1, 7), (2, 16), (2, 15), (5, 4), (9, 8), (5, 3), (8, 10), (2, 14), (6, 5), (7, 6), (11, 9), (4, 1), (0, 8), (8, 13), (7, 9), (13, 8), (4, 6), (12, 10), (4, 8), (0, 14), (4, 12), (9, 5), (9, 7), (4, 7), (12, 8), (1, 5), (2, 4), (9, 14), (5, 16), (6, 13), (13, 5), (4, 17), (11, 3), (4, 9), (8, 18), (10, 3), (7, 2), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851262", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 11), (10, 10), (8, 1), (9, 6), (2, 2), (8, 10), (9, 5), (8, 7), (1, 9), (8, 9), (8, 3), (11, 0), (8, 4), (12, 0), (4, 9), (13, 8), (5, 7), (7, 5), (13, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96504", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (2, 5), (11, 6), (6, 9), (5, 11), (2, 9), (6, 12), (2, 1), (5, 8), (0, 2), (12, 7), (11, 2), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844387", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (1, 7), (4, 9), (1, 10), (11, 10), (2, 2), (12, 10), (11, 2), (4, 4), (6, 10), (1, 2), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143860", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 10), (4, 0), (5, 7), (12, 2), (10, 9), (2, 1), (2, 4), (10, 10), (11, 6), (12, 9), (10, 4), (3, 9), (9, 8), (2, 9), (4, 8), (6, 1), (2, 7), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20710", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (4, 15), (9, 3), (7, 6), (9, 1), (8, 13), (4, 1), (1, 14), (6, 4), (0, 4), (12, 6), (5, 7), (3, 8), (9, 2), (6, 11), (8, 4), (7, 11), (6, 14), (6, 0), (0, 12), (4, 0), (1, 15), (1, 6), (4, 12), (12, 2), (1, 11), (2, 15), (8, 3), (12, 13), (2, 1), (1, 4), (10, 7), (4, 9), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514582", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 11), (1, 6), (10, 5), (11, 0), (15, 3), (7, 11), (14, 0), (18, 11), (1, 3), (18, 1), (11, 12), (14, 7), (12, 10), (18, 2), (15, 6), (9, 3), (0, 6), (1, 5), (8, 7), (16, 6), (17, 13), (16, 8), (14, 12), (2, 3), (17, 12), (8, 9), (8, 11), (0, 1), (9, 11), (7, 5), (7, 3), (16, 9), (12, 9), (8, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979698", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 9), (3, 0), (1, 14), (13, 4), (8, 5), (12, 4), (13, 11), (6, 2), (4, 8), (3, 14), (7, 15), (13, 8), (10, 8), (1, 4), (5, 15), (6, 7), (9, 5), (6, 12), (11, 8), (5, 1), (8, 15), (9, 14), (0, 14), (4, 0), (5, 5), (9, 6), (10, 1), (7, 14), (1, 6), (11, 7), (10, 5), (8, 2), (1, 3), (0, 2), (9, 7), (4, 7), (12, 9), (11, 10), (7, 13), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "415074", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (8, 10), (5, 1), (9, 9), (4, 7), (1, 2), (1, 10), (1, 4), (3, 5), (6, 3), (2, 10), (0, 2), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42934", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (3, 9), (1, 0), (9, 0), (2, 9), (4, 3), (5, 3), (9, 6), (0, 9), (10, 10), (3, 7), (6, 9), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33475", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (2, 10), (1, 12), (0, 14), (4, 14), (5, 2), (3, 2), (7, 17), (2, 12), (4, 16), (7, 9), (5, 7), (2, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "952102", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (12, 3), (10, 2), (3, 2), (2, 3), (7, 9), (13, 10), (8, 0), (9, 3), (10, 4), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279174", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (5, 1), (13, 1), (12, 4), (7, 4), (5, 6), (11, 9), (6, 11), (1, 11), (4, 8), (2, 5), (17, 8), (2, 0), (7, 0), (13, 9), (5, 8), (1, 12), (11, 2), (8, 11), (12, 2), (14, 8), (10, 3), (13, 12), (10, 9), (14, 10), (10, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936692", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (5, 13), (6, 2), (2, 10), (3, 1), (10, 16), (3, 12), (9, 7), (2, 1), (12, 11), (12, 4), (7, 5), (7, 11), (15, 1), (3, 5), (13, 8), (7, 14), (12, 6), (1, 10), (9, 8), (13, 0), (7, 10), (8, 14), (5, 12), (6, 5), (4, 13), (10, 1), (4, 5), (0, 2), (13, 6), (1, 8), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928533", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (9, 10), (13, 1), (10, 1), (0, 14), (13, 11), (4, 6), (11, 5), (9, 5), (11, 11), (4, 14), (2, 9), (8, 10), (6, 12), (13, 5), (6, 1), (7, 6), (1, 12), (1, 4), (5, 14), (11, 13), (4, 9), (5, 2), (5, 0), (12, 0), (0, 12), (5, 11), (11, 1), (8, 11), (3, 0), (5, 8), (12, 8), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813893", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 12), (10, 4), (1, 12), (3, 0), (14, 5), (3, 7), (9, 16), (13, 5), (8, 7), (13, 13), (10, 11), (11, 10), (0, 2), (10, 14), (12, 1), (15, 7), (5, 2), (5, 11), (14, 2), (8, 12), (14, 4), (12, 5), (9, 9), (12, 15), (9, 4), (9, 13), (8, 5), (2, 1), (3, 18), (1, 18), (13, 10), (14, 14), (6, 3), (4, 6), (1, 6), (0, 16), (14, 10), (7, 11), (7, 18), (9, 14), (10, 10), (0, 15), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917712", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 15), (11, 13), (5, 6), (12, 0), (6, 8), (3, 16), (9, 9), (12, 8), (5, 9), (3, 1), (12, 1), (2, 1), (5, 15), (12, 2), (5, 16), (11, 8), (3, 15), (8, 12), (0, 14), (6, 11), (8, 0), (1, 4), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977768", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 12), (11, 7), (11, 11), (2, 13), (11, 1), (6, 4), (7, 9), (11, 12), (6, 7), (5, 10), (12, 4), (2, 0), (11, 3), (4, 13), (4, 2), (6, 2), (13, 3), (12, 8), (13, 9), (14, 5), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977446", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (4, 4), (3, 2), (0, 13), (2, 13), (8, 7), (10, 2), (1, 8), (11, 11), (10, 9), (3, 6), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676456", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 12), (4, 3), (16, 8), (5, 14), (8, 4), (3, 17), (13, 15), (6, 7), (13, 9), (12, 9), (3, 7), (6, 13), (4, 2), (0, 2), (3, 11), (1, 12), (2, 8), (1, 6), (11, 6), (11, 11), (15, 10), (5, 1), (10, 13), (10, 2), (16, 4), (5, 5), (7, 11), (13, 18), (4, 1), (15, 9), (14, 10), (6, 10), (15, 18), (1, 16), (8, 3), (12, 13), (9, 6), (7, 4), (13, 2), (7, 6), (6, 11), (14, 16), (13, 11), (1, 10), (13, 4), (16, 16), (10, 7), (7, 16), (9, 2), (7, 12), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "935608", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 10), (8, 16), (2, 8), (1, 6), (9, 1), (8, 13), (4, 7), (11, 7), (12, 14), (7, 18), (4, 17), (5, 0), (5, 3), (4, 5), (2, 4), (6, 16), (11, 2), (5, 7), (5, 4), (8, 5), (5, 10), (5, 1), (7, 8), (12, 6), (0, 15), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917900", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (12, 3), (0, 9), (16, 9), (15, 0), (12, 2), (9, 2), (12, 1), (16, 5), (12, 9), (16, 0), (4, 1), (6, 8), (1, 9), (13, 6), (10, 0), (4, 4), (11, 9), (7, 3), (16, 2), (10, 3), (5, 3), (6, 0), (17, 9), (13, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57236", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (2, 2), (7, 8), (1, 1), (2, 6), (2, 7), (9, 10), (2, 9), (9, 6), (0, 2), (9, 0), (4, 7), (5, 9), (5, 7), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6733", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 0), (14, 5), (6, 6), (10, 8), (0, 1), (7, 8), (13, 5), (12, 6), (5, 2), (4, 3), (11, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22370", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (14, 9), (9, 4), (10, 8), (1, 7), (13, 1), (7, 0), (0, 8), (15, 3), (5, 5), (3, 5), (5, 10), (2, 1), (11, 5), (6, 2), (7, 6), (3, 3), (3, 10), (5, 3), (16, 8), (10, 0), (16, 6), (11, 2), (6, 4), (5, 7), (1, 2), (9, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26148", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 8), (6, 4), (4, 5), (6, 0), (14, 2), (11, 2), (10, 11), (7, 11), (3, 0), (10, 9), (3, 12), (14, 9), (9, 0), (14, 11), (7, 12), (8, 0), (9, 12), (8, 3), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810045", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 2), (4, 7), (0, 3), (0, 6), (8, 5), (0, 4), (6, 4), (14, 7), (5, 1), (9, 9), (8, 0), (10, 8), (2, 7), (11, 5), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866754", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 1), (0, 2), (5, 12), (13, 13), (11, 2), (9, 9), (3, 5), (13, 10), (17, 14), (7, 4), (14, 14), (4, 8), (1, 1), (11, 11), (5, 1), (13, 8), (7, 9), (6, 9), (18, 8), (17, 7), (3, 2), (14, 13), (14, 8), (12, 4), (15, 3), (15, 13), (2, 1), (16, 7), (11, 8), (14, 2), (13, 2), (8, 15), (0, 1), (15, 0), (9, 12), (6, 12), (4, 12), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858046", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (1, 6), (11, 12), (11, 2), (5, 2), (7, 12), (7, 3), (4, 8), (1, 10), (6, 10), (2, 12), (3, 11), (10, 0), (10, 6), (0, 11), (9, 4), (4, 0), (3, 12), (4, 2), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732192", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (2, 8), (4, 9), (12, 5), (7, 6), (13, 4), (16, 0), (9, 5), (6, 1), (7, 9), (7, 8), (2, 11), (16, 6), (1, 0), (5, 11), (11, 2), (6, 3), (0, 9), (5, 5), (17, 6), (4, 7), (15, 8), (10, 9), (17, 8), (1, 2), (16, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260826", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (1, 2), (9, 3), (6, 4), (10, 5), (3, 0), (1, 8), (10, 9), (4, 9), (6, 9), (0, 2), (1, 7), (1, 5), (8, 6), (0, 7), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15360", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 11), (5, 12), (11, 3), (5, 4), (6, 11), (16, 8), (9, 9), (16, 6), (5, 11), (14, 0), (9, 3), (13, 7), (14, 4), (11, 6), (6, 6), (16, 2), (9, 4), (11, 4), (15, 0), (1, 6), (11, 10), (9, 6), (15, 8), (12, 10), (13, 10), (6, 9), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981999", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (6, 6), (12, 9), (13, 6), (4, 3), (12, 5), (10, 5), (2, 2), (4, 12), (8, 5), (3, 11), (2, 11), (14, 7), (7, 13), (12, 11), (3, 14), (15, 5), (0, 8), (0, 5), (5, 11), (6, 3), (7, 2), (11, 7), (15, 4), (9, 3), (1, 1), (6, 14), (12, 10), (3, 12), (5, 4), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839106", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (11, 2), (15, 7), (5, 5), (14, 3), (9, 6), (11, 5), (9, 1), (8, 3), (8, 2), (0, 6), (11, 9), (2, 6), (13, 7), (14, 4), (12, 0), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "460481", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (16, 9), (5, 5), (5, 16), (4, 10), (13, 7), (13, 10), (7, 14), (14, 12), (2, 14), (12, 0), (0, 4), (2, 8), (11, 1), (12, 10), (12, 9), (2, 16), (10, 4), (9, 4), (2, 17), (13, 4), (13, 15), (9, 3), (11, 7), (3, 7), (4, 3), (1, 11), (7, 16), (3, 9), (3, 14), (6, 14), (9, 1), (5, 3), (14, 6), (2, 0), (15, 13), (8, 9), (5, 12), (10, 2), (12, 3), (17, 11), (2, 15), (2, 10), (8, 0), (5, 7), (6, 5), (2, 6), (13, 13), (7, 3), (5, 15), (6, 6), (8, 14), (6, 7), (10, 6), (15, 12), (4, 0), (15, 14), (1, 7), (7, 17), (10, 14), (15, 17), (11, 6), (8, 4), (16, 15), (10, 0), (17, 15), (6, 16), (16, 4), (7, 1), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858494", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (8, 8), (8, 1), (9, 5), (0, 6), (4, 10), (2, 3), (4, 13), (8, 4), (11, 4), (8, 12), (5, 10), (9, 12), (6, 3), (2, 5), (1, 13), (0, 13), (7, 4), (1, 6), (0, 11), (10, 1), (8, 0), (11, 3), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749249", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (17, 5), (8, 5), (11, 4), (7, 1), (12, 2), (2, 8), (17, 4), (2, 0), (11, 11), (7, 3), (13, 7), (4, 1), (2, 9), (16, 5), (3, 1), (4, 6), (10, 3), (8, 0), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970629", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (8, 9), (1, 6), (4, 8), (2, 3), (4, 1), (8, 3), (5, 8), (5, 9), (3, 3), (8, 7), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5302", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (12, 10), (8, 0), (3, 6), (2, 8), (0, 12), (13, 8), (14, 12), (8, 2), (4, 2), (17, 11), (6, 7), (3, 12), (13, 1), (16, 11), (1, 3), (2, 7), (12, 12), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804189", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (13, 9), (16, 8), (18, 8), (12, 2), (0, 12), (8, 0), (2, 0), (7, 8), (4, 11), (11, 2), (1, 5), (3, 7), (18, 5), (16, 9), (8, 7), (11, 7), (4, 12), (12, 11), (14, 3), (1, 3), (11, 5), (6, 9), (10, 1), (4, 4), (5, 4), (15, 4), (14, 8), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851051", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (13, 4), (5, 3), (11, 17), (10, 8), (2, 1), (5, 8), (13, 11), (0, 3), (7, 4), (12, 17), (12, 0), (0, 9), (14, 7), (8, 8), (6, 1), (1, 2), (2, 4), (13, 17), (0, 16), (9, 10), (4, 8), (3, 16), (10, 0), (0, 4), (6, 13), (7, 13), (1, 15), (13, 8), (5, 10), (14, 14), (5, 1), (15, 6), (2, 7), (8, 6), (10, 2), (2, 8), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924466", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (3, 1), (3, 0), (5, 3), (0, 2), (11, 3), (4, 11), (7, 0), (13, 7), (1, 2), (9, 3), (0, 5), (13, 8), (10, 8), (13, 2), (10, 1), (11, 6), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559200", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (11, 11), (8, 15), (5, 1), (12, 9), (16, 2), (16, 5), (11, 6), (17, 2), (4, 4), (9, 1), (12, 13), (10, 15), (0, 1), (10, 6), (17, 3), (1, 7), (17, 5), (1, 15), (6, 3), (16, 6), (16, 10), (9, 6), (2, 9), (3, 12), (1, 1), (3, 0), (9, 8), (15, 15), (6, 5), (15, 7), (8, 2), (4, 8), (10, 10), (5, 6), (13, 3), (1, 13), (13, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853454", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (0, 13), (2, 14), (0, 7), (9, 11), (7, 8), (1, 8), (9, 6), (0, 8), (5, 13), (0, 9), (4, 14), (1, 7), (2, 11), (8, 10), (3, 11), (8, 3), (11, 10), (11, 7), (11, 12), (4, 10), (6, 6), (9, 10), (11, 15), (4, 12), (7, 10), (10, 12), (12, 3), (10, 10), (6, 5), (0, 15), (0, 2), (12, 12), (3, 13), (3, 16), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617400", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (8, 9), (11, 2), (1, 9), (7, 7), (2, 2), (0, 6), (13, 8), (10, 4), (3, 8), (13, 1), (5, 8), (7, 9), (0, 2), (6, 2), (1, 8), (2, 7), (5, 10), (8, 8), (3, 1), (8, 4), (17, 1), (12, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63970", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (15, 4), (11, 0), (16, 6), (1, 9), (12, 8), (14, 1), (11, 4), (4, 5), (15, 0), (7, 2), (7, 6), (13, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225289", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 4), (6, 2), (14, 0), (15, 0), (18, 4), (3, 4), (1, 7), (4, 3), (9, 8), (11, 8), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "910314", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (7, 4), (6, 12), (11, 5), (0, 1), (1, 5), (8, 14), (2, 12), (0, 6), (4, 8), (8, 6), (8, 1), (6, 3), (4, 9), (0, 14), (3, 8), (3, 13), (11, 8), (9, 3), (3, 2), (7, 14), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541590", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 11), (9, 0), (8, 9), (5, 1), (4, 2), (7, 4), (0, 5), (1, 7), (9, 9), (12, 0), (8, 2), (1, 1), (0, 7), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73426", "dataset": "MATH"}
{"messages": [{"content": "In a 16x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 11), (3, 12), (6, 0), (10, 2), (10, 12), (14, 10), (13, 3), (11, 2), (5, 3), (7, 12), (13, 7), (11, 8), (15, 8), (1, 6), (11, 3), (2, 11), (8, 1), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870752", "dataset": "MATH"}
{"messages": [{"content": "In a 11x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 12), (7, 11), (6, 9), (1, 3), (4, 9), (6, 11), (3, 7), (5, 8), (1, 8), (2, 5), (1, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478164", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (10, 6), (1, 9), (3, 0), (9, 0), (7, 0), (3, 6), (7, 9), (11, 0), (6, 6), (3, 3), (3, 5), (3, 1), (8, 7), (7, 5), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2136", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (4, 2), (3, 13), (10, 4), (2, 1), (4, 1), (8, 5), (7, 12), (10, 8), (11, 3), (0, 12), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757430", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (10, 7), (8, 11), (1, 5), (9, 11), (9, 0), (2, 11), (5, 2), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122477", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 6), (10, 9), (11, 3), (15, 3), (3, 8), (3, 3), (3, 5), (8, 3), (14, 1), (12, 2), (1, 6), (14, 4), (13, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "737501", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (12, 6), (11, 2), (2, 9), (12, 11), (3, 12), (0, 7), (3, 4), (10, 9), (13, 3), (7, 10), (10, 2), (10, 3), (7, 5), (5, 8), (1, 8), (10, 7), (5, 6), (0, 4), (11, 0), (0, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214917", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (9, 3), (2, 3), (1, 12), (0, 2), (1, 3), (6, 5), (8, 5), (8, 11), (7, 6), (6, 4), (6, 11), (8, 7), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2467", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 17), (3, 2), (7, 11), (9, 1), (6, 4), (10, 9), (7, 0), (8, 6), (4, 5), (5, 17), (8, 8), (8, 16), (5, 4), (4, 7), (5, 16), (8, 9), (2, 5), (8, 1), (11, 8), (6, 5), (3, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964648", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (10, 6), (3, 16), (10, 10), (8, 6), (8, 16), (11, 8), (2, 15), (10, 15), (3, 11), (8, 7), (9, 3), (6, 14), (7, 10), (4, 2), (1, 0), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649144", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 12), (6, 4), (1, 6), (12, 18), (13, 1), (0, 13), (3, 2), (5, 18), (13, 7), (2, 4), (5, 15), (1, 2), (4, 9), (10, 6), (0, 11), (10, 18), (11, 14), (7, 16), (10, 14), (5, 13), (8, 12), (11, 6), (8, 3), (5, 1), (1, 5), (12, 9), (4, 0), (1, 15), (11, 2), (4, 11), (2, 9), (5, 11), (12, 8), (2, 6), (11, 11), (10, 9), (8, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997443", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (9, 9), (16, 4), (16, 0), (7, 6), (9, 4), (7, 1), (0, 1), (11, 9), (12, 3), (12, 1), (3, 0), (2, 1), (8, 11), (0, 3), (13, 1), (12, 11), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410075", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (3, 2), (3, 3), (8, 4), (9, 2), (4, 4), (2, 4), (9, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21977", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (12, 8), (1, 14), (11, 8), (7, 8), (10, 14), (12, 13), (8, 10), (15, 3), (11, 16), (4, 8), (15, 0), (7, 16), (0, 8), (7, 11), (2, 16), (12, 0), (6, 4), (8, 0), (12, 15), (0, 1), (5, 15), (12, 11), (13, 13), (7, 2), (3, 4), (14, 16), (5, 6), (10, 13), (8, 16), (1, 5), (1, 11), (11, 10), (5, 16), (6, 7), (9, 4), (4, 16), (15, 6), (8, 13), (16, 2), (16, 13), (12, 7), (14, 9), (16, 10), (5, 10), (3, 9), (16, 12), (17, 4), (2, 7), (13, 1), (1, 8), (6, 10), (4, 12), (8, 4), (2, 6), (6, 8), (1, 10), (13, 11), (0, 14), (9, 16), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883915", "dataset": "MATH"}
{"messages": [{"content": "In a 17x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (15, 8), (14, 10), (16, 0), (3, 8), (14, 7), (1, 3), (4, 9), (8, 14), (3, 16), (15, 10), (0, 3), (5, 7), (11, 10), (12, 12), (12, 5), (8, 1), (7, 6), (5, 11), (16, 8), (15, 0), (11, 17), (15, 2), (1, 7), (4, 14), (6, 8), (2, 1), (11, 16), (7, 17), (11, 9), (10, 8), (10, 17), (11, 7), (0, 2), (5, 13), (9, 14), (2, 8), (1, 1), (16, 6), (12, 2), (14, 1), (6, 12), (14, 14), (2, 4), (11, 4), (13, 11), (2, 11), (1, 9), (6, 13), (14, 6), (8, 13), (5, 3), (6, 16), (0, 4), (3, 14), (9, 6), (10, 2), (14, 11), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609408", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (0, 10), (1, 6), (5, 8), (4, 8), (10, 1), (8, 13), (8, 2), (1, 1), (3, 12), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447529", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (3, 13), (6, 4), (1, 10), (3, 9), (3, 1), (0, 11), (3, 7), (3, 3), (7, 5), (6, 9), (8, 10), (2, 10), (4, 6), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13706", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (9, 3), (6, 11), (5, 0), (3, 6), (5, 3), (9, 12), (4, 12), (3, 4), (0, 10), (5, 6), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20709", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (11, 4), (0, 6), (15, 9), (14, 6), (1, 6), (15, 8), (0, 8), (9, 7), (5, 6), (9, 4), (9, 9), (12, 0), (13, 7), (5, 7), (1, 0), (15, 0), (12, 6), (0, 4), (12, 1), (2, 6), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155252", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (7, 17), (9, 11), (3, 1), (5, 13), (4, 3), (4, 16), (1, 0), (7, 11), (3, 16), (2, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "990909", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (1, 4), (11, 9), (13, 14), (15, 7), (6, 14), (7, 1), (5, 4), (8, 10), (7, 11), (6, 9), (14, 14), (11, 13), (9, 14), (12, 2), (15, 2), (1, 5), (11, 1), (4, 5), (8, 11), (5, 11), (14, 4), (7, 7), (4, 13), (11, 7), (6, 1), (6, 6), (13, 4), (15, 10), (2, 10), (3, 12), (5, 3), (13, 1), (0, 6), (3, 13), (10, 0), (10, 3), (7, 12), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578567", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (7, 1), (2, 13), (0, 8), (12, 5), (7, 11), (0, 11), (6, 3), (9, 5), (1, 15), (0, 7), (0, 16), (12, 13), (10, 6), (4, 11), (2, 0), (1, 10), (9, 12), (0, 15), (8, 0), (2, 3), (13, 11), (10, 0), (2, 9), (4, 10), (7, 8), (13, 9), (11, 14), (6, 0), (2, 11), (4, 13), (6, 14), (13, 0), (6, 12), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779801", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (6, 6), (1, 4), (6, 11), (10, 3), (12, 0), (7, 10), (2, 5), (7, 3), (10, 10), (7, 4), (3, 10), (3, 9), (3, 7), (5, 8), (7, 5), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49036", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (4, 6), (12, 3), (2, 1), (2, 14), (6, 4), (15, 11), (1, 5), (16, 9), (18, 10), (14, 17), (1, 9), (8, 6), (16, 7), (8, 14), (2, 13), (0, 8), (3, 16), (17, 0), (3, 11), (5, 1), (2, 9), (17, 16), (13, 8), (8, 4), (7, 4), (0, 13), (0, 15), (3, 3), (4, 4), (13, 15), (17, 4), (0, 18), (5, 9), (5, 4), (9, 13), (15, 8), (5, 7), (9, 6), (16, 3), (11, 16), (10, 9), (14, 7), (16, 6), (6, 18), (1, 13), (17, 11), (10, 4), (15, 4), (11, 10), (13, 4), (9, 14), (14, 8), (17, 17), (11, 9), (7, 11), (6, 9), (7, 6), (4, 5), (7, 17), (8, 0), (4, 11), (17, 14), (1, 15), (6, 12), (17, 5), (17, 12), (0, 7), (8, 2), (6, 10), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695327", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (12, 4), (5, 10), (15, 10), (3, 7), (1, 3), (0, 12), (0, 5), (7, 10), (13, 7), (7, 1), (4, 13), (14, 9), (7, 8), (6, 12), (9, 4), (14, 7), (9, 2), (9, 1), (6, 11), (14, 2), (10, 7), (8, 9), (4, 1), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992760", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 9), (11, 0), (13, 13), (10, 11), (3, 6), (10, 15), (13, 12), (3, 15), (6, 6), (13, 4), (10, 10), (3, 1), (3, 13), (12, 5), (7, 7), (2, 14), (12, 8), (7, 5), (8, 7), (5, 12), (10, 4), (3, 10), (6, 8), (7, 10), (5, 15), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485315", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (7, 2), (0, 4), (12, 4), (5, 10), (11, 6), (9, 0), (8, 8), (10, 3), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891795", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 9), (6, 4), (8, 2), (7, 0), (6, 6), (5, 4), (12, 7), (2, 7), (12, 0), (12, 4), (3, 1), (12, 5), (1, 8), (1, 2), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18431", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 15), (14, 8), (15, 0), (15, 14), (3, 11), (5, 1), (1, 8), (13, 15), (15, 1), (6, 2), (12, 16), (15, 17), (4, 14), (0, 3), (15, 10), (0, 15), (11, 1), (11, 16), (5, 10), (1, 9), (15, 15), (7, 5), (6, 8), (8, 1), (9, 15), (6, 0), (3, 4), (11, 18), (1, 13), (4, 6), (2, 1), (9, 12), (8, 14), (7, 2), (9, 17), (7, 10), (7, 3), (1, 12), (9, 5), (10, 4), (11, 2), (14, 12), (4, 7), (14, 10), (0, 12), (1, 11), (10, 13), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738603", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 5), (8, 5), (4, 6), (0, 11), (1, 11), (1, 2), (6, 2), (8, 14), (8, 3), (7, 7), (7, 10), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244997", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 5), (7, 11), (10, 9), (8, 1), (1, 3), (10, 16), (3, 2), (5, 14), (6, 1), (7, 1), (3, 10), (6, 6), (7, 5), (9, 10), (0, 8), (5, 1), (5, 2), (10, 5), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951181", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 0), (1, 10), (10, 13), (10, 12), (9, 10), (7, 2), (6, 14), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680348", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 16), (3, 3), (3, 11), (11, 11), (11, 7), (0, 9), (7, 10), (3, 17), (4, 3), (14, 7), (7, 15), (6, 17), (8, 13), (9, 14), (1, 16), (0, 12), (4, 13), (6, 3), (1, 0), (5, 15), (9, 17), (3, 12), (1, 10), (14, 9), (9, 10), (14, 3), (0, 16), (12, 2), (7, 4), (1, 7), (2, 8), (0, 15), (13, 15), (13, 12), (2, 11), (7, 17), (13, 14), (14, 15), (2, 17), (6, 16), (6, 9), (14, 8), (4, 1), (0, 2), (2, 9), (5, 1), (3, 6), (14, 16), (11, 12), (5, 12), (12, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "307107", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (10, 7), (2, 3), (7, 0), (8, 4), (11, 3), (3, 8), (10, 12), (2, 7), (15, 11), (4, 13), (3, 7), (9, 11), (9, 9), (13, 6), (1, 7), (6, 12), (0, 9), (11, 12), (3, 1), (5, 13), (4, 10), (14, 1), (6, 9), (5, 6), (2, 12), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892496", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 9), (7, 12), (13, 5), (12, 6), (8, 3), (7, 11), (14, 6), (16, 7), (11, 5), (9, 9), (13, 0), (6, 9), (16, 8), (15, 3), (3, 9), (14, 7), (11, 6), (4, 6), (15, 6), (9, 11), (9, 1), (15, 5), (8, 11), (16, 3), (12, 3), (3, 1), (1, 12), (16, 4), (0, 11), (3, 7), (13, 12), (4, 11), (0, 3), (12, 4), (11, 0), (12, 8), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "802578", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 2), (12, 7), (13, 12), (10, 0), (17, 6), (11, 12), (12, 2), (12, 11), (11, 8), (8, 1), (6, 11), (6, 12), (17, 2), (1, 9), (9, 9), (10, 10), (13, 3), (16, 4), (8, 5), (14, 0), (15, 11), (6, 3), (11, 6), (4, 1), (13, 5), (13, 6), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931083", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 10), (10, 11), (9, 9), (7, 7), (1, 11), (4, 11), (1, 8), (2, 1), (11, 6), (7, 13), (9, 13), (0, 2), (1, 9), (14, 2), (1, 10), (5, 13), (6, 13), (12, 6), (6, 7), (10, 12), (8, 4), (13, 1), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538858", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (8, 1), (6, 7), (9, 0), (8, 9), (0, 5), (6, 4), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10755", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 14), (10, 6), (2, 5), (3, 1), (5, 12), (3, 7), (11, 9), (6, 8), (9, 12), (10, 8), (3, 10), (1, 9), (1, 10), (0, 9), (8, 11), (11, 14), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992675", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (11, 13), (8, 7), (5, 6), (13, 3), (3, 3), (3, 11), (10, 2), (10, 5), (11, 4), (5, 5), (1, 9), (5, 13), (5, 10), (13, 5), (0, 2), (13, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917352", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (4, 12), (0, 7), (3, 8), (12, 8), (4, 11), (7, 15), (0, 12), (8, 11), (0, 15), (7, 4), (10, 4), (6, 14), (0, 3), (13, 1), (5, 12), (7, 8), (4, 13), (11, 7), (1, 15), (8, 13), (8, 7), (12, 11), (12, 0), (0, 8), (2, 15), (4, 14), (2, 11), (2, 14), (2, 13), (5, 7), (10, 2), (4, 9), (13, 6), (2, 10), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897945", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (7, 2), (5, 3), (6, 8), (3, 1), (4, 7), (14, 8), (12, 7), (11, 9), (1, 9), (15, 8), (4, 9), (11, 1), (9, 5), (15, 7), (11, 6), (10, 0), (15, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44157", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 13), (0, 15), (16, 6), (1, 6), (9, 4), (4, 11), (15, 0), (17, 7), (8, 13), (2, 3), (6, 4), (13, 12), (3, 17), (1, 13), (15, 6), (7, 2), (17, 2), (17, 1), (17, 4), (10, 8), (10, 0), (16, 4), (4, 6), (14, 16), (5, 4), (5, 7), (12, 3), (1, 5), (15, 17), (0, 4), (3, 2), (10, 13), (3, 3), (4, 15), (0, 12), (15, 10), (15, 5), (6, 10), (17, 16), (5, 0), (4, 12), (8, 1), (10, 11), (16, 13), (13, 6), (13, 4), (14, 14), (17, 0), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670976", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (1, 10), (8, 8), (12, 4), (6, 10), (1, 4), (11, 7), (10, 5), (9, 10), (7, 0), (2, 12), (0, 10), (4, 3), (9, 5), (6, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211730", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 8), (7, 7), (4, 2), (8, 5), (2, 1), (6, 9), (3, 4), (10, 5), (2, 2), (2, 3), (6, 4), (4, 0), (2, 5), (6, 1), (1, 10), (10, 2), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2936", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (8, 0), (11, 11), (5, 0), (11, 4), (8, 6), (8, 9), (9, 7), (6, 10), (4, 10), (11, 6), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114421", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (1, 14), (9, 0), (12, 9), (8, 14), (1, 0), (2, 17), (3, 14), (0, 12), (10, 12), (5, 14), (11, 12), (8, 4), (0, 17), (8, 11), (7, 7), (0, 5), (1, 10), (5, 8), (3, 16), (3, 9), (0, 8), (6, 10), (9, 9), (8, 9), (2, 0), (5, 17), (10, 9), (0, 13), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967878", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 16), (5, 15), (5, 12), (7, 3), (7, 15), (1, 4), (5, 17), (8, 3), (9, 7), (3, 13), (8, 18), (7, 14), (6, 13), (4, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813760", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 14), (9, 12), (8, 5), (9, 2), (0, 12), (8, 3), (9, 9), (9, 3), (8, 13), (5, 6), (11, 0), (3, 7), (7, 4), (3, 6), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197452", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (6, 6), (2, 5), (6, 12), (8, 6), (6, 5), (1, 7), (7, 6), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447107", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 14), (0, 4), (9, 13), (0, 8), (0, 14), (7, 4), (0, 10), (1, 0), (8, 9), (9, 7), (9, 8), (2, 2), (4, 2), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77356", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (10, 17), (18, 13), (13, 14), (1, 7), (2, 6), (6, 10), (10, 5), (12, 17), (13, 1), (0, 2), (9, 1), (3, 16), (7, 18), (9, 13), (10, 12), (5, 0), (4, 8), (9, 17), (2, 2), (9, 5), (4, 16), (4, 18), (3, 1), (0, 7), (8, 4), (17, 2), (9, 18), (6, 18), (17, 8), (6, 0), (6, 8), (12, 16), (16, 3), (2, 8), (3, 8), (6, 12), (9, 12), (13, 2), (11, 13), (13, 8), (18, 10), (8, 12), (1, 18), (9, 10), (0, 11), (9, 7), (18, 17), (6, 6), (13, 5), (2, 7), (5, 11), (6, 15), (5, 17), (0, 12), (15, 8), (11, 11), (2, 14), (5, 5), (18, 5), (18, 14), (18, 8), (18, 4), (14, 13), (15, 6), (16, 8), (15, 0), (4, 15), (9, 2), (10, 6), (9, 0), (17, 15), (5, 10), (15, 1), (14, 8), (8, 15), (4, 6), (13, 0), (17, 6), (10, 10), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960763", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (8, 9), (8, 1), (11, 0), (2, 7), (3, 5), (9, 7), (7, 3), (3, 1), (1, 9), (5, 8), (9, 2), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56906", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (16, 12), (16, 1), (11, 12), (12, 4), (7, 12), (8, 6), (8, 8), (16, 0), (1, 14), (13, 5), (1, 4), (11, 10), (17, 3), (9, 1), (4, 10), (11, 13), (7, 7), (9, 9), (6, 8), (16, 13), (9, 12), (4, 3), (9, 11), (10, 10), (17, 0), (4, 6), (7, 2), (3, 0), (16, 11), (10, 6), (2, 7), (6, 1), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875766", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 9), (7, 11), (4, 5), (5, 5), (8, 0), (4, 8), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21073", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 3), (9, 3), (16, 4), (8, 9), (8, 7), (8, 10), (17, 2), (0, 7), (7, 0), (1, 1), (2, 9), (11, 5), (10, 0), (9, 8), (5, 10), (10, 1), (16, 1), (0, 4), (3, 10), (13, 0), (1, 6), (15, 7), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839756", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (11, 6), (2, 5), (15, 7), (16, 7), (12, 5), (0, 7), (16, 3), (3, 11), (5, 6), (3, 9), (3, 6), (2, 7), (15, 8), (1, 1), (12, 11), (8, 4), (4, 7), (16, 12), (10, 0), (9, 7), (11, 12), (0, 6), (10, 3), (6, 10), (16, 6), (8, 7), (13, 11), (8, 2), (3, 10), (0, 12), (3, 0), (12, 9), (11, 15), (9, 13), (5, 2), (4, 6), (5, 13), (10, 15), (2, 11), (11, 4), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "856398", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (5, 2), (2, 4), (7, 10), (1, 6), (7, 8), (3, 1), (14, 8), (12, 12), (12, 11), (5, 8), (13, 7), (1, 5), (8, 0), (12, 4), (0, 6), (4, 8), (10, 10), (15, 0), (1, 3), (6, 1), (11, 3), (6, 3), (10, 1), (1, 12), (6, 12), (7, 11), (16, 9), (10, 7), (11, 12), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640917", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (12, 1), (1, 4), (2, 11), (2, 7), (9, 3), (2, 4), (3, 10), (10, 2), (16, 5), (8, 8), (3, 8), (6, 10), (6, 2), (14, 9), (16, 10), (9, 4), (15, 9), (17, 8), (15, 10), (7, 8), (18, 7), (10, 1), (1, 8), (7, 2), (17, 7), (1, 7), (18, 2), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978168", "dataset": "MATH"}
{"messages": [{"content": "In a 11x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 10), (7, 12), (4, 1), (9, 13), (6, 8), (6, 11), (10, 6), (6, 0), (6, 12), (9, 12), (2, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172949", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (13, 9), (2, 9), (9, 15), (9, 14), (1, 3), (8, 0), (11, 12), (13, 5), (13, 6), (15, 11), (13, 0), (7, 11), (9, 2), (4, 14), (10, 10), (2, 1), (0, 12), (0, 14), (1, 2), (6, 3), (0, 5), (3, 7), (2, 12), (0, 15), (0, 11), (4, 5), (15, 3), (8, 12), (6, 1), (1, 7), (3, 11), (6, 13), (2, 8), (12, 8), (11, 0), (10, 3), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993850", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (0, 15), (1, 5), (12, 2), (1, 15), (7, 12), (14, 10), (0, 16), (3, 9), (3, 3), (5, 8), (6, 10), (15, 6), (15, 14), (10, 7), (9, 5), (14, 5), (0, 14), (6, 1), (11, 3), (10, 4), (16, 7), (17, 13), (16, 10), (11, 11), (16, 2), (10, 8), (14, 4), (15, 11), (6, 12), (2, 8), (7, 14), (13, 5), (13, 14), (15, 2), (2, 14), (9, 6), (3, 11), (11, 1), (15, 4), (2, 6), (13, 6), (13, 0), (15, 10), (12, 0), (4, 3), (16, 4), (6, 2), (8, 8), (5, 7), (12, 3), (3, 6), (7, 6), (17, 11), (4, 7), (7, 16), (17, 1), (6, 3), (10, 12), (11, 5), (10, 1), (5, 0), (17, 5), (12, 12), (2, 10), (13, 10), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484421", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 14), (8, 5), (7, 14), (8, 0), (9, 8), (11, 10), (11, 3), (5, 9), (5, 7), (4, 6), (10, 4), (3, 14), (6, 7), (9, 12), (4, 0), (3, 12), (0, 12), (12, 4), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720792", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (8, 5), (12, 6), (13, 5), (10, 3), (1, 3), (9, 6), (0, 17), (4, 12), (14, 8), (9, 3), (4, 13), (1, 13), (10, 8), (12, 10), (4, 6), (5, 0), (14, 10), (7, 9), (5, 15), (2, 1), (3, 3), (1, 5), (7, 1), (1, 16), (4, 3), (7, 16), (9, 11), (4, 2), (14, 2), (9, 13), (11, 8), (3, 11), (13, 2), (1, 10), (5, 7), (14, 9), (2, 8), (1, 8), (1, 7), (0, 11), (3, 12), (0, 7), (2, 17), (2, 16), (0, 12), (9, 8), (10, 10), (14, 0), (6, 8), (14, 13), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427527", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 13), (12, 12), (11, 13), (7, 0), (8, 14), (3, 15), (2, 8), (9, 15), (7, 8), (6, 4), (2, 4), (9, 9), (11, 2), (14, 13), (0, 2), (5, 15), (11, 3), (12, 11), (5, 7), (10, 3), (1, 7), (5, 10), (6, 13), (10, 9), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612004", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 1), (3, 11), (3, 1), (0, 4), (4, 11), (2, 9), (7, 6), (12, 11), (13, 2), (2, 1), (10, 5), (6, 10), (7, 2), (3, 7), (11, 2), (12, 10), (8, 1), (12, 8), (6, 11), (8, 9), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37311", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (11, 5), (6, 5), (7, 5), (4, 4), (14, 6), (8, 4), (6, 3), (1, 1), (12, 11), (7, 0), (10, 0), (4, 8), (5, 0), (5, 2), (8, 2), (12, 3), (13, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188698", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (7, 7), (9, 12), (1, 2), (7, 4), (2, 11), (1, 10), (6, 10), (3, 8), (1, 1), (6, 5), (8, 4), (6, 11), (7, 13), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4967", "dataset": "MATH"}
{"messages": [{"content": "In a 17x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (12, 15), (5, 16), (1, 13), (0, 15), (5, 15), (10, 17), (2, 14), (8, 8), (5, 9), (1, 11), (5, 1), (11, 16), (0, 9), (0, 14), (0, 3), (2, 8), (14, 15), (12, 2), (10, 5), (14, 3), (10, 15), (1, 2), (7, 4), (9, 9), (13, 9), (8, 4), (11, 14), (0, 5), (4, 15), (14, 12), (3, 15), (8, 7), (16, 10), (11, 5), (14, 16), (11, 7), (10, 3), (12, 6), (13, 8), (8, 5), (10, 6), (10, 4), (6, 17), (13, 0), (8, 9), (10, 1), (13, 12), (7, 13), (4, 4), (14, 8), (12, 10), (4, 3), (8, 12), (15, 0), (8, 14), (15, 9), (0, 1), (2, 12), (14, 6), (12, 5), (7, 5), (11, 0), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556961", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 5), (14, 10), (7, 6), (1, 8), (16, 5), (8, 3), (17, 8), (1, 3), (3, 3), (15, 0), (15, 3), (5, 3), (3, 4), (9, 0), (0, 1), (6, 9), (11, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695524", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (2, 10), (3, 8), (4, 8), (4, 10), (4, 2), (8, 4), (1, 5), (3, 2), (1, 10), (0, 9), (7, 3), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158516", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (10, 14), (6, 12), (9, 5), (3, 4), (7, 12), (8, 0), (3, 9), (6, 2), (10, 10), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243857", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 1), (3, 3), (5, 3), (3, 2), (6, 4), (8, 14), (17, 12), (2, 5), (1, 11), (8, 7), (2, 11), (18, 12), (0, 10), (8, 15), (14, 5), (2, 6), (0, 11), (6, 8), (9, 11), (17, 8), (13, 10), (6, 6), (16, 15), (11, 13), (12, 5), (2, 2), (3, 13), (9, 5), (18, 5), (13, 14), (1, 12), (18, 6), (8, 0), (12, 12), (2, 0), (14, 0), (13, 1), (2, 13), (18, 4), (17, 5), (17, 7), (13, 3), (18, 10), (14, 6), (16, 3), (9, 2), (2, 1), (8, 2), (3, 8), (1, 5), (5, 8), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977840", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 2), (11, 8), (10, 4), (9, 7), (8, 12), (8, 5), (12, 0), (2, 9), (0, 10), (7, 5), (3, 0), (6, 12), (1, 11), (8, 6), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810058", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 13), (9, 9), (1, 13), (5, 16), (6, 2), (3, 16), (3, 14), (8, 4), (4, 15), (4, 5), (6, 11), (1, 11), (7, 9), (5, 0), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980728", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (7, 3), (3, 13), (9, 3), (6, 2), (9, 13), (6, 12), (1, 5), (0, 8), (9, 1), (6, 11), (1, 15), (4, 12), (8, 17), (2, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285007", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 15), (6, 14), (6, 12), (5, 18), (1, 18), (10, 5), (4, 0), (0, 10), (2, 6), (7, 17), (0, 9), (1, 16), (11, 18), (11, 4), (9, 18), (3, 1), (9, 3), (7, 18), (7, 0), (3, 2), (6, 0), (9, 10), (10, 13), (5, 12), (9, 7), (5, 8), (11, 9), (5, 16), (12, 12), (6, 13), (6, 11), (2, 3), (13, 14), (9, 6), (7, 1), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981120", "dataset": "MATH"}
{"messages": [{"content": "In a 17x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (0, 14), (3, 12), (6, 6), (15, 7), (10, 5), (12, 10), (11, 3), (13, 9), (8, 9), (16, 3), (9, 2), (12, 9), (7, 3), (6, 14), (7, 13), (10, 0), (0, 6), (13, 4), (9, 4), (8, 12), (14, 9), (13, 0), (0, 3), (15, 11), (15, 10), (11, 7), (3, 13), (3, 6), (6, 8), (10, 9), (10, 4), (8, 0), (14, 12), (11, 12), (15, 13), (2, 11), (11, 4), (0, 5), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914079", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (1, 5), (9, 0), (8, 7), (5, 7), (9, 3), (10, 1), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153154", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (2, 0), (5, 5), (0, 7), (5, 8), (7, 7), (0, 1), (6, 2), (4, 5), (9, 0), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1665", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (12, 8), (7, 12), (5, 10), (5, 6), (5, 4), (13, 1), (8, 13), (1, 13), (4, 7), (13, 7), (8, 3), (12, 0), (9, 16), (15, 6), (2, 17), (4, 6), (6, 7), (7, 11), (15, 3), (4, 3), (11, 1), (5, 14), (7, 15), (8, 4), (11, 9), (10, 9), (8, 9), (11, 13), (14, 11), (13, 5), (6, 10), (5, 16), (1, 4), (2, 0), (7, 4), (8, 14), (2, 16), (6, 9), (4, 1), (15, 14), (5, 12), (14, 2), (1, 5), (13, 17), (7, 2), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246729", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (12, 4), (7, 1), (14, 1), (14, 0), (7, 4), (8, 0), (13, 8), (4, 6), (15, 10), (12, 0), (1, 5), (12, 12), (10, 0), (10, 5), (7, 14), (4, 0), (6, 1), (8, 13), (14, 12), (9, 7), (5, 10), (8, 5), (15, 1), (11, 9), (15, 9), (15, 14), (3, 5), (14, 4), (0, 14), (11, 11), (2, 13), (1, 10), (4, 10), (15, 5), (0, 16), (3, 15), (6, 4), (7, 6), (2, 11), (13, 12), (3, 3), (0, 2), (10, 13), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886240", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 10), (13, 3), (7, 11), (16, 10), (5, 11), (7, 3), (17, 2), (7, 5), (8, 12), (7, 1), (14, 5), (4, 12), (10, 12), (13, 8), (8, 5), (0, 10), (15, 12), (2, 2), (0, 8), (3, 6), (10, 1), (4, 7), (17, 1), (9, 3), (0, 12), (11, 8), (6, 8), (7, 10), (8, 7), (2, 8), (11, 5), (14, 6), (15, 13), (18, 3), (2, 7), (2, 9), (15, 2), (6, 12), (18, 2), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "802317", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (8, 8), (12, 3), (2, 9), (6, 3), (8, 6), (2, 8), (11, 5), (1, 1), (11, 2), (2, 5), (10, 8), (10, 3), (4, 7), (7, 9), (1, 7), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9870", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 13), (5, 3), (6, 12), (4, 13), (6, 7), (4, 3), (9, 0), (9, 7), (8, 14), (4, 1), (1, 13), (9, 5), (2, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296871", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (12, 6), (6, 1), (5, 3), (6, 3), (9, 5), (7, 3), (8, 4), (12, 1), (10, 6), (3, 9), (13, 9), (8, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328053", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 7), (12, 9), (9, 12), (3, 12), (3, 5), (9, 3), (0, 2), (7, 0), (10, 6), (3, 1), (3, 10), (1, 9), (3, 2), (2, 12), (13, 5), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "835048", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (5, 5), (8, 5), (6, 9), (5, 11), (0, 2), (5, 10), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77869", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 9), (2, 2), (9, 6), (3, 16), (4, 7), (4, 11), (8, 3), (1, 7), (8, 2), (9, 10), (4, 0), (3, 15), (10, 3), (1, 13), (4, 3), (9, 16), (4, 5), (4, 12), (10, 10), (8, 7), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676047", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (10, 4), (0, 8), (14, 3), (15, 12), (15, 10), (10, 13), (14, 5), (12, 5), (7, 10), (12, 8), (3, 1), (12, 12), (4, 13), (14, 13), (0, 5), (7, 12), (2, 0), (7, 2), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619077", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 12), (2, 13), (3, 12), (6, 9), (7, 10), (5, 3), (13, 8), (13, 10), (0, 4), (7, 4), (13, 11), (1, 11), (10, 0), (12, 8), (10, 10), (6, 10), (7, 1), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875495", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 3), (8, 9), (1, 2), (13, 2), (3, 11), (10, 5), (7, 10), (12, 6), (10, 11), (11, 10), (3, 3), (8, 13), (0, 3), (7, 6), (12, 8), (6, 14), (3, 13), (1, 5), (3, 10), (2, 12), (0, 8), (1, 11), (11, 2), (2, 2), (3, 2), (2, 8), (8, 8), (6, 8), (2, 9), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "686809", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 17), (14, 16), (5, 16), (7, 16), (10, 9), (13, 8), (9, 12), (0, 16), (8, 13), (11, 8), (5, 11), (9, 9), (1, 2), (12, 5), (14, 13), (12, 6), (10, 16), (7, 18), (5, 17), (2, 1), (10, 12), (1, 17), (1, 14), (6, 3), (7, 14), (6, 5), (5, 6), (0, 7), (6, 7), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931216", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 1), (5, 1), (5, 3), (1, 9), (11, 7), (7, 9), (4, 8), (4, 1), (7, 1), (12, 6), (5, 5), (10, 5), (3, 4), (0, 8), (2, 1), (13, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22711", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 9), (8, 7), (9, 6), (7, 2), (12, 1), (1, 5), (1, 11), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383515", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 0), (11, 17), (9, 17), (9, 7), (2, 15), (12, 8), (12, 14), (4, 1), (0, 13), (14, 1), (9, 14), (5, 7), (7, 13), (5, 12), (5, 16), (4, 7), (4, 3), (2, 14), (12, 15), (10, 8), (6, 3), (13, 3), (9, 5), (7, 9), (12, 12), (12, 17), (14, 12), (10, 6), (7, 10), (4, 12), (9, 12), (13, 12), (5, 0), (0, 17), (7, 3), (14, 10), (1, 17), (12, 2), (2, 6), (6, 8), (8, 13), (3, 13), (11, 8), (2, 13), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "735127", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 7), (8, 3), (9, 4), (6, 11), (0, 13), (13, 12), (14, 4), (6, 12), (17, 9), (7, 14), (12, 0), (4, 14), (4, 10), (8, 14), (3, 11), (17, 13), (2, 4), (9, 3), (9, 9), (4, 2), (11, 6), (15, 2), (16, 1), (6, 8), (7, 4), (18, 4), (10, 14), (13, 8), (4, 6), (8, 1), (5, 9), (14, 10), (6, 13), (1, 9), (11, 7), (8, 5), (17, 10), (0, 4), (7, 5), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270276", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (3, 4), (0, 4), (7, 6), (9, 6), (13, 5), (9, 9), (2, 1), (11, 1), (14, 1), (2, 6), (3, 8), (6, 8), (12, 10), (6, 7), (0, 3), (7, 2), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66266", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 3), (8, 9), (12, 3), (11, 11), (12, 9), (8, 0), (7, 1), (4, 0), (14, 11), (10, 10), (2, 4), (2, 12), (4, 8), (11, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606787", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 2), (12, 5), (6, 10), (3, 5), (11, 0), (11, 6), (6, 2), (11, 8), (10, 6), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110725", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 14), (3, 6), (17, 3), (13, 1), (14, 10), (11, 2), (4, 15), (12, 0), (17, 13), (17, 5), (11, 4), (0, 2), (8, 9), (4, 8), (9, 10), (15, 5), (15, 2), (10, 0), (15, 12), (9, 7), (3, 12), (9, 0), (7, 5), (1, 7), (3, 2), (17, 14), (2, 10), (4, 2), (13, 7), (4, 9), (9, 15), (15, 7), (6, 0), (13, 14), (3, 4), (11, 5), (8, 8), (13, 2), (2, 7), (6, 15), (10, 5), (1, 9), (15, 10), (18, 0), (0, 5), (2, 11), (5, 14), (17, 7), (12, 3), (0, 10), (1, 14), (12, 2), (2, 9), (7, 10), (17, 9), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896144", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (3, 9), (10, 1), (4, 3), (9, 0), (9, 6), (11, 5), (6, 11), (2, 0), (1, 3), (7, 6), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104228", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 15), (10, 2), (5, 11), (7, 8), (8, 2), (12, 15), (11, 12), (10, 9), (9, 11), (11, 11), (5, 5), (9, 12), (7, 1), (7, 0), (9, 4), (11, 15), (4, 3), (8, 0), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932621", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (8, 2), (11, 8), (1, 9), (2, 13), (6, 6), (6, 2), (5, 14), (2, 7), (5, 8), (6, 11), (0, 12), (10, 15), (0, 13), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923530", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (11, 1), (3, 0), (7, 3), (0, 3), (2, 0), (5, 4), (6, 5), (3, 4), (9, 0), (9, 9), (2, 1), (14, 5), (6, 6), (14, 8), (10, 2), (13, 8), (3, 3), (13, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6420", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 4), (10, 7), (11, 0), (2, 6), (4, 5), (14, 1), (10, 8), (9, 6), (2, 8), (5, 9), (0, 2), (6, 7), (8, 2), (3, 5), (7, 7), (9, 0), (0, 11), (10, 10), (3, 6), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "955531", "dataset": "MATH"}
{"messages": [{"content": "In a 15x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (8, 11), (1, 7), (6, 9), (13, 8), (10, 10), (9, 12), (10, 7), (10, 6), (8, 6), (2, 2), (6, 7), (1, 5), (4, 2), (12, 13), (7, 1), (3, 9), (9, 10), (7, 6), (10, 12), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370299", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 11), (3, 15), (5, 2), (9, 5), (5, 0), (5, 5), (3, 1), (10, 8), (6, 8), (9, 11), (5, 1), (6, 5), (10, 1), (4, 15), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913217", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (9, 10), (6, 8), (2, 11), (2, 4), (2, 1), (0, 2), (10, 1), (9, 8), (4, 1), (1, 6), (11, 3), (4, 10), (12, 7), (3, 8), (7, 8), (8, 2), (4, 7), (11, 7), (13, 6), (5, 7), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97930", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (7, 5), (7, 4), (3, 6), (0, 4), (5, 6), (8, 7), (0, 3), (2, 10), (1, 9), (6, 9), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7960", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (15, 2), (8, 12), (7, 7), (6, 2), (15, 8), (18, 6), (14, 5), (18, 11), (2, 7), (1, 7), (3, 7), (3, 0), (3, 11), (3, 5), (11, 4), (11, 11), (10, 10), (3, 4), (9, 10), (18, 7), (3, 6), (4, 10), (13, 11), (17, 3), (12, 1), (16, 7), (13, 3), (0, 5), (5, 0), (16, 5), (9, 7), (15, 11), (0, 7), (4, 9), (12, 11), (8, 3), (17, 8), (14, 2), (5, 12), (13, 8), (4, 6), (4, 7), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742735", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (13, 16), (6, 3), (17, 14), (6, 13), (13, 10), (2, 11), (6, 0), (14, 16), (5, 14), (10, 5), (10, 10), (2, 15), (7, 12), (14, 4), (11, 3), (4, 11), (15, 17), (12, 8), (7, 1), (1, 7), (3, 4), (4, 0), (15, 8), (9, 0), (11, 13), (0, 11), (1, 12), (14, 12), (3, 13), (8, 12), (14, 1), (4, 8), (8, 5), (15, 2), (16, 8), (4, 6), (11, 9), (1, 14), (12, 14), (10, 3), (5, 10), (6, 5), (12, 4), (7, 10), (16, 3), (7, 5), (0, 10), (17, 6), (2, 14), (0, 12), (7, 14), (16, 2), (7, 2), (17, 15), (10, 4), (14, 14), (3, 9), (13, 9), (1, 8), (11, 8), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "653922", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 9), (14, 1), (17, 2), (5, 10), (13, 5), (14, 11), (0, 9), (4, 10), (16, 5), (13, 7), (1, 12), (6, 10), (9, 4), (2, 4), (7, 11), (18, 4), (6, 11), (0, 4), (9, 13), (1, 14), (5, 11), (2, 7), (10, 10), (11, 6), (2, 8), (7, 10), (10, 11), (17, 4), (17, 11), (6, 6), (0, 12), (18, 12), (8, 11), (13, 6), (11, 3), (3, 11), (8, 12), (10, 6), (1, 13), (12, 13), (15, 0), (17, 12), (3, 13), (13, 12), (2, 2), (15, 8), (4, 14), (14, 14), (17, 10), (0, 11), (2, 0), (9, 12), (15, 14), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "568590", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (6, 1), (10, 5), (10, 0), (0, 7), (9, 2), (11, 3), (3, 5), (15, 6), (4, 6), (17, 0), (0, 8), (11, 0), (7, 0), (18, 1), (0, 4), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969716", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 9), (12, 7), (7, 5), (0, 1), (4, 0), (5, 2), (9, 7), (0, 11), (8, 8), (3, 11), (9, 3), (10, 3), (6, 4), (7, 7), (6, 10), (6, 8), (6, 9), (10, 0), (6, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52333", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (7, 6), (9, 13), (0, 13), (13, 6), (1, 5), (11, 12), (6, 6), (5, 11), (2, 7), (14, 4), (4, 7), (5, 2), (13, 13), (10, 10), (4, 11), (4, 12), (14, 9), (15, 0), (9, 1), (15, 9), (1, 7), (1, 1), (0, 9), (13, 1), (5, 1), (6, 3), (14, 10), (14, 3), (11, 13), (2, 12), (15, 5), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507492", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 1), (2, 7), (6, 8), (4, 9), (0, 5), (4, 3), (7, 2), (0, 10), (9, 0), (8, 10), (2, 9), (10, 4), (8, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72423", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (9, 0), (10, 7), (6, 8), (9, 4), (4, 2), (11, 6), (0, 8), (10, 0), (4, 1), (2, 0), (0, 1), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3951", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (2, 10), (11, 8), (10, 4), (11, 2), (8, 0), (6, 11), (6, 3), (12, 5), (4, 11), (1, 13), (1, 3), (9, 6), (14, 11), (5, 1), (2, 8), (2, 1), (1, 10), (14, 1), (8, 14), (14, 0), (0, 13), (0, 5), (5, 8), (10, 1), (13, 5), (5, 0), (14, 9), (10, 6), (8, 13), (1, 7), (8, 6), (4, 1), (7, 12), (13, 13), (3, 2), (8, 11), (12, 8), (11, 14), (4, 15), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "702545", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (7, 9), (9, 5), (10, 4), (3, 9), (3, 6), (4, 1), (3, 2), (0, 7), (5, 2), (7, 7), (9, 4), (8, 1), (10, 2), (8, 0), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12433", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (15, 8), (14, 8), (6, 8), (2, 1), (10, 6), (10, 7), (3, 5), (6, 0), (7, 0), (17, 1), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "678086", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (10, 3), (9, 0), (13, 3), (12, 14), (12, 15), (13, 2), (3, 15), (1, 0), (10, 4), (6, 0), (9, 1), (11, 12), (4, 15), (11, 3), (2, 8), (4, 1), (8, 14), (2, 0), (0, 7), (6, 18), (7, 1), (4, 12), (8, 10), (3, 6), (5, 11), (10, 12), (7, 7), (2, 7), (11, 9), (6, 13), (10, 5), (5, 3), (12, 3), (5, 10), (11, 17), (0, 2), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454307", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (8, 8), (16, 5), (6, 6), (11, 10), (14, 5), (11, 1), (0, 1), (2, 9), (3, 0), (9, 10), (4, 2), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784641", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (6, 9), (3, 5), (17, 10), (11, 10), (13, 0), (13, 8), (2, 9), (10, 1), (13, 7), (2, 1), (0, 9), (5, 2), (11, 2), (16, 3), (13, 10), (0, 10), (16, 2), (11, 9), (17, 9), (18, 9), (10, 10), (11, 6), (14, 0), (2, 11), (0, 6), (9, 5), (15, 1), (6, 3), (1, 7), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931941", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 7), (1, 3), (12, 1), (0, 5), (8, 3), (7, 1), (6, 2), (2, 6), (6, 3), (11, 3), (11, 0), (11, 1), (9, 8), (4, 4), (2, 1), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19127", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (0, 1), (14, 7), (5, 5), (12, 3), (3, 7), (0, 3), (2, 6), (13, 4), (10, 9), (11, 8), (8, 4), (12, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92925", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (8, 7), (5, 1), (3, 4), (0, 3), (11, 8), (9, 4), (2, 0), (2, 9), (9, 1), (9, 0), (12, 1), (0, 5), (13, 10), (7, 5), (11, 12), (8, 0), (6, 2), (10, 9), (5, 6), (11, 0), (6, 1), (4, 9), (10, 4), (5, 12), (1, 0), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "856252", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (5, 9), (10, 11), (9, 2), (6, 14), (6, 1), (10, 7), (0, 17), (0, 15), (9, 12), (1, 17), (5, 6), (7, 12), (4, 14), (10, 12), (5, 2), (1, 8), (6, 16), (1, 14), (9, 14), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884072", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 8), (3, 4), (11, 14), (11, 4), (1, 3), (3, 13), (5, 1), (2, 4), (2, 14), (5, 8), (8, 9), (3, 7), (3, 14), (9, 5), (2, 10), (12, 10), (15, 0), (2, 1), (15, 11), (10, 15), (6, 7), (1, 5), (4, 6), (0, 15), (12, 1), (7, 8), (9, 15), (7, 6), (12, 12), (9, 2), (16, 5), (5, 5), (7, 0), (9, 16), (14, 9), (1, 14), (9, 1), (12, 4), (2, 9), (13, 13), (5, 0), (15, 12), (14, 1), (6, 12), (9, 3), (14, 3), (11, 2), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944335", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (5, 8), (0, 8), (8, 3), (8, 7), (0, 10), (0, 5), (1, 5), (6, 6), (2, 6), (1, 2), (3, 2), (8, 5), (2, 0), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3447", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (8, 11), (11, 1), (16, 2), (12, 4), (6, 6), (10, 9), (15, 5), (11, 2), (5, 1), (2, 11), (16, 10), (7, 4), (8, 6), (10, 7), (6, 10), (7, 0), (14, 10), (0, 4), (2, 2), (9, 3), (8, 10), (17, 0), (5, 6), (11, 5), (6, 9), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60622", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (4, 7), (1, 15), (5, 11), (8, 18), (8, 12), (3, 5), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676242", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 3), (1, 9), (14, 0), (11, 3), (1, 11), (14, 10), (15, 9), (2, 2), (0, 1), (8, 4), (11, 10), (14, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369070", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (14, 3), (6, 7), (14, 4), (4, 4), (15, 10), (16, 8), (6, 2), (5, 9), (2, 3), (12, 2), (5, 8), (3, 7), (4, 5), (5, 5), (16, 9), (15, 1), (7, 5), (15, 7), (10, 5), (7, 7), (15, 0), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244747", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (9, 7), (5, 11), (4, 6), (7, 12), (10, 12), (1, 12), (1, 10), (1, 9), (1, 1), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "692006", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (6, 7), (8, 10), (13, 11), (3, 8), (9, 13), (12, 2), (0, 18), (10, 3), (8, 4), (9, 4), (4, 8), (4, 13), (9, 1), (12, 16), (2, 15), (5, 17), (0, 9), (12, 5), (1, 10), (8, 8), (9, 8), (4, 2), (0, 13), (1, 7), (0, 5), (3, 10), (3, 9), (10, 1), (3, 14), (2, 4), (8, 9), (2, 9), (12, 17), (7, 8), (1, 8), (8, 12), (3, 1), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "703540", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 7), (2, 9), (6, 5), (10, 10), (6, 1), (5, 7), (5, 11), (4, 9), (3, 10), (7, 2), (11, 5), (2, 14), (7, 7), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508339", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (2, 9), (1, 2), (4, 7), (6, 9), (3, 5), (10, 4), (8, 7), (12, 1), (5, 6), (13, 9), (6, 2), (1, 3), (7, 2), (12, 8), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45200", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (6, 3), (11, 2), (2, 11), (9, 7), (4, 13), (13, 11), (7, 6), (7, 12), (10, 12), (6, 0), (8, 8), (7, 14), (2, 12), (11, 11), (7, 1), (15, 8), (14, 0), (2, 6), (16, 2), (16, 6), (5, 5), (0, 15), (10, 0), (11, 13), (5, 0), (16, 13), (5, 13), (15, 7), (4, 8), (16, 11), (10, 2), (1, 6), (13, 5), (9, 14), (6, 7), (2, 1), (15, 9), (8, 13), (16, 15), (15, 15), (13, 4), (17, 0), (15, 1), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785341", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (17, 7), (2, 5), (11, 8), (16, 5), (2, 9), (9, 7), (5, 0), (1, 8), (5, 8), (3, 3), (9, 4), (10, 0), (15, 5), (7, 6), (3, 10), (7, 5), (5, 11), (18, 7), (10, 7), (1, 9), (16, 7), (7, 1), (14, 7), (16, 12), (10, 2), (15, 9), (16, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928978", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 6), (5, 0), (1, 2), (2, 3), (7, 6), (4, 8), (7, 11), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117031", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (9, 16), (9, 9), (6, 2), (4, 10), (5, 10), (8, 2), (9, 8), (2, 11), (1, 0), (4, 0), (6, 8), (10, 0), (7, 15), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235005", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (7, 8), (2, 10), (2, 9), (9, 16), (9, 1), (1, 5), (4, 3), (0, 1), (5, 0), (7, 16), (5, 13), (2, 17), (3, 9), (10, 14), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996493", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (7, 4), (1, 10), (3, 6), (10, 7), (6, 4), (0, 10), (4, 7), (1, 9), (3, 7), (11, 10), (4, 10), (11, 9), (10, 5), (10, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12947", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 5), (10, 0), (2, 7), (7, 3), (13, 6), (8, 0), (0, 5), (0, 4), (9, 4), (1, 3), (10, 5), (15, 2), (1, 6), (12, 1), (9, 1), (9, 8), (13, 4), (0, 6), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143513", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 10), (6, 3), (9, 2), (15, 1), (5, 4), (5, 3), (15, 0), (3, 11), (10, 10), (9, 6), (6, 4), (8, 8), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377330", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (2, 5), (2, 0), (1, 2), (5, 5), (4, 3), (3, 7), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306648", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (2, 3), (8, 1), (16, 8), (15, 6), (1, 4), (6, 11), (8, 3), (4, 8), (11, 0), (0, 7), (15, 0), (0, 9), (2, 0), (11, 5), (6, 2), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792709", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (6, 2), (2, 1), (7, 8), (9, 1), (10, 2), (6, 7), (2, 3), (9, 7), (3, 5), (1, 7), (3, 10), (2, 7), (7, 7), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46273", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (2, 0), (2, 6), (7, 1), (8, 2), (5, 8), (3, 10), (4, 11), (10, 5), (10, 1), (0, 9), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150616", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (8, 12), (6, 8), (1, 7), (1, 3), (7, 7), (4, 5), (9, 2), (2, 10), (8, 7), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46674", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (8, 11), (12, 5), (0, 4), (6, 8), (7, 11), (1, 6), (1, 5), (0, 7), (12, 3), (6, 0), (3, 6), (7, 8), (2, 5), (7, 10), (1, 9), (11, 8), (7, 1), (10, 8), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980025", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (6, 2), (7, 5), (3, 4), (7, 3), (1, 5), (0, 9), (6, 8), (8, 6), (8, 1), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15942", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (13, 11), (3, 0), (3, 7), (11, 0), (9, 7), (11, 7), (2, 4), (6, 5), (5, 4), (11, 1), (8, 7), (3, 2), (5, 6), (7, 10), (3, 13), (2, 9), (9, 9), (9, 8), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128001", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (6, 10), (1, 0), (0, 15), (11, 14), (6, 16), (8, 2), (7, 2), (7, 7), (9, 12), (3, 5), (4, 16), (8, 8), (8, 15), (5, 7), (6, 1), (10, 12), (4, 17), (1, 8), (1, 7), (7, 13), (12, 0), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712854", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (10, 9), (0, 7), (1, 17), (8, 6), (1, 7), (1, 1), (7, 16), (1, 14), (12, 6), (8, 2), (5, 10), (2, 6), (6, 10), (8, 4), (3, 10), (6, 1), (8, 8), (6, 2), (10, 13), (6, 5), (9, 13), (11, 10), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643716", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 6), (5, 0), (10, 1), (1, 3), (3, 4), (15, 6), (14, 12), (0, 4), (4, 0), (14, 0), (0, 10), (5, 12), (9, 10), (0, 3), (1, 11), (10, 5), (8, 7), (16, 7), (8, 10), (16, 6), (1, 5), (15, 0), (11, 7), (9, 2), (4, 8), (13, 7), (12, 12), (6, 0), (8, 0), (8, 6), (14, 2), (1, 9), (12, 4), (16, 0), (14, 11), (12, 2), (7, 4), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947192", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (7, 5), (10, 2), (8, 9), (8, 7), (1, 7), (4, 8), (6, 8), (9, 9), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657152", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (1, 9), (8, 0), (9, 0), (6, 2), (4, 3), (2, 7), (3, 1), (0, 8), (8, 3), (1, 8), (8, 2), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14389", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (3, 6), (12, 5), (0, 15), (1, 0), (12, 12), (1, 8), (14, 8), (3, 10), (1, 3), (2, 4), (9, 14), (14, 1), (15, 0), (12, 15), (4, 14), (6, 6), (4, 10), (0, 13), (2, 14), (7, 3), (7, 10), (12, 0), (2, 6), (11, 1), (9, 12), (8, 4), (6, 13), (10, 8), (6, 3), (3, 5), (12, 4), (13, 9), (13, 6), (4, 12), (7, 8), (5, 2), (1, 11), (9, 3), (14, 9), (15, 4), (5, 6), (11, 5), (1, 6), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907392", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 13), (11, 6), (3, 14), (7, 14), (2, 7), (18, 13), (2, 10), (0, 8), (9, 12), (18, 6), (7, 5), (15, 9), (8, 15), (6, 5), (8, 4), (14, 14), (16, 14), (4, 9), (9, 4), (17, 10), (10, 15), (7, 1), (1, 6), (3, 9), (4, 13), (14, 0), (10, 0), (8, 10), (11, 4), (12, 7), (9, 11), (13, 11), (18, 10), (15, 7), (5, 5), (9, 10), (15, 1), (3, 12), (7, 8), (15, 12), (12, 14), (0, 12), (12, 11), (13, 4), (14, 6), (13, 5), (16, 11), (1, 14), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720876", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (2, 5), (5, 12), (4, 5), (8, 13), (4, 14), (0, 9), (3, 13), (2, 3), (2, 8), (0, 11), (0, 7), (7, 12), (5, 1), (3, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179318", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 11), (6, 3), (6, 4), (6, 0), (2, 2), (7, 2), (1, 3), (2, 8), (4, 0), (3, 7), (5, 6), (5, 8), (1, 5), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4383", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 12), (4, 2), (0, 10), (5, 8), (9, 9), (11, 4), (5, 6), (3, 8), (7, 8), (8, 2), (2, 12), (7, 12), (3, 10), (1, 14), (4, 10), (0, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "446373", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 9), (8, 3), (4, 0), (8, 11), (6, 12), (13, 10), (12, 3), (9, 1), (5, 12), (2, 10), (7, 2), (15, 0), (6, 1), (12, 7), (11, 10), (5, 2), (12, 1), (12, 13), (1, 1), (12, 11), (10, 6), (16, 0), (12, 5), (12, 2), (7, 11), (7, 7), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "961335", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 2), (10, 9), (13, 12), (1, 5), (8, 8), (7, 11), (10, 4), (1, 3), (2, 2), (6, 0), (11, 6), (1, 13), (5, 6), (3, 9), (8, 0), (14, 5), (12, 14), (13, 6), (9, 7), (5, 8), (0, 11), (12, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875648", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (2, 13), (6, 8), (0, 1), (1, 1), (4, 1), (0, 15), (9, 16), (1, 2), (6, 2), (5, 5), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54796", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (3, 5), (5, 10), (0, 12), (3, 15), (1, 11), (0, 14), (5, 1), (2, 7), (5, 15), (4, 12), (8, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541626", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 5), (17, 11), (6, 10), (3, 10), (4, 12), (2, 7), (16, 12), (13, 6), (15, 11), (2, 2), (4, 0), (6, 13), (17, 3), (17, 8), (17, 6), (12, 4), (1, 6), (12, 2), (13, 3), (3, 8), (5, 11), (7, 2), (0, 9), (8, 11), (14, 11), (14, 6), (18, 0), (5, 10), (3, 6), (5, 4), (0, 4), (13, 13), (9, 6), (14, 4), (3, 2), (4, 1), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "741668", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (8, 1), (9, 9), (17, 7), (8, 11), (12, 8), (8, 3), (8, 0), (9, 4), (2, 1), (2, 11), (4, 6), (0, 2), (3, 1), (13, 10), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969425", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 7), (0, 1), (9, 7), (6, 0), (13, 4), (4, 1), (8, 5), (6, 9), (8, 2), (0, 10), (11, 12), (4, 9), (8, 4), (6, 18), (11, 15), (9, 1), (13, 12), (3, 7), (6, 7), (5, 13), (4, 6), (13, 8), (12, 6), (3, 12), (11, 9), (7, 5), (8, 10), (10, 8), (4, 18), (1, 18), (0, 12), (11, 6), (12, 12), (1, 17), (8, 7), (11, 11), (13, 14), (12, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "995087", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (8, 4), (5, 6), (4, 4), (9, 6), (0, 6), (0, 2), (1, 5), (9, 0), (9, 4), (4, 8), (0, 8), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16115", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (4, 5), (0, 5), (1, 13), (9, 14), (1, 9), (6, 8), (5, 10), (5, 8), (2, 10), (9, 1), (3, 17), (4, 0), (2, 8), (9, 16), (8, 3), (10, 10), (3, 15), (5, 6), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "665944", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (0, 11), (2, 11), (5, 15), (5, 4), (0, 15), (3, 7), (8, 9), (6, 3), (0, 12), (1, 7), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338584", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 2), (8, 6), (16, 5), (4, 6), (6, 7), (15, 9), (7, 7), (6, 9), (5, 8), (6, 0), (0, 9), (17, 9), (1, 10), (6, 10), (8, 9), (1, 7), (3, 10), (1, 3), (15, 0), (12, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896167", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (11, 9), (2, 10), (8, 3), (12, 8), (5, 9), (7, 0), (7, 5), (8, 10), (7, 10), (4, 9), (11, 2), (2, 8), (5, 1), (8, 0), (13, 4), (11, 8), (7, 3), (11, 10), (2, 4), (9, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54564", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 2), (6, 2), (10, 7), (5, 16), (6, 1), (11, 2), (12, 16), (4, 6), (14, 3), (13, 4), (6, 13), (8, 0), (1, 15), (15, 5), (9, 3), (9, 13), (0, 1), (7, 12), (1, 9), (7, 4), (15, 9), (5, 2), (1, 6), (1, 5), (15, 0), (8, 1), (9, 4), (3, 0), (13, 10), (4, 1), (2, 12), (14, 16), (0, 5), (6, 8), (13, 1), (12, 14), (10, 0), (15, 11), (12, 3), (11, 16), (9, 15), (5, 9), (0, 13), (3, 15), (0, 11), (6, 17), (3, 4), (14, 0), (2, 13), (10, 9), (12, 8), (14, 13), (9, 2), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548868", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 7), (8, 4), (5, 6), (10, 0), (9, 4), (9, 0), (0, 9), (9, 7), (12, 6), (15, 0), (14, 0), (12, 2), (0, 2), (1, 8), (11, 3), (6, 0), (3, 3), (11, 8), (11, 6), (13, 7), (8, 8), (15, 9), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57648", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (7, 0), (12, 1), (4, 2), (4, 4), (10, 1), (4, 10), (9, 8), (15, 12), (11, 13), (14, 10), (10, 2), (15, 2), (6, 14), (1, 12), (13, 3), (13, 13), (12, 15), (8, 1), (15, 3), (5, 0), (5, 9), (3, 15), (7, 8), (13, 8), (0, 15), (3, 2), (14, 6), (17, 2), (10, 12), (5, 15), (8, 11), (2, 0), (4, 13), (8, 13), (4, 5), (3, 5), (10, 5), (11, 12), (3, 13), (10, 15), (2, 14), (3, 1), (11, 14), (14, 8), (11, 0), (12, 13), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767929", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 12), (10, 2), (12, 12), (13, 2), (0, 5), (2, 14), (1, 0), (10, 0), (1, 5), (5, 3), (6, 0), (10, 10), (1, 9), (13, 0), (13, 6), (3, 2), (4, 3), (10, 8), (12, 5), (12, 8), (13, 12), (2, 9), (1, 4), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656190", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (14, 7), (1, 10), (7, 7), (4, 5), (12, 1), (13, 12), (3, 10), (5, 1), (15, 5), (6, 15), (1, 15), (3, 3), (12, 7), (4, 10), (6, 1), (9, 9), (6, 6), (14, 15), (15, 11), (12, 3), (9, 10), (9, 13), (10, 13), (9, 14), (6, 9), (8, 10), (10, 16), (2, 16), (8, 17), (1, 0), (8, 0), (7, 0), (1, 5), (12, 5), (5, 11), (4, 17), (2, 0), (6, 8), (2, 13), (14, 4), (7, 11), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851024", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (8, 2), (5, 10), (7, 12), (16, 2), (1, 9), (4, 10), (2, 9), (3, 11), (1, 0), (11, 3), (9, 5), (8, 12), (6, 9), (15, 0), (14, 2), (16, 10), (9, 0), (5, 1), (10, 1), (12, 7), (17, 0), (6, 3), (15, 8), (11, 9), (1, 1), (14, 7), (7, 9), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "911024", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (13, 16), (1, 7), (5, 2), (5, 6), (7, 13), (1, 1), (2, 15), (12, 6), (0, 16), (9, 1), (7, 16), (10, 16), (0, 9), (10, 2), (8, 1), (12, 3), (0, 12), (11, 4), (8, 9), (10, 5), (4, 8), (3, 2), (13, 14), (9, 11), (8, 4), (2, 6), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947196", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 12), (3, 11), (4, 5), (13, 6), (0, 2), (8, 10), (13, 4), (13, 0), (13, 14), (5, 0), (9, 7), (9, 1), (2, 13), (5, 15), (9, 2), (6, 6), (5, 13), (5, 5), (4, 7), (1, 10), (1, 6), (3, 0), (7, 11), (8, 2), (6, 0), (4, 14), (7, 14), (10, 3), (0, 16), (10, 7), (4, 2), (11, 0), (0, 12), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "869686", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (0, 7), (12, 8), (10, 1), (10, 3), (3, 3), (1, 0), (5, 2), (6, 5), (12, 10), (5, 3), (1, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "442718", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (5, 0), (12, 10), (7, 12), (10, 3), (8, 7), (5, 1), (3, 14), (8, 15), (7, 9), (10, 4), (1, 5), (4, 3), (3, 8), (3, 15), (11, 15), (2, 14), (8, 14), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "861322", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (6, 2), (0, 5), (7, 0), (12, 0), (9, 1), (9, 11), (10, 7), (15, 9), (3, 8), (1, 2), (14, 10), (4, 5), (2, 8), (3, 6), (12, 8), (10, 1), (7, 7), (1, 5), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127554", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 15), (10, 7), (6, 15), (13, 5), (11, 0), (1, 16), (2, 17), (8, 0), (5, 15), (11, 8), (1, 13), (2, 6), (4, 7), (5, 2), (4, 5), (3, 12), (5, 1), (4, 3), (8, 7), (13, 12), (2, 18), (6, 8), (9, 12), (11, 16), (15, 5), (9, 6), (2, 14), (15, 9), (10, 12), (11, 12), (3, 11), (5, 13), (9, 4), (12, 7), (14, 17), (4, 14), (7, 11), (0, 4), (12, 15), (4, 10), (0, 10), (0, 6), (11, 7), (13, 7), (12, 14), (13, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804368", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (1, 12), (9, 2), (5, 6), (6, 6), (4, 5), (5, 5), (4, 3), (3, 11), (8, 16), (9, 1), (7, 16), (7, 1), (7, 12), (1, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271291", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 12), (12, 4), (11, 11), (1, 3), (3, 10), (5, 11), (8, 7), (12, 8), (5, 9), (7, 12), (7, 14), (9, 10), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749866", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (8, 1), (5, 8), (4, 7), (7, 8), (4, 2), (9, 8), (2, 7), (6, 8), (3, 11), (0, 1), (2, 10), (2, 5), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18273", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (15, 1), (7, 7), (14, 0), (6, 7), (11, 6), (13, 6), (3, 9), (5, 9), (10, 3), (4, 1), (9, 4), (1, 6), (1, 4), (7, 8), (11, 8), (3, 7), (9, 5), (7, 1), (13, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123005", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (10, 3), (8, 13), (2, 7), (10, 12), (11, 1), (0, 13), (13, 2), (9, 7), (4, 2), (11, 12), (1, 1), (3, 3), (11, 6), (12, 5), (2, 2), (12, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492526", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 16), (9, 15), (12, 3), (8, 9), (9, 10), (11, 15), (8, 4), (8, 8), (6, 0), (7, 2), (17, 15), (2, 2), (8, 15), (1, 6), (15, 8), (1, 17), (7, 10), (12, 18), (8, 6), (5, 2), (10, 9), (15, 11), (8, 3), (7, 12), (13, 13), (10, 10), (0, 3), (10, 8), (15, 7), (2, 18), (2, 3), (7, 8), (12, 13), (6, 6), (5, 6), (12, 14), (15, 16), (5, 7), (11, 10), (4, 18), (17, 14), (11, 12), (3, 8), (12, 16), (8, 14), (14, 7), (10, 1), (4, 17), (15, 15), (15, 1), (10, 4), (13, 3), (16, 2), (4, 6), (14, 0), (4, 1), (16, 5), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386890", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (14, 1), (8, 11), (12, 5), (1, 13), (2, 10), (16, 11), (2, 3), (8, 12), (3, 13), (9, 10), (3, 5), (12, 2), (10, 0), (2, 8), (6, 13), (3, 8), (10, 10), (11, 10), (13, 11), (7, 9), (2, 1), (2, 7), (6, 11), (16, 2), (9, 3), (1, 5), (0, 1), (13, 5), (0, 13), (8, 9), (7, 12), (12, 13), (9, 1), (7, 8), (1, 12), (11, 12), (11, 7), (2, 4), (9, 2), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777384", "dataset": "MATH"}
{"messages": [{"content": "In a 15x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (11, 8), (6, 11), (10, 3), (11, 3), (9, 6), (6, 8), (1, 11), (3, 4), (5, 8), (10, 14), (6, 12), (6, 7), (9, 10), (4, 10), (0, 14), (10, 6), (13, 14), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993587", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (2, 6), (15, 8), (14, 2), (2, 7), (0, 6), (13, 6), (8, 1), (0, 4), (9, 5), (13, 10), (18, 12), (12, 12), (17, 15), (3, 1), (4, 14), (6, 15), (12, 14), (11, 10), (1, 9), (3, 6), (9, 8), (16, 14), (13, 12), (0, 7), (18, 7), (0, 9), (12, 0), (15, 12), (1, 3), (10, 12), (3, 5), (10, 8), (18, 11), (17, 1), (8, 12), (17, 0), (13, 13), (3, 0), (12, 13), (14, 13), (3, 8), (15, 9), (13, 3), (6, 0), (1, 11), (12, 2), (0, 14), (9, 7), (12, 5), (5, 11), (17, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707430", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 7), (4, 4), (1, 5), (7, 1), (6, 3), (4, 6), (8, 5), (5, 5), (8, 0), (5, 3), (3, 0), (2, 9), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1865", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (0, 1), (4, 12), (12, 5), (4, 1), (9, 6), (4, 0), (8, 6), (11, 9), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574155", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 14), (2, 7), (7, 12), (8, 2), (16, 8), (5, 3), (10, 12), (11, 8), (6, 8), (6, 1), (12, 0), (7, 13), (0, 9), (14, 12), (3, 5), (2, 14), (14, 11), (7, 7), (11, 7), (13, 7), (16, 14), (5, 9), (4, 6), (0, 14), (4, 4), (11, 2), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "795474", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (9, 9), (4, 7), (11, 4), (13, 5), (7, 4), (3, 1), (0, 9), (10, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235094", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 0), (11, 4), (2, 15), (4, 6), (18, 5), (12, 2), (18, 10), (8, 3), (16, 11), (5, 1), (15, 1), (0, 2), (3, 15), (17, 4), (8, 5), (5, 6), (0, 10), (16, 9), (8, 7), (2, 7), (12, 4), (9, 12), (7, 13), (11, 14), (18, 13), (16, 13), (4, 8), (5, 5), (15, 2), (10, 10), (12, 8), (3, 9), (18, 9), (16, 5), (8, 6), (8, 12), (8, 8), (8, 1), (12, 15), (1, 1), (9, 14), (13, 4), (4, 2), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970323", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (3, 8), (8, 15), (2, 12), (1, 6), (5, 12), (9, 10), (4, 0), (5, 7), (1, 5), (4, 16), (6, 1), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193240", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (2, 2), (8, 9), (9, 8), (3, 5), (6, 13), (0, 12), (1, 5), (6, 11), (0, 6), (10, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550302", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (3, 1), (9, 3), (2, 8), (3, 11), (9, 11), (3, 5), (7, 5), (3, 3), (4, 4), (0, 3), (8, 8), (0, 2), (5, 7), (7, 3), (10, 5), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11987", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 16), (6, 3), (3, 5), (17, 0), (8, 14), (5, 17), (1, 5), (3, 7), (11, 0), (6, 12), (8, 17), (10, 13), (6, 0), (15, 7), (10, 6), (7, 11), (3, 12), (1, 8), (8, 1), (16, 16), (10, 0), (1, 13), (5, 11), (12, 9), (3, 15), (17, 1), (17, 11), (4, 6), (6, 5), (15, 10), (15, 17), (7, 0), (14, 15), (13, 6), (13, 13), (8, 8), (15, 16), (2, 13), (0, 14), (15, 13), (1, 17), (2, 1), (2, 14), (14, 1), (4, 8), (15, 0), (5, 8), (11, 12), (0, 13), (13, 3), (12, 1), (4, 4), (4, 2), (5, 13), (4, 14), (4, 7), (3, 2), (11, 15), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "686271", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (3, 8), (3, 1), (6, 1), (1, 8), (11, 10), (2, 2), (0, 3), (8, 7), (2, 8), (4, 9), (0, 9), (5, 4), (6, 0), (11, 1), (5, 1), (8, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12460", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (8, 10), (5, 13), (0, 6), (0, 12), (0, 15), (11, 0), (9, 5), (7, 8), (6, 4), (10, 5), (0, 7), (10, 4), (10, 8), (11, 11), (8, 1), (1, 12), (11, 1), (5, 7), (4, 2), (2, 10), (12, 8), (5, 5), (8, 13), (9, 9), (6, 8), (7, 1), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839227", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (3, 11), (0, 10), (5, 16), (3, 15), (3, 4), (6, 10), (8, 6), (2, 4), (2, 10), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "389848", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (0, 8), (9, 8), (5, 8), (6, 2), (4, 0), (7, 1), (4, 11), (5, 7), (11, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240228", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 7), (2, 6), (6, 1), (3, 7), (3, 6), (1, 3), (11, 3), (15, 10), (12, 0), (2, 2), (1, 10), (11, 1), (10, 0), (18, 6), (17, 11), (14, 10), (7, 3), (17, 6), (14, 3), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "827028", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (6, 14), (1, 2), (7, 3), (3, 4), (13, 1), (9, 13), (4, 1), (6, 15), (9, 0), (1, 15), (3, 2), (15, 6), (14, 4), (1, 10), (6, 12), (8, 8), (7, 10), (12, 13), (4, 9), (7, 7), (14, 0), (11, 3), (9, 1), (7, 16), (12, 1), (15, 1), (12, 14), (2, 6), (6, 16), (1, 4), (7, 0), (13, 14), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "965486", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 9), (4, 11), (3, 8), (7, 5), (6, 8), (3, 1), (8, 8), (7, 4), (4, 4), (0, 10), (3, 6), (0, 7), (2, 7), (4, 1), (1, 9), (5, 5), (0, 3), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62451", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 12), (3, 10), (4, 2), (14, 8), (8, 9), (6, 7), (4, 8), (9, 5), (5, 3), (13, 7), (13, 12), (3, 6), (5, 16), (5, 0), (10, 13), (15, 9), (14, 3), (12, 7), (7, 13), (7, 11), (11, 15), (13, 5), (11, 4), (7, 2), (11, 6), (12, 11), (1, 11), (10, 8), (9, 2), (1, 13), (13, 9), (6, 0), (14, 7), (9, 15), (10, 15), (8, 11), (2, 4), (11, 10), (13, 16), (4, 3), (10, 16), (11, 16), (3, 1), (14, 1), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917789", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (0, 6), (4, 6), (5, 0), (2, 1), (10, 10), (1, 11), (4, 4), (14, 4), (10, 3), (7, 6), (12, 0), (12, 11), (13, 6), (14, 11), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289545", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 13), (11, 5), (15, 6), (14, 15), (5, 9), (10, 3), (11, 3), (8, 15), (14, 6), (10, 5), (16, 2), (8, 12), (17, 4), (10, 7), (4, 14), (8, 9), (13, 5), (10, 15), (8, 3), (14, 5), (0, 9), (5, 1), (12, 11), (5, 4), (2, 8), (15, 7), (14, 9), (16, 8), (6, 12), (6, 2), (8, 7), (13, 3), (6, 5), (8, 13), (16, 0), (5, 3), (10, 0), (12, 8), (5, 11), (3, 10), (14, 7), (1, 1), (9, 15), (8, 4), (12, 10), (1, 15), (3, 8), (10, 6), (4, 3), (7, 0), (6, 6), (4, 2), (17, 5), (6, 11), (15, 0), (17, 13), (1, 9), (5, 0), (3, 12), (2, 6), (16, 4), (6, 15), (1, 8), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798822", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (2, 7), (11, 0), (9, 3), (4, 2), (1, 8), (7, 4), (3, 0), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317991", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (9, 5), (5, 10), (0, 13), (11, 1), (1, 0), (15, 8), (13, 10), (16, 13), (12, 13), (5, 0), (2, 1), (5, 5), (8, 10), (1, 12), (3, 4), (6, 10), (17, 11), (1, 13), (9, 4), (17, 8), (10, 5), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734846", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (2, 12), (7, 5), (7, 1), (7, 8), (0, 14), (0, 10), (9, 2), (10, 14), (1, 6), (10, 3), (15, 15), (1, 7), (2, 14), (2, 5), (0, 11), (7, 0), (2, 11), (3, 1), (5, 11), (14, 13), (16, 0), (4, 4), (1, 3), (3, 12), (2, 2), (8, 12), (6, 5), (4, 15), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641809", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 12), (8, 13), (4, 5), (1, 8), (3, 2), (5, 0), (7, 16), (8, 4), (8, 16), (8, 10), (1, 5), (7, 10), (8, 6), (2, 3), (10, 16), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208736", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (14, 14), (7, 9), (13, 8), (12, 1), (4, 6), (13, 0), (5, 2), (15, 2), (0, 1), (2, 6), (10, 12), (13, 5), (6, 16), (8, 16), (13, 12), (15, 17), (16, 14), (10, 2), (10, 11), (3, 2), (5, 10), (14, 7), (4, 2), (5, 3), (14, 5), (5, 7), (11, 18), (9, 6), (9, 10), (6, 6), (15, 14), (1, 8), (2, 17), (13, 7), (14, 4), (6, 2), (3, 11), (11, 7), (6, 17), (6, 11), (12, 4), (13, 4), (4, 7), (11, 15), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915613", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (1, 6), (17, 5), (4, 1), (14, 9), (12, 2), (6, 12), (16, 7), (11, 12), (14, 1), (10, 0), (16, 5), (12, 10), (15, 1), (9, 2), (11, 7), (5, 12), (8, 8), (17, 10), (12, 6), (12, 12), (17, 8), (2, 0), (16, 6), (7, 1), (2, 10), (14, 12), (4, 0), (8, 6), (9, 3), (9, 10), (8, 3), (10, 3), (0, 8), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586568", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (4, 13), (7, 10), (3, 10), (17, 2), (17, 9), (10, 4), (6, 14), (1, 0), (8, 13), (7, 18), (7, 7), (5, 13), (2, 8), (1, 4), (17, 4), (9, 9), (8, 15), (11, 15), (13, 13), (3, 2), (3, 12), (7, 9), (3, 1), (4, 11), (14, 5), (17, 10), (11, 11), (10, 13), (14, 10), (9, 17), (12, 4), (8, 18), (16, 9), (16, 0), (9, 11), (15, 7), (1, 9), (4, 17), (16, 3), (4, 1), (15, 6), (6, 7), (8, 0), (12, 6), (5, 10), (16, 15), (0, 18), (17, 12), (12, 15), (14, 13), (10, 1), (6, 13), (10, 6), (10, 15), (1, 8), (16, 2), (17, 0), (15, 17), (7, 17), (11, 3), (0, 15), (1, 5), (5, 5), (13, 5), (8, 1), (6, 18), (15, 18), (7, 13), (3, 17), (7, 8), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820327", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (9, 9), (15, 1), (3, 8), (13, 10), (9, 11), (11, 2), (1, 11), (11, 1), (16, 8), (14, 2), (7, 12), (3, 13), (11, 10), (15, 8), (1, 8), (4, 5), (8, 7), (15, 13), (16, 0), (11, 7), (11, 3), (2, 9), (13, 2), (10, 6), (10, 11), (4, 9), (15, 7), (9, 3), (16, 3), (2, 3), (13, 6), (15, 12), (14, 8), (16, 14), (8, 9), (7, 2), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565059", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 7), (8, 0), (0, 2), (17, 6), (0, 5), (14, 4), (10, 2), (7, 6), (9, 14), (3, 6), (13, 0), (6, 16), (9, 18), (4, 5), (13, 17), (18, 3), (2, 11), (10, 1), (0, 12), (12, 13), (4, 4), (18, 4), (5, 6), (17, 0), (14, 16), (15, 11), (12, 4), (2, 6), (3, 17), (9, 8), (17, 9), (16, 4), (12, 15), (1, 0), (2, 8), (8, 12), (2, 15), (11, 9), (10, 5), (10, 10), (2, 1), (15, 15), (5, 13), (7, 10), (6, 8), (18, 0), (7, 18), (4, 11), (2, 4), (5, 4), (5, 11), (14, 5), (10, 14), (10, 8), (18, 15), (18, 2), (18, 8), (14, 2), (5, 17), (14, 15), (12, 2), (10, 7), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759657", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 9), (18, 7), (12, 3), (0, 1), (10, 5), (15, 9), (18, 4), (0, 2), (15, 11), (9, 1), (0, 5), (17, 3), (8, 9), (0, 4), (8, 6), (13, 3), (18, 0), (6, 12), (4, 11), (11, 4), (6, 9), (1, 11), (4, 9), (11, 3), (17, 9), (5, 7), (6, 0), (1, 9), (18, 5), (1, 8), (8, 12), (14, 4), (13, 1), (11, 7), (13, 2), (15, 10), (17, 5), (13, 9), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768957", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 17), (3, 11), (10, 11), (12, 13), (9, 0), (7, 1), (9, 15), (7, 4), (0, 3), (3, 7), (1, 13), (0, 15), (5, 5), (2, 13), (1, 1), (1, 7), (8, 15), (8, 5), (1, 2), (11, 0), (6, 11), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "772740", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (7, 0), (8, 3), (5, 8), (0, 13), (9, 11), (5, 10), (5, 9), (7, 9), (2, 5), (5, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112014", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (0, 16), (9, 4), (12, 9), (8, 1), (4, 2), (6, 11), (10, 10), (8, 2), (2, 5), (2, 7), (8, 8), (0, 6), (6, 1), (11, 1), (5, 4), (9, 13), (1, 12), (6, 15), (3, 12), (4, 7), (4, 1), (1, 4), (10, 3), (4, 12), (11, 5), (4, 8), (0, 12), (3, 6), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "823772", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (4, 5), (8, 8), (4, 17), (12, 11), (10, 0), (12, 2), (8, 9), (7, 17), (12, 1), (10, 4), (0, 14), (4, 9), (9, 0), (8, 1), (7, 12), (8, 5), (3, 5), (1, 8), (7, 11), (12, 14), (5, 10), (10, 12), (6, 5), (9, 12), (0, 12), (5, 4), (12, 9), (6, 0), (1, 10), (7, 4), (3, 15), (8, 16), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "849582", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (1, 6), (6, 7), (8, 0), (5, 7), (8, 7), (2, 0), (7, 1), (6, 8), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17542", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (15, 13), (1, 16), (7, 0), (13, 3), (15, 4), (6, 4), (9, 15), (12, 14), (15, 15), (8, 7), (0, 15), (10, 15), (2, 8), (3, 15), (15, 14), (8, 12), (14, 0), (4, 14), (3, 8), (2, 16), (1, 14), (2, 1), (3, 5), (11, 1), (13, 4), (4, 2), (1, 9), (9, 4), (12, 12), (14, 13), (9, 0), (1, 4), (12, 6), (8, 9), (15, 2), (4, 10), (11, 7), (4, 0), (5, 13), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991529", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (1, 4), (2, 5), (3, 4), (16, 11), (9, 1), (9, 2), (0, 7), (5, 5), (17, 4), (0, 3), (6, 10), (14, 2), (2, 10), (16, 1), (2, 6), (5, 12), (12, 9), (7, 6), (7, 9), (6, 12), (5, 0), (8, 2), (13, 4), (11, 10), (15, 3), (7, 10), (9, 10), (3, 12), (6, 2), (5, 9), (7, 1), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624420", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (4, 3), (3, 13), (1, 8), (6, 12), (6, 7), (10, 1), (0, 8), (10, 5), (2, 4), (8, 4), (3, 3), (11, 1), (5, 12), (13, 8), (9, 8), (5, 14), (13, 12), (6, 8), (5, 11), (14, 12), (8, 15), (5, 3), (4, 1), (0, 15), (12, 13), (8, 0), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838777", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 12), (6, 6), (10, 11), (8, 6), (4, 13), (5, 9), (4, 8), (12, 14), (13, 2), (5, 8), (11, 15), (4, 11), (10, 10), (5, 13), (12, 4), (8, 14), (7, 9), (9, 4), (10, 8), (0, 6), (14, 12), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876711", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 10), (6, 4), (0, 4), (11, 8), (0, 8), (8, 2), (5, 1), (11, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182528", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 11), (9, 0), (11, 9), (7, 8), (8, 1), (14, 11), (3, 9), (7, 10), (7, 0), (3, 5), (4, 8), (7, 2), (5, 1), (8, 11), (4, 4), (6, 2), (9, 11), (6, 7), (14, 7), (13, 4), (6, 6), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238167", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 18), (6, 16), (6, 8), (10, 16), (10, 8), (3, 0), (1, 5), (3, 9), (11, 14), (4, 3), (2, 5), (0, 14), (13, 14), (12, 10), (6, 13), (7, 15), (8, 7), (4, 18), (8, 1), (0, 10), (9, 0), (3, 2), (1, 13), (12, 4), (5, 12), (9, 7), (11, 16), (6, 5), (2, 18), (11, 15), (1, 9), (0, 4), (7, 17), (10, 6), (4, 10), (7, 5), (13, 4), (0, 12), (6, 7), (3, 17), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915588", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 13), (6, 1), (4, 13), (13, 8), (0, 8), (15, 0), (2, 11), (16, 6), (6, 11), (10, 5), (7, 1), (1, 6), (15, 9), (3, 12), (2, 3), (6, 13), (2, 7), (0, 14), (17, 12), (11, 1), (0, 2), (6, 7), (1, 8), (9, 9), (14, 9), (17, 7), (1, 4), (11, 8), (9, 1), (3, 7), (2, 8), (15, 1), (4, 11), (11, 12), (4, 4), (14, 7), (3, 10), (18, 9), (12, 5), (6, 2), (12, 8), (8, 7), (3, 5), (7, 4), (15, 13), (18, 2), (13, 0), (11, 3), (3, 9), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "871643", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (7, 4), (9, 9), (11, 11), (8, 8), (5, 3), (3, 1), (2, 10), (1, 6), (6, 5), (6, 0), (1, 12), (11, 2), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87815", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 0), (15, 12), (13, 4), (11, 4), (9, 11), (7, 12), (14, 5), (13, 2), (1, 4), (7, 8), (2, 3), (4, 13), (3, 4), (0, 2), (14, 10), (10, 0), (0, 11), (14, 3), (4, 0), (0, 9), (3, 11), (3, 12), (10, 9), (0, 4), (13, 7), (10, 1), (1, 11), (3, 10), (11, 1), (14, 6), (13, 6), (15, 11), (4, 10), (9, 2), (14, 9), (5, 3), (5, 10), (6, 7), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647647", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 5), (2, 11), (2, 6), (10, 3), (11, 4), (13, 5), (2, 10), (5, 10), (13, 2), (8, 4), (2, 0), (10, 7), (8, 9), (4, 11), (4, 9), (10, 5), (7, 8), (13, 0), (10, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168910", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 1), (0, 13), (2, 8), (11, 12), (0, 9), (12, 12), (1, 7), (11, 5), (7, 9), (5, 7), (4, 14), (9, 10), (6, 13), (8, 6), (13, 0), (0, 4), (7, 0), (1, 8), (2, 7), (6, 1), (11, 0), (14, 8), (11, 2), (7, 14), (6, 11), (8, 9), (0, 8), (6, 6), (14, 10), (10, 4), (12, 4), (7, 15), (1, 6), (10, 9), (10, 18), (10, 8), (0, 10), (11, 3), (0, 5), (2, 3), (4, 5), (15, 5), (2, 14), (15, 16), (14, 18), (8, 18), (1, 4), (2, 6), (4, 9), (10, 11), (15, 13), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749070", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 4), (0, 12), (16, 1), (6, 5), (4, 3), (14, 10), (14, 11), (13, 12), (7, 2), (5, 2), (11, 10), (5, 11), (11, 7), (4, 2), (5, 3), (8, 10), (10, 0), (7, 12), (15, 4), (15, 10), (3, 7), (8, 1), (6, 7), (10, 10), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94055", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 18), (4, 5), (3, 10), (7, 15), (8, 14), (10, 13), (1, 10), (9, 2), (5, 14), (4, 16), (3, 2), (1, 13), (3, 11), (8, 9), (8, 17), (8, 2), (8, 5), (7, 3), (0, 14), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95360", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 11), (13, 11), (1, 7), (8, 6), (6, 6), (2, 3), (13, 6), (8, 0), (3, 11), (9, 4), (2, 9), (11, 3), (2, 12), (0, 10), (7, 11), (7, 7), (2, 1), (5, 9), (2, 14), (4, 13), (10, 5), (10, 3), (3, 14), (2, 10), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "881804", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (6, 10), (13, 4), (7, 5), (9, 10), (16, 6), (13, 8), (6, 11), (6, 3), (10, 10), (14, 3), (16, 5), (13, 5), (7, 1), (12, 4), (3, 0), (11, 8), (8, 10), (14, 10), (0, 11), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755646", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 16), (6, 3), (5, 10), (1, 2), (8, 8), (6, 6), (10, 8), (3, 12), (4, 2), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919986", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (9, 9), (9, 2), (11, 1), (6, 3), (2, 17), (0, 16), (2, 1), (1, 12), (2, 15), (1, 14), (0, 8), (14, 2), (4, 1), (9, 17), (11, 14), (14, 9), (5, 1), (4, 0), (10, 0), (2, 9), (8, 4), (3, 5), (7, 18), (3, 12), (2, 12), (6, 8), (6, 13), (6, 2), (4, 10), (8, 5), (13, 11), (5, 0), (4, 8), (2, 13), (14, 6), (2, 0), (8, 10), (8, 8), (4, 9), (11, 11), (1, 9), (4, 2), (11, 6), (9, 0), (5, 12), (0, 5), (5, 13), (12, 1), (6, 11), (1, 8), (13, 12), (6, 4), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948410", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (6, 8), (13, 8), (0, 7), (2, 6), (11, 6), (4, 7), (7, 9), (13, 5), (0, 6), (9, 1), (8, 10), (3, 3), (7, 4), (8, 0), (2, 9), (12, 2), (2, 7), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966438", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (7, 4), (0, 9), (11, 7), (4, 6), (12, 5), (7, 0), (10, 1), (10, 3), (12, 6), (11, 2), (2, 7), (10, 6), (8, 1), (3, 3), (6, 7), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48092", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 7), (5, 10), (9, 12), (15, 0), (1, 6), (0, 5), (16, 4), (1, 0), (2, 12), (16, 14), (1, 8), (14, 4), (16, 10), (12, 9), (17, 2), (1, 13), (14, 5), (13, 0), (13, 3), (15, 10), (14, 8), (0, 3), (7, 13), (12, 16), (13, 8), (10, 4), (17, 10), (7, 10), (16, 13), (3, 6), (1, 4), (4, 15), (8, 13), (17, 9), (17, 15), (7, 4), (16, 15), (12, 11), (9, 11), (17, 1), (13, 13), (12, 4), (5, 6), (1, 7), (1, 14), (17, 7), (16, 12), (5, 11), (12, 13), (10, 11), (12, 3), (8, 2), (9, 4), (13, 15), (2, 6), (2, 11), (11, 3), (15, 2), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632442", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 6), (8, 5), (6, 8), (10, 3), (5, 1), (13, 8), (0, 1), (8, 1), (3, 3), (12, 2), (17, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308354", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (7, 13), (5, 13), (16, 4), (16, 10), (4, 0), (8, 7), (15, 15), (9, 8), (5, 10), (11, 9), (12, 8), (6, 7), (14, 8), (7, 3), (9, 2), (17, 2), (17, 14), (14, 2), (2, 7), (2, 0), (4, 5), (15, 1), (14, 13), (3, 2), (14, 15), (10, 13), (10, 0), (2, 14), (9, 1), (11, 15), (16, 11), (6, 8), (12, 4), (13, 13), (15, 10), (16, 5), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972477", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (10, 17), (9, 4), (2, 5), (0, 12), (3, 11), (3, 10), (4, 12), (2, 17), (3, 6), (10, 15), (9, 13), (5, 4), (1, 4), (5, 12), (1, 13), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592332", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 4), (5, 14), (3, 4), (8, 14), (8, 11), (3, 3), (0, 6), (1, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140154", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (0, 6), (3, 11), (9, 9), (5, 12), (4, 5), (5, 11), (3, 3), (9, 6), (3, 5), (7, 4), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99246", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (15, 9), (13, 5), (8, 1), (14, 2), (2, 7), (0, 11), (8, 9), (1, 7), (3, 13), (14, 14), (5, 9), (9, 14), (10, 7), (0, 12), (6, 1), (6, 7), (15, 7), (11, 14), (7, 11), (6, 2), (11, 4), (14, 8), (2, 9), (11, 1), (8, 13), (2, 3), (13, 2), (12, 13), (1, 9), (3, 2), (15, 4), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908903", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (2, 6), (6, 4), (4, 0), (2, 0), (9, 2), (1, 0), (8, 5), (6, 9), (9, 1), (4, 5), (10, 4), (8, 8), (3, 0), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5531", "dataset": "MATH"}
{"messages": [{"content": "In a 11x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (8, 11), (4, 1), (7, 3), (7, 10), (2, 4), (5, 8), (6, 17), (10, 16), (1, 15), (1, 9), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798314", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 9), (16, 12), (11, 6), (8, 10), (5, 4), (2, 10), (7, 1), (1, 0), (8, 5), (0, 2), (3, 10), (9, 8), (2, 6), (14, 2), (1, 2), (10, 8), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882405", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (2, 12), (10, 11), (1, 2), (3, 10), (1, 8), (0, 7), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710661", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (8, 13), (3, 5), (1, 1), (1, 11), (8, 3), (6, 6), (0, 6), (6, 4), (4, 4), (6, 5), (12, 6), (2, 8), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354770", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (4, 8), (12, 9), (11, 4), (11, 1), (12, 10), (3, 12), (8, 8), (6, 11), (4, 9), (8, 9), (12, 13), (3, 3), (1, 10), (3, 5), (9, 14), (0, 1), (13, 13), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239890", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 9), (9, 9), (7, 13), (5, 12), (11, 8), (8, 6), (7, 12), (5, 4), (7, 11), (1, 12), (0, 3), (6, 11), (10, 9), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895458", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 5), (12, 2), (3, 12), (0, 10), (10, 12), (4, 11), (9, 4), (1, 5), (8, 10), (11, 4), (5, 1), (8, 7), (0, 9), (10, 2), (0, 12), (5, 0), (4, 13), (0, 11), (9, 11), (7, 0), (4, 9), (10, 7), (2, 7), (4, 2), (8, 6), (4, 1), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738139", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (1, 1), (9, 1), (4, 10), (11, 8), (2, 11), (5, 3), (6, 10), (4, 5), (6, 11), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65490", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 12), (12, 15), (5, 1), (4, 10), (9, 0), (6, 12), (10, 13), (12, 5), (12, 13), (4, 11), (10, 14), (11, 1), (2, 10), (12, 0), (13, 17), (6, 7), (1, 8), (13, 4), (2, 12), (2, 16), (1, 10), (8, 7), (13, 12), (9, 13), (0, 7), (8, 17), (6, 5), (2, 1), (3, 16), (8, 11), (3, 1), (11, 3), (7, 17), (6, 16), (10, 0), (5, 0), (13, 8), (5, 13), (14, 10), (8, 0), (2, 9), (5, 4), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884350", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (9, 14), (14, 6), (11, 16), (1, 2), (9, 6), (9, 7), (5, 0), (5, 14), (12, 8), (13, 8), (3, 14), (8, 9), (2, 14), (14, 14), (7, 11), (3, 17), (12, 16), (13, 7), (3, 13), (10, 17), (1, 0), (0, 5), (1, 12), (0, 3), (11, 0), (3, 16), (3, 3), (6, 1), (4, 15), (4, 13), (8, 15), (8, 12), (6, 15), (1, 13), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913314", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (4, 5), (8, 3), (7, 14), (1, 15), (7, 0), (5, 15), (2, 15), (0, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587774", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 5), (7, 6), (9, 1), (6, 2), (3, 10), (9, 10), (1, 6), (12, 3), (4, 11), (11, 5), (4, 9), (3, 0), (4, 2), (8, 7), (6, 11), (6, 10), (8, 0), (10, 4), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209628", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 9), (7, 0), (7, 13), (3, 13), (1, 6), (10, 3), (4, 12), (9, 5), (10, 2), (8, 4), (8, 10), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578562", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 13), (2, 8), (12, 6), (3, 1), (5, 14), (3, 4), (1, 5), (13, 8), (1, 11), (13, 0), (8, 8), (0, 9), (8, 3), (6, 13), (4, 12), (3, 2), (3, 0), (13, 12), (13, 13), (3, 13), (11, 9), (12, 3), (5, 12), (12, 7), (9, 5), (1, 7), (0, 7), (5, 3), (10, 10), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209142", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (0, 5), (3, 11), (8, 10), (8, 7), (5, 13), (5, 11), (16, 1), (14, 4), (7, 1), (9, 3), (3, 0), (13, 0), (1, 5), (15, 0), (16, 6), (13, 3), (13, 5), (0, 12), (16, 10), (0, 6), (15, 4), (10, 0), (1, 2), (15, 6), (10, 11), (5, 5), (3, 10), (9, 1), (3, 7), (13, 6), (8, 3), (16, 5), (8, 9), (3, 8), (2, 7), (6, 4), (16, 8), (11, 13), (4, 3), (12, 10), (0, 2), (6, 11), (7, 11), (9, 10), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496026", "dataset": "MATH"}
{"messages": [{"content": "In a 11x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (8, 7), (4, 15), (0, 1), (9, 4), (1, 12), (4, 1), (5, 1), (9, 11), (10, 1), (1, 2), (10, 11), (6, 1), (4, 2), (2, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925915", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (8, 12), (10, 17), (14, 3), (13, 7), (15, 0), (10, 2), (5, 0), (9, 0), (0, 18), (3, 0), (3, 4), (15, 1), (15, 12), (8, 10), (7, 6), (11, 6), (16, 10), (10, 18), (9, 6), (4, 13), (8, 4), (2, 17), (4, 0), (16, 3), (1, 17), (12, 3), (12, 8), (14, 18), (16, 8), (2, 2), (9, 13), (8, 2), (0, 6), (6, 10), (16, 17), (4, 2), (6, 7), (14, 8), (10, 11), (16, 2), (8, 16), (7, 11), (1, 18), (0, 1), (5, 18), (13, 12), (15, 17), (13, 11), (6, 6), (4, 6), (7, 9), (8, 15), (10, 10), (14, 0), (18, 15), (5, 4), (8, 13), (9, 9), (16, 18), (4, 15), (7, 4), (18, 13), (3, 16), (1, 16), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "837507", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 6), (4, 13), (0, 13), (1, 2), (0, 7), (4, 12), (8, 13), (3, 5), (2, 6), (2, 9), (6, 5), (8, 10), (0, 12), (4, 0), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23957", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (11, 1), (6, 10), (9, 16), (2, 16), (2, 7), (2, 11), (2, 3), (11, 2), (17, 10), (8, 16), (5, 15), (5, 0), (10, 7), (13, 4), (13, 10), (12, 13), (2, 17), (2, 0), (5, 2), (6, 5), (2, 1), (16, 11), (9, 8), (15, 13), (2, 9), (13, 2), (0, 9), (13, 16), (0, 13), (10, 16), (10, 3), (1, 0), (6, 6), (1, 6), (17, 13), (15, 18), (7, 6), (15, 11), (13, 8), (14, 9), (9, 11), (10, 0), (8, 14), (8, 4), (0, 5), (17, 14), (10, 15), (15, 12), (12, 5), (6, 7), (4, 12), (5, 14), (11, 14), (0, 10), (8, 1), (5, 8), (12, 18), (13, 7), (9, 0), (0, 14), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814588", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (3, 1), (7, 0), (10, 5), (1, 11), (4, 4), (8, 9), (14, 10), (1, 7), (5, 8), (2, 7), (1, 5), (2, 13), (13, 13), (14, 9), (3, 3), (12, 12), (9, 5), (3, 6), (12, 4), (5, 0), (4, 12), (0, 14), (14, 7), (8, 8), (0, 10), (3, 8), (11, 9), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882322", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (4, 3), (13, 11), (4, 4), (17, 12), (3, 0), (12, 0), (5, 3), (4, 9), (3, 6), (4, 0), (4, 8), (9, 12), (12, 8), (16, 15), (7, 14), (6, 2), (7, 7), (1, 7), (16, 8), (8, 12), (10, 13), (18, 11), (1, 15), (5, 14), (12, 14), (5, 5), (0, 7), (6, 13), (0, 1), (4, 6), (12, 9), (11, 7), (4, 11), (9, 10), (2, 10), (12, 15), (12, 13), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953802", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 14), (11, 16), (7, 16), (12, 15), (1, 13), (17, 14), (7, 15), (14, 6), (10, 3), (8, 5), (14, 9), (10, 2), (16, 13), (14, 16), (3, 5), (6, 11), (16, 10), (0, 1), (5, 0), (3, 0), (8, 0), (2, 15), (3, 2), (16, 7), (17, 8), (13, 4), (2, 11), (9, 11), (7, 7), (12, 6), (4, 13), (9, 3), (9, 7), (7, 2), (14, 11), (12, 14), (3, 8), (7, 0), (12, 7), (3, 9), (4, 12), (10, 9), (15, 6), (7, 5), (2, 0), (17, 9), (0, 8), (0, 10), (5, 8), (13, 9), (1, 10), (10, 10), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877763", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 6), (13, 4), (1, 1), (13, 3), (9, 9), (8, 6), (5, 5), (13, 2), (8, 2), (2, 10), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479565", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 12), (3, 10), (10, 12), (14, 17), (13, 0), (3, 7), (0, 5), (1, 17), (1, 14), (13, 15), (13, 13), (4, 0), (12, 7), (2, 13), (6, 8), (10, 17), (2, 14), (7, 2), (6, 10), (5, 3), (8, 14), (7, 5), (5, 13), (17, 2), (4, 14), (4, 4), (2, 9), (1, 0), (1, 11), (0, 7), (7, 3), (11, 4), (10, 11), (11, 12), (18, 2), (1, 3), (8, 5), (8, 17), (3, 2), (5, 7), (4, 16), (7, 17), (16, 11), (4, 3), (9, 11), (9, 8), (16, 1), (2, 17), (18, 9), (3, 1), (6, 0), (2, 15), (14, 9), (3, 13), (16, 10), (7, 6), (12, 0), (4, 17), (6, 4), (5, 8), (9, 13), (8, 8), (12, 5), (10, 0), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764630", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (9, 11), (0, 1), (5, 12), (7, 7), (9, 6), (0, 10), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277509", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 4), (1, 11), (13, 5), (17, 3), (11, 1), (6, 1), (6, 0), (2, 0), (10, 10), (6, 8), (2, 4), (9, 6), (15, 3), (15, 5), (0, 1), (3, 4), (7, 2), (7, 8), (13, 3), (15, 6), (5, 3), (15, 11), (9, 0), (14, 0), (18, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522790", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 4), (2, 3), (10, 8), (10, 10), (11, 0), (9, 3), (6, 5), (13, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221485", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (6, 6), (3, 5), (10, 15), (2, 9), (3, 7), (1, 2), (15, 11), (16, 6), (7, 18), (12, 0), (4, 18), (14, 3), (10, 18), (5, 7), (13, 11), (12, 18), (4, 0), (3, 12), (9, 7), (5, 3), (16, 14), (9, 12), (4, 6), (3, 4), (14, 14), (12, 11), (5, 2), (11, 15), (16, 0), (13, 3), (15, 12), (3, 10), (4, 15), (6, 15), (9, 18), (5, 15), (1, 15), (3, 6), (8, 5), (2, 17), (5, 10), (8, 6), (11, 14), (2, 3), (13, 12), (5, 16), (1, 10), (13, 2), (7, 1), (15, 10), (6, 9), (8, 0), (12, 1), (6, 8), (11, 7), (0, 3), (13, 8), (9, 13), (12, 5), (5, 5), (16, 13), (16, 7), (2, 18), (0, 17), (7, 0), (10, 0), (0, 7), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624112", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 9), (12, 1), (11, 5), (2, 3), (3, 3), (6, 9), (12, 8), (16, 9), (15, 7), (13, 2), (7, 7), (14, 8), (8, 8), (7, 2), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70273", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 15), (5, 8), (9, 6), (1, 15), (2, 12), (1, 13), (4, 11), (6, 6), (8, 6), (2, 5), (1, 11), (8, 7), (11, 13), (9, 1), (2, 0), (0, 8), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "819398", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (5, 3), (5, 13), (11, 4), (3, 12), (0, 8), (11, 1), (2, 16), (10, 14), (9, 12), (4, 16), (1, 1), (0, 9), (10, 0), (6, 2), (6, 11), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "625068", "dataset": "MATH"}
{"messages": [{"content": "In a 15x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 12), (11, 11), (11, 6), (1, 7), (14, 9), (6, 14), (10, 7), (1, 0), (13, 10), (11, 1), (9, 2), (5, 4), (6, 13), (11, 12), (6, 1), (1, 4), (7, 3), (6, 12), (2, 13), (9, 9), (0, 5), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623189", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 13), (2, 8), (3, 16), (5, 11), (5, 15), (0, 7), (4, 1), (6, 15), (9, 5), (8, 16), (3, 15), (4, 5), (9, 8), (2, 14), (2, 11), (4, 9), (5, 6), (8, 12), (3, 12), (5, 0), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "869235", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (6, 6), (14, 3), (12, 5), (14, 9), (11, 3), (9, 5), (0, 10), (14, 2), (3, 6), (9, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455845", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 4), (11, 2), (1, 1), (1, 5), (5, 0), (8, 5), (6, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432917", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 10), (6, 6), (2, 1), (5, 4), (7, 4), (8, 8), (6, 10), (5, 12), (3, 1), (6, 13), (7, 12), (3, 14), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122855", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 14), (13, 15), (17, 3), (12, 9), (1, 9), (12, 1), (8, 2), (1, 6), (12, 6), (16, 14), (17, 4), (14, 2), (10, 16), (1, 10), (3, 14), (14, 12), (1, 17), (10, 6), (3, 7), (17, 1), (16, 8), (3, 12), (14, 11), (0, 2), (0, 5), (13, 14), (18, 8), (12, 3), (18, 10), (17, 0), (14, 16), (6, 3), (18, 4), (3, 2), (17, 2), (10, 2), (9, 0), (1, 8), (10, 9), (17, 13), (17, 12), (13, 2), (5, 14), (17, 11), (0, 12), (13, 16), (1, 3), (7, 11), (3, 10), (3, 11), (4, 7), (0, 18), (3, 8), (8, 9), (2, 18), (5, 3), (12, 11), (8, 15), (18, 14), (12, 15), (0, 7), (5, 18), (9, 17), (11, 4), (2, 12), (14, 7), (16, 5), (3, 1), (4, 4), (4, 13), (6, 11), (18, 1), (8, 16), (9, 13), (3, 16), (9, 8), (18, 17), (11, 7), (8, 0), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557418", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 12), (6, 3), (2, 5), (4, 3), (5, 0), (10, 11), (0, 3), (7, 10), (5, 1), (4, 11), (10, 3), (10, 5), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485636", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (9, 3), (8, 2), (4, 12), (11, 9), (4, 8), (18, 5), (7, 3), (3, 5), (17, 5), (5, 15), (10, 10), (5, 5), (5, 1), (2, 8), (11, 6), (10, 1), (4, 1), (1, 0), (6, 1), (15, 12), (12, 0), (2, 13), (17, 14), (8, 6), (4, 3), (15, 14), (2, 3), (13, 12), (8, 11), (8, 10), (1, 12), (16, 14), (12, 11), (12, 5), (13, 8), (14, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870763", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (3, 17), (4, 0), (3, 16), (4, 11), (8, 3), (7, 9), (7, 2), (0, 12), (6, 11), (2, 3), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816037", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 2), (6, 2), (7, 4), (9, 4), (2, 0), (11, 0), (2, 9), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292239", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 2), (3, 8), (3, 2), (4, 7), (6, 2), (3, 1), (4, 2), (1, 5), (1, 6), (11, 4), (7, 0), (11, 2), (5, 4), (1, 4), (3, 10), (7, 8), (2, 1), (7, 7), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76429", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (6, 11), (8, 7), (1, 9), (0, 8), (3, 5), (2, 12), (2, 14), (5, 7), (3, 3), (0, 11), (9, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860272", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (7, 16), (7, 10), (0, 13), (7, 0), (2, 15), (5, 8), (3, 6), (3, 0), (4, 5), (9, 10), (8, 14), (5, 5), (9, 1), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579603", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 6), (7, 4), (4, 3), (1, 6), (4, 1), (8, 1), (5, 4), (14, 9), (14, 13), (11, 12), (8, 5), (5, 13), (9, 8), (5, 2), (14, 11), (1, 7), (6, 3), (7, 9), (13, 12), (6, 2), (1, 1), (15, 3), (0, 13), (10, 1), (11, 0), (4, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999089", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 11), (8, 0), (7, 9), (5, 13), (11, 7), (10, 3), (11, 12), (2, 7), (5, 9), (0, 4), (10, 6), (10, 4), (0, 5), (1, 10), (4, 13), (6, 6), (3, 12), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229205", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 5), (18, 3), (8, 4), (13, 7), (3, 2), (7, 8), (15, 7), (17, 8), (0, 12), (1, 13), (14, 8), (18, 1), (8, 7), (3, 10), (7, 4), (15, 11), (6, 7), (2, 3), (2, 7), (8, 1), (14, 14), (5, 7), (13, 10), (9, 11), (17, 5), (9, 14), (4, 1), (12, 0), (12, 4), (2, 10), (7, 2), (10, 12), (12, 2), (0, 7), (5, 1), (1, 9), (11, 12), (8, 5), (4, 2), (16, 2), (11, 14), (16, 0), (2, 8), (14, 0), (3, 1), (18, 5), (9, 13), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892928", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 10), (13, 8), (9, 1), (18, 3), (4, 15), (3, 10), (4, 5), (9, 9), (16, 10), (15, 2), (4, 9), (15, 15), (10, 5), (14, 14), (9, 13), (0, 10), (4, 0), (0, 7), (11, 4), (5, 7), (4, 2), (3, 8), (9, 12), (18, 9), (7, 14), (18, 8), (8, 13), (16, 11), (6, 4), (16, 8), (17, 3), (10, 11), (4, 14), (4, 1), (16, 0), (17, 0), (2, 6), (12, 9), (3, 2), (8, 3), (17, 13), (13, 1), (1, 6), (16, 7), (12, 5), (11, 11), (18, 1), (14, 2), (12, 0), (5, 1), (17, 6), (14, 15), (7, 15), (15, 14), (16, 5), (1, 14), (11, 13), (6, 8), (11, 12), (14, 8), (4, 13), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522994", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 2), (3, 3), (12, 6), (12, 5), (11, 9), (9, 3), (2, 2), (0, 6), (0, 9), (6, 5), (14, 9), (16, 2), (13, 5), (5, 7), (1, 5), (6, 9), (16, 6), (2, 6), (5, 2), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53347", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (3, 8), (4, 7), (4, 0), (4, 4), (1, 1), (8, 5), (0, 3), (9, 11), (8, 7), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17368", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (10, 3), (2, 11), (7, 8), (8, 5), (6, 6), (3, 10), (10, 7), (6, 1), (3, 8), (9, 9), (7, 1), (9, 3), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57361", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 14), (16, 10), (15, 10), (15, 5), (13, 5), (0, 11), (3, 8), (4, 11), (16, 1), (6, 10), (12, 14), (11, 14), (3, 12), (9, 1), (13, 10), (12, 2), (12, 8), (16, 12), (14, 8), (8, 13), (17, 0), (6, 0), (3, 11), (14, 7), (7, 8), (12, 11), (7, 6), (9, 6), (2, 5), (13, 2), (7, 1), (2, 10), (14, 2), (11, 9), (10, 13), (7, 7), (14, 5), (7, 13), (14, 11), (1, 8), (5, 2), (4, 4), (9, 2), (5, 1), (3, 7), (16, 6), (4, 9), (14, 3), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785492", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (10, 16), (0, 8), (5, 0), (11, 8), (0, 1), (8, 1), (1, 17), (10, 13), (4, 12), (4, 14), (6, 16), (9, 2), (1, 8), (7, 7), (7, 3), (10, 5), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "846379", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (9, 6), (2, 7), (7, 4), (1, 6), (0, 5), (3, 5), (7, 6), (8, 9), (6, 0), (5, 1), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5200", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 14), (0, 7), (6, 10), (11, 5), (2, 12), (5, 0), (5, 8), (8, 2), (12, 3), (12, 8), (9, 9), (4, 6), (2, 16), (4, 10), (2, 6), (6, 9), (2, 17), (2, 2), (8, 3), (2, 13), (12, 9), (11, 11), (2, 14), (11, 0), (3, 15), (6, 17), (7, 4), (6, 13), (12, 11), (8, 11), (3, 10), (2, 15), (5, 14), (10, 1), (12, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610320", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (14, 1), (12, 8), (6, 4), (11, 6), (8, 4), (11, 3), (9, 0), (7, 4), (7, 8), (8, 0), (11, 8), (15, 3), (3, 6), (8, 2), (7, 5), (16, 7), (3, 8), (11, 2), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88576", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (1, 7), (6, 10), (1, 10), (1, 11), (4, 5), (7, 5), (2, 0), (4, 0), (1, 8), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115038", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (3, 7), (13, 12), (10, 15), (4, 5), (0, 14), (6, 6), (7, 4), (8, 2), (1, 4), (10, 14), (11, 12), (7, 13), (2, 8), (2, 13), (5, 14), (2, 2), (11, 3), (2, 4), (9, 14), (0, 9), (3, 17), (2, 3), (10, 12), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956296", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (8, 1), (2, 8), (4, 9), (2, 3), (10, 0), (9, 5), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34920", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 12), (2, 17), (2, 7), (9, 17), (10, 12), (2, 15), (10, 8), (0, 3), (4, 11), (4, 15), (12, 4), (4, 7), (10, 15), (6, 2), (5, 1), (9, 7), (0, 1), (0, 12), (1, 16), (7, 10), (4, 10), (10, 9), (0, 7), (11, 7), (2, 8), (6, 0), (10, 1), (3, 5), (7, 2), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960959", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (10, 4), (9, 9), (4, 3), (1, 2), (11, 14), (3, 16), (7, 4), (8, 3), (13, 8), (0, 4), (5, 12), (12, 11), (2, 8), (8, 12), (2, 13), (2, 11), (6, 0), (1, 11), (10, 10), (10, 6), (10, 9), (0, 16), (1, 1), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867230", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (11, 5), (7, 8), (11, 2), (2, 15), (3, 15), (13, 1), (8, 14), (3, 12), (16, 7), (12, 12), (0, 10), (6, 11), (3, 8), (14, 1), (12, 14), (0, 8), (16, 14), (13, 13), (12, 5), (10, 0), (9, 9), (7, 13), (13, 12), (5, 5), (1, 2), (0, 2), (3, 14), (6, 10), (13, 11), (10, 2), (3, 2), (9, 3), (13, 0), (0, 11), (14, 9), (7, 6), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956408", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 4), (13, 1), (10, 7), (3, 0), (5, 4), (6, 7), (4, 0), (14, 9), (3, 5), (0, 2), (12, 10), (13, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97319", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (5, 9), (5, 11), (8, 6), (4, 12), (12, 9), (7, 3), (5, 0), (1, 2), (2, 2), (13, 7), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854927", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 9), (9, 8), (8, 3), (7, 3), (8, 10), (1, 17), (6, 5), (11, 5), (15, 6), (18, 4), (11, 11), (9, 13), (17, 6), (5, 17), (1, 1), (3, 1), (2, 3), (12, 9), (10, 1), (17, 16), (6, 1), (7, 4), (2, 4), (16, 11), (2, 8), (13, 7), (10, 8), (12, 7), (18, 2), (4, 10), (16, 3), (1, 16), (6, 2), (6, 0), (10, 2), (17, 12), (5, 9), (8, 11), (14, 2), (17, 17), (15, 14), (4, 14), (0, 7), (4, 15), (12, 4), (16, 0), (2, 11), (13, 4), (3, 9), (16, 9), (16, 5), (9, 10), (13, 1), (0, 15), (15, 17), (0, 10), (17, 2), (9, 5), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971765", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 9), (0, 5), (13, 0), (17, 11), (2, 18), (17, 17), (4, 15), (12, 2), (17, 7), (15, 15), (11, 12), (1, 7), (10, 3), (1, 2), (1, 10), (5, 1), (6, 13), (12, 16), (0, 7), (17, 4), (13, 11), (15, 12), (14, 7), (11, 16), (13, 12), (9, 13), (5, 17), (10, 12), (13, 17), (6, 12), (11, 18), (6, 1), (17, 15), (0, 15), (7, 5), (13, 14), (11, 17), (3, 1), (14, 3), (13, 3), (15, 1), (12, 13), (15, 11), (0, 12), (4, 10), (11, 11), (14, 16), (9, 18), (11, 14), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996267", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (2, 10), (1, 2), (0, 5), (6, 7), (3, 5), (1, 0), (4, 1), (4, 9), (0, 10), (8, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5338", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (1, 4), (7, 14), (6, 8), (3, 5), (8, 13), (10, 13), (10, 8), (7, 2), (10, 14), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246082", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 9), (12, 5), (10, 3), (1, 4), (17, 6), (15, 13), (15, 2), (1, 3), (10, 4), (14, 13), (1, 13), (3, 1), (1, 5), (6, 2), (3, 5), (8, 16), (7, 15), (7, 8), (13, 5), (3, 7), (17, 13), (7, 13), (1, 11), (11, 16), (7, 6), (14, 6), (17, 0), (2, 13), (11, 6), (13, 2), (7, 5), (10, 2), (2, 9), (15, 14), (11, 1), (13, 4), (9, 10), (4, 12), (4, 15), (3, 11), (3, 15), (0, 1), (2, 5), (11, 14), (10, 7), (5, 13), (7, 9), (2, 8), (14, 1), (4, 6), (3, 6), (15, 8), (13, 16), (5, 16), (7, 1), (16, 9), (14, 2), (10, 11), (0, 8), (6, 12), (9, 6), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907482", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 4), (13, 9), (6, 5), (3, 8), (10, 7), (6, 9), (6, 12), (18, 12), (0, 3), (4, 2), (2, 4), (5, 9), (3, 10), (15, 5), (14, 4), (18, 4), (1, 13), (10, 1), (10, 10), (11, 12), (9, 6), (8, 9), (14, 0), (12, 9), (5, 13), (7, 5), (14, 2), (8, 13), (2, 2), (17, 3), (0, 10), (8, 12), (15, 2), (15, 0), (1, 0), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "989573", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (4, 17), (5, 16), (8, 15), (7, 2), (5, 9), (9, 0), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371642", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (13, 1), (11, 2), (11, 5), (13, 0), (10, 5), (0, 8), (7, 5), (12, 5), (11, 10), (3, 3), (8, 1), (5, 1), (17, 3), (8, 0), (4, 0), (18, 7), (13, 4), (15, 4), (16, 4), (5, 8), (5, 6), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "754463", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 16), (5, 14), (1, 14), (5, 8), (4, 17), (3, 6), (8, 11), (5, 17), (10, 11), (8, 9), (5, 5), (5, 15), (10, 14), (2, 1), (2, 0), (11, 12), (10, 2), (2, 8), (6, 12), (5, 11), (0, 11), (10, 0), (10, 16), (0, 18), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608876", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (3, 1), (8, 0), (5, 7), (6, 8), (2, 4), (8, 7), (7, 2), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11316", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (11, 8), (9, 2), (11, 2), (6, 2), (0, 13), (11, 10), (9, 15), (8, 1), (5, 7), (8, 6), (10, 2), (2, 12), (11, 4), (3, 15), (1, 12), (4, 15), (8, 3), (14, 1), (1, 7), (0, 15), (4, 8), (9, 0), (7, 3), (14, 13), (8, 4), (4, 9), (10, 7), (2, 0), (6, 11), (7, 8), (5, 1), (3, 5), (0, 11), (8, 13), (3, 14), (9, 4), (12, 5), (10, 5), (12, 3), (1, 14), (1, 11), (0, 5), (5, 14), (8, 8), (4, 7), (9, 3), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566066", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (10, 12), (12, 2), (11, 8), (4, 2), (0, 6), (7, 5), (14, 5), (4, 1), (14, 9), (9, 9), (15, 4), (7, 10), (8, 9), (3, 5), (18, 8), (14, 11), (6, 2), (7, 8), (15, 11), (8, 6), (6, 0), (9, 5), (0, 10), (17, 9), (6, 10), (8, 5), (16, 8), (16, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "727351", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 4), (13, 10), (8, 1), (9, 6), (1, 6), (3, 1), (12, 4), (7, 8), (3, 4), (14, 0), (1, 5), (1, 7), (9, 5), (8, 6), (1, 3), (10, 5), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99544", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 9), (7, 1), (8, 12), (9, 1), (10, 9), (1, 4), (8, 10), (0, 6), (5, 10), (8, 6), (4, 0), (4, 8), (1, 9), (0, 8), (10, 3), (6, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109082", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 9), (2, 9), (1, 9), (4, 12), (2, 0), (9, 2), (9, 1), (5, 10), (6, 11), (7, 8), (8, 8), (8, 4), (4, 8), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54155", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (15, 2), (5, 6), (1, 3), (1, 1), (5, 1), (3, 6), (4, 8), (6, 3), (11, 8), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285201", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (4, 8), (1, 3), (9, 7), (9, 2), (8, 10), (2, 4), (5, 8), (1, 0), (1, 6), (1, 4), (1, 8), (3, 5), (6, 8), (9, 0), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8103", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (4, 6), (9, 0), (7, 5), (5, 1), (2, 4), (9, 4), (4, 0), (0, 3), (8, 3), (3, 5), (6, 9), (5, 5), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9403", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (13, 1), (0, 2), (1, 5), (4, 9), (9, 4), (4, 1), (3, 2), (0, 5), (7, 1), (8, 0), (10, 0), (0, 3), (10, 1), (6, 1), (6, 7), (0, 6), (2, 3), (5, 2), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11094", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 10), (8, 6), (11, 3), (7, 10), (9, 0), (9, 4), (10, 1), (10, 5), (2, 8), (9, 3), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180017", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 4), (0, 7), (1, 2), (6, 0), (3, 6), (7, 9), (2, 1), (4, 3), (11, 15), (5, 2), (0, 14), (3, 5), (0, 10), (9, 14), (7, 4), (9, 8), (2, 2), (18, 10), (14, 17), (8, 4), (6, 17), (15, 12), (18, 5), (17, 4), (11, 3), (11, 12), (3, 8), (1, 4), (12, 14), (14, 6), (13, 1), (11, 5), (3, 9), (18, 16), (15, 10), (0, 15), (9, 13), (18, 14), (12, 10), (7, 7), (11, 7), (7, 1), (3, 2), (18, 1), (5, 0), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705898", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 4), (5, 9), (7, 16), (0, 10), (12, 8), (6, 9), (10, 6), (10, 12), (13, 14), (12, 9), (16, 14), (15, 6), (7, 15), (14, 18), (4, 10), (16, 3), (1, 5), (6, 18), (14, 17), (11, 12), (11, 8), (13, 3), (4, 6), (1, 18), (6, 6), (11, 14), (6, 7), (13, 15), (11, 9), (11, 13), (13, 17), (11, 1), (4, 11), (2, 6), (7, 12), (12, 3), (14, 2), (11, 7), (1, 4), (6, 13), (8, 10), (3, 6), (16, 7), (0, 16), (11, 0), (13, 9), (15, 11), (2, 0), (3, 14), (3, 17), (16, 13), (3, 12), (7, 5), (16, 15), (12, 6), (5, 6), (10, 2), (1, 6), (5, 0), (6, 14), (14, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865758", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (5, 4), (12, 3), (0, 5), (3, 1), (10, 5), (2, 9), (9, 10), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167154", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (3, 2), (1, 12), (9, 0), (4, 9), (1, 4), (13, 10), (0, 16), (9, 17), (2, 14), (0, 3), (4, 11), (11, 11), (9, 13), (10, 17), (0, 14), (2, 2), (13, 8), (1, 0), (9, 4), (1, 15), (1, 11), (9, 10), (4, 7), (2, 6), (9, 6), (12, 9), (12, 5), (4, 0), (6, 7), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780708", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (11, 8), (8, 5), (12, 8), (6, 2), (11, 4), (9, 5), (1, 8), (8, 1), (2, 5), (11, 3), (1, 3), (6, 6), (4, 9), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30423", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 17), (4, 6), (1, 7), (4, 18), (4, 15), (2, 2), (3, 9), (8, 1), (7, 14), (1, 1), (4, 4), (2, 13), (1, 2), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41392", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (4, 13), (15, 8), (13, 11), (10, 5), (9, 0), (6, 5), (13, 12), (9, 12), (2, 11), (7, 8), (8, 9), (15, 1), (14, 13), (3, 10), (1, 13), (11, 4), (17, 9), (10, 6), (14, 11), (4, 10), (1, 11), (13, 13), (7, 5), (3, 8), (8, 13), (12, 2), (11, 1), (8, 7), (1, 8), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822630", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (5, 9), (8, 2), (9, 2), (5, 5), (3, 8), (0, 8), (10, 4), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41300", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (9, 3), (3, 1), (7, 9), (2, 7), (1, 11), (6, 3), (5, 5), (1, 5), (1, 9), (5, 9), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330089", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (6, 16), (0, 14), (4, 9), (3, 8), (2, 4), (5, 17), (14, 7), (6, 14), (3, 4), (6, 6), (3, 9), (12, 11), (12, 3), (13, 4), (1, 1), (13, 10), (3, 16), (8, 6), (11, 8), (8, 5), (5, 0), (10, 4), (6, 1), (2, 16), (11, 14), (4, 17), (8, 12), (13, 2), (3, 13), (6, 4), (14, 16), (11, 4), (0, 3), (6, 3), (14, 17), (2, 5), (9, 7), (6, 9), (8, 10), (7, 16), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "990723", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 14), (3, 2), (11, 12), (6, 8), (6, 7), (8, 2), (13, 2), (0, 16), (1, 18), (7, 0), (7, 13), (7, 18), (6, 11), (13, 8), (1, 9), (6, 6), (13, 10), (3, 6), (11, 0), (7, 14), (3, 15), (12, 12), (8, 17), (13, 0), (11, 15), (0, 15), (7, 17), (12, 6), (13, 15), (4, 4), (5, 5), (8, 3), (3, 8), (8, 13), (10, 12), (7, 2), (10, 5), (7, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "809703", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (0, 10), (1, 8), (5, 8), (15, 6), (14, 1), (8, 2), (0, 7), (9, 7), (9, 8), (6, 2), (11, 2), (13, 1), (12, 3), (11, 0), (5, 7), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752475", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (15, 8), (12, 4), (7, 9), (2, 9), (7, 6), (9, 3), (5, 7), (9, 2), (17, 0), (15, 6), (1, 2), (13, 0), (17, 9), (11, 5), (18, 6), (3, 8), (17, 6), (1, 10), (13, 3), (0, 8), (16, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981696", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (16, 5), (1, 8), (2, 3), (10, 2), (11, 7), (7, 4), (9, 1), (12, 1), (13, 6), (2, 1), (2, 7), (1, 6), (16, 8), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102781", "dataset": "MATH"}
{"messages": [{"content": "In a 13x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (10, 2), (6, 9), (3, 6), (6, 10), (4, 7), (11, 3), (3, 3), (1, 8), (2, 6), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156800", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (10, 4), (2, 0), (1, 2), (9, 5), (8, 2), (12, 0), (0, 6), (12, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150292", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 14), (4, 10), (6, 4), (15, 2), (14, 4), (5, 7), (10, 6), (7, 14), (7, 16), (5, 4), (10, 5), (15, 4), (11, 11), (7, 9), (13, 9), (16, 4), (10, 17), (11, 2), (7, 5), (4, 17), (3, 3), (9, 10), (14, 15), (10, 9), (15, 3), (13, 3), (12, 4), (6, 0), (15, 14), (4, 0), (2, 16), (16, 2), (8, 14), (10, 2), (5, 16), (15, 16), (13, 0), (8, 13), (12, 7), (8, 4), (3, 0), (4, 3), (14, 2), (16, 9), (8, 7), (16, 11), (0, 5), (11, 4), (14, 6), (0, 10), (4, 5), (2, 10), (2, 2), (0, 9), (16, 10), (12, 9), (3, 5), (6, 9), (11, 18), (1, 16), (10, 8), (3, 9), (16, 12), (16, 16), (0, 13), (16, 0), (5, 15), (4, 6), (6, 12), (13, 18), (5, 18), (13, 13), (5, 1), (14, 1), (10, 7), (9, 7), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610215", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (7, 0), (9, 6), (2, 7), (0, 3), (4, 6), (9, 0), (8, 8), (2, 9), (2, 8), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8787", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (6, 0), (12, 5), (8, 2), (12, 4), (4, 0), (4, 12), (15, 2), (3, 8), (14, 9), (1, 3), (11, 11), (11, 1), (0, 10), (1, 12), (13, 0), (3, 12), (14, 5), (14, 8), (5, 7), (4, 8), (5, 13), (12, 0), (9, 0), (5, 5), (5, 8), (2, 9), (13, 9), (8, 12), (1, 7), (3, 6), (13, 12), (2, 5), (14, 0), (14, 7), (7, 10), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445790", "dataset": "MATH"}
{"messages": [{"content": "In a 14x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 17), (0, 11), (3, 5), (4, 11), (5, 3), (5, 10), (2, 11), (12, 10), (1, 2), (8, 12), (0, 12), (1, 5), (8, 8), (0, 10), (5, 14), (13, 0), (9, 8), (6, 17), (8, 14), (3, 7), (10, 14), (6, 13), (13, 1), (1, 13), (8, 16), (6, 14), (0, 3), (11, 4), (13, 15), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999371", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 0), (3, 9), (9, 5), (2, 3), (3, 0), (2, 11), (8, 3), (7, 6), (7, 4), (5, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227801", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 14), (9, 7), (12, 7), (5, 14), (15, 10), (13, 15), (11, 4), (13, 12), (8, 8), (3, 1), (12, 4), (5, 1), (3, 5), (4, 2), (16, 2), (8, 12), (2, 10), (11, 10), (10, 5), (9, 2), (0, 13), (11, 14), (16, 3), (8, 5), (4, 14), (2, 2), (0, 4), (16, 5), (8, 15), (9, 15), (14, 5), (5, 7), (10, 15), (1, 12), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547403", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 13), (1, 6), (1, 3), (2, 9), (8, 10), (5, 15), (13, 15), (15, 9), (15, 11), (1, 11), (5, 10), (4, 7), (4, 12), (18, 9), (3, 5), (8, 4), (17, 8), (14, 3), (9, 3), (2, 14), (7, 7), (11, 8), (3, 6), (4, 8), (5, 11), (18, 8), (1, 0), (8, 7), (13, 1), (9, 2), (11, 0), (14, 8), (13, 12), (18, 10), (9, 13), (12, 4), (4, 4), (15, 10), (7, 2), (13, 10), (7, 4), (1, 7), (5, 13), (5, 6), (9, 1), (10, 0), (7, 11), (4, 14), (13, 9), (5, 7), (15, 3), (16, 8), (17, 2), (10, 14), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981110", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 9), (1, 8), (8, 0), (7, 8), (12, 11), (5, 11), (13, 8), (2, 6), (16, 13), (14, 3), (16, 11), (4, 10), (4, 0), (7, 10), (0, 7), (1, 10), (12, 1), (17, 3), (12, 3), (6, 1), (2, 8), (0, 2), (12, 13), (7, 1), (4, 13), (4, 5), (8, 12), (17, 4), (12, 12), (6, 9), (2, 5), (1, 2), (6, 4), (12, 10), (12, 2), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913234", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (6, 15), (1, 16), (4, 1), (1, 7), (0, 6), (1, 12), (9, 4), (0, 7), (8, 13), (3, 13), (6, 5), (3, 16), (4, 10), (8, 4), (2, 2), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707835", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (9, 6), (2, 9), (10, 13), (1, 1), (6, 7), (6, 6), (10, 2), (5, 3), (4, 3), (9, 8), (0, 8), (3, 16), (5, 5), (12, 4), (2, 1), (12, 6), (10, 0), (9, 5), (6, 3), (8, 2), (1, 0), (7, 6), (2, 11), (5, 13), (4, 13), (4, 14), (6, 10), (6, 4), (7, 4), (9, 10), (10, 8), (1, 9), (2, 12), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658189", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (3, 0), (2, 2), (1, 7), (7, 1), (12, 2), (10, 10), (5, 8), (8, 3), (15, 3), (2, 11), (16, 10), (1, 6), (2, 5), (5, 9), (12, 11), (15, 2), (6, 3), (9, 5), (3, 3), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257562", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (15, 1), (6, 0), (6, 11), (12, 3), (9, 5), (16, 0), (10, 12), (16, 10), (12, 12), (7, 3), (3, 2), (10, 0), (14, 1), (3, 1), (7, 12), (9, 12), (10, 7), (9, 9), (16, 1), (17, 6), (11, 3), (10, 4), (8, 7), (4, 6), (15, 8), (14, 9), (11, 9), (4, 10), (10, 8), (4, 9), (13, 13), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977550", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 2), (14, 4), (2, 1), (9, 7), (0, 7), (8, 0), (1, 6), (6, 7), (0, 1), (1, 9), (13, 4), (3, 2), (8, 1), (3, 9), (12, 4), (4, 1), (10, 3), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28318", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 12), (8, 12), (4, 0), (6, 2), (5, 4), (7, 1), (2, 14), (2, 1), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450430", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (9, 7), (5, 5), (5, 3), (7, 14), (0, 17), (5, 1), (8, 6), (5, 10), (0, 16), (1, 12), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "637759", "dataset": "MATH"}
{"messages": [{"content": "In a 17x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (10, 9), (4, 3), (2, 3), (12, 0), (5, 2), (9, 3), (9, 11), (12, 7), (12, 12), (1, 13), (5, 3), (13, 0), (2, 5), (3, 2), (9, 4), (12, 6), (5, 5), (14, 5), (14, 7), (10, 4), (2, 9), (14, 3), (1, 11), (8, 13), (9, 13), (0, 10), (6, 3), (13, 1), (8, 2), (13, 12), (7, 6), (2, 12), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "983476", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (10, 12), (5, 8), (10, 10), (4, 15), (8, 11), (8, 3), (5, 16), (0, 11), (11, 7), (5, 12), (2, 12), (5, 7), (11, 4), (3, 0), (3, 7), (5, 1), (7, 8), (7, 4), (1, 2), (10, 13), (6, 1), (8, 1), (7, 7), (8, 2), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "852333", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (14, 9), (7, 2), (3, 12), (12, 2), (13, 1), (9, 2), (1, 14), (0, 6), (1, 13), (8, 14), (15, 9), (15, 10), (8, 6), (5, 0), (13, 9), (7, 4), (13, 11), (14, 5), (0, 7), (7, 13), (10, 11), (12, 12), (8, 3), (3, 1), (11, 3), (6, 5), (9, 10), (10, 14), (6, 11), (14, 4), (8, 4), (7, 9), (9, 11), (12, 5), (12, 8), (0, 13), (13, 2), (12, 0), (14, 3), (0, 5), (13, 10), (5, 1), (14, 14), (9, 4), (10, 7), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836577", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 5), (2, 8), (13, 2), (15, 5), (17, 6), (16, 8), (8, 6), (9, 1), (0, 4), (14, 9), (11, 6), (10, 8), (12, 1), (14, 1), (15, 0), (10, 0), (8, 10), (16, 11), (9, 3), (3, 8), (10, 13), (6, 14), (4, 10), (9, 13), (13, 4), (8, 8), (2, 5), (10, 1), (0, 8), (10, 10), (10, 6), (7, 5), (7, 11), (16, 5), (15, 13), (9, 9), (13, 11), (2, 10), (2, 6), (12, 4), (5, 12), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521741", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 13), (4, 3), (8, 9), (10, 2), (8, 16), (4, 4), (2, 5), (7, 17), (0, 14), (1, 8), (0, 12), (1, 11), (2, 2), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951658", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (9, 4), (14, 3), (3, 10), (3, 14), (2, 11), (5, 8), (8, 4), (6, 4), (3, 3), (15, 7), (4, 7), (2, 13), (3, 4), (7, 6), (14, 14), (4, 11), (14, 10), (14, 0), (8, 2), (1, 9), (4, 2), (16, 4), (9, 5), (8, 5), (13, 13), (10, 6), (11, 0), (12, 4), (8, 13), (0, 4), (3, 1), (5, 3), (10, 14), (5, 7), (10, 13), (6, 12), (17, 4), (3, 11), (10, 1), (5, 12), (7, 11), (3, 12), (7, 5), (16, 5), (17, 8), (2, 7), (9, 10), (17, 9), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "962836", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (9, 5), (8, 6), (3, 0), (1, 5), (4, 1), (1, 3), (2, 9), (11, 0), (6, 7), (9, 8), (3, 8), (0, 3), (9, 3), (10, 0), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10626", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (7, 10), (7, 0), (5, 15), (5, 1), (9, 7), (1, 10), (6, 7), (1, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705274", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (10, 3), (12, 14), (4, 12), (6, 13), (0, 8), (2, 0), (7, 5), (12, 0), (6, 1), (8, 3), (3, 11), (13, 0), (2, 2), (7, 13), (10, 4), (8, 1), (7, 12), (7, 11), (11, 13), (11, 8), (13, 9), (12, 3), (1, 7), (8, 14), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "828997", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (8, 11), (8, 12), (2, 8), (5, 6), (0, 3), (4, 4), (4, 1), (0, 6), (0, 2), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31120", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 0), (3, 6), (5, 0), (2, 7), (1, 5), (10, 7), (0, 4), (8, 7), (2, 6), (10, 9), (8, 8), (5, 3), (5, 12), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155261", "dataset": "MATH"}
{"messages": [{"content": "In a 19x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 2), (5, 9), (13, 11), (9, 8), (11, 8), (0, 2), (7, 9), (16, 5), (13, 7), (5, 13), (13, 8), (3, 4), (3, 13), (18, 12), (4, 8), (17, 16), (1, 6), (5, 1), (0, 9), (15, 3), (2, 6), (13, 2), (2, 15), (7, 8), (1, 5), (13, 4), (4, 15), (8, 0), (18, 8), (0, 14), (3, 15), (0, 16), (2, 2), (13, 6), (1, 14), (16, 2), (17, 4), (0, 15), (8, 16), (11, 1), (2, 7), (12, 1), (0, 10), (8, 5), (1, 1), (7, 4), (12, 14), (17, 13), (11, 5), (7, 6), (15, 7), (9, 4), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "880762", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (9, 7), (3, 10), (9, 0), (14, 0), (17, 0), (11, 3), (4, 6), (6, 6), (7, 4), (12, 6), (15, 6), (5, 0), (4, 7), (3, 2), (2, 2), (13, 9), (0, 3), (2, 0), (0, 2), (9, 1), (4, 3), (6, 9), (1, 10), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119778", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (6, 0), (5, 11), (5, 6), (4, 10), (4, 11), (2, 6), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187079", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (7, 1), (4, 2), (10, 13), (10, 5), (8, 13), (8, 10), (3, 1), (7, 4), (0, 9), (12, 0), (1, 0), (8, 4), (11, 1), (5, 2), (2, 15), (10, 9), (0, 7), (5, 10), (5, 13), (3, 10), (3, 4), (1, 12), (11, 16), (12, 15), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661611", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (8, 2), (4, 13), (1, 7), (7, 16), (10, 9), (9, 10), (8, 15), (6, 5), (8, 11), (11, 8), (10, 2), (7, 1), (2, 11), (5, 6), (1, 12), (7, 10), (3, 1), (10, 8), (0, 16), (7, 2), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730081", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (9, 12), (3, 9), (0, 3), (7, 12), (8, 1), (10, 7), (7, 10), (5, 6), (4, 6), (3, 6), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425152", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (1, 2), (3, 1), (10, 11), (15, 5), (15, 2), (11, 3), (7, 8), (14, 4), (13, 0), (17, 1), (17, 2), (4, 1), (11, 5), (4, 8), (15, 4), (1, 5), (13, 1), (6, 5), (8, 2), (14, 10), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877530", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (10, 3), (11, 2), (3, 0), (10, 8), (3, 1), (11, 6), (3, 5), (9, 4), (7, 8), (6, 1), (4, 9), (3, 8), (2, 1), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27957", "dataset": "MATH"}
{"messages": [{"content": "In a 17x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 8), (2, 1), (6, 3), (5, 4), (3, 7), (5, 8), (11, 7), (6, 1), (2, 3), (16, 1), (16, 0), (6, 8), (3, 1), (11, 3), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50247", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 13), (4, 1), (3, 8), (11, 1), (9, 11), (15, 6), (12, 0), (7, 7), (8, 7), (1, 7), (9, 12), (3, 14), (2, 5), (7, 10), (16, 1), (18, 11), (18, 5), (8, 4), (12, 11), (10, 0), (3, 2), (18, 8), (7, 14), (11, 3), (11, 12), (2, 2), (16, 8), (10, 8), (16, 2), (9, 10), (9, 4), (5, 1), (12, 9), (9, 13), (13, 1), (12, 10), (14, 1), (10, 7), (7, 2), (11, 0), (17, 7), (14, 3), (11, 7), (17, 4), (10, 1), (5, 7), (0, 10), (4, 10), (4, 13), (12, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242550", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (15, 1), (11, 2), (5, 3), (2, 6), (16, 3), (9, 5), (3, 5), (8, 10), (16, 2), (3, 9), (10, 4), (8, 11), (7, 4), (3, 6), (14, 4), (9, 4), (6, 7), (3, 2), (1, 7), (8, 3), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536196", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 0), (13, 6), (3, 10), (15, 0), (13, 7), (5, 3), (1, 0), (0, 10), (8, 3), (13, 9), (1, 10), (7, 2), (15, 5), (11, 7), (2, 9), (1, 1), (4, 0), (12, 3), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114484", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (7, 5), (8, 2), (7, 1), (2, 0), (12, 0), (4, 8), (7, 3), (3, 6), (8, 5), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72159", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 8), (9, 2), (7, 2), (9, 11), (5, 0), (9, 4), (9, 7), (13, 7), (13, 2), (8, 12), (2, 1), (4, 12), (1, 8), (12, 6), (7, 12), (4, 9), (0, 5), (11, 0), (5, 11), (13, 9), (4, 1), (9, 6), (7, 1), (14, 2), (5, 5), (18, 7), (8, 8), (18, 10), (6, 1), (15, 3), (2, 10), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734411", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (6, 1), (6, 10), (3, 10), (2, 2), (0, 5), (11, 4), (1, 5), (8, 3), (8, 5), (0, 10), (5, 2), (5, 8), (11, 8), (9, 4), (8, 10), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118639", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 10), (11, 4), (3, 12), (14, 9), (0, 9), (12, 8), (0, 13), (12, 1), (0, 7), (11, 11), (2, 11), (9, 12), (3, 7), (14, 13), (9, 5), (4, 6), (8, 10), (3, 15), (7, 5), (1, 8), (6, 11), (8, 1), (12, 10), (6, 15), (9, 9), (10, 3), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799045", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 4), (7, 9), (10, 7), (6, 2), (2, 5), (9, 6), (10, 1), (6, 11), (4, 3), (10, 4), (0, 9), (0, 5), (10, 3), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16250", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (14, 14), (4, 10), (0, 7), (9, 9), (9, 14), (9, 8), (4, 5), (7, 3), (1, 2), (10, 6), (0, 5), (11, 6), (15, 3), (4, 0), (5, 3), (0, 1), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940972", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 5), (10, 10), (4, 11), (13, 1), (7, 6), (12, 14), (11, 8), (0, 12), (11, 10), (11, 12), (7, 4), (2, 10), (3, 10), (13, 14), (3, 4), (14, 0), (10, 3), (17, 9), (16, 2), (4, 0), (6, 13), (1, 11), (17, 4), (13, 7), (0, 11), (16, 13), (16, 0), (7, 11), (12, 5), (16, 8), (14, 6), (4, 2), (15, 10), (13, 10), (3, 8), (10, 2), (13, 5), (3, 14), (0, 3), (9, 3), (2, 11), (16, 10), (5, 4), (2, 14), (1, 8), (16, 14), (4, 8), (14, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "765680", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (7, 2), (11, 6), (9, 8), (7, 9), (12, 11), (9, 1), (3, 5), (8, 7), (3, 9), (3, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185836", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 6), (0, 8), (8, 1), (9, 11), (0, 9), (2, 10), (15, 6), (7, 4), (17, 0), (11, 2), (9, 9), (0, 11), (3, 10), (16, 3), (4, 9), (17, 8), (5, 0), (15, 2), (7, 0), (17, 7), (4, 5), (2, 3), (3, 3), (3, 6), (9, 6), (3, 0), (14, 11), (6, 2), (4, 7), (9, 1), (6, 7), (15, 10), (10, 6), (9, 0), (0, 2), (5, 11), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941822", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 11), (16, 8), (17, 11), (2, 9), (3, 8), (9, 11), (18, 5), (18, 1), (3, 2), (11, 1), (15, 0), (9, 10), (1, 8), (11, 5), (15, 9), (18, 8), (18, 9), (0, 10), (14, 6), (13, 12), (7, 6), (10, 11), (14, 3), (4, 8), (5, 11), (8, 12), (6, 5), (5, 5), (8, 4), (12, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994807", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 12), (3, 7), (1, 1), (5, 12), (7, 5), (10, 8), (0, 12), (1, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184184", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (9, 3), (15, 0), (11, 11), (7, 4), (0, 5), (3, 4), (1, 2), (11, 10), (4, 4), (4, 14), (1, 15), (10, 8), (2, 1), (3, 11), (2, 0), (11, 13), (11, 8), (16, 14), (14, 4), (5, 16), (11, 1), (15, 8), (7, 0), (14, 1), (13, 3), (15, 9), (10, 6), (7, 8), (8, 10), (1, 8), (10, 12), (3, 14), (10, 5), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874864", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (11, 4), (4, 11), (6, 9), (2, 0), (10, 8), (3, 8), (6, 3), (6, 2), (4, 9), (4, 6), (3, 6), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319609", "dataset": "MATH"}
{"messages": [{"content": "In a 16x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 16), (7, 9), (7, 6), (15, 3), (6, 8), (1, 10), (3, 13), (6, 1), (2, 3), (2, 5), (2, 7), (0, 11), (15, 14), (1, 3), (3, 4), (15, 0), (0, 2), (0, 5), (13, 11), (9, 7), (7, 8), (13, 10), (8, 13), (0, 15), (5, 8), (12, 5), (6, 11), (12, 7), (2, 14), (5, 5), (15, 11), (8, 5), (6, 7), (9, 0), (13, 6), (15, 13), (5, 4), (0, 7), (9, 15), (5, 9), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624845", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 11), (2, 3), (8, 5), (11, 9), (4, 3), (3, 1), (11, 5), (5, 11), (9, 14), (8, 6), (11, 3), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455017", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (10, 10), (3, 6), (3, 7), (0, 3), (9, 8), (5, 2), (6, 9), (11, 11), (12, 9), (3, 4), (7, 3), (10, 11), (4, 3), (11, 8), (11, 10), (12, 8), (7, 8), (2, 11), (1, 6), (2, 9), (7, 9), (6, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58244", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 16), (1, 5), (3, 1), (11, 1), (5, 5), (10, 5), (2, 0), (11, 13), (17, 13), (16, 5), (11, 14), (15, 16), (8, 14), (11, 9), (3, 4), (9, 10), (7, 15), (18, 13), (14, 2), (9, 2), (6, 11), (13, 1), (4, 3), (11, 7), (16, 1), (13, 11), (8, 12), (0, 6), (0, 9), (12, 8), (10, 1), (18, 0), (5, 2), (16, 16), (14, 13), (15, 3), (16, 2), (13, 16), (6, 18), (9, 1), (11, 10), (3, 11), (9, 9), (16, 8), (14, 8), (13, 17), (12, 9), (8, 6), (8, 0), (11, 5), (11, 16), (9, 3), (4, 13), (4, 14), (5, 10), (14, 0), (13, 8), (0, 18), (14, 6), (7, 13), (5, 11), (2, 1), (15, 18), (11, 2), (12, 13), (4, 17), (6, 5), (0, 10), (12, 1), (0, 15), (5, 6), (15, 7), (6, 13), (0, 13), (15, 2), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574596", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (8, 1), (8, 5), (0, 1), (5, 1), (3, 1), (2, 5), (9, 1), (4, 5), (2, 8), (5, 4), (5, 5), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1884", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (9, 3), (0, 15), (1, 12), (3, 15), (3, 12), (1, 15), (5, 9), (9, 4), (0, 8), (2, 3), (1, 7), (3, 5), (4, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311429", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 12), (6, 9), (1, 7), (5, 5), (8, 7), (6, 5), (2, 4), (11, 6), (7, 3), (5, 14), (7, 16), (0, 14), (4, 16), (10, 4), (0, 4), (9, 5), (2, 15), (7, 15), (11, 4), (3, 8), (5, 6), (8, 3), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997899", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 1), (12, 6), (1, 10), (4, 1), (6, 6), (12, 10), (8, 2), (12, 8), (15, 2), (14, 8), (9, 10), (5, 9), (7, 5), (11, 10), (5, 6), (5, 4), (1, 2), (6, 4), (15, 6), (11, 4), (10, 0), (9, 0), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108623", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (3, 9), (11, 5), (3, 5), (2, 7), (7, 11), (2, 6), (8, 12), (11, 16), (3, 18), (10, 14), (10, 10), (7, 8), (7, 10), (3, 4), (7, 1), (3, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866454", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (8, 14), (5, 6), (3, 11), (7, 13), (9, 13), (7, 15), (1, 6), (10, 10), (11, 2), (11, 9), (3, 15), (7, 12), (10, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "795111", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (6, 9), (7, 11), (9, 7), (1, 8), (5, 12), (7, 9), (9, 12), (6, 6), (2, 8), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301106", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 4), (13, 2), (6, 7), (4, 6), (9, 8), (8, 7), (1, 4), (8, 6), (9, 2), (4, 5), (13, 3), (8, 1), (9, 9), (11, 7), (3, 2), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12525", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (2, 12), (10, 12), (1, 1), (2, 13), (3, 7), (0, 1), (6, 15), (5, 4), (6, 4), (3, 9), (1, 15), (9, 6), (5, 1), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138404", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 10), (9, 12), (14, 10), (13, 12), (6, 3), (8, 8), (11, 12), (3, 9), (8, 6), (9, 16), (1, 7), (3, 13), (10, 2), (11, 7), (14, 1), (11, 10), (0, 6), (10, 16), (0, 11), (9, 8), (3, 4), (12, 4), (13, 5), (15, 17), (3, 8), (4, 16), (1, 12), (10, 6), (14, 12), (0, 4), (2, 11), (15, 3), (13, 17), (15, 13), (5, 15), (12, 9), (8, 13), (8, 0), (1, 1), (4, 15), (2, 4), (0, 15), (4, 12), (7, 13), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890480", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 10), (8, 11), (5, 8), (7, 5), (16, 4), (1, 11), (0, 3), (3, 1), (16, 3), (13, 10), (14, 3), (1, 4), (13, 3), (4, 3), (12, 0), (8, 0), (0, 7), (16, 2), (16, 1), (3, 4), (7, 3), (3, 7), (14, 0), (11, 3), (5, 7), (13, 0), (17, 3), (6, 7), (9, 1), (7, 9), (6, 8), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "697417", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (3, 9), (2, 1), (1, 4), (8, 12), (8, 2), (0, 9), (3, 7), (3, 2), (0, 1), (0, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32053", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 14), (4, 5), (8, 8), (14, 2), (2, 3), (0, 8), (2, 7), (2, 1), (5, 4), (1, 14), (0, 14), (2, 8), (15, 9), (9, 9), (1, 13), (9, 0), (11, 1), (13, 14), (10, 0), (4, 10), (7, 14), (10, 1), (12, 14), (7, 8), (10, 13), (1, 2), (2, 5), (5, 9), (6, 7), (5, 14), (7, 6), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87020", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 3), (9, 3), (8, 6), (3, 10), (2, 4), (6, 7), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10138", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 10), (7, 9), (1, 14), (0, 6), (7, 3), (8, 5), (6, 14), (0, 10), (2, 5), (10, 4), (10, 13), (1, 4), (6, 6), (3, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153899", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (7, 0), (5, 11), (1, 10), (6, 10), (2, 1), (7, 9), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146725", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 14), (9, 6), (7, 12), (3, 9), (0, 2), (7, 2), (3, 13), (0, 15), (2, 15), (2, 9), (2, 0), (0, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471050", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 14), (15, 11), (2, 8), (4, 6), (15, 8), (3, 16), (7, 10), (12, 7), (2, 12), (12, 1), (11, 4), (4, 16), (14, 1), (10, 9), (5, 2), (2, 4), (5, 12), (15, 2), (6, 14), (8, 7), (2, 11), (12, 15), (0, 2), (9, 5), (3, 4), (12, 11), (5, 7), (9, 4), (5, 0), (7, 6), (15, 14), (3, 12), (7, 12), (2, 16), (3, 8), (2, 14), (14, 7), (4, 2), (6, 2), (1, 15), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994505", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (3, 16), (10, 11), (1, 3), (8, 3), (2, 1), (2, 6), (0, 9), (1, 7), (7, 6), (11, 0), (4, 17), (3, 9), (5, 3), (5, 14), (1, 10), (3, 13), (6, 5), (1, 8), (5, 4), (3, 18), (10, 0), (2, 10), (7, 10), (11, 10), (5, 15), (10, 14), (3, 10), (4, 13), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844175", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 8), (4, 2), (9, 8), (1, 5), (8, 5), (2, 9), (10, 9), (1, 1), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18298", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (5, 11), (5, 12), (2, 11), (7, 2), (6, 3), (9, 6), (9, 7), (9, 12), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174782", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 10), (1, 4), (5, 16), (3, 0), (9, 9), (7, 9), (0, 4), (5, 9), (0, 2), (3, 15), (3, 3), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91147", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (17, 13), (11, 12), (5, 6), (16, 5), (1, 1), (13, 7), (14, 15), (12, 10), (17, 7), (13, 1), (17, 6), (2, 12), (14, 3), (4, 13), (4, 4), (16, 6), (5, 3), (8, 14), (13, 6), (3, 15), (7, 3), (3, 6), (3, 0), (7, 9), (15, 3), (15, 16), (6, 0), (11, 2), (9, 14), (13, 5), (15, 1), (17, 0), (8, 3), (8, 13), (13, 15), (8, 12), (15, 0), (6, 13), (5, 15), (12, 12), (17, 9), (12, 9), (0, 15), (14, 11), (9, 4), (0, 6), (10, 13), (10, 14), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942824", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (11, 14), (7, 0), (2, 7), (15, 1), (4, 10), (13, 11), (7, 3), (9, 1), (14, 11), (4, 8), (15, 9), (7, 14), (0, 10), (4, 12), (10, 3), (0, 6), (16, 6), (8, 8), (3, 7), (7, 12), (9, 11), (13, 10), (6, 8), (11, 11), (9, 3), (8, 11), (6, 11), (16, 1), (1, 10), (10, 6), (7, 5), (5, 11), (6, 12), (14, 4), (12, 13), (9, 7), (4, 9), (10, 0), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "762044", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 8), (5, 1), (2, 2), (3, 7), (1, 6), (0, 8), (3, 5), (3, 1), (1, 5), (8, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5210", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (11, 8), (1, 0), (8, 18), (0, 9), (3, 2), (6, 15), (1, 12), (1, 13), (3, 15), (1, 4), (7, 2), (0, 2), (5, 14), (0, 14), (10, 8), (5, 10), (10, 1), (10, 6), (7, 9), (6, 2), (4, 14), (5, 5), (2, 17), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "725467", "dataset": "MATH"}
{"messages": [{"content": "In a 10x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (8, 1), (8, 9), (9, 1), (5, 10), (6, 4), (1, 2), (9, 7), (9, 4), (6, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10405", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (10, 1), (6, 1), (7, 10), (8, 5), (0, 4), (9, 8), (6, 9), (9, 2), (2, 13), (3, 3), (4, 3), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153401", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 10), (15, 11), (11, 5), (9, 3), (2, 3), (9, 1), (17, 10), (4, 3), (7, 0), (16, 5), (13, 1), (16, 11), (9, 5), (17, 3), (15, 10), (7, 7), (6, 3), (3, 1), (10, 2), (15, 1), (15, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183722", "dataset": "MATH"}
{"messages": [{"content": "In a 13x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 13), (5, 11), (3, 8), (5, 9), (11, 0), (12, 11), (4, 8), (7, 5), (6, 13), (12, 7), (1, 3), (9, 8), (1, 7), (6, 7), (11, 8), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "392451", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (0, 11), (2, 1), (3, 9), (14, 3), (6, 0), (9, 11), (8, 6), (9, 0), (12, 4), (0, 5), (5, 6), (0, 9), (16, 11), (16, 10), (2, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648602", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 11), (5, 8), (8, 0), (3, 14), (3, 8), (11, 14), (4, 9), (2, 13), (11, 5), (5, 9), (9, 7), (0, 12), (7, 0), (2, 5), (7, 2), (7, 8), (1, 6), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980250", "dataset": "MATH"}
{"messages": [{"content": "In a 16x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (5, 8), (13, 10), (14, 1), (9, 3), (13, 8), (5, 4), (8, 2), (11, 8), (10, 6), (0, 4), (15, 2), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121139", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 6), (6, 3), (6, 4), (3, 5), (8, 1), (6, 5), (0, 8), (2, 8), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86711", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 9), (9, 8), (9, 1), (8, 12), (9, 3), (8, 16), (4, 16), (5, 2), (8, 7), (0, 11), (3, 8), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874254", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 4), (5, 9), (10, 0), (8, 7), (12, 8), (3, 8), (11, 14), (8, 15), (7, 11), (13, 2), (5, 2), (7, 1), (4, 3), (12, 9), (3, 7), (12, 12), (7, 7), (13, 10), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587118", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (11, 3), (5, 1), (6, 3), (10, 7), (11, 11), (18, 4), (10, 10), (1, 12), (1, 9), (13, 6), (6, 12), (0, 7), (11, 9), (13, 10), (13, 8), (4, 10), (2, 12), (16, 0), (15, 6), (17, 2), (7, 0), (10, 3), (11, 7), (6, 9), (8, 7), (17, 1), (8, 6), (8, 3), (5, 3), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739397", "dataset": "MATH"}
{"messages": [{"content": "In a 14x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (7, 3), (5, 0), (13, 7), (11, 7), (4, 7), (1, 10), (12, 0), (0, 6), (2, 1), (4, 9), (1, 4), (9, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152008", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (3, 8), (7, 11), (8, 2), (7, 3), (8, 10), (8, 0), (0, 12), (2, 5), (9, 1), (1, 5), (0, 1), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275300", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (0, 3), (5, 6), (3, 4), (11, 9), (3, 3), (8, 9), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29303", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (6, 7), (4, 3), (17, 3), (16, 5), (5, 10), (9, 10), (10, 10), (17, 4), (5, 12), (16, 3), (17, 6), (2, 3), (8, 2), (16, 16), (15, 14), (4, 15), (0, 6), (8, 6), (14, 7), (0, 1), (14, 3), (6, 0), (6, 17), (6, 9), (0, 10), (14, 17), (15, 2), (4, 9), (3, 9), (12, 17), (5, 2), (6, 2), (3, 0), (7, 4), (2, 11), (13, 15), (13, 9), (15, 10), (8, 11), (0, 9), (1, 13), (1, 15), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920022", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (7, 10), (4, 8), (0, 6), (3, 0), (5, 4), (1, 11), (8, 6), (10, 10), (8, 7), (6, 0), (7, 2), (0, 3), (2, 4), (9, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17719", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (2, 4), (2, 8), (8, 9), (1, 1), (4, 11), (6, 9), (11, 9), (4, 0), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117359", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (10, 6), (10, 8), (5, 1), (7, 5), (10, 12), (3, 0), (9, 5), (11, 12), (3, 14), (0, 9), (0, 13), (9, 2), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "905938", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (8, 16), (7, 15), (8, 8), (3, 5), (5, 5), (6, 6), (4, 7), (3, 12), (9, 4), (4, 11), (5, 12), (3, 0), (0, 8), (5, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87199", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (11, 0), (1, 10), (4, 5), (0, 10), (8, 3), (14, 6), (10, 9), (5, 9), (12, 9), (11, 4), (4, 4), (2, 4), (15, 10), (17, 3), (0, 1), (3, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907581", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 15), (8, 17), (2, 13), (6, 17), (5, 10), (0, 18), (4, 15), (3, 18), (8, 10), (0, 16), (9, 8), (0, 15), (9, 1), (8, 18), (9, 6), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845550", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (3, 0), (9, 10), (12, 4), (4, 12), (10, 4), (7, 5), (7, 6), (5, 0), (2, 5), (3, 8), (6, 1), (12, 6), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891301", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (4, 0), (10, 11), (0, 6), (4, 1), (6, 7), (6, 5), (5, 7), (6, 8), (8, 9), (5, 2), (0, 9), (0, 1), (1, 9), (10, 9), (8, 0), (1, 6), (9, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31732", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 11), (3, 11), (1, 6), (1, 5), (2, 6), (7, 9), (0, 12), (11, 6), (6, 1), (3, 4), (12, 4), (10, 10), (4, 0), (4, 6), (8, 8), (7, 12), (2, 2), (16, 8), (15, 5), (4, 12), (6, 3), (13, 9), (14, 1), (0, 8), (3, 8), (10, 9), (1, 11), (16, 4), (14, 5), (5, 12), (2, 11), (8, 9), (16, 2), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "989383", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (9, 7), (2, 6), (3, 6), (8, 12), (0, 8), (5, 2), (6, 8), (6, 9), (9, 0), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131676", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (2, 4), (3, 4), (5, 0), (8, 6), (9, 6), (12, 5), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534467", "dataset": "MATH"}
{"messages": [{"content": "In a 11x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (4, 9), (3, 12), (1, 17), (9, 13), (4, 0), (10, 16), (0, 17), (10, 12), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953223", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 12), (1, 9), (6, 6), (10, 8), (5, 5), (2, 2), (10, 5), (10, 2), (9, 11), (3, 13), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553623", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 14), (6, 1), (4, 11), (11, 2), (6, 15), (9, 10), (10, 18), (16, 0), (4, 4), (4, 13), (15, 4), (6, 10), (5, 18), (8, 11), (0, 15), (2, 3), (10, 12), (13, 1), (15, 9), (10, 5), (2, 9), (2, 5), (16, 17), (12, 15), (0, 5), (14, 1), (15, 14), (9, 0), (2, 10), (14, 15), (16, 9), (1, 3), (2, 18), (12, 3), (6, 0), (6, 3), (4, 17), (12, 18), (10, 16), (0, 17), (15, 13), (6, 9), (2, 8), (5, 2), (3, 17), (5, 7), (14, 9), (15, 3), (10, 11), (3, 5), (7, 0), (1, 14), (0, 7), (15, 5), (4, 10), (6, 14), (9, 6), (16, 2), (3, 16), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704223", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 3), (12, 8), (8, 9), (6, 3), (1, 8), (10, 4), (0, 9), (7, 2), (1, 9), (11, 0), (10, 7), (2, 4), (10, 10), (6, 6), (2, 5), (7, 8), (9, 7), (3, 11), (5, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151592", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (3, 5), (10, 10), (8, 5), (7, 6), (11, 3), (4, 1), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36586", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 6), (11, 8), (7, 11), (11, 1), (3, 3), (5, 3), (10, 3), (12, 10), (5, 1), (9, 2), (1, 8), (2, 0), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810593", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 12), (2, 5), (3, 11), (9, 8), (4, 10), (10, 2), (5, 13), (2, 7), (2, 3), (10, 7), (4, 4), (0, 5), (8, 9), (5, 2), (16, 14), (11, 6), (13, 8), (0, 6), (15, 12), (16, 2), (15, 6), (12, 4), (16, 8), (16, 11), (8, 6), (3, 7), (4, 0), (1, 13), (1, 11), (5, 8), (7, 1), (7, 6), (4, 14), (14, 3), (11, 3), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860947", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (1, 9), (2, 9), (8, 7), (1, 6), (3, 13), (5, 8), (10, 5), (2, 4), (9, 10), (9, 6), (7, 0), (1, 0), (0, 4), (10, 13), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94306", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 1), (14, 3), (13, 10), (8, 6), (7, 10), (2, 9), (12, 7), (10, 7), (13, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "773321", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (9, 9), (7, 8), (9, 15), (0, 16), (7, 15), (1, 9), (1, 3), (0, 17), (2, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400910", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 6), (2, 0), (9, 7), (8, 8), (3, 2), (9, 0), (12, 3), (8, 6), (14, 7), (16, 4), (0, 5), (0, 9), (12, 6), (4, 1), (17, 5), (10, 8), (11, 8), (9, 8), (10, 5), (7, 5), (12, 2), (2, 7), (2, 4), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15040", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (5, 7), (3, 2), (1, 4), (9, 11), (8, 11), (0, 10), (11, 10), (11, 12), (8, 9), (12, 7), (12, 0), (12, 10), (14, 9), (2, 4), (6, 7), (10, 7), (5, 8), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963637", "dataset": "MATH"}
{"messages": [{"content": "In a 14x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (6, 0), (8, 11), (13, 7), (1, 11), (0, 5), (11, 5), (0, 4), (6, 6), (11, 6), (2, 8), (12, 2), (0, 2), (2, 12), (3, 4), (8, 2), (9, 4), (2, 11), (9, 12), (8, 10), (4, 11), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738494", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 12), (7, 5), (11, 8), (4, 0), (11, 2), (6, 13), (7, 9), (4, 14), (8, 11), (3, 13), (14, 4), (4, 6), (12, 2), (1, 2), (2, 2), (5, 11), (2, 13), (9, 8), (5, 8), (12, 13), (5, 10), (8, 7), (5, 1), (0, 12), (9, 12), (13, 5), (2, 8), (1, 13), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930372", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 12), (4, 6), (8, 12), (0, 6), (5, 10), (2, 10), (6, 6), (6, 0), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147207", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 10), (11, 7), (13, 0), (0, 2), (8, 8), (1, 11), (9, 1), (1, 4), (9, 4), (6, 9), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538371", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 14), (3, 11), (10, 2), (3, 3), (14, 9), (9, 12), (1, 15), (1, 13), (14, 13), (14, 7), (2, 14), (5, 11), (2, 10), (13, 12), (10, 3), (15, 0), (15, 7), (3, 6), (8, 1), (12, 3), (5, 2), (13, 8), (3, 5), (6, 10), (2, 7), (12, 6), (7, 8), (14, 11), (4, 11), (14, 12), (6, 14), (1, 8), (11, 14), (11, 8), (15, 11), (15, 10), (8, 15), (12, 12), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "957244", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 10), (7, 11), (0, 5), (3, 8), (10, 6), (6, 2), (2, 10), (7, 5), (2, 8), (6, 6), (0, 10), (2, 5), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38598", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 10), (10, 5), (2, 5), (15, 10), (6, 10), (8, 5), (3, 2), (11, 10), (10, 0), (10, 6), (11, 7), (1, 2), (11, 13), (7, 4), (2, 11), (7, 5), (14, 6), (1, 1), (0, 4), (0, 10), (16, 3), (15, 3), (13, 13), (9, 12), (13, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908864", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (15, 9), (15, 12), (14, 7), (4, 4), (0, 2), (11, 6), (2, 4), (16, 2), (1, 9), (2, 12), (15, 5), (14, 11), (5, 9), (8, 12), (0, 10), (1, 12), (10, 11), (1, 10), (2, 13), (2, 11), (14, 5), (7, 9), (6, 5), (17, 2), (6, 12), (8, 1), (4, 13), (16, 9), (14, 13), (11, 13), (1, 5), (6, 2), (12, 9), (13, 5), (15, 13), (18, 10), (6, 3), (9, 4), (9, 0), (13, 6), (15, 6), (9, 5), (10, 5), (0, 6), (9, 14), (0, 5), (5, 13), (17, 5), (7, 4), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841624", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (3, 1), (10, 9), (16, 6), (10, 0), (8, 1), (14, 2), (9, 17), (17, 12), (15, 14), (2, 9), (3, 12), (16, 8), (12, 13), (17, 1), (0, 9), (15, 15), (3, 15), (15, 0), (15, 4), (17, 2), (2, 1), (6, 13), (12, 12), (10, 13), (8, 17), (7, 15), (9, 6), (3, 7), (17, 0), (12, 14), (9, 2), (5, 13), (13, 17), (0, 13), (15, 13), (3, 5), (9, 1), (2, 7), (17, 4), (11, 1), (14, 3), (4, 9), (0, 5), (14, 0), (10, 14), (1, 14), (8, 12), (7, 7), (10, 2), (3, 13), (5, 3), (15, 6), (16, 17), (2, 5), (6, 3), (12, 5), (7, 10), (4, 12), (7, 1), (14, 9), (8, 0), (0, 15), (8, 2), (6, 17), (15, 7), (5, 14), (13, 16), (11, 16), (7, 16), (16, 10), (11, 17), (17, 14), (0, 16), (9, 11), (2, 8), (16, 11), (1, 6), (16, 2), (7, 12), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "761337", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (2, 9), (12, 11), (8, 7), (6, 8), (9, 1), (6, 6), (13, 4), (12, 7), (5, 0), (6, 2), (8, 1), (7, 4), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "889506", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (17, 7), (9, 0), (18, 2), (13, 6), (11, 6), (7, 3), (6, 8), (2, 8), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "633549", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 17), (1, 2), (7, 6), (0, 14), (6, 1), (10, 5), (8, 1), (3, 16), (2, 15), (6, 2), (0, 15), (8, 18), (5, 10), (3, 3), (9, 18), (7, 10), (3, 4), (1, 8), (6, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964409", "dataset": "MATH"}
{"messages": [{"content": "In a 10x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 10), (1, 2), (6, 9), (3, 6), (7, 5), (4, 6), (5, 8), (0, 12), (5, 4), (9, 3), (5, 11), (5, 12), (2, 9), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17134", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (9, 13), (12, 8), (5, 0), (4, 11), (4, 13), (5, 9), (6, 16), (9, 10), (4, 16), (9, 11), (6, 10), (6, 3), (5, 4), (4, 5), (6, 15), (0, 15), (8, 8), (11, 6), (10, 5), (10, 17), (2, 16), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660537", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 11), (10, 11), (12, 2), (9, 2), (14, 16), (12, 6), (4, 2), (11, 9), (1, 7), (11, 0), (3, 15), (10, 18), (2, 8), (7, 1), (11, 3), (4, 5), (6, 10), (7, 15), (8, 10), (11, 15), (9, 3), (1, 15), (3, 6), (14, 7), (5, 3), (5, 17), (8, 5), (12, 11), (9, 4), (1, 8), (10, 9), (13, 13), (6, 1), (9, 16), (5, 0), (4, 8), (11, 2), (0, 12), (4, 1), (0, 6), (12, 9), (0, 5), (5, 5), (2, 0), (4, 18), (11, 18), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894600", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 9), (5, 1), (13, 10), (3, 6), (15, 15), (12, 11), (2, 8), (12, 9), (1, 5), (10, 13), (1, 4), (3, 7), (4, 16), (15, 8), (3, 14), (1, 9), (16, 13), (12, 16), (16, 6), (16, 16), (7, 12), (12, 2), (6, 8), (1, 0), (9, 5), (2, 18), (0, 15), (8, 12), (8, 10), (16, 11), (11, 6), (15, 1), (2, 10), (4, 2), (14, 2), (14, 11), (2, 3), (1, 11), (2, 15), (6, 13), (15, 3), (12, 14), (15, 5), (17, 0), (0, 8), (6, 16), (17, 9), (14, 14), (8, 6), (9, 11), (7, 17), (5, 3), (12, 6), (15, 6), (11, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111988", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 15), (6, 13), (16, 10), (15, 4), (9, 11), (5, 10), (16, 6), (2, 0), (1, 8), (2, 6), (6, 11), (12, 13), (15, 5), (6, 0), (13, 4), (2, 1), (10, 0), (1, 9), (6, 8), (11, 8), (14, 12), (9, 5), (14, 3), (7, 4), (5, 3), (10, 7), (14, 6), (1, 16), (10, 15), (11, 14), (10, 1), (7, 2), (14, 7), (6, 6), (0, 7), (3, 7), (12, 3), (14, 8), (3, 12), (3, 10), (9, 16), (4, 14), (10, 8), (11, 0), (6, 15), (10, 12), (5, 7), (13, 14), (3, 8), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695192", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (5, 4), (1, 4), (12, 0), (14, 12), (7, 1), (6, 8), (12, 11), (14, 0), (14, 5), (9, 4), (11, 4), (1, 13), (13, 3), (2, 10), (16, 9), (8, 6), (10, 1), (5, 2), (7, 13), (6, 0), (14, 4), (0, 1), (5, 9), (9, 12), (1, 9), (12, 13), (14, 13), (7, 10), (4, 13), (8, 11), (3, 5), (8, 12), (10, 0), (15, 6), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913143", "dataset": "MATH"}
{"messages": [{"content": "In a 15x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 12), (1, 10), (8, 12), (13, 8), (11, 7), (8, 15), (7, 11), (2, 8), (0, 12), (8, 4), (11, 6), (4, 11), (9, 13), (10, 11), (1, 12), (12, 2), (1, 2), (12, 7), (12, 3), (11, 16), (5, 3), (1, 16), (4, 8), (7, 5), (12, 16), (5, 6), (5, 0), (3, 12), (9, 11), (0, 8), (8, 3), (1, 4), (0, 2), (5, 13), (9, 10), (6, 1), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787700", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 11), (4, 1), (3, 2), (6, 6), (13, 4), (1, 5), (12, 10), (1, 7), (8, 6), (10, 1), (3, 7), (6, 7), (8, 3), (5, 1), (0, 4), (7, 11), (16, 3), (11, 0), (10, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "893264", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 12), (8, 9), (6, 1), (11, 8), (11, 18), (10, 4), (4, 0), (3, 3), (13, 15), (12, 7), (9, 12), (7, 9), (1, 2), (13, 8), (7, 10), (0, 11), (13, 16), (13, 11), (4, 12), (6, 17), (5, 5), (3, 9), (11, 3), (12, 14), (9, 2), (13, 12), (3, 11), (10, 17), (6, 13), (7, 15), (0, 18), (10, 18), (11, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779646", "dataset": "MATH"}
{"messages": [{"content": "In a 12x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (2, 4), (3, 7), (7, 5), (8, 6), (4, 2), (10, 8), (2, 5), (1, 8), (9, 1), (1, 1), (7, 11), (7, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59920", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (9, 7), (4, 3), (1, 8), (0, 2), (11, 4), (3, 8), (8, 5), (0, 4), (4, 5), (10, 8), (6, 9), (1, 3), (1, 0), (7, 11), (10, 5), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29758", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 12), (7, 0), (18, 6), (8, 1), (9, 1), (5, 6), (14, 6), (1, 6), (12, 1), (15, 2), (18, 8), (13, 5), (14, 9), (14, 2), (15, 11), (2, 12), (8, 0), (1, 7), (4, 3), (2, 10), (0, 5), (17, 7), (13, 11), (16, 3), (14, 8), (2, 2), (3, 9), (16, 6), (11, 3), (0, 11), (12, 11), (1, 4), (5, 12), (18, 9), (4, 10), (7, 11), (2, 6), (1, 5), (12, 7), (10, 10), (6, 4), (17, 8), (6, 9), (11, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920905", "dataset": "MATH"}
{"messages": [{"content": "In a 15x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (9, 7), (9, 13), (13, 12), (9, 4), (7, 10), (11, 4), (5, 7), (11, 10), (10, 10), (12, 14), (11, 5), (4, 13), (2, 9), (10, 13), (9, 6), (6, 7), (5, 11), (0, 5), (0, 6), (4, 7), (5, 6), (5, 5), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913770", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 5), (6, 8), (8, 11), (8, 2), (9, 14), (4, 4), (6, 6), (6, 10), (6, 12), (2, 7), (3, 4), (4, 11), (5, 11), (4, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46965", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (3, 6), (15, 4), (14, 8), (13, 0), (6, 5), (10, 9), (6, 6), (13, 7), (14, 3), (3, 9), (13, 4), (11, 5), (7, 0), (7, 3), (1, 9), (2, 1), (12, 0), (16, 9), (3, 1), (8, 7), (9, 7), (13, 2), (0, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62273", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (12, 0), (4, 14), (14, 6), (10, 4), (6, 11), (10, 6), (6, 15), (4, 3), (12, 15), (10, 7), (0, 11), (10, 14), (1, 15), (2, 9), (0, 1), (7, 3), (10, 13), (2, 8), (2, 11), (8, 3), (9, 4), (12, 11), (5, 7), (0, 10), (3, 3), (7, 9), (4, 2), (11, 15), (12, 9), (8, 6), (4, 1), (2, 13), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778155", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (6, 5), (11, 6), (6, 12), (12, 5), (6, 15), (4, 16), (12, 2), (2, 2), (12, 15), (8, 6), (9, 3), (11, 4), (9, 10), (8, 0), (8, 8), (0, 7), (1, 14), (12, 1), (4, 15), (0, 15), (11, 5), (0, 14), (12, 10), (6, 8), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984287", "dataset": "MATH"}
{"messages": [{"content": "In a 11x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (6, 9), (7, 10), (4, 7), (8, 9), (6, 10), (4, 9), (8, 8), (1, 13), (10, 0), (3, 1), (10, 14), (4, 3), (3, 7), (6, 2), (10, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370846", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (3, 5), (2, 9), (6, 0), (10, 8), (8, 9), (10, 5), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73975", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (1, 8), (5, 2), (11, 6), (3, 16), (2, 6), (1, 7), (2, 12), (8, 7), (11, 2), (9, 8), (9, 0), (1, 6), (8, 17), (7, 7), (2, 18), (0, 18), (4, 2), (6, 16), (10, 18), (0, 6), (9, 9), (5, 17), (11, 10), (10, 11), (4, 0), (0, 10), (9, 7), (3, 8), (5, 15), (10, 16), (2, 9), (3, 0), (11, 11), (12, 13), (3, 11), (8, 4), (8, 10), (10, 13), (4, 3), (4, 6), (8, 8), (3, 13), (8, 6), (8, 11), (3, 1), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942806", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 3), (2, 8), (0, 9), (8, 9), (5, 7), (2, 3), (7, 7), (9, 0), (3, 3), (2, 2), (11, 0), (9, 7), (6, 4), (1, 4), (0, 6), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12134", "dataset": "MATH"}
{"messages": [{"content": "In a 12x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (9, 7), (8, 8), (5, 10), (3, 9), (10, 2), (7, 10), (5, 2), (8, 2), (6, 3), (3, 1), (1, 0), (2, 9), (10, 5), (3, 0), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12097", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 10), (3, 5), (13, 11), (0, 7), (10, 1), (8, 11), (15, 10), (8, 3), (8, 7), (12, 3), (1, 11), (7, 2), (4, 15), (5, 12), (11, 5), (0, 17), (13, 0), (0, 10), (9, 14), (4, 10), (1, 13), (3, 7), (8, 14), (13, 3), (7, 11), (7, 15), (15, 4), (12, 12), (2, 5), (13, 13), (15, 7), (10, 5), (2, 10), (11, 16), (13, 15), (11, 12), (3, 14), (13, 16), (8, 9), (9, 2), (14, 5), (12, 17), (7, 17), (14, 9), (3, 11), (6, 17), (11, 14), (13, 17), (15, 2), (9, 13), (2, 0), (15, 12), (12, 16), (14, 7), (5, 1), (9, 15), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628730", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 6), (2, 3), (10, 6), (1, 2), (1, 10), (10, 3), (2, 7), (5, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108590", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 1), (1, 16), (9, 8), (1, 8), (3, 8), (1, 1), (0, 11), (8, 0), (11, 14), (5, 2), (2, 5), (12, 12), (7, 3), (8, 13), (1, 9), (3, 6), (5, 8), (3, 9), (4, 11), (8, 6), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760146", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (6, 9), (5, 4), (7, 0), (5, 10), (9, 9), (9, 6), (9, 4), (9, 0), (8, 7), (2, 1), (4, 1), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11428", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (13, 7), (18, 6), (17, 1), (4, 8), (3, 0), (8, 7), (1, 7), (13, 1), (5, 3), (9, 8), (11, 1), (4, 7), (9, 9), (6, 7), (16, 1), (18, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "731843", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 8), (15, 7), (14, 9), (5, 5), (4, 3), (1, 2), (0, 9), (5, 1), (6, 4), (3, 0), (14, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587327", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (12, 2), (2, 5), (1, 5), (6, 7), (12, 7), (8, 0), (1, 9), (8, 8), (3, 2), (12, 3), (2, 2), (3, 7), (5, 7), (6, 6), (5, 3), (3, 10), (9, 8), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69228", "dataset": "MATH"}
{"messages": [{"content": "In a 19x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (4, 17), (13, 12), (9, 5), (14, 14), (12, 9), (10, 2), (16, 6), (0, 17), (12, 5), (7, 3), (8, 9), (2, 6), (1, 10), (5, 8), (3, 15), (13, 0), (11, 12), (2, 5), (0, 13), (14, 6), (2, 14), (15, 3), (16, 4), (11, 0), (14, 2), (5, 18), (0, 11), (7, 2), (8, 2), (3, 0), (17, 18), (2, 15), (11, 8), (1, 16), (15, 14), (5, 12), (8, 5), (15, 13), (17, 6), (5, 4), (12, 16), (15, 2), (12, 14), (12, 4), (4, 10), (9, 7), (4, 12), (17, 1), (8, 7), (15, 15), (8, 17), (12, 13), (2, 0), (6, 4), (8, 16), (13, 8), (1, 3), (1, 1), (4, 8), (5, 10), (18, 0), (17, 2), (2, 10), (3, 3), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626466", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (16, 7), (6, 8), (4, 10), (1, 4), (16, 17), (6, 14), (14, 4), (17, 2), (11, 12), (15, 17), (14, 16), (4, 17), (13, 1), (6, 12), (8, 11), (16, 15), (5, 16), (16, 12), (14, 3), (16, 6), (12, 2), (12, 1), (11, 13), (10, 13), (17, 7), (14, 17), (17, 5), (16, 9), (17, 14), (12, 8), (8, 3), (3, 9), (3, 12), (0, 8), (2, 16), (8, 0), (14, 0), (3, 16), (7, 2), (11, 6), (14, 13), (15, 14), (11, 16), (12, 11), (9, 5), (7, 1), (13, 5), (17, 10), (4, 9), (7, 17), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960723", "dataset": "MATH"}
{"messages": [{"content": "In a 18x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (12, 2), (3, 0), (1, 4), (4, 1), (3, 9), (2, 8), (9, 4), (2, 10), (4, 5), (16, 2), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996110", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 3), (17, 7), (9, 2), (5, 10), (13, 8), (14, 7), (9, 3), (12, 2), (11, 14), (12, 13), (10, 3), (7, 5), (5, 13), (5, 8), (16, 4), (12, 9), (7, 6), (0, 1), (17, 8), (18, 3), (4, 0), (1, 1), (12, 14), (14, 8), (15, 0), (15, 7), (7, 12), (17, 4), (15, 5), (4, 10), (10, 2), (2, 12), (15, 9), (15, 13), (4, 14), (4, 4), (12, 0), (14, 14), (8, 14), (11, 0), (16, 10), (12, 1), (10, 7), (11, 15), (9, 11), (5, 14), (2, 8), (18, 1), (14, 6), (17, 1), (3, 0), (15, 6), (4, 5), (17, 15), (0, 2), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966980", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 3), (6, 11), (9, 1), (3, 7), (1, 3), (9, 6), (0, 3), (0, 7), (0, 8), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88238", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (3, 9), (12, 5), (1, 1), (9, 8), (18, 8), (15, 4), (11, 2), (18, 6), (6, 8), (1, 2), (13, 8), (3, 8), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273237", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (12, 14), (10, 10), (0, 12), (14, 3), (15, 5), (14, 2), (8, 4), (5, 15), (9, 12), (15, 6), (7, 10), (0, 6), (16, 3), (12, 13), (8, 15), (8, 0), (5, 9), (9, 7), (14, 0), (10, 13), (15, 4), (14, 4), (16, 12), (7, 11), (0, 2), (4, 16), (2, 4), (10, 3), (6, 8), (12, 5), (8, 11), (12, 8), (5, 3), (7, 7), (16, 9), (6, 12), (2, 7), (5, 1), (10, 7), (15, 11), (5, 4), (3, 10), (3, 11), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883422", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 6), (4, 4), (18, 5), (7, 4), (14, 7), (17, 2), (17, 3), (15, 2), (4, 2), (12, 5), (8, 2), (3, 5), (18, 1), (13, 0), (12, 8), (1, 0), (14, 1), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30259", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (9, 9), (2, 9), (4, 12), (15, 7), (5, 11), (9, 6), (16, 14), (2, 11), (5, 0), (3, 1), (14, 3), (1, 10), (6, 7), (13, 3), (9, 3), (15, 5), (3, 6), (2, 12), (10, 14), (3, 12), (8, 13), (6, 9), (11, 9), (7, 2), (10, 1), (16, 10), (3, 3), (14, 1), (7, 3), (0, 10), (15, 12), (12, 7), (17, 9), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774121", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 1), (16, 9), (16, 10), (11, 2), (6, 6), (7, 2), (10, 1), (6, 4), (17, 13), (3, 0), (2, 0), (0, 15), (13, 12), (11, 15), (6, 15), (7, 8), (7, 13), (4, 11), (8, 13), (17, 10), (16, 4), (16, 6), (13, 16), (16, 16), (15, 11), (9, 6), (12, 16), (5, 0), (15, 1), (7, 10), (1, 6), (11, 12), (12, 8), (6, 1), (2, 4), (15, 7), (2, 10), (4, 15), (17, 11), (6, 7), (8, 4), (4, 12), (6, 9), (11, 5), (0, 1), (5, 8), (12, 15), (15, 4), (3, 6), (16, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416920", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (2, 6), (3, 2), (10, 8), (7, 7), (11, 8), (8, 9), (1, 0), (1, 5), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255978", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (4, 7), (2, 10), (14, 7), (11, 10), (4, 9), (16, 6), (14, 9), (12, 1), (10, 5), (8, 6), (15, 7), (11, 4), (9, 4), (3, 5), (7, 2), (5, 5), (2, 0), (8, 10), (4, 0), (4, 1), (5, 9), (4, 3), (17, 8), (14, 8), (10, 3), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11970", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 16), (5, 5), (5, 14), (12, 0), (9, 2), (7, 9), (0, 10), (13, 12), (13, 17), (4, 4), (12, 8), (11, 10), (13, 1), (6, 16), (1, 12), (6, 7), (12, 1), (15, 11), (2, 6), (5, 7), (4, 10), (4, 14), (3, 13), (4, 17), (14, 3), (10, 11), (6, 10), (5, 17), (0, 5), (6, 12), (6, 17), (10, 8), (14, 8), (5, 0), (15, 6), (10, 2), (6, 0), (5, 10), (15, 8), (14, 2), (14, 16), (9, 17), (3, 14), (3, 1), (13, 5), (10, 13), (6, 1), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973453", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (12, 6), (16, 15), (16, 12), (9, 16), (12, 13), (4, 12), (8, 16), (1, 1), (6, 5), (16, 18), (13, 13), (2, 5), (17, 16), (4, 18), (0, 4), (9, 7), (7, 3), (12, 15), (0, 8), (5, 0), (8, 3), (5, 17), (13, 11), (14, 12), (1, 10), (3, 11), (1, 14), (8, 1), (6, 18), (7, 1), (4, 5), (9, 8), (12, 1), (4, 13), (0, 7), (11, 8), (12, 8), (12, 9), (13, 14), (0, 10), (12, 14), (15, 14), (6, 4), (1, 9), (3, 5), (3, 0), (0, 14), (17, 7), (11, 18), (4, 8), (15, 6), (8, 7), (9, 14), (10, 2), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "961430", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 4), (15, 0), (13, 14), (5, 15), (12, 14), (9, 12), (10, 15), (6, 10), (8, 13), (6, 4), (6, 14), (1, 12), (7, 9), (15, 12), (15, 6), (7, 1), (1, 1), (1, 6), (2, 4), (4, 3), (7, 8), (8, 0), (6, 8), (5, 12), (4, 5), (5, 11), (15, 1), (8, 12), (14, 11), (10, 2), (15, 3), (9, 4), (2, 2), (6, 11), (1, 5), (6, 7), (10, 6), (12, 6), (12, 4), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942964", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 13), (14, 1), (15, 9), (6, 0), (3, 7), (6, 5), (15, 2), (3, 4), (6, 11), (10, 6), (13, 13), (4, 4), (6, 14), (13, 3), (12, 2), (7, 3), (8, 10), (3, 9), (5, 13), (0, 13), (5, 4), (3, 8), (1, 10), (3, 12), (7, 8), (4, 5), (7, 5), (12, 0), (7, 12), (6, 4), (12, 8), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948280", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (10, 6), (5, 5), (12, 3), (14, 7), (7, 9), (4, 6), (3, 0), (5, 8), (2, 9), (1, 3), (14, 4), (8, 3), (11, 0), (15, 1), (7, 7), (1, 8), (1, 5), (4, 8), (5, 10), (14, 1), (6, 9), (7, 4), (0, 9), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178561", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (10, 1), (5, 7), (9, 16), (13, 9), (14, 0), (13, 7), (14, 11), (9, 5), (7, 13), (1, 12), (2, 11), (11, 2), (3, 14), (13, 0), (14, 15), (12, 2), (3, 18), (0, 5), (5, 0), (2, 8), (2, 1), (15, 10), (11, 9), (11, 10), (12, 16), (4, 1), (5, 2), (14, 14), (13, 11), (15, 5), (1, 10), (2, 10), (6, 0), (8, 16), (2, 0), (8, 0), (11, 16), (12, 5), (14, 1), (13, 1), (3, 4), (8, 9), (0, 14), (15, 16), (12, 1), (4, 17), (12, 17), (1, 18), (14, 4), (1, 0), (9, 17), (12, 15), (5, 12), (0, 16), (2, 4), (7, 9), (15, 9), (3, 10), (13, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953584", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (6, 17), (7, 2), (7, 8), (7, 7), (11, 2), (12, 6), (8, 3), (2, 13), (8, 16), (12, 16), (4, 6), (0, 8), (1, 5), (11, 3), (5, 11), (5, 0), (10, 13), (8, 1), (1, 1), (3, 1), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770427", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 9), (3, 6), (5, 2), (4, 4), (9, 8), (0, 9), (3, 1), (4, 11), (13, 4), (11, 2), (1, 10), (6, 5), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "911295", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 11), (3, 0), (3, 13), (5, 13), (6, 7), (3, 10), (11, 13), (1, 5), (2, 11), (6, 10), (4, 10), (3, 4), (2, 7), (7, 5), (1, 7), (6, 9), (4, 8), (10, 5), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900991", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 1), (8, 9), (11, 11), (0, 4), (9, 3), (1, 8), (8, 12), (16, 0), (10, 16), (16, 6), (15, 8), (10, 6), (2, 16), (11, 9), (9, 10), (5, 14), (14, 11), (2, 10), (14, 10), (15, 13), (10, 5), (6, 3), (2, 14), (0, 11), (5, 16), (1, 4), (14, 15), (16, 2), (10, 8), (10, 15), (6, 16), (5, 3), (5, 2), (13, 16), (1, 15), (5, 10), (14, 0), (5, 9), (6, 1), (3, 2), (10, 9), (7, 5), (6, 6), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908534", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 6), (0, 1), (0, 10), (10, 5), (2, 7), (9, 9), (1, 2), (4, 10), (12, 13), (11, 12), (4, 5), (11, 18), (12, 6), (9, 8), (10, 4), (2, 4), (5, 11), (11, 11), (2, 2), (12, 16), (8, 9), (10, 1), (7, 10), (13, 15), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824992", "dataset": "MATH"}
{"messages": [{"content": "In a 15x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (6, 3), (3, 7), (12, 7), (12, 5), (5, 0), (8, 4), (13, 3), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220714", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (5, 4), (6, 10), (7, 9), (4, 0), (2, 11), (12, 9), (1, 6), (13, 13), (11, 2), (6, 4), (10, 4), (5, 11), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804156", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 12), (6, 0), (3, 14), (13, 7), (8, 4), (13, 14), (4, 0), (10, 1), (10, 6), (8, 2), (5, 16), (5, 7), (9, 12), (11, 1), (13, 10), (1, 14), (1, 2), (1, 15), (6, 10), (9, 10), (5, 15), (5, 13), (6, 11), (4, 6), (10, 11), (8, 9), (12, 3), (11, 14), (11, 0), (3, 12), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "988992", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 5), (17, 0), (4, 11), (2, 10), (3, 7), (2, 0), (7, 5), (15, 1), (1, 8), (10, 5), (4, 6), (5, 9), (2, 7), (12, 9), (10, 9), (9, 5), (9, 0), (18, 9), (14, 10), (16, 11), (0, 3), (17, 4), (8, 4), (1, 7), (0, 10), (12, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721892", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 4), (13, 13), (7, 10), (11, 4), (2, 6), (8, 12), (2, 8), (4, 11), (1, 7), (12, 2), (12, 12), (5, 5), (8, 3), (1, 6), (16, 13), (10, 13), (10, 3), (13, 16), (2, 5), (8, 9), (0, 1), (6, 0), (7, 0), (7, 9), (10, 14), (16, 5), (8, 16), (3, 1), (8, 2), (1, 1), (6, 8), (8, 13), (5, 7), (12, 1), (9, 4), (14, 13), (3, 3), (0, 6), (15, 3), (5, 6), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742758", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (13, 11), (8, 0), (9, 5), (7, 5), (8, 2), (9, 12), (6, 6), (5, 5), (12, 14), (13, 7), (14, 15), (2, 5), (12, 3), (1, 14), (5, 11), (3, 14), (4, 11), (16, 7), (12, 6), (4, 0), (10, 10), (5, 1), (11, 1), (2, 12), (12, 13), (14, 7), (4, 16), (14, 2), (1, 9), (8, 3), (3, 2), (4, 8), (8, 14), (4, 3), (7, 7), (3, 10), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839858", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (9, 9), (11, 11), (3, 4), (8, 12), (4, 3), (4, 8), (5, 13), (11, 2), (7, 9), (4, 7), (1, 0), (11, 1), (3, 10), (1, 10), (8, 1), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42952", "dataset": "MATH"}
{"messages": [{"content": "In a 19x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 11), (4, 1), (3, 6), (12, 12), (8, 6), (3, 12), (9, 13), (13, 3), (9, 5), (16, 1), (11, 7), (13, 4), (14, 8), (11, 6), (13, 13), (17, 6), (6, 8), (9, 9), (17, 10), (12, 2), (16, 12), (5, 12), (15, 2), (12, 6), (1, 3), (6, 1), (0, 7), (7, 6), (7, 2), (14, 9), (3, 0), (14, 5), (3, 1), (16, 10), (3, 9), (11, 13), (18, 7), (12, 3), (3, 11), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836188", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (5, 3), (10, 13), (9, 1), (7, 5), (9, 2), (0, 10), (2, 10), (6, 13), (6, 4), (5, 12), (7, 4), (6, 0), (4, 9), (1, 6), (6, 9), (8, 11), (4, 12), (12, 12), (11, 7), (0, 3), (12, 8), (12, 11), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732127", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 10), (5, 11), (12, 13), (8, 14), (7, 0), (5, 2), (12, 1), (1, 4), (3, 11), (4, 7), (4, 12), (6, 16), (3, 2), (3, 15), (10, 13), (4, 15), (2, 2), (11, 10), (3, 14), (0, 11), (7, 3), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694646", "dataset": "MATH"}
{"messages": [{"content": "In a 17x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (2, 8), (14, 11), (7, 4), (12, 11), (4, 2), (9, 5), (9, 13), (0, 6), (10, 6), (5, 9), (2, 5), (5, 4), (9, 7), (13, 12), (6, 7), (7, 5), (5, 3), (11, 11), (3, 12), (1, 14), (3, 14), (6, 4), (7, 12), (16, 12), (11, 14), (6, 3), (16, 8), (9, 1), (1, 5), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749550", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 1), (14, 9), (15, 4), (17, 5), (0, 9), (14, 3), (7, 9), (0, 7), (15, 9), (2, 5), (13, 1), (9, 9), (13, 3), (16, 6), (12, 6), (0, 6), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763300", "dataset": "MATH"}
{"messages": [{"content": "In a 12x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (8, 10), (5, 5), (0, 6), (10, 6), (2, 0), (2, 1), (2, 8), (6, 7), (4, 11), (9, 6), (1, 0), (11, 5), (11, 10), (10, 4), (10, 7), (5, 10), (7, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25093", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (1, 9), (2, 10), (9, 9), (1, 15), (2, 12), (1, 1), (7, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "911534", "dataset": "MATH"}
{"messages": [{"content": "In a 16x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (11, 0), (5, 7), (0, 12), (6, 1), (5, 5), (15, 4), (13, 3), (3, 2), (14, 2), (0, 5), (9, 3), (6, 10), (4, 0), (9, 10), (2, 0), (8, 6), (15, 11), (1, 12), (3, 9), (8, 13), (3, 13), (8, 1), (1, 8), (7, 0), (10, 0), (6, 3), (1, 7), (8, 5), (0, 2), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948382", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (1, 12), (14, 4), (16, 6), (5, 4), (8, 10), (10, 6), (0, 10), (6, 10), (2, 9), (5, 2), (5, 5), (8, 8), (1, 2), (1, 10), (10, 3), (8, 2), (13, 2), (7, 10), (4, 3), (15, 13), (7, 14), (5, 11), (11, 12), (14, 10), (6, 15), (13, 0), (5, 7), (12, 1), (7, 6), (11, 4), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930439", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (12, 2), (11, 12), (9, 13), (15, 11), (17, 9), (5, 15), (9, 0), (1, 3), (15, 5), (2, 16), (10, 8), (10, 5), (10, 6), (1, 17), (8, 7), (9, 3), (1, 14), (1, 10), (1, 6), (10, 10), (11, 8), (8, 13), (13, 16), (14, 5), (4, 0), (5, 17), (4, 13), (4, 15), (5, 11), (5, 9), (7, 1), (0, 15), (13, 7), (10, 16), (2, 17), (14, 3), (0, 13), (11, 16), (12, 13), (1, 9), (12, 3), (8, 0), (11, 9), (3, 4), (13, 9), (17, 12), (16, 3), (15, 6), (14, 14), (4, 7), (7, 4), (17, 17), (6, 1), (13, 17), (6, 10), (9, 14), (17, 10), (6, 13), (18, 9), (10, 11), (16, 2), (5, 6), (2, 12), (6, 4), (4, 10), (14, 2), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997606", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (7, 2), (2, 5), (0, 5), (8, 6), (3, 10), (1, 5), (8, 4), (7, 4), (7, 6), (5, 10), (2, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66393", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 10), (1, 8), (9, 11), (8, 6), (1, 5), (0, 1), (4, 1), (7, 5), (6, 9), (8, 2), (1, 1), (5, 1), (2, 14), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44769", "dataset": "MATH"}
{"messages": [{"content": "In a 12x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (8, 1), (10, 7), (1, 0), (3, 7), (0, 3), (6, 8), (4, 7), (9, 8), (3, 0), (5, 7), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4070", "dataset": "MATH"}
{"messages": [{"content": "In a 10x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 3), (0, 4), (0, 2), (3, 5), (9, 1), (6, 3), (0, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244873", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (9, 11), (5, 12), (5, 1), (4, 10), (5, 0), (12, 4), (3, 2), (1, 11), (3, 1), (7, 9), (5, 4), (11, 10), (4, 2), (8, 1), (6, 7), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136004", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (1, 8), (6, 9), (0, 5), (8, 4), (11, 4), (11, 2), (7, 13), (4, 11), (5, 16), (2, 9), (0, 2), (1, 9), (5, 11), (1, 10), (11, 1), (4, 13), (2, 1), (1, 13), (5, 2), (6, 2), (10, 15), (3, 8), (3, 11), (7, 16), (5, 0), (5, 15), (12, 2), (5, 8), (6, 6), (2, 13), (4, 2), (9, 6), (2, 14), (10, 6), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "975452", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (13, 9), (1, 5), (10, 13), (13, 10), (10, 6), (6, 0), (11, 9), (3, 10), (2, 10), (14, 4), (9, 11), (5, 8), (11, 0), (6, 13), (14, 9), (11, 12), (2, 8), (13, 2), (7, 12), (3, 12), (10, 8), (13, 5), (12, 6), (0, 12), (13, 0), (12, 5), (3, 0), (1, 7), (5, 13), (10, 2), (4, 12), (8, 4), (8, 6), (5, 2), (4, 1), (7, 0), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816798", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (8, 9), (17, 1), (9, 1), (1, 10), (7, 3), (17, 0), (5, 6), (12, 7), (10, 10), (3, 2), (2, 0), (14, 5), (6, 5), (2, 7), (14, 2), (10, 8), (1, 6), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413276", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (6, 10), (10, 7), (12, 11), (8, 4), (3, 12), (11, 5), (13, 11), (16, 11), (15, 8), (5, 13), (7, 1), (12, 8), (5, 5), (1, 0), (14, 3), (14, 6), (15, 15), (9, 9), (11, 13), (9, 10), (6, 3), (15, 12), (6, 5), (16, 5), (5, 11), (9, 14), (11, 1), (10, 4), (7, 9), (6, 8), (11, 2), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876227", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 14), (12, 1), (0, 11), (2, 10), (6, 12), (13, 13), (3, 13), (10, 14), (0, 9), (4, 5), (3, 4), (14, 0), (16, 7), (2, 5), (4, 4), (3, 6), (17, 3), (2, 0), (18, 14), (2, 14), (2, 9), (14, 10), (1, 6), (17, 2), (17, 5), (8, 15), (10, 9), (14, 7), (13, 11), (1, 8), (15, 11), (6, 9), (12, 15), (18, 0), (4, 10), (2, 8), (12, 3), (1, 9), (5, 13), (17, 13), (9, 0), (17, 10), (10, 2), (13, 2), (1, 10), (10, 3), (1, 7), (13, 10), (17, 14), (0, 3), (4, 2), (11, 14), (3, 14), (7, 12), (5, 4), (16, 10), (9, 15), (18, 2), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842928", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (15, 6), (12, 8), (16, 2), (13, 8), (12, 3), (16, 12), (7, 2), (0, 4), (4, 2), (6, 5), (10, 2), (9, 8), (12, 12), (16, 9), (5, 6), (15, 1), (2, 2), (16, 6), (10, 9), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "834682", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (0, 12), (0, 11), (3, 5), (9, 3), (7, 14), (9, 1), (9, 2), (0, 1), (9, 13), (1, 10), (9, 5), (5, 13), (1, 1), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93002", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (17, 6), (14, 18), (4, 7), (0, 10), (12, 13), (5, 17), (8, 11), (0, 15), (13, 4), (14, 4), (17, 10), (15, 13), (14, 1), (10, 2), (0, 1), (7, 2), (13, 2), (12, 12), (1, 1), (12, 6), (9, 7), (13, 9), (9, 3), (1, 8), (10, 16), (15, 0), (15, 3), (17, 1), (13, 14), (16, 10), (16, 17), (8, 6), (9, 9), (10, 12), (14, 13), (4, 10), (15, 9), (12, 2), (7, 13), (4, 4), (5, 6), (11, 12), (17, 12), (10, 10), (8, 4), (3, 7), (15, 1), (7, 17), (12, 18), (4, 17), (13, 0), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832600", "dataset": "MATH"}
{"messages": [{"content": "In a 16x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 14), (7, 6), (13, 9), (7, 2), (6, 5), (0, 13), (15, 0), (13, 15), (1, 10), (10, 1), (4, 9), (4, 0), (6, 4), (5, 7), (15, 10), (1, 1), (0, 7), (11, 9), (14, 14), (14, 5), (12, 9), (8, 8), (6, 0), (10, 0), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946525", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (13, 3), (12, 0), (0, 3), (6, 8), (13, 4), (8, 1), (5, 0), (4, 0), (8, 4), (3, 4), (4, 7), (10, 9), (14, 0), (14, 11), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "595958", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (13, 7), (11, 5), (5, 10), (2, 3), (6, 9), (11, 9), (12, 9), (9, 10), (2, 0), (5, 6), (7, 8), (5, 1), (6, 4), (5, 4), (1, 4), (13, 8), (14, 6), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4528", "dataset": "MATH"}
{"messages": [{"content": "In a 19x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 12), (12, 5), (11, 10), (6, 11), (16, 12), (6, 8), (14, 10), (11, 2), (2, 3), (2, 11), (2, 0), (5, 0), (8, 5), (11, 3), (16, 5), (12, 7), (17, 0), (7, 12), (3, 9), (16, 11), (9, 4), (11, 12), (17, 2), (18, 2), (5, 3), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661190", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 9), (9, 8), (8, 0), (5, 11), (0, 9), (6, 13), (4, 9), (2, 7), (0, 7), (1, 14), (9, 7), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289778", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (15, 3), (5, 9), (16, 0), (15, 2), (8, 8), (8, 2), (4, 6), (3, 9), (5, 10), (14, 0), (10, 11), (4, 2), (12, 9), (15, 11), (7, 9), (14, 11), (6, 1), (17, 5), (12, 7), (10, 7), (8, 9), (12, 6), (2, 9), (13, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475320", "dataset": "MATH"}
{"messages": [{"content": "In a 10x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 10), (7, 0), (5, 3), (9, 9), (4, 9), (7, 8), (6, 6), (6, 11), (5, 7), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42503", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 17), (9, 7), (1, 13), (10, 5), (1, 2), (1, 5), (12, 9), (3, 2), (7, 17), (12, 2), (8, 13), (10, 6), (3, 8), (5, 0), (5, 1), (3, 18), (3, 5), (12, 1), (0, 3), (7, 10), (9, 11), (5, 16), (9, 10), (2, 9), (7, 12), (2, 6), (12, 4), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959752", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (9, 12), (0, 4), (11, 9), (9, 10), (4, 12), (2, 2), (10, 7), (9, 6), (9, 13), (1, 9), (7, 12), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239892", "dataset": "MATH"}
{"messages": [{"content": "In a 14x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (5, 4), (9, 6), (5, 11), (1, 12), (1, 14), (2, 8), (10, 1), (12, 3), (2, 0), (1, 6), (1, 3), (0, 12), (13, 5), (13, 12), (7, 13), (10, 2), (5, 9), (8, 1), (3, 8), (12, 7), (10, 13), (6, 12), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701350", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 8), (1, 6), (9, 1), (1, 1), (9, 5), (10, 7), (3, 6), (13, 4), (4, 2), (5, 12), (2, 10), (9, 11), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993575", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 16), (7, 6), (3, 0), (2, 17), (6, 13), (4, 10), (0, 13), (14, 16), (1, 3), (11, 7), (11, 2), (11, 12), (7, 2), (14, 0), (3, 6), (14, 3), (1, 4), (7, 5), (11, 4), (5, 8), (0, 8), (6, 11), (13, 2), (0, 14), (8, 2), (8, 15), (2, 4), (13, 7), (2, 7), (6, 10), (6, 1), (0, 11), (14, 4), (14, 14), (10, 12), (10, 13), (13, 9), (5, 13), (9, 5), (7, 8), (2, 18), (1, 11), (5, 10), (2, 16), (6, 12), (8, 14), (7, 9), (3, 10), (13, 8), (14, 15), (9, 0), (9, 18), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933408", "dataset": "MATH"}
{"messages": [{"content": "In a 15x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (13, 2), (5, 12), (12, 2), (5, 2), (4, 8), (2, 2), (2, 1), (5, 8), (3, 13), (3, 12), (6, 8), (8, 8), (6, 10), (6, 6), (3, 8), (2, 7), (14, 3), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "857271", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 8), (12, 2), (3, 3), (2, 2), (9, 0), (10, 7), (10, 6), (16, 6), (6, 8), (8, 7), (15, 8), (13, 6), (14, 8), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248679", "dataset": "MATH"}
{"messages": [{"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (8, 8), (2, 3), (3, 8), (9, 4), (2, 4), (2, 9), (1, 1), (8, 7), (9, 7), (6, 7), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 0), (14, 1), (8, 0), (4, 7), (14, 9), (12, 5), (7, 9), (13, 7), (4, 2), (10, 4), (2, 8), (6, 1), (2, 1), (13, 2), (6, 2), (11, 8), (10, 8), (7, 8), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13075", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 6), (6, 0), (8, 0), (6, 4), (8, 2), (8, 1), (6, 1), (6, 8), (4, 7), (9, 0), (5, 7), (2, 3), (12, 10), (2, 10), (11, 10), (9, 11), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22351", "dataset": "MATH"}
{"messages": [{"content": "In a 18x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (11, 6), (12, 4), (16, 12), (2, 9), (1, 11), (4, 16), (2, 5), (4, 7), (14, 16), (14, 3), (6, 13), (11, 8), (4, 12), (15, 5), (8, 4), (2, 8), (0, 8), (16, 11), (3, 15), (4, 6), (5, 6), (11, 12), (7, 9), (7, 14), (12, 1), (11, 0), (10, 4), (3, 12), (1, 0), (2, 10), (9, 5), (2, 7), (0, 16), (14, 14), (12, 9), (10, 3), (6, 8), (5, 12), (14, 1), (12, 5), (13, 3), (8, 14), (15, 12), (9, 7), (15, 16), (1, 7), (12, 13), (0, 12), (16, 15), (7, 2), (0, 3), (17, 1), (16, 7), (16, 16), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954507", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (2, 10), (12, 1), (1, 6), (10, 9), (5, 4), (0, 9), (11, 9), (7, 11), (12, 2), (3, 9), (2, 6), (6, 9), (3, 4), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176518", "dataset": "MATH"}
{"messages": [{"content": "In a 19x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 16), (9, 14), (14, 12), (11, 13), (18, 4), (10, 8), (6, 0), (5, 2), (16, 8), (3, 7), (17, 14), (11, 15), (3, 6), (7, 1), (7, 15), (16, 14), (12, 10), (12, 12), (2, 12), (15, 9), (10, 15), (13, 4), (5, 12), (7, 10), (0, 9), (15, 6), (18, 14), (4, 12), (16, 0), (8, 2), (13, 2), (5, 15), (17, 9), (9, 4), (14, 1), (15, 4), (1, 8), (4, 16), (6, 1), (10, 11), (8, 11), (14, 10), (0, 16), (18, 2), (16, 3), (17, 3), (6, 14), (15, 2), (10, 14), (1, 0), (1, 6), (15, 8), (12, 13), (2, 11), (17, 0), (18, 13), (5, 8), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540352", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 17), (4, 4), (7, 2), (5, 2), (9, 13), (7, 9), (6, 6), (5, 16), (7, 18), (11, 10), (6, 15), (5, 17), (10, 13), (7, 12), (10, 5), (14, 8), (3, 12), (7, 17), (2, 1), (9, 18), (10, 14), (2, 10), (12, 17), (5, 4), (14, 5), (10, 7), (11, 15), (6, 7), (10, 0), (13, 4), (5, 11), (9, 12), (1, 3), (4, 2), (8, 4), (8, 5), (11, 5), (8, 3), (2, 9), (7, 8), (12, 3), (11, 2), (3, 15), (12, 11), (2, 18), (6, 13), (13, 1), (2, 17), (4, 13), (6, 3), (8, 1), (0, 16), (14, 12), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619112", "dataset": "MATH"}
{"messages": [{"content": "In a 17x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (2, 6), (15, 4), (10, 2), (5, 1), (1, 7), (13, 0), (0, 6), (8, 0), (15, 7), (16, 5), (9, 9), (8, 4), (4, 1), (13, 2), (16, 1), (10, 0), (0, 3), (10, 4), (13, 1), (0, 7), (9, 7), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "903262", "dataset": "MATH"}
{"messages": [{"content": "In a 12x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 15), (8, 3), (5, 8), (4, 0), (5, 17), (11, 5), (3, 8), (7, 3), (3, 17), (11, 2), (3, 1), (10, 7), (5, 6), (6, 2), (5, 11), (2, 14), (5, 14), (7, 12), (3, 13), (3, 9), (5, 1), (8, 13), (7, 10), (8, 14), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "642347", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (13, 9), (1, 2), (4, 5), (0, 12), (6, 10), (6, 1), (3, 6), (3, 7), (5, 12), (4, 4), (12, 8), (6, 14), (14, 0), (10, 4), (18, 13), (9, 11), (7, 0), (2, 1), (14, 9), (12, 0), (0, 3), (17, 11), (3, 10), (15, 9), (6, 6), (13, 6), (14, 6), (6, 5), (15, 6), (16, 7), (11, 14), (15, 12), (12, 12), (3, 3), (0, 14), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943281", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 7), (9, 4), (10, 10), (8, 3), (15, 4), (5, 4), (5, 7), (10, 7), (0, 1), (13, 7), (9, 0), (8, 6), (9, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753195", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (7, 14), (8, 5), (7, 1), (9, 3), (3, 13), (0, 6), (2, 11), (4, 10), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922925", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 4), (8, 1), (6, 10), (7, 4), (7, 3), (1, 4), (7, 7), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108687", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 4), (13, 8), (16, 1), (16, 0), (5, 4), (4, 7), (10, 3), (6, 5), (1, 0), (3, 3), (11, 0), (17, 6), (0, 5), (12, 8), (4, 4), (5, 9), (15, 8), (13, 0), (8, 0), (16, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78353", "dataset": "MATH"}
{"messages": [{"content": "In a 18x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 11), (15, 12), (14, 3), (4, 10), (7, 5), (8, 14), (7, 11), (3, 1), (16, 11), (7, 0), (7, 7), (0, 14), (3, 5), (0, 9), (15, 11), (6, 12), (16, 9), (12, 2), (9, 0), (4, 11), (8, 8), (10, 5), (8, 6), (2, 4), (7, 14), (5, 9), (2, 11), (5, 11), (0, 11), (5, 8), (12, 9), (8, 12), (1, 2), (12, 13), (11, 12), (13, 6), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "821409", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (10, 13), (2, 12), (11, 7), (1, 4), (1, 1), (1, 8), (11, 16), (0, 4), (9, 11), (0, 6), (11, 2), (6, 3), (7, 13), (3, 17), (1, 14), (4, 17), (11, 12), (9, 2), (5, 11), (12, 10), (4, 7), (7, 5), (9, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971170", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (3, 11), (1, 7), (4, 6), (6, 0), (9, 9), (10, 2), (5, 7), (0, 9), (8, 3), (5, 3), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "771077", "dataset": "MATH"}
{"messages": [{"content": "In a 15x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 3), (1, 1), (7, 3), (1, 9), (7, 10), (12, 3), (8, 7), (8, 8), (12, 4), (3, 10), (2, 6), (7, 5), (9, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787846", "dataset": "MATH"}
{"messages": [{"content": "In a 19x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 14), (3, 4), (12, 11), (3, 2), (14, 0), (4, 8), (4, 7), (3, 0), (5, 9), (18, 1), (11, 10), (7, 13), (2, 6), (1, 7), (9, 8), (5, 12), (1, 10), (17, 14), (6, 4), (14, 13), (10, 0), (16, 2), (4, 12), (12, 0), (18, 9), (17, 9), (13, 13), (12, 12), (15, 15), (7, 15), (16, 11), (0, 15), (17, 12), (3, 12), (16, 8), (4, 4), (6, 6), (12, 2), (17, 3), (17, 2), (15, 6), (14, 6), (15, 3), (11, 11), (7, 3), (18, 0), (9, 5), (6, 2), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744729", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 12), (6, 11), (5, 3), (0, 10), (1, 5), (7, 2), (5, 11), (11, 1), (5, 10), (9, 10), (10, 4), (11, 5), (1, 2), (1, 1), (9, 0), (0, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "747558", "dataset": "MATH"}
{"messages": [{"content": "In a 11x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 15), (10, 9), (6, 0), (6, 11), (8, 12), (1, 6), (4, 10), (0, 2), (3, 9), (8, 13), (8, 2), (4, 9), (2, 15), (4, 12), (5, 0), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "633829", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (4, 1), (5, 10), (4, 7), (3, 4), (5, 8), (3, 1), (2, 0), (2, 8), (10, 1), (5, 1), (6, 13), (10, 10), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256953", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 3), (1, 2), (3, 8), (11, 10), (12, 10), (2, 7), (5, 6), (9, 10), (15, 7), (9, 8), (13, 9), (12, 7), (10, 0), (14, 5), (8, 13), (4, 10), (0, 7), (5, 0), (1, 7), (4, 6), (3, 11), (0, 3), (10, 1), (12, 13), (6, 6), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "985095", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (9, 0), (11, 8), (8, 9), (6, 9), (0, 15), (5, 12), (4, 13), (5, 2), (6, 3), (11, 0), (4, 1), (0, 12), (2, 1), (3, 12), (6, 12), (10, 4), (4, 3), (4, 8), (10, 5), (10, 3), (9, 1), (12, 9), (12, 2), (2, 15), (3, 14), (3, 8), (8, 15), (1, 10), (0, 8), (7, 3), (12, 10), (3, 13), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760406", "dataset": "MATH"}
{"messages": [{"content": "In a 17x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (3, 2), (10, 1), (14, 5), (14, 8), (4, 0), (15, 3), (0, 11), (8, 4), (2, 4), (16, 5), (0, 9), (11, 6), (5, 5), (12, 4), (9, 9), (7, 0), (6, 2), (7, 5), (2, 12), (0, 12), (6, 4), (11, 3), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922691", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (4, 10), (3, 9), (1, 2), (17, 4), (8, 6), (3, 3), (12, 10), (12, 9), (7, 5), (4, 9), (14, 11), (18, 9), (16, 2), (13, 10), (9, 1), (7, 6), (10, 7), (5, 9), (2, 6), (5, 3), (15, 0), (0, 11), (18, 1), (13, 8), (16, 6), (14, 5), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "893218", "dataset": "MATH"}
{"messages": [{"content": "In a 14x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 11), (0, 3), (7, 12), (10, 7), (1, 8), (11, 3), (5, 9), (10, 1), (8, 2), (5, 4), (5, 1), (0, 7), (13, 6), (5, 13), (7, 8), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "806310", "dataset": "MATH"}
{"messages": [{"content": "In a 18x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 0), (3, 3), (3, 8), (15, 0), (0, 7), (11, 9), (16, 2), (8, 0), (9, 10), (7, 4), (5, 2), (5, 11), (2, 7), (4, 6), (0, 1), (10, 10), (14, 7), (4, 4), (8, 4), (13, 11), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "729744", "dataset": "MATH"}
{"messages": [{"content": "In a 19x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (17, 4), (4, 12), (16, 1), (18, 4), (5, 13), (12, 8), (4, 11), (5, 14), (14, 4), (18, 8), (2, 9), (3, 3), (12, 4), (11, 5), (8, 7), (10, 11), (3, 11), (14, 10), (10, 6), (6, 3), (5, 5), (9, 12), (5, 4), (0, 7), (17, 6), (0, 6), (13, 13), (18, 6), (13, 2), (14, 3), (7, 6), (3, 14), (7, 4), (6, 13), (1, 3), (13, 7), (9, 4), (8, 14), (13, 12), (15, 2), (8, 13), (16, 10), (6, 6), (13, 1), (10, 0), (11, 2), (5, 6), (9, 1), (17, 0), (2, 12), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656630", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 5), (0, 7), (0, 4), (7, 1), (10, 4), (0, 1), (0, 6), (8, 1), (6, 9), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37978", "dataset": "MATH"}
{"messages": [{"content": "In a 10x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 13), (4, 11), (4, 5), (1, 10), (8, 7), (1, 8), (0, 10), (0, 6), (5, 7), (7, 1), (3, 10), (1, 2), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165365", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 8), (9, 4), (12, 0), (14, 1), (1, 4), (3, 1), (11, 4), (5, 9), (11, 8), (0, 4), (0, 1), (12, 5), (2, 4), (8, 8), (4, 8), (7, 1), (10, 3), (13, 3), (9, 1), (12, 4), (12, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90180", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 10), (9, 1), (4, 13), (5, 6), (8, 6), (6, 13), (9, 10), (5, 7), (5, 1), (10, 13), (7, 11), (1, 1), (0, 4), (8, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82661", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 7), (1, 11), (7, 1), (0, 3), (6, 2), (3, 13), (3, 11), (2, 11), (9, 12), (5, 13), (8, 9), (0, 2), (10, 15), (11, 4), (12, 15), (12, 17), (12, 2), (4, 8), (8, 0), (4, 16), (11, 3), (0, 18), (0, 6), (8, 6), (7, 5), (2, 3), (12, 3), (3, 16), (2, 8), (7, 14), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872112", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (4, 2), (5, 4), (8, 7), (1, 6), (6, 14), (2, 2), (2, 6), (0, 9), (1, 11), (11, 1), (8, 4), (4, 13), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606801", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 7), (1, 7), (6, 10), (13, 2), (8, 8), (8, 6), (2, 1), (12, 8), (3, 7), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362792", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 3), (1, 10), (3, 8), (1, 3), (7, 1), (12, 7), (18, 8), (6, 5), (4, 5), (3, 4), (15, 5), (10, 1), (5, 7), (14, 2), (4, 0), (17, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "829610", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (1, 13), (1, 10), (3, 8), (6, 8), (2, 9), (3, 11), (2, 8), (9, 6), (4, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302799", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 3), (6, 4), (0, 8), (14, 14), (3, 14), (1, 3), (8, 14), (2, 10), (12, 8), (10, 5), (14, 8), (13, 13), (1, 11), (2, 0), (8, 10), (3, 10), (11, 14), (6, 12), (9, 7), (14, 5), (8, 5), (12, 10), (9, 16), (7, 7), (4, 8), (11, 6), (5, 3), (6, 14), (0, 10), (3, 4), (3, 13), (5, 5), (5, 11), (4, 1), (0, 4), (11, 11), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757386", "dataset": "MATH"}
{"messages": [{"content": "In a 16x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 6), (15, 12), (2, 14), (8, 8), (9, 9), (7, 7), (3, 12), (14, 0), (12, 10), (9, 10), (3, 9), (2, 13), (9, 11), (6, 4), (2, 12), (6, 3), (11, 9), (3, 14), (13, 5), (13, 7), (5, 8), (4, 6), (6, 6), (13, 0), (9, 0), (14, 5), (12, 14), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "683879", "dataset": "MATH"}
{"messages": [{"content": "In a 14x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (12, 11), (2, 2), (12, 2), (4, 3), (11, 10), (7, 8), (1, 3), (11, 1), (7, 0), (7, 10), (5, 7), (3, 1), (12, 5), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24808", "dataset": "MATH"}
{"messages": [{"content": "In a 13x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (6, 4), (1, 11), (2, 6), (7, 1), (12, 4), (11, 3), (8, 8), (3, 8), (6, 9), (1, 5), (8, 9), (5, 3), (11, 0), (0, 11), (9, 4), (3, 9), (5, 10), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797354", "dataset": "MATH"}
{"messages": [{"content": "In a 13x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (12, 13), (8, 14), (9, 11), (11, 13), (0, 5), (0, 16), (10, 12), (2, 1), (8, 6), (6, 9), (4, 10), (1, 5), (5, 13), (9, 7), (7, 7), (5, 12), (6, 15), (2, 7), (9, 8), (0, 8), (11, 8), (3, 16), (6, 0), (6, 7), (10, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860919", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 10), (7, 1), (8, 11), (7, 12), (3, 11), (10, 12), (8, 7), (1, 3), (3, 4), (2, 14), (10, 3), (1, 9), (6, 8), (4, 0), (1, 5), (11, 12), (3, 7), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45049", "dataset": "MATH"}
{"messages": [{"content": "In a 14x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (12, 7), (10, 3), (0, 11), (3, 14), (4, 6), (6, 6), (5, 4), (0, 14), (3, 10), (8, 11), (0, 2), (12, 11), (5, 6), (3, 15), (9, 11), (13, 14), (7, 14), (9, 4), (8, 9), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732165", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (12, 1), (4, 0), (8, 1), (15, 4), (4, 7), (11, 2), (2, 1), (10, 8), (14, 3), (18, 8), (16, 6), (6, 0), (9, 5), (17, 8), (4, 1), (16, 1), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978115", "dataset": "MATH"}
{"messages": [{"content": "In a 15x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 7), (4, 5), (11, 0), (12, 14), (13, 12), (11, 11), (14, 9), (7, 4), (1, 12), (12, 9), (7, 5), (10, 2), (10, 7), (4, 3), (7, 8), (9, 12), (6, 8), (10, 12), (8, 6), (14, 8), (11, 8), (12, 16), (10, 11), (2, 7), (3, 10), (9, 13), (3, 2), (1, 4), (3, 17), (7, 11), (12, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "506738", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 5), (10, 7), (11, 2), (9, 1), (10, 0), (13, 3), (10, 12), (11, 5), (16, 6), (11, 4), (14, 13), (14, 0), (3, 11), (4, 11), (4, 3), (11, 13), (5, 0), (9, 10), (0, 7), (16, 4), (11, 9), (3, 6), (15, 9), (17, 5), (6, 5), (16, 8), (9, 3), (12, 9), (15, 12), (6, 4), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607067", "dataset": "MATH"}
{"messages": [{"content": "In a 16x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 0), (0, 4), (13, 4), (10, 8), (13, 1), (10, 6), (4, 4), (1, 0), (11, 2), (7, 3), (0, 6), (13, 5), (12, 3), (7, 6), (7, 8), (1, 3), (5, 0), (1, 8), (12, 7), (8, 9), (2, 9), (4, 7), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9595", "dataset": "MATH"}
{"messages": [{"content": "In a 16x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 9), (14, 4), (1, 10), (7, 5), (9, 2), (8, 4), (8, 10), (9, 1), (3, 0), (6, 4), (1, 8), (3, 11), (12, 8), (1, 2), (8, 5), (3, 1), (11, 4), (5, 2), (2, 6), (5, 1), (14, 8), (12, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471671", "dataset": "MATH"}
{"messages": [{"content": "In a 12x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 0), (4, 7), (6, 8), (7, 11), (8, 11), (7, 2), (8, 7), (2, 9), (10, 7), (6, 6), (3, 4), (2, 5), (8, 2), (6, 11), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254407", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (5, 4), (7, 11), (8, 1), (0, 5), (9, 8), (8, 4), (2, 13), (2, 0), (3, 4), (9, 9), (2, 2), (5, 0), (7, 9), (5, 5), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47702", "dataset": "MATH"}
{"messages": [{"content": "In a 11x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 7), (6, 7), (7, 6), (8, 5), (1, 2), (4, 8), (4, 4), (2, 6), (1, 8), (4, 5), (2, 5), (5, 5), (9, 3), (7, 8), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2846", "dataset": "MATH"}
{"messages": [{"content": "In a 12x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (1, 8), (4, 7), (9, 15), (11, 12), (0, 5), (5, 9), (6, 0), (0, 15), (0, 12), (5, 1), (1, 6), (2, 4), (9, 11), (2, 13), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984975", "dataset": "MATH"}
{"messages": [{"content": "In a 19x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 5), (8, 0), (14, 5), (16, 1), (7, 8), (5, 3), (2, 7), (13, 6), (10, 3), (5, 9), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575969", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (6, 14), (7, 9), (2, 14), (7, 14), (7, 4), (5, 7), (7, 6), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978541", "dataset": "MATH"}
{"messages": [{"content": "In a 13x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 11), (5, 13), (7, 15), (7, 12), (0, 14), (5, 9), (6, 18), (3, 10), (0, 10), (11, 13), (6, 6), (8, 11), (12, 1), (5, 0), (6, 8), (8, 2), (10, 0), (11, 15), (3, 5), (6, 15), (1, 2), (5, 1), (4, 0), (11, 7), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "856062", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (10, 0), (11, 6), (4, 11), (5, 11), (11, 9), (5, 1), (6, 10), (0, 4), (1, 11), (6, 5), (0, 6), (2, 4), (9, 4), (8, 14), (6, 3), (5, 3), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610879", "dataset": "MATH"}
{"messages": [{"content": "In a 10x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (0, 11), (8, 4), (2, 2), (1, 12), (9, 3), (9, 5), (8, 5), (2, 5), (4, 7), (7, 3), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182677", "dataset": "MATH"}
{"messages": [{"content": "In a 13x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (12, 0), (4, 9), (5, 4), (9, 3), (7, 9), (3, 7), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279333", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (5, 6), (17, 4), (9, 2), (10, 5), (15, 14), (7, 9), (16, 3), (14, 1), (4, 8), (3, 10), (4, 14), (8, 4), (13, 1), (8, 11), (9, 14), (7, 12), (15, 6), (5, 11), (15, 7), (9, 7), (10, 3), (8, 7), (10, 2), (7, 11), (13, 3), (4, 10), (4, 5), (7, 1), (16, 6), (7, 8), (12, 12), (0, 10), (3, 8), (10, 11), (1, 4), (4, 1), (6, 10), (12, 4), (0, 7), (1, 8), (17, 10), (13, 6), (17, 8), (5, 7), (10, 9), (1, 7), (5, 9), (12, 6), (1, 12), (16, 8), (11, 14), (17, 5), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155004", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 5), (3, 7), (5, 5), (4, 7), (5, 15), (5, 7), (2, 10), (10, 1), (6, 14), (1, 15), (5, 14), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "644340", "dataset": "MATH"}
{"messages": [{"content": "In a 17x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (14, 8), (1, 4), (8, 11), (2, 12), (3, 12), (0, 11), (9, 3), (8, 12), (7, 3), (3, 2), (0, 16), (15, 12), (6, 6), (16, 5), (2, 2), (3, 6), (11, 5), (10, 17), (7, 10), (13, 17), (7, 1), (15, 14), (7, 7), (8, 17), (10, 7), (16, 9), (8, 13), (7, 18), (0, 12), (16, 0), (1, 6), (10, 16), (15, 6), (5, 1), (16, 7), (2, 17), (6, 15), (7, 12), (2, 0), (13, 12), (4, 17), (1, 17), (15, 16), (7, 9), (3, 16), (9, 0), (6, 11), (4, 3), (8, 0), (13, 2), (0, 8), (7, 11), (10, 8), (0, 6), (8, 8), (13, 8), (4, 0), (5, 17), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836834", "dataset": "MATH"}
{"messages": [{"content": "In a 17x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (7, 6), (1, 2), (8, 7), (16, 2), (15, 8), (7, 8), (14, 4), (14, 1), (12, 2), (12, 10), (10, 2), (8, 2), (9, 3), (4, 2), (4, 5), (8, 5), (13, 0), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252728", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (11, 4), (1, 2), (1, 8), (17, 6), (14, 8), (14, 0), (14, 11), (5, 4), (7, 0), (13, 7), (12, 8), (16, 11), (17, 5), (0, 6), (8, 4), (12, 1), (11, 10), (7, 8), (16, 1), (11, 6), (11, 0), (2, 2), (16, 5), (13, 11), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895646", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (8, 9), (8, 4), (13, 1), (2, 1), (10, 4), (13, 2), (11, 17), (3, 10), (5, 16), (15, 0), (6, 0), (13, 3), (3, 6), (15, 7), (11, 10), (9, 15), (10, 9), (0, 1), (10, 3), (4, 2), (10, 10), (4, 9), (7, 17), (7, 10), (2, 8), (7, 0), (12, 4), (5, 10), (4, 6), (5, 12), (0, 16), (2, 13), (7, 5), (4, 16), (0, 12), (1, 11), (10, 1), (9, 16), (6, 8), (15, 10), (5, 2), (5, 17), (3, 8), (8, 1), (1, 6), (11, 16), (1, 9), (0, 8), (11, 8), (11, 0), (14, 8), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538996", "dataset": "MATH"}
{"messages": [{"content": "In a 11x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 8), (6, 4), (9, 8), (7, 8), (0, 2), (1, 6), (7, 2), (2, 6), (2, 11), (5, 9), (3, 5), (6, 0), (0, 3), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49228", "dataset": "MATH"}
{"messages": [{"content": "In a 13x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 11), (0, 1), (2, 0), (10, 6), (11, 11), (12, 2), (2, 7), (1, 4), (5, 6), (4, 14), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759507", "dataset": "MATH"}
{"messages": [{"content": "In a 19x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 16), (2, 1), (14, 2), (13, 15), (12, 14), (2, 13), (5, 2), (12, 10), (12, 7), (6, 9), (3, 14), (10, 14), (2, 6), (4, 9), (0, 2), (1, 12), (7, 6), (0, 1), (11, 5), (5, 3), (6, 10), (3, 3), (12, 0), (16, 6), (4, 13), (4, 4), (9, 3), (2, 15), (6, 3), (7, 17), (14, 9), (8, 1), (10, 17), (2, 0), (0, 4), (9, 17), (4, 1), (0, 15), (5, 9), (18, 12), (2, 7), (12, 9), (8, 17), (10, 11), (16, 2), (6, 1), (8, 0), (5, 5), (15, 7), (10, 10), (14, 10), (14, 3), (1, 5), (13, 3), (0, 3), (8, 12), (7, 3), (6, 6), (0, 5), (0, 11), (6, 13), (13, 2), (10, 12), (16, 8), (12, 15), (4, 14), (6, 17), (4, 8), (7, 2), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564450", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 12), (14, 5), (9, 5), (1, 0), (5, 1), (14, 3), (15, 4), (7, 5), (6, 13), (5, 2), (1, 4), (4, 5), (4, 4), (2, 6), (11, 2), (11, 10), (13, 2), (4, 14), (8, 15), (3, 2), (6, 14), (2, 4), (8, 12), (8, 14), (11, 3), (2, 7), (5, 0), (14, 15), (16, 1), (16, 10), (0, 13), (13, 15), (13, 7), (6, 6), (14, 11), (6, 8), (0, 11), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864967", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (4, 5), (10, 4), (3, 10), (2, 10), (0, 1), (4, 0), (0, 9), (8, 7), (5, 5), (12, 0), (8, 4), (5, 12), (9, 8), (11, 9), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146688", "dataset": "MATH"}
{"messages": [{"content": "In a 18x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 17), (10, 0), (8, 1), (10, 8), (8, 15), (0, 5), (7, 15), (14, 17), (0, 12), (13, 17), (17, 14), (6, 15), (14, 10), (16, 17), (13, 15), (8, 16), (4, 12), (12, 17), (5, 6), (4, 6), (8, 5), (9, 11), (10, 17), (0, 4), (8, 17), (10, 7), (16, 11), (4, 10), (11, 3), (2, 0), (13, 13), (15, 17), (6, 12), (6, 9), (11, 17), (5, 17), (11, 11), (1, 3), (4, 0), (10, 2), (1, 17), (1, 5), (9, 12), (15, 8), (14, 16), (1, 4), (14, 6), (2, 3), (10, 6), (0, 2), (10, 9), (9, 7), (8, 6), (10, 3), (16, 4), (10, 15), (16, 9), (9, 10), (0, 9), (7, 16), (2, 17), (8, 11), (15, 7), (6, 8), (9, 16), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998054", "dataset": "MATH"}
{"messages": [{"content": "In a 13x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (0, 10), (0, 1), (8, 2), (4, 13), (12, 11), (6, 5), (1, 11), (0, 7), (3, 7), (5, 5), (1, 13), (6, 6), (4, 7), (5, 11), (10, 1), (11, 15), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810236", "dataset": "MATH"}
{"messages": [{"content": "In a 15x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (5, 2), (14, 8), (1, 15), (5, 17), (6, 16), (12, 8), (10, 14), (11, 17), (2, 9), (2, 12), (13, 17), (5, 10), (14, 0), (14, 17), (3, 6), (1, 12), (13, 0), (1, 3), (6, 7), (12, 15), (7, 18), (8, 18), (13, 10), (4, 7), (11, 10), (7, 1), (4, 15), (0, 9), (9, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953337", "dataset": "MATH"}
{"messages": [{"content": "In a 13x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (10, 1), (11, 6), (6, 8), (8, 5), (12, 3), (11, 0), (2, 6), (1, 3), (1, 4), (0, 11), (8, 3), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437379", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 10), (0, 4), (15, 8), (3, 7), (9, 5), (13, 3), (5, 4), (3, 6), (16, 7), (8, 10), (1, 13), (16, 14), (13, 4), (1, 4), (4, 11), (12, 14), (5, 11), (3, 3), (9, 3), (11, 12), (2, 2), (5, 1), (13, 7), (0, 12), (12, 6), (16, 10), (8, 3), (12, 12), (13, 2), (1, 8), (13, 9), (15, 6), (1, 7), (4, 14), (7, 15), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760451", "dataset": "MATH"}
{"messages": [{"content": "In a 10x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (3, 6), (8, 12), (5, 11), (0, 4), (4, 13), (5, 6), (7, 14), (9, 3), (2, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251430", "dataset": "MATH"}
{"messages": [{"content": "In a 11x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 18), (9, 0), (5, 13), (4, 10), (10, 14), (2, 17), (9, 3), (4, 1), (3, 9), (2, 3), (10, 2), (4, 16), (10, 4), (2, 9), (3, 16), (2, 12), (3, 8), (9, 4), (1, 17), (6, 0), (7, 9), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768835", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (11, 0), (12, 16), (0, 15), (14, 8), (8, 9), (6, 2), (14, 10), (11, 17), (3, 2), (8, 17), (8, 15), (10, 2), (10, 9), (15, 8), (7, 10), (14, 5), (6, 11), (11, 15), (5, 5), (8, 13), (10, 12), (7, 1), (13, 3), (0, 16), (7, 13), (9, 2), (15, 2), (0, 2), (9, 16), (9, 11), (12, 7), (8, 4), (6, 10), (2, 7), (0, 3), (10, 11), (3, 14), (1, 15), (12, 2), (2, 11), (12, 17), (8, 1), (7, 7), (3, 13), (7, 8), (7, 6), (6, 0), (1, 13), (13, 2), (13, 17), (0, 10), (3, 4), (9, 17), (4, 14), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708373", "dataset": "MATH"}
{"messages": [{"content": "In a 11x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 6), (10, 12), (4, 15), (8, 5), (3, 5), (3, 11), (3, 8), (10, 9), (0, 15), (9, 5), (4, 4), (7, 14), (5, 2), (3, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "435456", "dataset": "MATH"}
{"messages": [{"content": "In a 17x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 3), (7, 3), (10, 1), (3, 0), (16, 13), (1, 10), (10, 11), (6, 14), (12, 10), (1, 14), (12, 8), (7, 16), (4, 14), (7, 8), (15, 9), (15, 3), (0, 11), (8, 1), (3, 3), (7, 11), (16, 1), (10, 2), (4, 7), (4, 3), (3, 13), (15, 4), (2, 14), (0, 5), (12, 7), (13, 11), (8, 8), (14, 8), (14, 16), (15, 11), (6, 5), (9, 7), (14, 6), (9, 2), (1, 12), (9, 10), (4, 1), (7, 7), (11, 14), (7, 9), (10, 4), (11, 9), (2, 12), (9, 1), (3, 16), (8, 0), (9, 6), (0, 14), (2, 13), (13, 16), (2, 5), (16, 11), (14, 3), (7, 5), (4, 13), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775048", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (7, 13), (6, 2), (3, 7), (3, 12), (4, 12), (3, 9), (11, 12), (7, 2), (7, 15), (4, 14), (9, 5), (9, 7), (4, 6), (7, 5), (9, 15), (11, 14), (4, 2), (1, 5), (1, 8), (7, 4), (8, 2), (4, 7), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793814", "dataset": "MATH"}
{"messages": [{"content": "In a 11x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (8, 9), (1, 6), (6, 4), (5, 3), (8, 4), (3, 7), (8, 10), (6, 2), (2, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46737", "dataset": "MATH"}
{"messages": [{"content": "In a 18x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 11), (8, 2), (1, 12), (1, 13), (11, 4), (6, 2), (6, 1), (8, 4), (13, 0), (8, 12), (4, 6), (7, 7), (9, 4), (11, 0), (0, 5), (8, 1), (5, 0), (16, 12), (6, 3), (6, 7), (17, 1), (15, 13), (0, 8), (5, 11), (7, 9), (1, 9), (2, 9), (6, 13), (11, 5), (7, 13), (13, 1), (1, 8), (14, 7), (11, 3), (17, 8), (17, 10), (4, 13), (7, 12), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936215", "dataset": "MATH"}
{"messages": [{"content": "In a 15x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (4, 6), (12, 3), (11, 8), (11, 4), (0, 4), (8, 6), (3, 2), (8, 4), (1, 9), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195305", "dataset": "MATH"}
{"messages": [{"content": "In a 13x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (12, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (12, 4), (5, 7), (11, 3), (4, 7), (11, 0), (0, 1), (12, 8), (6, 9), (9, 4), (8, 9), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53352", "dataset": "MATH"}
{"messages": [{"content": "In a 12x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (6, 2), (0, 2), (0, 12), (4, 3), (2, 12), (9, 0), (6, 4), (3, 7), (8, 0), (0, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766164", "dataset": "MATH"}
{"messages": [{"content": "In a 18x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 5), (1, 12), (12, 9), (9, 8), (9, 6), (12, 14), (8, 3), (15, 4), (2, 3), (3, 6), (8, 2), (0, 14), (13, 5), (0, 12), (9, 15), (3, 10), (11, 10), (0, 6), (10, 1), (9, 14), (17, 2), (1, 13), (10, 9), (4, 0), (17, 5), (7, 3), (3, 13), (1, 10), (3, 7), (8, 9), (6, 9), (11, 13), (8, 11), (11, 14), (15, 6), (14, 7), (5, 6), (11, 9), (15, 11), (2, 15), (10, 7), (9, 3), (3, 15), (9, 7), (5, 0), (3, 9), (6, 4), (6, 14), (9, 0), (0, 15), (12, 15), (1, 9), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913610", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (4, 3), (1, 10), (1, 4), (8, 3), (2, 2), (5, 10), (5, 6), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15688", "dataset": "MATH"}
{"messages": [{"content": "In a 17x16 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 15), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (16, 6), (0, 12), (12, 11), (3, 14), (0, 11), (4, 7), (15, 1), (11, 10), (7, 3), (10, 4), (3, 10), (12, 5), (4, 10), (15, 7), (3, 8), (7, 2), (14, 13), (3, 11), (8, 8), (6, 10), (3, 12), (10, 15), (15, 14), (5, 4), (4, 4), (1, 12), (1, 10), (5, 6), (1, 9), (1, 0), (16, 7), (1, 3), (10, 5), (14, 7), (1, 8), (5, 8), (12, 3), (2, 13), (9, 14), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943633", "dataset": "MATH"}
{"messages": [{"content": "In a 14x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (10, 2), (5, 0), (6, 6), (7, 4), (5, 1), (12, 4), (9, 6), (8, 1), (11, 3), (13, 8), (10, 9), (1, 1), (0, 3), (0, 6), (0, 8), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13308", "dataset": "MATH"}
{"messages": [{"content": "In a 17x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 11), (12, 9), (4, 13), (12, 8), (2, 12), (14, 5), (1, 5), (10, 1), (3, 2), (12, 12), (3, 0), (13, 9), (7, 9), (5, 7), (3, 14), (15, 0), (6, 4), (16, 5), (13, 12), (8, 5), (5, 8), (12, 11), (10, 4), (2, 11), (12, 5), (5, 10), (15, 14), (13, 6), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863738", "dataset": "MATH"}
{"messages": [{"content": "In a 18x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 8), (5, 2), (3, 8), (13, 17), (8, 16), (16, 4), (14, 9), (5, 18), (11, 10), (2, 15), (8, 5), (17, 11), (0, 18), (17, 12), (11, 0), (1, 13), (4, 12), (11, 17), (2, 3), (0, 6), (1, 11), (3, 9), (8, 3), (7, 7), (2, 0), (5, 9), (14, 5), (12, 13), (13, 0), (16, 15), (10, 12), (4, 16), (4, 1), (16, 13), (16, 0), (9, 8), (3, 17), (3, 7), (6, 12), (17, 10), (8, 8), (14, 4), (0, 16), (13, 2), (8, 0), (12, 5), (6, 6), (8, 18), (15, 8), (5, 6), (2, 1), (14, 3), (6, 10), (7, 17), (11, 18), (16, 14), (12, 11), (0, 7), (9, 14), (5, 13), (12, 18), (8, 14), (17, 6), (0, 11), (8, 6), (13, 14), (5, 16), (9, 10), (0, 17), (13, 3), (4, 4), (6, 7), (4, 5), (10, 16), (13, 11), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504212", "dataset": "MATH"}
{"messages": [{"content": "In a 16x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 5), (14, 15), (15, 2), (11, 7), (11, 15), (13, 15), (2, 3), (2, 8), (1, 2), (4, 14), (11, 16), (14, 5), (15, 1), (3, 15), (11, 12), (1, 1), (12, 13), (2, 17), (0, 14), (15, 0), (11, 13), (13, 12), (9, 13), (5, 13), (15, 10), (0, 9), (0, 12), (15, 7), (9, 15), (6, 2), (8, 9), (6, 9), (3, 9), (1, 8), (14, 13), (2, 4), (2, 14), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265734", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (3, 15), (13, 5), (8, 8), (4, 8), (11, 7), (3, 16), (13, 14), (10, 8), (8, 3), (14, 16), (4, 1), (15, 17), (13, 9), (5, 8), (11, 5), (1, 1), (0, 2), (12, 3), (8, 10), (2, 18), (5, 5), (15, 10), (13, 2), (15, 6), (9, 1), (8, 7), (9, 17), (9, 18), (9, 15), (14, 4), (6, 5), (15, 1), (11, 16), (2, 8), (10, 4), (5, 1), (1, 17), (13, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208508", "dataset": "MATH"}
{"messages": [{"content": "In a 12x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 5), (2, 9), (5, 11), (4, 0), (6, 9), (0, 13), (9, 9), (10, 4), (7, 1), (6, 3), (6, 1), (1, 8), (9, 7), (11, 13), (2, 3), (7, 12), (1, 0), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125717", "dataset": "MATH"}
{"messages": [{"content": "In a 15x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (14, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 8), (1, 1), (2, 5), (3, 3), (4, 2), (10, 0), (10, 6), (5, 4), (11, 11), (1, 9), (6, 1), (11, 10), (14, 4), (10, 7), (7, 7), (11, 7), (14, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41100", "dataset": "MATH"}
{"messages": [{"content": "In a 18x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (9, 7), (1, 8), (9, 0), (1, 3), (1, 2), (11, 5), (16, 2), (7, 2), (7, 8), (12, 4), (9, 8), (6, 4), (8, 1), (4, 9), (4, 3), (6, 2), (8, 9), (5, 8), (4, 6), (14, 5), (0, 2), (6, 3), (4, 1), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36000", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 13), (13, 5), (0, 9), (0, 5), (12, 12), (2, 5), (6, 14), (6, 6), (4, 2), (2, 8), (4, 11), (2, 4), (7, 6), (3, 5), (11, 15), (10, 10), (12, 2), (11, 0), (12, 3), (8, 1), (6, 3), (10, 2), (7, 7), (9, 8), (4, 1), (1, 11), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820722", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 11), (4, 1), (3, 0), (10, 5), (6, 4), (16, 5), (2, 10), (12, 13), (1, 13), (8, 11), (13, 3), (8, 7), (16, 3), (2, 3), (4, 3), (0, 2), (12, 3), (4, 13), (14, 13), (1, 5), (4, 9), (9, 13), (13, 10), (0, 3), (5, 0), (3, 12), (15, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485060", "dataset": "MATH"}
{"messages": [{"content": "In a 14x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 9), (6, 8), (1, 13), (13, 12), (13, 10), (11, 14), (5, 13), (5, 4), (5, 16), (12, 7), (9, 17), (5, 11), (3, 6), (9, 10), (8, 12), (5, 3), (4, 14), (10, 2), (4, 4), (0, 7), (5, 15), (3, 5), (10, 12), (11, 1), (0, 16), (8, 15), (1, 16), (1, 2), (1, 9), (5, 14), (3, 18), (5, 7), (12, 12), (6, 4), (10, 11), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247377", "dataset": "MATH"}
{"messages": [{"content": "In a 16x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (15, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (2, 1), (12, 18), (15, 17), (3, 10), (7, 12), (10, 1), (4, 18), (8, 15), (5, 16), (15, 16), (9, 0), (13, 6), (9, 4), (1, 2), (6, 15), (4, 5), (4, 14), (12, 3), (9, 15), (0, 8), (6, 3), (10, 4), (1, 5), (11, 3), (6, 8), (6, 0), (8, 10), (8, 2), (10, 0), (13, 10), (1, 11), (7, 2), (7, 13), (4, 7), (10, 15), (3, 0), (5, 6), (2, 0), (7, 10), (4, 13), (3, 17), (3, 13), (15, 2), (5, 8), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854928", "dataset": "MATH"}
{"messages": [{"content": "In a 12x19 grid, how many different paths are there from the bottom left (0, 0) to the top right (11, 18), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (6, 8), (4, 9), (11, 9), (7, 16), (4, 11), (1, 9), (4, 16), (9, 13), (1, 10), (1, 17), (6, 5), (1, 4), (9, 14), (2, 2), (10, 16), (8, 7), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818373", "dataset": "MATH"}
{"messages": [{"content": "In a 11x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (2, 8), (3, 4), (8, 9), (8, 0), (7, 6), (6, 7), (9, 3), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15466", "dataset": "MATH"}
{"messages": [{"content": "In a 17x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (16, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 12), (15, 7), (14, 7), (12, 8), (12, 0), (15, 10), (11, 0), (6, 5), (14, 6), (1, 2), (14, 8), (10, 9), (13, 10), (4, 9), (5, 3), (3, 3), (7, 13), (0, 9), (5, 9), (16, 10), (8, 12), (13, 7), (16, 4), (10, 5), (11, 7), (1, 7), (16, 3), (11, 1), (1, 13), (7, 0), (4, 8), (12, 2), (11, 5), (14, 11), (1, 10), (7, 7), (9, 0), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841732", "dataset": "MATH"}
{"messages": [{"content": "In a 18x13 grid, how many different paths are there from the bottom left (0, 0) to the top right (17, 12), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (7, 10), (10, 8), (7, 5), (0, 8), (7, 2), (1, 2), (9, 3), (17, 9), (2, 8), (1, 12), (14, 12), (15, 1), (4, 2), (5, 0), (15, 4), (0, 2), (4, 7), (6, 7), (12, 10), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717531", "dataset": "MATH"}
{"messages": [{"content": "In a 19x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (2, 5), (4, 10), (17, 10), (18, 8), (8, 8), (8, 10), (15, 2), (6, 8), (18, 3), (16, 6), (12, 10), (7, 5), (3, 7), (10, 3), (13, 9), (15, 10), (13, 4), (4, 7), (1, 8), (15, 7), (17, 3), (9, 2), (16, 4), (10, 8), (18, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986889", "dataset": "MATH"}
{"messages": [{"content": "In a 14x17 grid, how many different paths are there from the bottom left (0, 0) to the top right (13, 16), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 7), (12, 12), (10, 0), (11, 4), (10, 3), (13, 10), (9, 9), (1, 2), (11, 15), (9, 12), (4, 15), (8, 11), (8, 4), (13, 1), (5, 1), (3, 13), (11, 14), (5, 15), (11, 6), (6, 10), (7, 3), (10, 16), (10, 6), (1, 5), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906702", "dataset": "MATH"}
{"messages": [{"content": "In a 10x12 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 11), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (3, 5), (1, 6), (2, 7), (4, 0), (4, 6), (1, 9), (3, 6), (5, 11), (3, 11), (6, 8), (2, 6), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26878", "dataset": "MATH"}
{"messages": [{"content": "In a 10x18 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 17), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 10), (6, 8), (4, 10), (0, 17), (8, 0), (1, 10), (2, 17), (3, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "905004", "dataset": "MATH"}
{"messages": [{"content": "In a 19x11 grid, how many different paths are there from the bottom left (0, 0) to the top right (18, 10), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (0, 10), (11, 3), (15, 9), (15, 8), (13, 5), (7, 7), (7, 10), (14, 1), (5, 6), (15, 2), (18, 5), (9, 10), (8, 10), (5, 5), (3, 5), (9, 2), (18, 4), (13, 9), (3, 10), (14, 10), (6, 8), (1, 6), (6, 9), (13, 6), (3, 1), (17, 10), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82014", "dataset": "MATH"}
{"messages": [{"content": "In a 11x14 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 13), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 0), (3, 0), (7, 2), (0, 7), (4, 4), (0, 4), (0, 1), (6, 1), (2, 11), (8, 0), (9, 6), (1, 6), (7, 13), (2, 9), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222491", "dataset": "MATH"}
{"messages": [{"content": "In a 11x15 grid, how many different paths are there from the bottom left (0, 0) to the top right (10, 14), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (0, 11), (0, 1), (1, 3), (8, 6), (6, 5), (2, 10), (9, 9), (9, 13), (1, 4), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123434", "dataset": "MATH"}