{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (8, 10), (2, 4), (12, 2), (4, 10), (4, 4), (12, 19), (5, 9), (18, 3), (9, 14), (9, 9), (13, 17), (14, 10), (11, 12), (11, 1), (4, 0), (6, 19), (1, 20), (10, 6), (2, 7), (14, 6), (17, 12), (4, 21), (4, 9), (1, 1), (14, 2), (18, 21), (5, 11), (6, 1), (5, 16), (5, 0), (8, 20), (16, 2), (8, 13), (19, 9), (6, 13), (14, 7), (8, 0), (15, 10), (7, 0), (12, 17), (15, 15), (3, 2), (7, 4), (2, 0), (14, 19), (17, 18), (1, 7), (10, 8), (0, 9), (13, 18), (0, 4), (8, 21), (1, 15), (3, 1), (15, 19), (18, 17), (12, 20), (8, 15), (7, 17), (18, 11), (5, 15), (11, 3), (5, 2), (14, 15), (3, 7), (11, 20), (12, 0), (6, 4), (19, 12), (9, 15), (16, 15), (2, 10), (11, 17), (7, 9), (16, 9), (11, 13), (9, 18), (0, 8), (13, 4), (13, 3), (6, 15), (5, 13), (3, 20), (3, 19), (16, 5), (10, 20), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752952", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 16), (17, 17), (3, 13), (9, 16), (1, 10), (1, 8), (6, 1), (2, 21), (14, 16), (17, 13), (7, 1), (12, 8), (3, 3), (17, 21), (0, 13), (14, 7), (1, 11), (18, 2), (4, 18), (3, 15), (12, 6), (1, 4), (21, 5), (0, 15), (16, 5), (3, 14), (9, 10), (20, 6), (15, 6), (0, 14), (9, 5), (6, 17), (20, 18), (6, 9), (4, 2), (6, 7), (12, 17), (1, 17), (4, 10), (8, 14), (9, 12), (6, 6), (7, 19), (13, 6), (20, 13), (2, 9), (2, 15), (7, 21), (9, 17), (8, 16), (16, 8), (21, 11), (2, 11), (4, 11), (8, 18), (0, 20), (13, 0), (20, 5), (10, 14), (11, 5), (16, 17), (3, 0), (0, 3), (1, 3), (20, 16), (17, 12), (13, 1), (1, 2), (6, 16), (13, 13), (14, 15), (9, 13), (20, 20), (5, 16), (6, 11), (3, 12), (15, 17), (20, 2), (13, 12), (20, 21), (10, 19), (15, 19), (9, 21), (14, 20), (11, 14), (11, 1), (6, 0), (2, 18), (19, 11), (19, 19), (8, 15), (10, 21), (0, 1), (11, 18), (4, 21), (19, 6), (4, 5), (6, 20), (10, 0), (16, 2), (14, 3), (17, 5), (4, 4), (4, 20), (2, 16), (5, 11), (21, 12), (7, 13), (8, 9), (13, 21), (7, 20), (5, 8), (18, 12), (5, 21), (17, 20), (21, 14), (11, 2), (11, 13), (4, 13), (17, 15), (13, 14), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913325", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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), (15, 21), (18, 2), (9, 8), (14, 17), (3, 16), (14, 15), (6, 20), (3, 18), (5, 16), (4, 6), (12, 20), (8, 6), (14, 5), (5, 19), (1, 9), (5, 0), (14, 10), (18, 3), (0, 4), (16, 12), (19, 18), (5, 21), (1, 11), (2, 19), (19, 5), (0, 11), (4, 14), (9, 15), (17, 8), (5, 12), (14, 13), (15, 15), (0, 16), (4, 8), (2, 14), (20, 11), (9, 2), (1, 17), (4, 4), (1, 6), (16, 5), (8, 3), (2, 11), (3, 19), (19, 7), (4, 20), (12, 9), (4, 19), (19, 8), (20, 0), (1, 12), (20, 1), (17, 12), (18, 17), (7, 8), (20, 12), (16, 4), (1, 13), (18, 7), (13, 3), (9, 7), (16, 6), (16, 3), (11, 4), (15, 13), (8, 11), (6, 3), (11, 13), (1, 5), (17, 0), (5, 9), (2, 5), (20, 20), (4, 7), (7, 9), (17, 6), (7, 5), (7, 14), (15, 11), (4, 9), (11, 9), (17, 20), (12, 18), (7, 10), (19, 9), (18, 11), (5, 10), (20, 10), (6, 12), (14, 7), (3, 12), (4, 11), (6, 6), (19, 2), (1, 20), (0, 13), (15, 9), (4, 18), (8, 18), (3, 6), (6, 19), (6, 8), (12, 16), (18, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406143", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 18), (9, 23), (16, 17), (2, 12), (10, 0), (10, 23), (7, 4), (11, 15), (17, 20), (11, 2), (14, 8), (12, 7), (2, 16), (14, 4), (7, 13), (8, 2), (18, 21), (15, 4), (10, 15), (20, 8), (12, 23), (12, 19), (10, 9), (9, 24), (10, 24), (7, 21), (3, 8), (7, 8), (17, 22), (14, 21), (5, 10), (4, 24), (16, 13), (3, 0), (6, 7), (16, 8), (1, 24), (0, 23), (1, 8), (18, 12), (21, 20), (19, 18), (16, 0), (8, 6), (10, 2), (18, 2), (7, 5), (17, 3), (2, 0), (12, 6), (15, 23), (2, 10), (4, 0), (3, 6), (11, 4), (13, 7), (13, 22), (8, 5), (16, 9), (0, 20), (2, 18), (21, 7), (2, 2), (0, 16), (13, 19), (11, 13), (15, 12), (5, 21), (20, 24), (17, 19), (14, 11), (13, 14), (5, 24), (13, 5), (17, 6), (21, 11), (0, 22), (19, 12), (11, 8), (21, 8), (13, 24), (8, 15), (8, 9), (18, 17), (4, 19), (19, 13), (9, 12), (13, 6), (5, 22), (6, 2), (20, 14), (1, 11), (19, 7), (3, 9), (7, 22), (19, 3), (5, 6), (1, 6), (2, 8), (15, 5), (18, 20), (3, 5), (20, 2), (12, 9), (5, 19), (1, 12), (11, 19), (0, 17), (2, 22), (19, 9), (1, 2), (3, 24), (17, 15), (17, 10), (0, 14), (9, 14), (4, 18), (4, 22), (14, 14), (6, 10), (19, 17), (15, 11), (2, 7), (12, 3), (19, 21), (6, 5), (19, 1), (1, 17), (18, 5), (13, 23), (11, 10), (9, 1), (20, 13), (11, 9), (19, 22), (5, 7), (11, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987402", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), 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), (24, 21), (16, 20), (13, 17), (16, 9), (10, 8), (27, 6), (5, 5), (14, 12), (2, 3), (12, 0), (26, 19), (23, 4), (22, 19), (4, 0), (6, 12), (26, 21), (22, 22), (17, 17), (20, 5), (3, 19), (23, 19), (7, 20), (2, 4), (10, 21), (23, 8), (10, 4), (4, 5), (7, 22), (1, 9), (22, 23), (15, 4), (19, 10), (0, 7), (3, 11), (14, 10), (17, 12), (13, 11), (24, 10), (14, 21), (20, 9), (12, 9), (18, 16), (5, 11), (3, 21), (4, 17), (3, 5), (10, 5), (10, 13), (14, 8), (18, 0), (5, 8), (19, 1), (24, 16), (13, 18), (9, 12), (0, 15), (21, 13), (12, 6), (20, 15), (28, 22), (0, 19), (19, 17), (1, 3), (16, 12), (13, 23), (12, 14), (24, 4), (25, 0), (21, 15), (21, 12), (12, 10), (5, 9), (25, 1), (9, 10), (9, 11), (21, 2), (1, 18), (8, 7), (5, 19), (28, 4), (2, 13), (7, 2), (4, 10), (11, 6), (27, 17), (20, 21), (25, 23), (5, 6), (28, 18), (20, 23), (24, 22), (7, 7), (15, 10), (22, 14), (1, 17), (6, 6), (25, 7), (22, 16), (22, 9), (26, 2), (26, 5), (14, 19), (0, 16), (8, 17), (6, 11), (25, 8), (18, 2), (23, 11), (7, 4), (26, 3), (4, 11), (2, 15), (3, 14), (19, 7), (8, 19), (11, 2), (11, 0), (15, 14), (15, 0), (0, 2), (14, 7), (7, 17), (20, 1), (24, 5), (16, 5), (6, 5), (28, 15), (8, 6), (18, 13), (22, 2), (4, 7), (23, 9), (16, 19), (13, 22), (14, 18), (5, 18), (3, 8), (9, 21), (13, 19), (20, 6), (22, 12), (5, 4), (21, 4), (17, 7), (23, 7), (1, 8), (22, 11), (21, 1), (11, 20), (23, 21), (24, 12), (14, 16), (15, 20), (21, 0), (14, 22), (20, 4), (8, 1), (24, 20), (25, 2), (20, 20), (2, 10), (19, 4), (4, 8), (1, 5), (25, 17), (5, 7), (13, 14), (19, 6), (25, 5), (18, 18), (11, 5), (9, 23), (26, 13), (24, 3), (13, 13), (8, 14), (13, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907560", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 9), (4, 9), (2, 12), (15, 3), (2, 13), (22, 7), (1, 15), (20, 2), (23, 9), (23, 5), (11, 13), (1, 9), (0, 13), (7, 8), (4, 14), (8, 0), (10, 14), (16, 19), (20, 3), (21, 17), (15, 11), (1, 4), (13, 1), (9, 3), (10, 13), (24, 16), (18, 14), (17, 0), (23, 12), (2, 5), (0, 11), (3, 14), (0, 6), (20, 6), (21, 1), (14, 17), (20, 12), (3, 12), (2, 7), (16, 16), (0, 8), (10, 1), (15, 7), (13, 17), (21, 0), (20, 20), (4, 19), (15, 4), (6, 5), (9, 12), (14, 6), (13, 3), (5, 3), (6, 15), (3, 10), (9, 9), (4, 17), (7, 12), (5, 8), (18, 5), (22, 6), (21, 16), (15, 16), (17, 11), (10, 8), (24, 15), (9, 1), (6, 9), (13, 20), (10, 19), (9, 19), (11, 0), (7, 13), (18, 15), (9, 0), (16, 5), (6, 10), (22, 10), (7, 14), (19, 10), (15, 15), (12, 1), (15, 13), (11, 5), (11, 14), (8, 8), (6, 14), (20, 1), (17, 13), (10, 3), (4, 3), (22, 15), (16, 12), (5, 7), (1, 18), (22, 4), (12, 20), (20, 9), (13, 12), (12, 18), (16, 15), (13, 18), (3, 1), (21, 10), (0, 10), (0, 19), (12, 13), (11, 7), (8, 4), (8, 10), (20, 4), (20, 16), (13, 8), (17, 12), (9, 11), (20, 8), (4, 2), (19, 17), (6, 12), (13, 19), (17, 19), (6, 11), (14, 20), (17, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970772", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 22), (20, 15), (1, 28), (17, 22), (8, 15), (15, 2), (7, 13), (13, 26), (2, 5), (4, 22), (7, 10), (5, 25), (18, 7), (5, 6), (6, 28), (12, 17), (16, 24), (17, 17), (13, 3), (21, 22), (15, 4), (20, 16), (9, 9), (4, 7), (20, 0), (9, 26), (14, 7), (18, 21), (5, 7), (5, 1), (21, 7), (4, 12), (14, 24), (14, 1), (21, 3), (8, 9), (1, 23), (20, 1), (15, 27), (10, 12), (9, 7), (1, 10), (17, 6), (18, 9), (19, 23), (11, 15), (4, 8), (4, 6), (8, 7), (0, 24), (8, 19), (12, 14), (8, 23), (2, 21), (18, 5), (9, 11), (5, 17), (11, 22), (6, 13), (8, 13), (3, 14), (7, 26), (3, 21), (17, 27), (5, 20), (17, 23), (21, 6), (12, 26), (3, 28), (11, 2), (7, 15), (12, 4), (15, 26), (10, 2), (0, 17), (10, 16), (16, 7), (8, 6), (17, 4), (10, 27), (14, 27), (21, 24), (8, 4), (1, 12), (19, 13), (18, 0), (13, 16), (17, 8), (10, 11), (3, 10), (12, 9), (7, 11), (4, 5), (11, 9), (14, 15), (10, 22), (13, 14), (3, 1), (19, 20), (4, 2), (15, 28), (10, 3), (3, 20), (21, 1), (5, 11), (12, 24), (6, 16), (11, 28), (6, 10), (4, 28), (7, 23), (17, 21), (20, 28), (17, 10), (2, 16), (1, 3), (9, 14), (6, 25), (2, 3), (0, 1), (4, 27), (9, 5), (20, 26), (10, 10), (8, 14), (10, 17), (7, 5), (15, 11), (6, 7), (15, 19), (16, 13), (16, 18), (18, 14), (3, 13), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "462858", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), 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), (12, 0), (12, 18), (13, 0), (7, 9), (11, 14), (1, 12), (8, 10), (11, 1), (17, 5), (17, 22), (10, 0), (19, 16), (13, 13), (8, 14), (9, 15), (19, 1), (5, 24), (8, 8), (20, 11), (20, 18), (3, 6), (21, 23), (6, 22), (4, 14), (13, 18), (11, 12), (5, 12), (16, 8), (8, 16), (16, 20), (7, 22), (12, 1), (17, 0), (21, 3), (1, 10), (18, 2), (14, 13), (8, 12), (3, 19), (13, 12), (22, 23), (22, 8), (16, 4), (0, 3), (21, 6), (12, 21), (3, 10), (1, 6), (16, 11), (10, 24), (5, 2), (7, 1), (11, 3), (12, 15), (6, 2), (0, 14), (12, 9), (17, 2), (8, 4), (0, 8), (11, 23), (14, 20), (0, 6), (12, 7), (20, 3), (8, 9), (6, 17), (16, 0), (17, 17), (2, 15), (11, 20), (10, 17), (18, 3), (8, 11), (5, 6), (20, 0), (5, 13), (14, 24), (19, 21), (16, 18), (17, 4), (9, 20), (0, 10), (22, 10), (1, 3), (5, 20), (20, 15), (3, 4), (12, 13), (11, 11), (4, 22), (2, 18), (19, 13), (6, 21), (15, 11), (8, 15), (14, 9), (6, 20), (7, 7), (10, 13), (17, 20), (14, 11), (10, 1), (16, 1), (6, 7), (19, 11), (22, 5), (15, 6), (20, 20), (21, 20), (7, 11), (17, 10), (3, 7), (16, 13), (12, 8), (12, 19), (14, 17), (5, 14), (9, 21), (21, 17), (8, 6), (5, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944474", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), 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), (18, 15), (14, 3), (20, 16), (2, 21), (16, 1), (3, 9), (24, 3), (11, 22), (8, 23), (10, 8), (15, 14), (7, 4), (21, 10), (22, 19), (0, 20), (4, 2), (19, 20), (10, 6), (5, 0), (19, 14), (13, 22), (4, 4), (16, 11), (16, 16), (14, 16), (24, 14), (12, 2), (8, 16), (24, 1), (1, 1), (23, 8), (1, 8), (22, 24), (9, 14), (24, 11), (2, 1), (0, 3), (17, 20), (9, 23), (1, 14), (1, 5), (4, 13), (14, 17), (12, 18), (11, 2), (0, 24), (7, 13), (11, 7), (23, 18), (16, 23), (22, 1), (7, 9), (17, 18), (1, 10), (24, 18), (1, 22), (14, 15), (6, 21), (6, 8), (6, 22), (8, 1), (6, 2), (3, 14), (16, 13), (13, 10), (15, 3), (3, 12), (19, 10), (0, 13), (9, 5), (13, 18), (9, 17), (21, 2), (18, 21), (12, 17), (19, 4), (17, 1), (19, 9), (20, 1), (23, 12), (3, 20), (14, 10), (20, 14), (5, 24), (11, 13), (16, 9), (10, 18), (0, 10), (11, 20), (15, 20), (7, 3), (0, 23), (13, 6), (2, 2), (23, 10), (23, 1), (17, 6), (11, 5), (13, 24), (15, 7), (20, 11), (8, 11), (17, 4), (9, 4), (0, 9), (22, 7), (6, 11), (5, 17), (23, 6), (15, 12), (16, 8), (11, 17), (24, 4), (0, 15), (6, 18), (14, 4), (8, 13), (16, 18), (13, 5), (11, 24), (11, 3), (1, 0), (12, 20), (5, 19), (20, 6), (14, 22), (14, 19), (5, 16), (5, 21), (3, 21), (7, 24), (21, 5), (19, 5), (3, 15), (24, 13), (13, 9), (24, 0), (15, 9), (1, 15), (13, 23), (1, 17), (15, 16), (3, 1), (12, 15), (18, 8), (19, 3), (1, 9), (12, 13), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728940", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 13), (17, 10), (8, 6), (18, 1), (2, 5), (2, 11), (6, 2), (10, 13), (8, 19), (5, 11), (5, 17), (13, 7), (16, 15), (20, 17), (5, 16), (13, 5), (7, 3), (0, 11), (12, 13), (2, 4), (10, 11), (18, 8), (7, 20), (2, 13), (8, 2), (4, 9), (12, 10), (1, 5), (18, 7), (19, 4), (11, 18), (12, 16), (15, 19), (6, 8), (3, 0), (15, 0), (3, 16), (15, 12), (17, 18), (3, 4), (16, 19), (4, 17), (10, 5), (17, 16), (0, 15), (15, 17), (13, 3), (13, 12), (6, 11), (12, 11), (0, 16), (7, 1), (16, 20), (2, 1), (11, 4), (4, 19), (5, 4), (19, 16), (15, 14), (19, 0), (16, 13), (3, 15), (5, 0), (15, 20), (4, 14), (12, 0), (18, 16), (8, 1), (5, 2), (9, 9), (19, 19), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736192", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (19, 5), (9, 3), (5, 21), (19, 4), (15, 17), (10, 0), (11, 13), (10, 4), (17, 11), (18, 12), (10, 16), (12, 13), (12, 21), (19, 10), (0, 17), (3, 21), (14, 8), (4, 7), (1, 21), (11, 10), (18, 3), (6, 5), (9, 6), (1, 12), (19, 17), (15, 7), (2, 12), (9, 14), (1, 17), (3, 17), (5, 17), (16, 10), (18, 17), (18, 7), (16, 1), (16, 16), (3, 8), (0, 20), (19, 12), (14, 15), (0, 18), (1, 1), (11, 0), (0, 21), (17, 2), (2, 14), (5, 0), (19, 8), (4, 3), (8, 5), (9, 12), (18, 20), (8, 9), (4, 16), (18, 8), (16, 3), (4, 17), (8, 6), (3, 18), (9, 21), (13, 15), (7, 15), (15, 21), (8, 0), (3, 3), (19, 20), (3, 19), (10, 2), (3, 5), (15, 11), (2, 16), (15, 6), (10, 7), (4, 11), (19, 15), (13, 9), (15, 15), (17, 3), (14, 5), (3, 7), (12, 20), (12, 12), (14, 21), (15, 18), (15, 10), (9, 11), (9, 1), (16, 17), (7, 0), (17, 13), (8, 19), (5, 7), (4, 2), (7, 5), (7, 18), (14, 10), (2, 11), (14, 9), (13, 3), (12, 17), (19, 6), (1, 4), (1, 7), (5, 16), (16, 14), (15, 19), (19, 7), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912658", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 23), (21, 4), (4, 19), (3, 20), (28, 24), (7, 26), (13, 19), (8, 23), (10, 8), (5, 7), (6, 17), (8, 8), (24, 25), (14, 20), (20, 26), (19, 6), (8, 13), (17, 3), (23, 21), (22, 0), (26, 0), (10, 9), (24, 10), (0, 13), (10, 17), (10, 19), (28, 6), (13, 24), (16, 6), (11, 15), (9, 6), (22, 13), (4, 25), (10, 24), (21, 27), (1, 4), (20, 27), (22, 20), (17, 27), (10, 4), (3, 2), (23, 13), (20, 16), (11, 19), (24, 21), (27, 5), (2, 3), (9, 4), (10, 2), (24, 15), (18, 20), (13, 14), (10, 0), (20, 4), (25, 11), (4, 7), (13, 27), (3, 15), (3, 11), (13, 20), (18, 26), (11, 11), (21, 17), (4, 17), (4, 1), (28, 10), (27, 16), (20, 6), (8, 20), (21, 24), (3, 13), (2, 20), (12, 14), (7, 6), (15, 3), (5, 2), (9, 9), (26, 11), (22, 15), (10, 27), (13, 21), (24, 5), (19, 10), (25, 20), (24, 24), (5, 13), (11, 10), (6, 19), (13, 11), (12, 18), (16, 20), (6, 9), (24, 7), (26, 25), (10, 12), (0, 15), (25, 9), (27, 8), (3, 17), (12, 3), (7, 4), (21, 6), (16, 8), (6, 18), (11, 26), (4, 10), (4, 21), (25, 12), (6, 5), (0, 14), (3, 7), (24, 4), (6, 7), (24, 26), (21, 21), (6, 25), (15, 5), (11, 25), (16, 13), (27, 18), (18, 18), (8, 18), (0, 25), (27, 6), (6, 4), (21, 0), (20, 19), (4, 6), (7, 25), (6, 21), (16, 22), (26, 22), (18, 11), (19, 14), (0, 8), (6, 26), (3, 1), (27, 9), (4, 2), (1, 19), (16, 2), (0, 17), (26, 1), (7, 1), (0, 6), (11, 5), (22, 21), (8, 14), (16, 17), (20, 11), (20, 22), (5, 15), (2, 1), (24, 18), (8, 1), (16, 27), (27, 26), (26, 19), (9, 15), (18, 23), (1, 27), (28, 11), (2, 8), (28, 19), (23, 25), (24, 8), (14, 24), (3, 27), (15, 24), (1, 10), (25, 0), (9, 12), (21, 9), (27, 3), (26, 4), (15, 14), (14, 5), (3, 25), (15, 21), (2, 21), (16, 18), (23, 6), (10, 25), (0, 2), (22, 14), (25, 19), (7, 10), (24, 14), (20, 15), (26, 7), (21, 8), (28, 23), (10, 1), (18, 0), (3, 18), (10, 18), (27, 25), (27, 4), (2, 10), (3, 12), (18, 27), (25, 10), (8, 11), (8, 5), (19, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527040", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), 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), (6, 12), (10, 10), (3, 8), (0, 10), (12, 1), (15, 6), (17, 5), (19, 0), (19, 17), (0, 8), (12, 17), (4, 5), (11, 12), (8, 12), (18, 4), (5, 15), (0, 9), (16, 12), (12, 0), (17, 10), (15, 10), (1, 16), (15, 1), (9, 5), (6, 10), (10, 8), (3, 19), (16, 2), (10, 17), (4, 6), (15, 16), (6, 2), (11, 14), (16, 11), (0, 11), (14, 16), (18, 17), (16, 9), (11, 9), (15, 17), (18, 2), (8, 14), (7, 5), (15, 15), (13, 16), (7, 10), (11, 2), (6, 5), (10, 12), (0, 6), (10, 15), (16, 13), (11, 4), (8, 4), (19, 4), (13, 15), (15, 5), (16, 7), (2, 7), (19, 8), (17, 19), (17, 14), (5, 1), (6, 17), (14, 4), (9, 11), (11, 18), (9, 13), (4, 17), (18, 11), (8, 11), (9, 1), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "873600", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 19), (20, 22), (19, 22), (1, 3), (22, 0), (19, 14), (12, 13), (23, 24), (0, 5), (15, 22), (12, 19), (17, 24), (16, 24), (21, 24), (19, 24), (25, 8), (9, 8), (21, 5), (4, 17), (4, 7), (26, 16), (10, 24), (20, 7), (4, 23), (6, 15), (17, 5), (27, 23), (15, 2), (7, 13), (5, 22), (1, 24), (25, 7), (7, 0), (11, 6), (18, 24), (25, 15), (5, 10), (15, 24), (22, 5), (11, 0), (12, 6), (6, 5), (10, 20), (18, 11), (16, 16), (22, 19), (13, 1), (24, 25), (24, 22), (13, 24), (3, 17), (19, 20), (16, 3), (5, 11), (11, 7), (6, 19), (22, 10), (2, 0), (12, 2), (0, 17), (7, 23), (18, 6), (12, 8), (23, 21), (3, 13), (15, 4), (11, 2), (13, 22), (20, 12), (2, 4), (23, 17), (27, 18), (11, 21), (24, 23), (16, 22), (12, 5), (8, 23), (10, 11), (6, 25), (24, 24), (16, 12), (22, 3), (0, 16), (17, 20), (14, 6), (20, 1), (23, 11), (17, 9), (21, 25), (19, 10), (0, 20), (9, 10), (0, 2), (25, 6), (18, 16), (27, 1), (9, 22), (20, 25), (11, 15), (13, 5), (12, 25), (1, 14), (14, 2), (22, 23), (19, 13), (11, 8), (18, 14), (26, 11), (13, 3), (23, 22), (10, 25), (21, 9), (13, 9), (24, 3), (8, 3), (6, 21), (26, 14), (6, 16), (2, 5), (3, 7), (21, 10), (21, 20), (0, 10), (21, 21), (16, 4), (8, 24), (25, 23), (1, 0), (5, 9), (11, 4), (7, 8), (3, 0), (21, 18), (16, 18), (1, 11), (6, 2), (11, 14), (14, 7), (7, 21), (14, 25), (18, 19), (15, 11), (19, 17), (10, 5), (4, 4), (6, 18), (4, 12), (22, 20), (14, 14), (16, 2), (24, 10), (12, 7), (4, 22), (7, 17), (19, 19), (7, 14), (6, 6), (5, 2), (2, 12), (0, 8), (17, 22), (17, 21), (11, 25), (8, 7), (4, 1), (2, 7), (20, 4), (16, 17), (6, 3), (24, 18), (16, 15), (5, 16), (24, 6), (9, 4), (27, 14), (21, 1), (18, 13), (3, 21), (13, 0), (24, 8), (20, 13), (18, 1), (14, 9), (0, 6), (11, 11), (12, 9), (5, 1), (15, 7), (22, 18), (3, 4), (21, 11), (19, 6), (17, 25), (17, 7), (14, 17), (15, 19), (16, 19), (19, 5), (0, 14), (23, 19), (1, 8), (22, 4), (2, 3), (23, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203904", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 5), (17, 22), (4, 20), (7, 16), (3, 8), (17, 12), (19, 7), (4, 13), (19, 14), (5, 18), (10, 23), (18, 10), (23, 15), (11, 9), (19, 3), (3, 17), (21, 23), (25, 20), (6, 19), (12, 8), (4, 14), (9, 14), (27, 19), (25, 1), (2, 14), (20, 8), (23, 20), (16, 2), (3, 23), (3, 6), (4, 17), (12, 12), (11, 13), (5, 11), (24, 14), (13, 17), (5, 20), (5, 21), (9, 13), (15, 3), (17, 1), (20, 6), (20, 17), (15, 10), (20, 15), (11, 8), (21, 18), (1, 11), (14, 21), (1, 9), (14, 22), (3, 20), (17, 4), (24, 7), (20, 13), (9, 15), (23, 3), (9, 18), (1, 20), (15, 6), (8, 8), (23, 5), (20, 0), (15, 11), (26, 11), (2, 2), (9, 5), (0, 8), (11, 1), (20, 4), (22, 4), (12, 7), (9, 10), (6, 0), (17, 23), (7, 21), (17, 19), (7, 3), (8, 20), (20, 1), (16, 19), (10, 14), (13, 22), (2, 15), (5, 17), (11, 3), (9, 16), (19, 8), (20, 12), (26, 7), (3, 12), (15, 16), (10, 18), (8, 1), (27, 22), (17, 9), (18, 5), (27, 8), (9, 2), (18, 9), (0, 2), (0, 10), (7, 10), (16, 22), (25, 7), (19, 4), (14, 4), (4, 22), (11, 23), (5, 22), (5, 7), (3, 2), (19, 17), (22, 20), (21, 13), (25, 21), (15, 7), (11, 2), (15, 1), (4, 3), (6, 23), (3, 10), (16, 8), (14, 9), (17, 16), (13, 6), (10, 3), (7, 5), (15, 17), (7, 22), (9, 7), (22, 10), (20, 3), (18, 7), (25, 22), (26, 15), (17, 15), (14, 17), (27, 16), (5, 0), (24, 18), (26, 10), (1, 22), (0, 7), (6, 10), (0, 18), (0, 9), (12, 15), (8, 21), (13, 2), (23, 6), (27, 21), (9, 4), (27, 11), (18, 21), (21, 6), (20, 9), (23, 14), (21, 10), (21, 5), (24, 6), (2, 12), (8, 7), (21, 9), (24, 10), (4, 12), (5, 6), (2, 1), (10, 13), (27, 15), (26, 2), (16, 16), (15, 23), (9, 6), (13, 9), (12, 18), (1, 13), (26, 14), (1, 15), (0, 1), (22, 16), (27, 18), (20, 14), (11, 12), (17, 20), (20, 11), (10, 6), (0, 12), (15, 9), (14, 5), (2, 20), (16, 6), (11, 19), (4, 9), (0, 21), (27, 13), (24, 11), (23, 21), (8, 3), (25, 16), (7, 8), (17, 6), (26, 21), (0, 14), (23, 16), (23, 10), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694008", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 20), (1, 18), (5, 0), (8, 26), (14, 3), (0, 1), (9, 0), (4, 12), (12, 19), (19, 2), (3, 16), (13, 4), (9, 14), (18, 7), (14, 25), (11, 14), (0, 15), (7, 0), (7, 10), (18, 24), (14, 5), (7, 9), (19, 25), (20, 8), (6, 22), (10, 20), (1, 23), (3, 4), (14, 13), (13, 3), (7, 7), (20, 14), (11, 3), (11, 25), (2, 16), (3, 26), (14, 4), (15, 5), (9, 23), (16, 8), (12, 14), (3, 0), (15, 0), (15, 18), (18, 16), (0, 5), (1, 17), (3, 1), (19, 23), (17, 27), (11, 12), (6, 5), (3, 10), (3, 20), (6, 18), (4, 14), (10, 12), (19, 14), (19, 3), (3, 6), (12, 4), (18, 8), (20, 22), (4, 21), (13, 1), (13, 16), (12, 3), (6, 12), (6, 2), (18, 22), (15, 12), (4, 19), (2, 26), (18, 10), (1, 25), (11, 9), (4, 20), (5, 20), (10, 4), (15, 6), (9, 24), (11, 0), (18, 27), (9, 4), (5, 11), (13, 12), (9, 9), (9, 21), (10, 2), (9, 27), (14, 0), (19, 21), (20, 10), (10, 18), (11, 6), (13, 2), (8, 11), (8, 15), (4, 0), (17, 21), (16, 12), (17, 3), (11, 18), (8, 6), (4, 9), (17, 19), (0, 17), (1, 16), (18, 2), (13, 7), (16, 24), (11, 7), (19, 15), (8, 13), (20, 13), (16, 15), (6, 7), (1, 22), (14, 27), (8, 8), (7, 18), (10, 11), (20, 23), (10, 21), (8, 1), (8, 25), (12, 23), (6, 16), (12, 6), (15, 11), (4, 13), (14, 10), (14, 23), (3, 19), (20, 25), (17, 16), (4, 24), (19, 22), (2, 19), (8, 19), (3, 27), (5, 6), (5, 27), (2, 27), (11, 26), (0, 26), (16, 9), (15, 24), (1, 21), (13, 21), (12, 21), (14, 24), (6, 14), (9, 7), (20, 11), (1, 13), (2, 11), (11, 2), (7, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999160", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), 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), (0, 21), (10, 10), (7, 2), (3, 20), (19, 9), (4, 6), (12, 12), (10, 15), (4, 0), (17, 14), (10, 4), (19, 16), (10, 8), (10, 3), (8, 7), (8, 8), (22, 7), (8, 13), (5, 20), (5, 0), (6, 15), (10, 1), (20, 3), (18, 13), (20, 8), (2, 1), (17, 0), (5, 17), (7, 6), (10, 20), (21, 4), (11, 14), (12, 9), (8, 2), (8, 18), (5, 2), (2, 18), (16, 14), (4, 12), (17, 20), (1, 15), (5, 8), (19, 2), (8, 12), (5, 11), (14, 5), (14, 1), (6, 4), (6, 6), (10, 13), (20, 19), (5, 15), (11, 1), (15, 3), (11, 19), (6, 3), (0, 1), (21, 12), (16, 11), (12, 11), (11, 17), (17, 6), (17, 9), (15, 11), (0, 15), (17, 19), (21, 15), (17, 15), (11, 15), (16, 0), (8, 21), (16, 10), (4, 7), (10, 11), (13, 4), (22, 1), (9, 20), (3, 21), (1, 5), (7, 3), (22, 4), (0, 11), (10, 0), (10, 6), (6, 20), (19, 6), (4, 3), (13, 14), (2, 19), (16, 13), (0, 4), (14, 10), (21, 19), (3, 15), (12, 5), (21, 1), (17, 7), (2, 5), (18, 21), (16, 9), (20, 2), (15, 18), (11, 13), (15, 8), (10, 5), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612007", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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, 19), (22, 3), (5, 12), (19, 20), (6, 16), (19, 2), (2, 11), (5, 18), (12, 15), (17, 11), (2, 13), (5, 7), (14, 11), (23, 19), (6, 14), (12, 20), (16, 18), (16, 15), (22, 24), (15, 2), (6, 5), (3, 14), (19, 3), (22, 20), (0, 17), (21, 0), (0, 15), (1, 2), (1, 22), (21, 3), (6, 19), (17, 23), (20, 13), (21, 20), (13, 23), (4, 17), (15, 21), (2, 10), (16, 0), (17, 14), (13, 14), (9, 20), (17, 4), (3, 23), (17, 8), (7, 18), (11, 7), (8, 4), (20, 15), (4, 3), (21, 12), (8, 15), (15, 24), (18, 12), (8, 11), (16, 9), (9, 19), (18, 11), (6, 24), (19, 10), (6, 9), (13, 6), (23, 0), (10, 21), (7, 14), (4, 11), (22, 11), (11, 13), (22, 16), (12, 21), (4, 16), (19, 19), (1, 17), (21, 22), (19, 14), (19, 0), (1, 21), (11, 9), (23, 15), (16, 11), (1, 3), (13, 9), (1, 6), (6, 12), (4, 21), (3, 19), (7, 6), (2, 0), (18, 23), (20, 3), (14, 4), (22, 2), (19, 12), (17, 12), (12, 16), (16, 8), (8, 6), (22, 13), (21, 13), (2, 23), (17, 9), (0, 7), (5, 8), (18, 14), (7, 11), (3, 0), (21, 6), (20, 10), (6, 4), (20, 9), (0, 8), (19, 15), (2, 14), (15, 10), (16, 14), (23, 4), (6, 8), (8, 8), (13, 4), (10, 22), (0, 24), (17, 17), (5, 6), (15, 12), (12, 17), (11, 6), (4, 22), (10, 6), (15, 8), (15, 3), (10, 17), (17, 7), (23, 11), (6, 13), (12, 14), (22, 23), (12, 24), (12, 1), (9, 8), (4, 8), (6, 7), (1, 16), (8, 13), (20, 16), (13, 7), (19, 1), (22, 22), (9, 21), (13, 20), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306414", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 18), (24, 15), (21, 5), (15, 11), (3, 18), (11, 19), (6, 3), (11, 25), (25, 0), (16, 11), (1, 12), (9, 3), (17, 18), (7, 26), (1, 13), (16, 15), (7, 23), (15, 12), (9, 22), (20, 7), (20, 18), (11, 1), (25, 2), (3, 1), (14, 8), (17, 2), (13, 18), (24, 13), (20, 19), (8, 22), (5, 13), (3, 20), (4, 17), (23, 13), (23, 6), (8, 3), (4, 23), (10, 5), (1, 18), (1, 2), (13, 4), (13, 1), (18, 19), (6, 2), (7, 24), (20, 26), (14, 11), (19, 20), (3, 3), (4, 5), (23, 12), (2, 23), (5, 22), (20, 14), (19, 22), (20, 22), (11, 4), (24, 20), (15, 3), (18, 6), (7, 1), (5, 23), (2, 7), (24, 12), (4, 9), (6, 1), (10, 14), (3, 14), (4, 4), (6, 11), (4, 11), (5, 16), (11, 9), (7, 19), (25, 25), (12, 12), (20, 1), (24, 11), (9, 2), (7, 16), (4, 19), (8, 4), (24, 22), (18, 20), (4, 7), (13, 13), (12, 2), (7, 5), (20, 20), (25, 5), (18, 11), (12, 24), (10, 24), (9, 25), (10, 11), (22, 14), (21, 21), (13, 19), (13, 23), (4, 6), (12, 18), (14, 19), (0, 24), (21, 14), (18, 16), (12, 3), (8, 23), (2, 22), (2, 3), (19, 23), (7, 21), (24, 10), (20, 8), (8, 24), (17, 10), (12, 10), (16, 23), (1, 0), (14, 4), (20, 5), (22, 12), (19, 1), (25, 11), (17, 23), (11, 21), (18, 26), (21, 23), (8, 8), (2, 4), (13, 9), (14, 17), (19, 13), (22, 24), (21, 12), (2, 5), (11, 26), (25, 17), (14, 7), (19, 9), (14, 3), (15, 1), (2, 9), (3, 0), (6, 24), (16, 3), (13, 21), (25, 12), (13, 15), (0, 8), (10, 4), (6, 8), (14, 23), (0, 16), (11, 23), (3, 21), (16, 21), (21, 26), (5, 11), (16, 12), (16, 18), (5, 10), (15, 15), (10, 22), (25, 3), (15, 4), (2, 12), (9, 20), (0, 9), (21, 6), (5, 4), (17, 13), (24, 2), (14, 18), (17, 16), (16, 5), (10, 9), (23, 10), (8, 0), (19, 14), (15, 13), (21, 20), (0, 4), (8, 21), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779298", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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), (14, 8), (8, 22), (18, 11), (19, 13), (7, 20), (22, 22), (18, 1), (14, 5), (20, 1), (19, 7), (19, 3), (19, 14), (18, 8), (10, 17), (8, 3), (15, 2), (13, 21), (2, 20), (14, 16), (12, 21), (13, 8), (13, 16), (3, 0), (6, 21), (14, 23), (10, 3), (21, 15), (9, 16), (6, 4), (4, 20), (8, 18), (4, 16), (18, 26), (6, 10), (9, 10), (8, 24), (0, 20), (6, 9), (22, 3), (13, 17), (22, 19), (16, 15), (2, 7), (13, 9), (17, 0), (9, 19), (22, 6), (1, 5), (2, 21), (14, 0), (10, 21), (18, 4), (19, 25), (16, 22), (19, 1), (5, 9), (14, 24), (0, 18), (10, 13), (11, 4), (17, 18), (20, 11), (6, 17), (14, 10), (2, 5), (18, 22), (17, 10), (20, 4), (21, 5), (3, 3), (15, 23), (20, 17), (13, 12), (11, 20), (5, 16), (0, 11), (6, 20), (22, 13), (13, 20), (10, 24), (22, 7), (12, 18), (13, 22), (1, 1), (12, 17), (13, 1), (13, 0), (21, 21), (6, 22), (9, 8), (4, 7), (11, 24), (12, 1), (21, 11), (5, 6), (18, 19), (8, 26), (7, 4), (4, 5), (11, 15), (10, 0), (18, 17), (14, 26), (11, 0), (20, 23), (16, 4), (22, 11), (21, 16), (2, 18), (15, 9), (9, 24), (12, 8), (1, 24), (0, 21), (3, 19), (14, 1), (19, 16), (14, 4), (22, 23), (12, 26), (13, 15), (11, 14), (0, 1), (8, 11), (16, 18), (11, 5), (22, 10), (6, 14), (16, 16), (9, 25), (13, 24), (20, 10), (15, 14), (6, 3), (20, 22), (6, 7), (2, 25), (9, 2), (21, 13), (7, 17), (10, 23), (5, 14), (0, 12), (13, 6), (18, 0), (0, 3), (12, 22), (20, 16), (21, 1), (2, 12), (10, 9), (7, 19), (3, 24), (12, 7), (17, 24), (11, 11), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759768", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (7, 23), (22, 9), (2, 18), (20, 5), (9, 25), (10, 4), (7, 25), (22, 11), (16, 5), (13, 4), (14, 1), (18, 26), (25, 17), (1, 3), (11, 22), (24, 0), (8, 22), (2, 16), (12, 4), (6, 13), (23, 6), (21, 12), (20, 6), (18, 21), (23, 7), (14, 16), (17, 20), (6, 8), (12, 6), (4, 12), (7, 22), (11, 26), (18, 8), (8, 9), (12, 5), (16, 13), (19, 25), (8, 6), (13, 9), (1, 13), (16, 20), (20, 18), (15, 19), (17, 7), (4, 25), (23, 5), (20, 2), (21, 15), (26, 7), (13, 6), (16, 2), (14, 3), (14, 25), (19, 23), (14, 8), (12, 13), (0, 13), (10, 5), (3, 12), (0, 23), (5, 5), (4, 17), (15, 9), (9, 3), (23, 19), (18, 9), (12, 3), (12, 0), (25, 11), (23, 17), (13, 13), (8, 25), (20, 16), (10, 22), (12, 11), (15, 1), (9, 7), (20, 10), (21, 26), (6, 9), (9, 22), (18, 11), (23, 16), (16, 6), (21, 7), (20, 20), (11, 3), (1, 11), (0, 21), (26, 5), (4, 16), (8, 15), (1, 4), (15, 12), (22, 3), (8, 16), (6, 18), (24, 3), (3, 13), (20, 7), (24, 13), (7, 4), (1, 16), (24, 21), (17, 19), (13, 16), (12, 8), (1, 17), (11, 0), (18, 15), (22, 13), (17, 14), (8, 12), (17, 22), (4, 6), (10, 23), (23, 24), (14, 0), (3, 26), (18, 25), (1, 19), (9, 2), (17, 1), (12, 19), (7, 24), (22, 23), (8, 0), (12, 10), (2, 10), (3, 11), (3, 15), (4, 20), (19, 11), (14, 23), (9, 24), (17, 3), (23, 15), (20, 11), (0, 18), (16, 24), (20, 0), (14, 18), (5, 0), (11, 11), (10, 24), (10, 25), (10, 0), (2, 25), (20, 12), (12, 15), (19, 4), (11, 17), (22, 25), (13, 1), (22, 16), (7, 18), (5, 4), (9, 18), (14, 19), (21, 3), (20, 24), (24, 1), (26, 25), (5, 14), (15, 5), (14, 7), (20, 21), (22, 4), (5, 10), (0, 25), (19, 26), (15, 3), (21, 2), (7, 10), (2, 0), (7, 20), (17, 25), (18, 18), (9, 11), (21, 11), (22, 20), (22, 17), (14, 11), (5, 9), (3, 24), (0, 15), (3, 2), (0, 17), (2, 6), (7, 8), (22, 7), (6, 12), (12, 1), (26, 1), (9, 1), (19, 3), (24, 24), (13, 7), (5, 17), (26, 24), (10, 17), (6, 21), (3, 10), (14, 12), (13, 15), (19, 14), (22, 15), (17, 24), (7, 19), (2, 9), (17, 11), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301608", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 18), (2, 7), (7, 8), (14, 12), (13, 16), (2, 17), (10, 19), (6, 8), (4, 6), (2, 3), (13, 10), (14, 14), (16, 5), (14, 9), (18, 4), (16, 10), (8, 18), (10, 12), (15, 14), (0, 14), (8, 4), (10, 8), (18, 16), (15, 16), (0, 19), (16, 7), (17, 17), (13, 6), (19, 5), (19, 3), (8, 17), (4, 3), (16, 4), (15, 8), (10, 13), (4, 16), (19, 18), (9, 19), (4, 12), (17, 18), (4, 4), (5, 14), (9, 13), (12, 19), (2, 9), (16, 2), (20, 8), (1, 5), (10, 10), (19, 2), (13, 17), (12, 15), (15, 11), (2, 4), (11, 1), (5, 7), (20, 16), (17, 7), (9, 4), (8, 1), (8, 12), (5, 9), (14, 15), (10, 0), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208446", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), 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), (9, 20), (7, 3), (17, 19), (18, 5), (5, 22), (5, 4), (6, 18), (6, 14), (10, 24), (6, 15), (13, 12), (20, 9), (16, 6), (11, 4), (8, 23), (0, 18), (0, 11), (24, 19), (23, 1), (15, 15), (8, 15), (6, 17), (7, 11), (11, 11), (25, 18), (18, 10), (4, 4), (21, 9), (10, 9), (9, 6), (18, 13), (24, 15), (20, 25), (3, 6), (14, 1), (14, 9), (6, 24), (15, 3), (1, 17), (10, 3), (12, 26), (22, 19), (1, 6), (7, 4), (19, 1), (0, 7), (22, 9), (7, 22), (11, 12), (21, 1), (20, 15), (1, 22), (17, 22), (10, 22), (13, 9), (22, 3), (24, 24), (5, 21), (11, 25), (23, 0), (19, 19), (20, 1), (6, 22), (2, 15), (5, 16), (23, 8), (20, 26), (13, 10), (15, 1), (9, 2), (21, 13), (16, 5), (18, 22), (3, 20), (14, 13), (20, 22), (4, 23), (4, 8), (8, 9), (9, 19), (8, 19), (8, 8), (23, 2), (17, 6), (19, 17), (8, 22), (5, 14), (18, 19), (9, 24), (22, 11), (1, 21), (8, 13), (21, 6), (4, 14), (4, 9), (18, 4), (6, 8), (8, 20), (12, 22), (1, 11), (6, 19), (12, 7), (25, 14), (15, 21), (5, 5), (20, 23), (17, 8), (0, 12), (9, 1), (25, 25), (0, 14), (9, 16), (19, 23), (14, 23), (14, 25), (3, 2), (16, 10), (1, 26), (22, 23), (19, 3), (19, 9), (2, 4), (13, 20), (9, 14), (15, 13), (11, 15), (11, 23), (6, 2), (13, 23), (0, 10), (20, 20), (24, 3), (10, 26), (18, 20), (7, 15), (19, 16), (7, 23), (18, 23), (1, 8), (8, 12), (8, 24), (4, 21), (24, 18), (13, 3), (25, 13), (0, 6), (9, 12), (13, 7), (2, 2), (17, 25), (5, 11), (6, 23), (19, 4), (1, 15), (18, 6), (12, 19), (24, 14), (4, 15), (4, 1), (21, 15), (5, 18), (11, 3), (0, 25), (9, 0), (22, 26), (8, 3), (10, 13), (2, 5), (10, 17), (2, 8), (21, 24), (11, 14), (6, 26), (20, 11), (18, 18), (13, 5), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132830", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (6, 13), (13, 5), (10, 16), (4, 14), (14, 2), (8, 9), (19, 6), (6, 8), (13, 7), (16, 2), (9, 3), (1, 10), (11, 3), (9, 18), (5, 11), (0, 16), (14, 0), (2, 3), (21, 8), (23, 12), (1, 4), (10, 4), (20, 6), (14, 4), (5, 17), (10, 3), (6, 10), (6, 4), (2, 1), (16, 17), (15, 15), (11, 1), (19, 3), (9, 15), (8, 12), (9, 12), (4, 9), (3, 12), (3, 9), (22, 9), (3, 18), (7, 9), (18, 7), (23, 9), (9, 17), (7, 12), (3, 3), (21, 14), (8, 2), (11, 9), (9, 11), (2, 16), (17, 16), (5, 8), (2, 18), (3, 6), (0, 15), (13, 17), (9, 9), (2, 7), (0, 11), (9, 7), (0, 17), (3, 4), (0, 7), (0, 13), (17, 14), (21, 18), (15, 17), (21, 7), (22, 4), (20, 1), (14, 19), (14, 12), (18, 0), (14, 9), (18, 3), (3, 5), (15, 13), (9, 0), (18, 6), (8, 18), (5, 5), (23, 8), (16, 14), (22, 15), (18, 13), (12, 15), (14, 11), (10, 11), (0, 8), (15, 0), (5, 4), (0, 10), (13, 10), (11, 15), (9, 16), (21, 0), (1, 9), (17, 6), (18, 14), (1, 14), (1, 3), (5, 19), (6, 6), (2, 5), (17, 9), (12, 0), (18, 12), (6, 17), (7, 18), (14, 15), (12, 19), (15, 5), (20, 18), (16, 1), (7, 4), (19, 2), (9, 5), (21, 3), (18, 16), (4, 15), (21, 17), (14, 5), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749676", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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), (25, 12), (0, 14), (20, 9), (21, 7), (15, 13), (21, 13), (12, 0), (5, 14), (19, 21), (14, 2), (18, 0), (11, 7), (20, 10), (5, 8), (0, 7), (1, 9), (15, 3), (11, 19), (11, 15), (17, 2), (14, 21), (26, 14), (10, 20), (19, 19), (18, 15), (26, 8), (17, 11), (4, 11), (21, 4), (3, 20), (13, 17), (12, 4), (6, 13), (20, 0), (13, 5), (13, 13), (16, 13), (7, 6), (21, 16), (21, 10), (19, 11), (2, 18), (1, 2), (19, 12), (17, 1), (14, 20), (7, 15), (14, 18), (19, 7), (22, 2), (20, 7), (19, 17), (12, 20), (19, 15), (7, 21), (25, 13), (26, 5), (23, 12), (10, 4), (7, 10), (11, 20), (10, 19), (23, 2), (26, 2), (7, 17), (6, 15), (22, 3), (10, 0), (1, 16), (24, 15), (19, 0), (22, 11), (10, 3), (17, 8), (6, 21), (6, 3), (24, 7), (9, 4), (3, 16), (2, 20), (8, 15), (25, 20), (14, 1), (7, 4), (10, 8), (8, 7), (20, 12), (6, 4), (13, 12), (3, 5), (22, 14), (13, 6), (20, 8), (19, 18), (1, 7), (10, 16), (10, 7), (5, 20), (14, 0), (5, 12), (18, 18), (7, 14), (4, 20), (15, 7), (24, 10), (9, 17), (20, 6), (17, 0), (4, 10), (19, 2), (22, 10), (14, 9), (22, 12), (21, 15), (7, 11), (11, 12), (5, 18), (14, 16), (1, 20), (9, 16), (1, 19), (8, 9), (21, 0), (5, 16), (2, 15), (6, 16), (11, 13), (0, 10), (16, 15), (20, 15), (2, 6), (13, 1), (18, 10), (16, 4), (11, 9), (5, 10), (8, 20), (17, 10), (1, 18), (16, 14), (24, 8), (0, 12), (3, 1), (1, 14), (25, 6), (12, 9), (6, 11), (17, 12), (22, 9), (3, 19), (26, 18), (5, 9), (3, 14), (2, 16), (7, 13), (14, 6), (15, 11), (11, 17), (1, 8), (20, 18), (5, 0), (4, 3), (25, 2), (21, 14), (0, 15), (4, 12), (4, 6), (7, 16), (16, 20), (0, 1), (8, 19), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901176", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (18, 24), (2, 4), (11, 5), (23, 20), (22, 3), (13, 23), (7, 22), (21, 22), (16, 7), (16, 3), (14, 17), (17, 10), (20, 17), (22, 18), (13, 17), (18, 0), (12, 9), (11, 18), (7, 14), (22, 12), (19, 16), (1, 24), (12, 19), (0, 14), (6, 7), (9, 9), (10, 19), (12, 13), (5, 16), (21, 9), (23, 6), (16, 24), (21, 7), (12, 24), (5, 13), (22, 19), (19, 12), (16, 18), (14, 4), (16, 13), (15, 25), (13, 0), (0, 26), (21, 5), (9, 2), (8, 16), (17, 4), (15, 15), (7, 20), (23, 1), (17, 6), (20, 21), (11, 10), (8, 10), (8, 6), (19, 19), (2, 7), (10, 0), (15, 20), (7, 0), (16, 6), (20, 9), (18, 22), (12, 14), (9, 22), (11, 14), (13, 20), (19, 17), (17, 18), (3, 7), (5, 4), (12, 7), (6, 5), (20, 11), (20, 3), (16, 0), (4, 6), (13, 7), (18, 4), (21, 25), (1, 4), (21, 18), (4, 13), (5, 27), (11, 17), (13, 12), (12, 23), (16, 8), (21, 15), (23, 21), (12, 5), (0, 15), (20, 10), (14, 16), (23, 17), (15, 4), (21, 10), (22, 20), (11, 27), (14, 2), (12, 4), (4, 22), (22, 16), (9, 4), (17, 16), (5, 8), (20, 26), (18, 20), (21, 23), (3, 1), (10, 21), (13, 25), (7, 25), (9, 10), (6, 23), (0, 24), (9, 17), (6, 9), (4, 9), (14, 26), (10, 27), (20, 22), (15, 24), (7, 26), (5, 17), (2, 9), (22, 27), (16, 26), (22, 1), (7, 21), (21, 2), (14, 18), (7, 4), (0, 4), (11, 23), (11, 26), (6, 25), (22, 14), (12, 22), (0, 20), (15, 14), (7, 12), (1, 3), (20, 6), (10, 16), (12, 25), (20, 2), (22, 11), (16, 12), (3, 5), (12, 0), (15, 13), (22, 15), (1, 14), (13, 27), (12, 20), (7, 1), (21, 0), (0, 25), (2, 11), (22, 2), (7, 6), (4, 21), (1, 19), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72960", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (4, 11), (5, 15), (4, 8), (6, 26), (8, 15), (18, 10), (8, 4), (11, 21), (2, 4), (10, 25), (6, 9), (19, 16), (3, 15), (14, 23), (14, 2), (13, 16), (25, 20), (19, 18), (8, 5), (8, 26), (8, 3), (16, 11), (22, 0), (5, 19), (18, 5), (11, 6), (24, 3), (22, 9), (4, 6), (26, 12), (20, 13), (13, 24), (22, 16), (16, 25), (4, 17), (25, 4), (15, 10), (1, 3), (11, 3), (1, 21), (18, 19), (9, 17), (1, 12), (13, 11), (18, 21), (19, 21), (11, 1), (25, 24), (26, 3), (24, 24), (1, 15), (5, 5), (15, 3), (0, 26), (11, 15), (11, 4), (4, 0), (8, 17), (12, 25), (21, 11), (18, 8), (3, 24), (24, 4), (3, 13), (3, 22), (10, 22), (0, 23), (25, 13), (25, 3), (12, 8), (2, 20), (14, 1), (16, 26), (20, 27), (22, 12), (2, 22), (11, 19), (16, 19), (23, 18), (21, 19), (9, 0), (7, 21), (9, 14), (16, 0), (2, 6), (18, 25), (12, 3), (20, 17), (1, 24), (19, 14), (14, 10), (8, 19), (12, 7), (0, 17), (24, 0), (25, 23), (4, 5), (18, 9), (15, 5), (15, 19), (19, 3), (6, 12), (7, 6), (1, 9), (14, 6), (21, 23), (16, 15), (23, 3), (12, 11), (5, 27), (21, 16), (23, 6), (15, 15), (7, 10), (5, 16), (1, 19), (1, 23), (12, 5), (2, 14), (7, 14), (12, 17), (17, 11), (21, 27), (6, 4), (24, 25), (20, 23), (6, 20), (13, 17), (14, 20), (21, 9), (0, 3), (15, 20), (10, 13), (3, 10), (3, 20), (0, 18), (11, 14), (25, 8), (17, 18), (26, 9), (17, 23), (21, 17), (7, 8), (10, 9), (8, 9), (14, 0), (11, 22), (6, 8), (15, 21), (15, 0), (7, 1), (23, 15), (14, 15), (17, 27), (25, 14), (6, 13), (9, 1), (13, 20), (21, 15), (20, 26), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918720", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 10), (10, 14), (11, 2), (14, 14), (14, 12), (6, 11), (15, 5), (2, 17), (5, 13), (13, 10), (3, 20), (5, 5), (5, 1), (1, 13), (3, 10), (1, 19), (1, 5), (18, 3), (16, 8), (3, 8), (1, 1), (17, 9), (1, 17), (2, 14), (12, 13), (9, 17), (5, 18), (13, 12), (0, 19), (6, 7), (11, 3), (18, 12), (3, 5), (6, 1), (1, 10), (5, 15), (4, 7), (2, 18), (16, 9), (7, 5), (16, 2), (6, 0), (9, 3), (0, 14), (19, 0), (14, 17), (15, 7), (16, 18), (19, 7), (13, 5), (14, 9), (4, 20), (0, 11), (9, 6), (4, 16), (17, 12), (15, 20), (7, 7), (8, 18), (12, 1), (12, 10), (8, 16), (19, 17), (10, 6), (5, 9), (15, 15), (6, 13), (4, 8), (6, 10), (16, 20), (14, 13), (7, 8), (2, 12), (14, 5), (3, 14), (1, 7), (8, 5), (11, 20), (16, 10), (12, 14), (9, 1), (13, 7), (6, 14), (10, 19), (13, 1), (11, 9), (5, 4), (11, 6), (1, 9), (8, 20), (17, 8), (3, 3), (14, 4), (12, 11), (0, 5), (13, 19), (9, 11), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619710", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 26), (10, 21), (12, 19), (20, 5), (19, 25), (9, 19), (10, 4), (22, 21), (3, 25), (1, 21), (18, 26), (15, 11), (16, 1), (9, 13), (21, 7), (6, 15), (12, 25), (14, 0), (27, 0), (2, 3), (11, 12), (5, 25), (19, 6), (25, 26), (7, 17), (6, 0), (23, 15), (13, 23), (13, 16), (23, 0), (16, 5), (9, 12), (25, 18), (25, 3), (23, 2), (21, 2), (26, 22), (9, 0), (10, 6), (16, 26), (21, 12), (8, 1), (8, 5), (5, 14), (5, 21), (21, 26), (13, 5), (27, 3), (24, 16), (7, 6), (19, 8), (18, 5), (18, 8), (0, 3), (24, 7), (16, 12), (3, 15), (10, 19), (13, 12), (27, 16), (6, 12), (4, 2), (18, 1), (21, 23), (1, 10), (12, 0), (18, 25), (26, 23), (20, 21), (17, 8), (24, 14), (10, 11), (5, 17), (10, 17), (1, 19), (5, 16), (27, 10), (2, 20), (6, 17), (9, 7), (22, 0), (18, 13), (9, 9), (23, 3), (5, 4), (25, 11), (27, 4), (7, 15), (25, 5), (23, 14), (27, 9), (18, 3), (17, 11), (14, 13), (27, 11), (26, 5), (19, 17), (22, 24), (26, 0), (27, 1), (23, 26), (8, 23), (2, 10), (0, 23), (22, 7), (0, 21), (20, 12), (14, 12), (2, 9), (25, 21), (27, 12), (15, 23), (15, 13), (16, 11), (2, 18), (11, 0), (13, 26), (9, 11), (2, 12), (24, 17), (17, 14), (0, 17), (23, 23), (19, 24), (1, 8), (12, 7), (13, 24), (9, 4), (0, 24), (3, 1), (16, 24), (4, 23), (0, 9), (7, 18), (15, 1), (13, 10), (10, 14), (21, 22), (18, 12), (13, 13), (9, 10), (2, 19), (10, 3), (26, 3), (25, 16), (27, 2), (14, 10), (0, 10), (14, 21), (7, 2), (7, 16), (9, 6), (14, 14), (7, 1), (15, 26), (17, 3), (1, 20), (11, 24), (22, 12), (26, 10), (21, 24), (26, 24), (3, 13), (16, 17), (22, 15), (22, 9), (5, 6), (14, 24), (19, 26), (0, 6), (13, 21), (12, 16), (18, 24), (1, 18), (11, 10), (0, 11), (8, 13), (3, 4), (20, 17), (21, 15), (12, 6), (24, 19), (3, 24), (14, 15), (11, 25), (4, 3), (16, 25), (0, 14), (9, 17), (19, 14), (10, 13), (5, 5), (10, 26), (17, 2), (16, 23), (26, 15), (0, 5), (22, 5), (4, 16), (17, 24), (16, 18), (2, 5), (18, 2), (12, 20), (25, 24), (5, 24), (1, 12), (0, 18), (12, 13), (7, 20), (0, 22), (1, 6), (16, 0), (8, 4), (26, 21), (22, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295050", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), 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, 8), (8, 19), (19, 15), (18, 17), (17, 16), (7, 16), (12, 8), (21, 13), (24, 0), (25, 17), (9, 14), (12, 1), (3, 2), (24, 6), (2, 7), (10, 10), (3, 1), (18, 1), (3, 6), (19, 8), (1, 12), (16, 2), (22, 7), (10, 3), (14, 3), (7, 0), (19, 11), (15, 7), (18, 18), (19, 0), (5, 5), (22, 15), (14, 19), (10, 19), (20, 9), (4, 16), (24, 19), (14, 15), (16, 10), (6, 3), (20, 3), (21, 15), (4, 8), (22, 13), (7, 14), (0, 8), (18, 19), (11, 9), (20, 12), (10, 7), (21, 12), (21, 9), (23, 3), (9, 1), (1, 20), (5, 1), (7, 15), (14, 13), (10, 14), (23, 9), (4, 18), (22, 5), (5, 11), (19, 20), (11, 12), (2, 1), (1, 7), (11, 7), (21, 4), (21, 7), (6, 0), (3, 0), (4, 7), (8, 3), (21, 8), (22, 14), (6, 10), (3, 13), (18, 14), (24, 20), (0, 3), (19, 2), (11, 15), (13, 7), (18, 15), (20, 1), (14, 16), (14, 14), (6, 6), (19, 18), (1, 6), (20, 7), (16, 11), (22, 11), (21, 3), (1, 15), (20, 17), (0, 11), (0, 20), (25, 3), (13, 12), (7, 4), (23, 19), (17, 5), (3, 12), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562620", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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), (16, 19), (4, 2), (18, 12), (8, 3), (17, 17), (0, 14), (4, 8), (12, 9), (13, 9), (16, 6), (15, 16), (11, 1), (12, 11), (8, 5), (12, 20), (12, 12), (0, 16), (21, 12), (22, 13), (10, 7), (15, 5), (20, 19), (15, 9), (0, 12), (7, 15), (6, 3), (20, 12), (7, 1), (22, 11), (20, 9), (3, 19), (24, 13), (5, 17), (20, 1), (13, 8), (3, 7), (22, 4), (3, 1), (21, 2), (0, 20), (10, 11), (13, 15), (16, 3), (8, 9), (23, 7), (23, 1), (19, 0), (21, 13), (1, 18), (1, 3), (18, 11), (0, 6), (0, 8), (17, 3), (0, 3), (17, 11), (10, 6), (3, 11), (12, 14), (24, 1), (10, 18), (12, 8), (17, 5), (9, 17), (13, 17), (1, 15), (10, 17), (20, 3), (17, 0), (11, 0), (23, 16), (21, 4), (24, 2), (13, 7), (9, 8), (1, 11), (13, 10), (10, 16), (2, 1), (8, 6), (19, 14), (11, 20), (17, 7), (3, 14), (14, 15), (7, 4), (13, 2), (17, 9), (8, 18), (18, 17), (3, 20), (14, 10), (2, 13), (13, 16), (22, 7), (12, 1), (3, 4), (7, 16), (1, 12), (6, 1), (1, 9), (22, 8), (19, 3), (20, 10), (4, 1), (24, 3), (15, 0), (18, 9), (23, 18), (0, 2), (6, 8), (19, 10), (16, 15), (9, 7), (22, 14), (23, 15), (22, 2), (10, 2), (18, 6), (17, 14), (17, 15), (6, 4), (22, 1), (13, 14), (7, 2), (19, 13), (10, 3), (14, 12), (1, 6), (1, 4), (15, 2), (7, 13), (0, 18), (6, 9), (21, 15), (22, 18), (9, 13), (3, 16), (9, 0), (22, 0), (17, 6), (19, 6), (3, 12), (15, 1), (0, 19), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "687407", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 21), (15, 7), (15, 12), (0, 6), (13, 0), (16, 12), (10, 7), (10, 5), (12, 12), (5, 4), (21, 5), (20, 11), (0, 19), (8, 9), (8, 6), (3, 13), (19, 18), (2, 1), (21, 17), (13, 21), (17, 7), (7, 7), (19, 6), (14, 16), (1, 2), (13, 11), (1, 1), (21, 11), (10, 2), (18, 10), (20, 17), (3, 3), (13, 2), (20, 7), (9, 19), (0, 8), (20, 1), (16, 9), (9, 17), (6, 13), (0, 14), (10, 21), (14, 17), (1, 17), (19, 1), (8, 19), (17, 16), (19, 0), (14, 20), (7, 17), (0, 4), (1, 9), (3, 7), (20, 12), (1, 12), (21, 14), (7, 1), (16, 4), (12, 3), (0, 15), (16, 2), (13, 6), (12, 1), (11, 10), (3, 18), (14, 19), (19, 20), (4, 10), (12, 18), (4, 3), (1, 18), (19, 15), (15, 14), (3, 20), (0, 18), (11, 19), (7, 21), (20, 14), (14, 8), (4, 18), (17, 18), (9, 20), (18, 11), (21, 12), (13, 10), (9, 1), (14, 2), (11, 17), (19, 13), (0, 3), (18, 6), (7, 12), (7, 18), (6, 18), (9, 13), (7, 15), (4, 17), (7, 16), (14, 10), (13, 20), (3, 2), (7, 5), (21, 15), (14, 1), (9, 7), (19, 3), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519296", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (0, 6), (20, 3), (19, 8), (14, 6), (3, 2), (3, 22), (5, 6), (19, 10), (2, 12), (11, 22), (20, 19), (4, 4), (8, 4), (6, 1), (5, 24), (0, 9), (6, 24), (0, 10), (15, 9), (20, 10), (5, 3), (0, 12), (1, 16), (14, 9), (1, 13), (14, 21), (12, 12), (4, 15), (1, 23), (4, 8), (13, 5), (3, 24), (2, 19), (5, 2), (8, 24), (4, 24), (11, 13), (11, 21), (1, 3), (15, 22), (18, 7), (3, 23), (7, 22), (15, 11), (20, 23), (1, 5), (3, 9), (8, 23), (6, 5), (10, 22), (18, 13), (15, 2), (12, 3), (8, 21), (4, 17), (4, 25), (12, 23), (1, 15), (1, 10), (7, 6), (19, 11), (16, 14), (10, 20), (9, 16), (17, 12), (14, 3), (0, 24), (12, 1), (18, 5), (14, 25), (18, 16), (3, 25), (4, 11), (20, 12), (14, 10), (14, 8), (10, 6), (11, 16), (2, 7), (15, 13), (18, 20), (9, 15), (13, 24), (9, 3), (11, 23), (0, 21), (6, 20), (19, 21), (5, 8), (9, 19), (10, 17), (18, 4), (11, 20), (10, 16), (20, 14), (18, 8), (0, 13), (10, 0), (16, 22), (13, 1), (12, 24), (2, 9), (7, 3), (6, 11), (19, 12), (11, 10), (16, 0), (0, 15), (14, 4), (1, 21), (15, 4), (20, 7), (16, 21), (16, 10), (14, 19), (17, 2), (13, 9), (1, 6), (2, 10), (1, 8), (19, 25), (9, 5), (7, 8), (12, 19), (10, 7), (9, 20), (20, 4), (12, 25), (12, 18), (11, 2), (11, 0), (11, 15), (18, 24), (13, 11), (10, 8), (6, 12), (18, 25), (0, 19), (9, 18), (17, 3), (1, 20), (3, 18), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73408", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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), (21, 1), (22, 19), (9, 19), (2, 17), (20, 0), (5, 15), (1, 7), (13, 10), (17, 2), (14, 8), (2, 19), (21, 2), (12, 14), (17, 20), (10, 3), (0, 5), (17, 6), (17, 10), (10, 16), (2, 8), (6, 7), (5, 7), (15, 15), (1, 12), (4, 19), (21, 18), (3, 18), (6, 18), (13, 14), (11, 3), (2, 15), (23, 12), (23, 19), (24, 4), (4, 7), (15, 16), (9, 2), (8, 7), (9, 16), (3, 7), (4, 10), (16, 0), (4, 6), (21, 19), (16, 16), (1, 6), (9, 18), (8, 1), (16, 19), (19, 0), (17, 3), (13, 9), (18, 0), (10, 1), (8, 3), (10, 10), (17, 4), (21, 3), (24, 6), (20, 16), (11, 8), (19, 13), (11, 15), (24, 0), (22, 8), (24, 16), (2, 20), (12, 5), (15, 1), (21, 10), (10, 12), (17, 18), (2, 18), (0, 6), (8, 17), (20, 15), (14, 1), (9, 17), (13, 6), (7, 19), (9, 8), (3, 15), (8, 2), (17, 16), (10, 6), (15, 4), (23, 10), (1, 4), (20, 6), (6, 13), (6, 2), (5, 8), (21, 8), (1, 13), (20, 10), (19, 18), (10, 18), (14, 4), (12, 4), (0, 9), (5, 12), (20, 11), (6, 5), (16, 20), (2, 0), (9, 9), (4, 11), (15, 14), (9, 14), (22, 5), (17, 5), (0, 11), (10, 4), (3, 3), (24, 11), (4, 14), (14, 14), (16, 13), (19, 11), (11, 9), (5, 16), (18, 18), (3, 1), (15, 10), (9, 5), (2, 13), (14, 2), (12, 2), (7, 12), (24, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120668", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (6, 9), (15, 20), (2, 26), (22, 7), (20, 9), (23, 18), (26, 9), (24, 1), (26, 25), (9, 11), (20, 2), (26, 20), (21, 14), (8, 12), (12, 11), (17, 10), (13, 9), (19, 10), (18, 7), (10, 21), (11, 21), (22, 12), (21, 2), (25, 4), (11, 8), (12, 15), (6, 12), (12, 14), (25, 8), (24, 20), (12, 9), (3, 18), (6, 11), (0, 8), (0, 1), (8, 10), (20, 14), (15, 22), (20, 8), (7, 13), (10, 23), (12, 24), (1, 12), (25, 16), (4, 19), (4, 21), (9, 6), (19, 17), (8, 6), (4, 0), (18, 9), (9, 12), (20, 22), (1, 6), (12, 12), (7, 14), (1, 8), (22, 17), (13, 22), (23, 22), (25, 1), (1, 14), (10, 4), (2, 14), (6, 17), (26, 5), (7, 25), (7, 18), (26, 2), (4, 5), (15, 8), (10, 13), (9, 0), (6, 25), (16, 1), (24, 2), (15, 19), (0, 12), (16, 12), (23, 27), (16, 21), (16, 17), (7, 15), (12, 23), (16, 0), (20, 18), (11, 18), (17, 23), (8, 13), (25, 27), (22, 5), (14, 3), (3, 2), (11, 1), (6, 13), (1, 16), (15, 4), (2, 15), (14, 7), (23, 0), (7, 6), (21, 11), (3, 8), (2, 10), (13, 2), (25, 14), (19, 2), (26, 16), (0, 18), (17, 9), (7, 16), (11, 23), (19, 16), (20, 7), (12, 6), (24, 22), (21, 8), (6, 8), (20, 4), (24, 19), (23, 12), (11, 5), (7, 27), (23, 13), (1, 15), (16, 23), (2, 5), (9, 2), (4, 8), (19, 21), (18, 4), (20, 21), (4, 2), (10, 9), (6, 15), (10, 2), (19, 4), (9, 21), (13, 13), (8, 15), (21, 3), (6, 6), (25, 24), (0, 2), (14, 18), (21, 9), (13, 12), (17, 12), (2, 13), (8, 20), (7, 22), (13, 16), (15, 9), (6, 4), (14, 8), (16, 26), (7, 17), (15, 7), (14, 25), (3, 5), (9, 17), (6, 19), (21, 7), (14, 2), (10, 26), (25, 17), (5, 22), (0, 23), (15, 6), (12, 8), (23, 4), (25, 22), (14, 13), (25, 15), (12, 1), (20, 16), (14, 11), (16, 25), (18, 11), (22, 3), (7, 12), (3, 20), (25, 21), (12, 21), (16, 19), (25, 23), (6, 20), (1, 23), (10, 5), (5, 16), (13, 10), (1, 24), (4, 13), (7, 23), (17, 0), (15, 15), (9, 16), (8, 25), (4, 27), (23, 10), (15, 0), (3, 1), (14, 22), (22, 2), (18, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547740", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (20, 27), (2, 26), (17, 2), (10, 8), (5, 9), (10, 5), (21, 21), (14, 18), (19, 11), (16, 25), (19, 15), (15, 13), (18, 1), (15, 8), (16, 2), (3, 10), (1, 9), (22, 27), (19, 22), (20, 12), (11, 14), (12, 24), (18, 7), (10, 17), (15, 24), (12, 5), (13, 22), (4, 20), (4, 23), (1, 20), (18, 6), (22, 6), (7, 7), (1, 21), (12, 19), (4, 6), (12, 0), (23, 20), (5, 7), (22, 22), (14, 2), (2, 27), (13, 19), (16, 12), (23, 12), (17, 19), (1, 17), (3, 1), (15, 17), (18, 12), (7, 11), (20, 26), (12, 13), (20, 0), (18, 16), (4, 24), (5, 6), (12, 7), (0, 27), (18, 26), (12, 26), (21, 18), (0, 15), (0, 18), (12, 23), (2, 8), (21, 15), (22, 14), (7, 15), (9, 12), (23, 16), (2, 12), (15, 6), (15, 23), (6, 10), (18, 2), (13, 14), (19, 7), (21, 11), (19, 26), (19, 0), (2, 6), (16, 21), (6, 15), (11, 5), (22, 5), (10, 12), (5, 14), (6, 5), (23, 22), (20, 2), (0, 9), (22, 12), (15, 4), (15, 2), (8, 11), (9, 0), (23, 5), (20, 24), (16, 18), (0, 19), (10, 27), (1, 10), (21, 7), (2, 15), (7, 17), (6, 22), (1, 4), (0, 1), (5, 12), (21, 20), (21, 16), (0, 23), (6, 0), (10, 0), (1, 25), (10, 14), (18, 10), (9, 11), (0, 11), (17, 10), (20, 9), (15, 18), (19, 1), (17, 8), (5, 27), (14, 8), (4, 17), (11, 7), (8, 1), (10, 4), (4, 16), (2, 3), (14, 19), (18, 22), (15, 14), (13, 2), (15, 22), (19, 17), (8, 4), (22, 18), (1, 26), (12, 18), (16, 0), (8, 20), (13, 8), (21, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118746", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 26), (19, 14), (19, 18), (15, 13), (1, 3), (7, 14), (4, 9), (6, 21), (19, 21), (5, 5), (7, 25), (15, 15), (12, 18), (0, 3), (18, 1), (6, 12), (5, 20), (7, 26), (12, 10), (1, 17), (12, 9), (10, 7), (5, 3), (8, 14), (2, 7), (13, 12), (6, 15), (4, 6), (5, 24), (8, 8), (0, 26), (2, 26), (8, 24), (10, 11), (20, 16), (5, 15), (10, 8), (18, 2), (14, 20), (13, 15), (19, 20), (5, 23), (18, 14), (9, 16), (16, 17), (1, 5), (13, 17), (11, 2), (6, 24), (19, 11), (3, 17), (2, 10), (2, 13), (9, 15), (13, 25), (6, 6), (19, 9), (14, 0), (1, 21), (4, 1), (14, 1), (10, 13), (1, 19), (2, 20), (16, 10), (8, 21), (11, 22), (2, 0), (7, 2), (18, 3), (4, 23), (13, 3), (6, 23), (17, 1), (19, 17), (18, 5), (9, 9), (0, 4), (18, 16), (1, 23), (10, 24), (0, 23), (6, 25), (15, 7), (1, 25), (7, 22), (20, 26), (12, 11), (20, 24), (0, 17), (2, 6), (7, 24), (17, 13), (14, 24), (15, 9), (0, 2), (0, 19), (11, 1), (19, 8), (10, 5), (5, 11), (15, 0), (20, 15), (15, 4), (3, 13), (7, 6), (20, 20), (1, 12), (10, 26), (3, 14), (0, 25), (12, 17), (6, 22), (10, 16), (20, 17), (19, 0), (3, 5), (13, 11), (11, 5), (13, 22), (20, 9), (12, 5), (13, 7), (6, 4), (12, 15), (0, 6), (14, 9), (15, 2), (11, 21), (9, 22), (9, 4), (2, 16), (12, 2), (5, 9), (4, 22), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443772", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (19, 10), (2, 17), (7, 11), (2, 18), (5, 4), (9, 1), (10, 15), (19, 5), (7, 12), (5, 8), (11, 5), (17, 0), (4, 5), (5, 9), (12, 13), (6, 7), (18, 0), (12, 16), (1, 8), (5, 2), (11, 7), (13, 18), (12, 19), (7, 1), (14, 18), (11, 19), (4, 3), (8, 8), (12, 8), (16, 8), (10, 0), (8, 4), (16, 6), (16, 18), (10, 11), (17, 20), (1, 5), (9, 16), (10, 5), (1, 10), (13, 20), (18, 14), (0, 19), (19, 6), (18, 6), (10, 17), (13, 4), (11, 0), (15, 19), (12, 1), (13, 17), (1, 6), (19, 16), (0, 11), (4, 1), (2, 10), (12, 4), (19, 3), (18, 11), (1, 9), (3, 10), (3, 15), (10, 10), (3, 0), (17, 11), (0, 18), (16, 13), (6, 13), (12, 14), (11, 17), (7, 17), (14, 11), (12, 12), (4, 14), (18, 10), (16, 1), (9, 3), (0, 15), (14, 13), (6, 18), (19, 9), (6, 1), (4, 12), (16, 19), (4, 8), (13, 1), (5, 15), (16, 10), (19, 12), (12, 5), (5, 18), (2, 16), (15, 18), (0, 12), (2, 15), (17, 7), (14, 2), (18, 5), (12, 7), (0, 4), (8, 2), (4, 20), (14, 19), (16, 12), (15, 7), (6, 8), (6, 3), (8, 14), (7, 15), (8, 6), (6, 11), (4, 2), (5, 10), (11, 1), (13, 19), (7, 10), (18, 1), (4, 19), (14, 3), (10, 14), (16, 5), (6, 16), (15, 0), (18, 4), (17, 5), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "722916", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 19), (3, 17), (3, 8), (0, 7), (2, 24), (10, 20), (22, 14), (8, 5), (14, 21), (16, 13), (8, 16), (20, 1), (5, 4), (23, 1), (10, 19), (18, 17), (22, 20), (11, 17), (21, 21), (21, 5), (15, 24), (16, 3), (21, 9), (5, 11), (4, 6), (3, 14), (4, 16), (0, 23), (13, 5), (16, 1), (6, 0), (3, 13), (15, 16), (11, 11), (4, 4), (17, 7), (7, 8), (10, 14), (17, 4), (7, 22), (21, 20), (18, 2), (6, 7), (9, 20), (18, 14), (10, 0), (19, 15), (4, 10), (0, 20), (13, 22), (23, 5), (3, 24), (7, 13), (2, 6), (6, 20), (5, 12), (11, 15), (14, 1), (10, 22), (22, 17), (13, 9), (2, 19), (6, 11), (23, 12), (1, 18), (14, 12), (10, 9), (6, 3), (1, 5), (22, 12), (11, 9), (10, 18), (3, 10), (5, 24), (13, 10), (15, 6), (9, 3), (12, 10), (7, 20), (14, 4), (13, 16), (10, 17), (15, 14), (7, 19), (7, 10), (22, 0), (15, 17), (23, 8), (15, 12), (16, 14), (12, 19), (2, 20), (15, 10), (19, 4), (18, 3), (13, 15), (8, 18), (12, 11), (14, 18), (6, 19), (20, 23), (1, 14), (23, 11), (1, 20), (11, 3), (2, 2), (13, 2), (19, 12), (19, 20), (11, 13), (4, 9), (19, 9), (20, 4), (21, 11), (5, 3), (0, 5), (7, 0), (21, 22), (2, 9), (22, 22), (22, 15), (10, 10), (15, 3), (0, 8), (10, 4), (5, 18), (16, 11), (1, 22), (1, 21), (5, 22), (11, 1), (7, 5), (5, 0), (2, 17), (18, 19), (13, 20), (15, 21), (20, 20), (23, 7), (14, 15), (9, 7), (13, 1), (18, 8), (23, 17), (20, 21), (21, 18), (4, 17), (7, 24), (19, 22), (23, 9), (1, 17), (18, 18), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707472", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), 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), (20, 22), (0, 5), (6, 14), (5, 16), (16, 17), (5, 17), (1, 22), (9, 25), (1, 19), (7, 1), (15, 3), (2, 2), (15, 1), (2, 8), (18, 10), (5, 6), (12, 21), (11, 21), (12, 15), (4, 0), (1, 24), (5, 12), (1, 12), (6, 18), (16, 14), (16, 7), (1, 1), (8, 13), (1, 26), (20, 20), (12, 19), (12, 8), (5, 22), (8, 15), (20, 15), (7, 14), (9, 6), (13, 10), (12, 2), (15, 5), (11, 13), (1, 17), (10, 21), (20, 17), (15, 9), (19, 13), (16, 25), (13, 15), (8, 16), (14, 11), (8, 5), (14, 3), (5, 1), (13, 18), (20, 12), (20, 6), (7, 2), (15, 0), (9, 4), (16, 5), (17, 9), (10, 24), (17, 24), (0, 3), (9, 19), (11, 11), (14, 22), (12, 5), (0, 13), (3, 24), (11, 2), (7, 3), (14, 10), (13, 1), (17, 17), (12, 6), (2, 12), (9, 21), (2, 18), (10, 20), (10, 2), (20, 9), (6, 8), (11, 22), (17, 18), (3, 25), (10, 26), (8, 8), (10, 11), (16, 6), (4, 13), (18, 8), (0, 7), (5, 3), (17, 12), (11, 16), (10, 17), (6, 0), (13, 5), (8, 1), (20, 11), (6, 7), (10, 13), (18, 3), (3, 13), (16, 15), (11, 14), (4, 3), (8, 26), (7, 21), (6, 1), (2, 9), (18, 26), (17, 22), (0, 22), (9, 11), (20, 0), (1, 20), (9, 15), (13, 17), (2, 1), (15, 20), (20, 19), (18, 5), (6, 10), (12, 11), (9, 22), (13, 2), (7, 7), (6, 15), (19, 19), (17, 2), (4, 15), (7, 20), (13, 13), (6, 5), (19, 9), (19, 17), (9, 3), (3, 20), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872472", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (16, 2), (2, 14), (4, 19), (12, 17), (3, 13), (15, 2), (2, 1), (19, 4), (19, 14), (17, 1), (5, 16), (9, 11), (3, 2), (15, 19), (11, 12), (1, 15), (15, 12), (15, 11), (5, 18), (13, 13), (14, 12), (13, 14), (18, 9), (6, 1), (10, 7), (7, 20), (10, 10), (15, 21), (4, 16), (18, 1), (5, 9), (2, 13), (10, 15), (14, 20), (5, 3), (12, 7), (16, 8), (14, 2), (4, 0), (13, 12), (6, 18), (6, 12), (5, 15), (8, 11), (11, 17), (10, 5), (10, 14), (6, 10), (1, 12), (3, 7), (1, 6), (7, 17), (11, 4), (14, 17), (6, 21), (15, 18), (15, 14), (18, 14), (4, 7), (4, 21), (15, 5), (16, 6), (3, 20), (6, 13), (11, 1), (16, 19), (17, 18), (3, 14), (12, 18), (11, 0), (4, 20), (9, 12), (3, 1), (9, 14), (19, 6), (9, 18), (0, 9), (0, 20), (15, 1), (11, 21), (7, 9), (9, 16), (11, 8), (11, 10), (10, 11), (11, 16), (13, 7), (6, 17), (2, 4), (8, 14), (14, 7), (18, 10), (6, 0), (6, 16), (11, 14), (18, 2), (14, 6), (19, 19), (15, 16), (12, 16), (17, 2), (10, 17), (9, 0), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308448", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 18), (9, 23), (16, 15), (15, 24), (4, 5), (7, 18), (25, 1), (4, 7), (0, 8), (17, 16), (3, 18), (14, 2), (22, 22), (22, 2), (15, 5), (8, 27), (9, 3), (15, 27), (20, 14), (22, 25), (4, 0), (21, 23), (4, 4), (10, 10), (11, 3), (14, 14), (23, 8), (9, 21), (9, 19), (20, 21), (19, 3), (20, 17), (23, 5), (9, 0), (1, 22), (4, 14), (16, 8), (11, 7), (8, 9), (8, 21), (14, 0), (5, 13), (22, 18), (25, 27), (3, 26), (23, 17), (11, 27), (26, 1), (19, 13), (24, 11), (2, 20), (13, 2), (15, 25), (8, 0), (14, 12), (2, 12), (24, 22), (23, 10), (21, 20), (2, 13), (18, 25), (10, 26), (9, 7), (13, 11), (23, 26), (11, 2), (25, 2), (9, 6), (10, 24), (3, 27), (14, 25), (3, 8), (16, 0), (16, 16), (13, 16), (14, 5), (19, 7), (18, 2), (2, 26), (12, 7), (5, 24), (10, 11), (11, 10), (6, 27), (12, 10), (13, 7), (13, 22), (0, 22), (9, 16), (2, 3), (23, 24), (26, 20), (10, 25), (17, 24), (3, 14), (7, 19), (20, 18), (18, 15), (22, 16), (15, 8), (4, 1), (16, 3), (25, 22), (24, 6), (13, 5), (1, 14), (8, 19), (17, 21), (26, 16), (0, 6), (1, 6), (7, 11), (13, 26), (12, 20), (21, 21), (16, 4), (12, 17), (14, 24), (2, 21), (19, 11), (19, 16), (12, 0), (7, 20), (18, 6), (9, 24), (18, 14), (17, 27), (21, 26), (14, 3), (3, 6), (11, 12), (16, 13), (8, 5), (1, 1), (10, 15), (9, 25), (13, 25), (6, 10), (13, 13), (7, 21), (18, 8), (16, 24), (21, 2), (14, 27), (25, 21), (3, 24), (22, 17), (17, 10), (18, 1), (7, 10), (16, 20), (11, 23), (8, 23), (3, 22), (14, 19), (4, 19), (26, 10), (7, 12), (3, 9), (4, 13), (26, 17), (24, 5), (7, 5), (3, 21), (21, 13), (6, 24), (3, 0), (2, 2), (17, 19), (5, 20), (8, 12), (15, 0), (2, 6), (9, 14), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617340", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (5, 2), (7, 18), (16, 22), (1, 19), (3, 7), (17, 24), (7, 23), (11, 14), (1, 2), (12, 21), (17, 7), (0, 16), (14, 13), (0, 6), (10, 19), (9, 2), (6, 18), (4, 4), (3, 6), (3, 24), (10, 21), (6, 20), (6, 16), (1, 11), (0, 8), (21, 0), (4, 0), (5, 19), (13, 10), (14, 21), (16, 12), (15, 3), (9, 20), (6, 3), (12, 17), (18, 15), (21, 4), (14, 15), (19, 23), (18, 16), (9, 19), (8, 0), (13, 5), (5, 11), (20, 10), (17, 23), (7, 3), (12, 19), (10, 13), (18, 7), (10, 22), (7, 10), (13, 12), (19, 7), (18, 22), (20, 17), (6, 14), (18, 17), (15, 19), (0, 21), (9, 5), (4, 6), (0, 24), (8, 7), (20, 7), (20, 3), (8, 5), (13, 2), (14, 20), (1, 24), (12, 7), (9, 11), (15, 14), (11, 12), (10, 0), (13, 19), (9, 1), (11, 21), (13, 15), (12, 4), (11, 7), (2, 18), (15, 10), (19, 13), (1, 12), (5, 5), (13, 4), (20, 8), (0, 20), (21, 5), (19, 17), (15, 13), (11, 19), (3, 16), (1, 13), (1, 15), (5, 13), (12, 6), (6, 19), (16, 3), (20, 2), (1, 9), (0, 4), (16, 20), (18, 23), (3, 9), (18, 1), (20, 1), (14, 9), (19, 18), (18, 2), (14, 17), (10, 2), (8, 21), (15, 4), (12, 9), (20, 14), (9, 9), (4, 18), (7, 13), (7, 4), (7, 5), (5, 20), (17, 19), (1, 16), (5, 7), (14, 12), (21, 22), (6, 0), (16, 7), (11, 10), (6, 6), (10, 4), (1, 14), (16, 21), (1, 22), (17, 1), (0, 15), (4, 2), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "438750", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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), (8, 17), (14, 21), (2, 2), (16, 11), (14, 24), (8, 11), (5, 6), (15, 2), (15, 14), (17, 9), (9, 21), (10, 5), (1, 5), (19, 1), (9, 18), (12, 13), (2, 16), (11, 6), (0, 18), (18, 12), (4, 4), (5, 17), (6, 7), (18, 20), (6, 5), (1, 18), (0, 8), (16, 9), (2, 10), (7, 3), (7, 4), (15, 10), (17, 14), (13, 16), (19, 13), (9, 20), (16, 17), (2, 13), (2, 7), (3, 2), (0, 10), (2, 9), (6, 24), (9, 6), (14, 9), (13, 24), (4, 15), (17, 7), (10, 14), (6, 4), (9, 15), (1, 24), (2, 11), (5, 11), (19, 12), (7, 8), (4, 10), (3, 16), (0, 15), (2, 6), (11, 21), (19, 21), (2, 19), (12, 24), (5, 21), (3, 6), (14, 22), (0, 11), (3, 1), (6, 17), (6, 21), (9, 12), (12, 2), (7, 0), (12, 9), (14, 4), (8, 8), (6, 18), (3, 10), (18, 8), (12, 3), (16, 2), (15, 15), (4, 13), (4, 21), (3, 20), (11, 0), (8, 6), (16, 10), (17, 23), (10, 4), (19, 20), (15, 3), (7, 12), (4, 22), (9, 10), (9, 3), (18, 9), (11, 9), (9, 22), (1, 17), (10, 1), (19, 17), (19, 18), (10, 2), (16, 19), (5, 5), (13, 14), (1, 15), (19, 22), (19, 11), (15, 7), (13, 1), (13, 10), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752714", "dataset": "MATH"}
{"messages": [{"content": "In a 29x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 1), (23, 11), (24, 2), (27, 9), (0, 14), (2, 12), (15, 10), (6, 18), (8, 3), (16, 14), (25, 10), (17, 16), (3, 17), (28, 15), (5, 4), (8, 15), (24, 16), (17, 10), (6, 5), (27, 20), (27, 2), (13, 1), (4, 18), (5, 3), (1, 11), (9, 15), (2, 2), (28, 0), (26, 21), (8, 22), (11, 6), (8, 10), (24, 18), (28, 3), (25, 13), (4, 1), (15, 16), (15, 17), (24, 10), (3, 11), (9, 5), (18, 0), (7, 14), (3, 2), (11, 10), (9, 18), (1, 9), (19, 1), (10, 11), (14, 12), (3, 10), (3, 5), (15, 19), (1, 20), (24, 22), (8, 12), (21, 13), (1, 1), (27, 10), (6, 16), (2, 20), (13, 3), (17, 18), (25, 0), (25, 4), (20, 13), (21, 19), (14, 19), (1, 2), (23, 2), (15, 11), (18, 16), (21, 21), (16, 7), (24, 11), (11, 15), (1, 3), (19, 22), (19, 15), (18, 8), (28, 1), (16, 9), (24, 4), (28, 18), (16, 8), (14, 10), (21, 2), (9, 6), (8, 8), (22, 1), (27, 14), (23, 6), (22, 10), (25, 8), (4, 14), (15, 15), (4, 8), (3, 18), (20, 20), (19, 0), (26, 0), (12, 22), (5, 6), (13, 9), (15, 6), (24, 17), (18, 9), (16, 11), (18, 3), (4, 21), (22, 4), (8, 6), (14, 20), (26, 11), (18, 5), (26, 3), (23, 17), (11, 22), (23, 18), (2, 7), (15, 0), (7, 7), (23, 13), (19, 2), (15, 1), (3, 1), (21, 16), (5, 20), (21, 7), (21, 11), (22, 20), (12, 14), (20, 15), (6, 22), (7, 6), (5, 17), (6, 20), (18, 18), (25, 17), (14, 18), (21, 12), (4, 16), (0, 2), (25, 19), (28, 2), (27, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220980", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 25), (7, 2), (15, 13), (3, 8), (12, 6), (10, 23), (22, 0), (22, 2), (17, 16), (2, 26), (8, 5), (11, 18), (1, 17), (14, 2), (10, 2), (7, 0), (24, 1), (20, 10), (7, 15), (14, 26), (1, 10), (2, 20), (8, 20), (2, 1), (2, 27), (5, 4), (17, 19), (4, 3), (22, 11), (14, 21), (2, 25), (2, 16), (0, 21), (19, 6), (10, 24), (14, 16), (2, 5), (3, 27), (11, 26), (4, 16), (14, 10), (4, 25), (6, 21), (8, 0), (1, 15), (18, 3), (14, 20), (3, 21), (4, 5), (11, 22), (24, 18), (13, 17), (9, 8), (4, 19), (9, 18), (19, 4), (8, 24), (9, 5), (16, 22), (15, 22), (11, 9), (16, 1), (12, 10), (13, 20), (19, 17), (1, 7), (12, 11), (3, 20), (13, 6), (23, 7), (17, 13), (7, 10), (2, 23), (5, 23), (2, 3), (22, 23), (11, 7), (1, 27), (10, 10), (20, 0), (13, 13), (15, 17), (15, 4), (14, 14), (22, 9), (3, 17), (15, 23), (11, 23), (6, 5), (15, 16), (14, 0), (20, 14), (3, 25), (12, 14), (6, 25), (8, 10), (21, 26), (9, 2), (4, 27), (14, 19), (0, 16), (5, 26), (21, 23), (6, 4), (7, 25), (18, 13), (13, 11), (24, 19), (24, 11), (18, 15), (11, 27), (3, 2), (10, 1), (4, 17), (20, 3), (20, 27), (11, 16), (20, 15), (9, 16), (7, 19), (19, 25), (14, 27), (20, 6), (5, 10), (0, 23), (24, 17), (14, 25), (2, 13), (15, 20), (10, 21), (16, 26), (20, 11), (24, 23), (1, 18), (18, 4), (4, 0), (4, 9), (4, 2), (9, 0), (16, 21), (7, 27), (20, 26), (7, 22), (16, 20), (19, 14), (1, 4), (21, 15), (8, 16), (5, 9), (16, 12), (13, 0), (2, 8), (8, 17), (2, 7), (19, 2), (5, 18), (16, 24), (20, 2), (20, 24), (11, 12), (12, 9), (15, 21), (4, 26), (1, 9), (15, 5), (1, 24), (19, 16), (17, 26), (3, 15), (7, 5), (4, 20), (13, 2), (16, 18), (17, 5), (0, 14), (10, 15), (13, 10), (7, 18), (0, 6), (14, 11), (14, 18), (17, 14), (10, 17), (22, 18), (7, 14), (8, 7), (9, 10), (20, 23), (22, 24), (10, 7), (15, 19), (19, 12), (11, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "939252", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 3), (10, 14), (22, 13), (7, 16), (22, 17), (25, 1), (18, 5), (8, 18), (27, 3), (2, 12), (23, 9), (14, 5), (9, 16), (5, 11), (11, 18), (13, 8), (4, 19), (21, 13), (4, 6), (3, 3), (20, 14), (16, 3), (9, 4), (10, 10), (25, 4), (17, 7), (9, 13), (23, 10), (16, 16), (1, 12), (20, 5), (22, 11), (23, 1), (13, 17), (11, 2), (11, 17), (1, 1), (17, 17), (14, 10), (18, 1), (24, 9), (23, 17), (9, 14), (9, 15), (0, 3), (5, 0), (7, 17), (10, 1), (14, 14), (12, 9), (23, 3), (24, 19), (3, 4), (26, 14), (11, 9), (20, 4), (7, 9), (16, 9), (14, 3), (4, 13), (24, 14), (14, 9), (7, 6), (15, 10), (20, 17), (3, 6), (11, 16), (1, 6), (22, 18), (15, 14), (24, 8), (10, 15), (19, 4), (18, 7), (27, 7), (7, 11), (23, 2), (21, 16), (4, 8), (25, 13), (16, 12), (4, 11), (20, 2), (17, 14), (1, 0), (18, 8), (17, 19), (8, 15), (23, 4), (2, 7), (25, 0), (13, 6), (22, 5), (24, 7), (6, 15), (20, 16), (7, 19), (8, 0), (14, 19), (9, 1), (3, 11), (19, 14), (11, 7), (6, 12), (2, 19), (17, 0), (8, 14), (10, 12), (27, 8), (12, 2), (21, 10), (5, 9), (19, 2), (18, 11), (7, 13), (5, 7), (22, 4), (11, 13), (6, 1), (8, 11), (5, 13), (5, 14), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388696", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 12), (10, 8), (5, 17), (24, 19), (6, 22), (8, 6), (12, 0), (13, 5), (21, 10), (9, 6), (21, 5), (20, 18), (8, 9), (11, 4), (21, 19), (14, 17), (10, 20), (0, 20), (20, 17), (0, 18), (7, 12), (4, 10), (14, 0), (10, 14), (13, 8), (26, 7), (25, 8), (27, 3), (18, 13), (26, 6), (17, 1), (7, 20), (4, 22), (3, 11), (0, 15), (20, 0), (15, 5), (17, 15), (23, 6), (15, 18), (23, 7), (4, 20), (19, 6), (14, 1), (24, 9), (9, 21), (1, 17), (4, 2), (15, 14), (11, 10), (9, 10), (8, 13), (23, 4), (14, 4), (5, 1), (2, 7), (25, 9), (13, 21), (1, 10), (6, 5), (7, 8), (28, 7), (27, 1), (10, 11), (11, 3), (26, 10), (26, 0), (6, 13), (26, 21), (24, 15), (4, 12), (26, 23), (9, 22), (23, 12), (9, 0), (19, 4), (1, 14), (21, 7), (3, 10), (22, 3), (5, 10), (0, 1), (7, 13), (24, 7), (5, 6), (21, 11), (16, 20), (11, 2), (7, 0), (5, 4), (28, 17), (4, 15), (0, 17), (15, 15), (22, 14), (28, 8), (24, 23), (19, 18), (23, 11), (17, 3), (18, 4), (28, 11), (22, 22), (22, 20), (16, 7), (26, 8), (21, 12), (21, 0), (28, 1), (15, 16), (5, 21), (9, 17), (12, 20), (8, 14), (17, 6), (14, 21), (3, 8), (27, 17), (25, 10), (7, 23), (20, 15), (14, 13), (21, 3), (27, 8), (18, 17), (6, 7), (23, 0), (26, 15), (3, 12), (6, 10), (11, 5), (9, 20), (11, 19), (25, 23), (18, 7), (19, 17), (21, 8), (24, 20), (25, 22), (3, 23), (5, 13), (4, 3), (8, 15), (21, 17), (5, 19), (25, 4), (21, 23), (14, 7), (16, 23), (20, 10), (2, 19), (27, 16), (26, 17), (17, 22), (20, 2), (0, 10), (15, 1), (18, 5), (19, 12), (1, 9), (16, 0), (1, 1), (13, 10), (12, 11), (16, 10), (16, 13), (26, 2), (8, 16), (2, 20), (6, 16), (10, 10), (5, 7), (27, 22), (3, 22), (9, 3), (26, 22), (1, 5), (1, 20), (27, 9), (19, 11), (7, 5), (28, 20), (21, 6), (23, 19), (9, 18), (11, 1), (1, 3), (17, 20), (21, 20), (24, 10), (22, 18), (0, 6), (22, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980730", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), 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), (0, 14), (2, 10), (23, 0), (8, 1), (12, 11), (14, 20), (22, 1), (6, 21), (25, 8), (27, 20), (25, 11), (26, 9), (22, 0), (7, 3), (0, 3), (28, 16), (7, 19), (12, 20), (18, 10), (13, 19), (2, 0), (12, 4), (7, 7), (12, 5), (3, 6), (2, 4), (18, 21), (4, 16), (8, 19), (7, 2), (12, 19), (9, 14), (1, 20), (2, 21), (3, 0), (8, 3), (4, 20), (10, 14), (1, 21), (7, 15), (11, 16), (19, 9), (23, 11), (18, 12), (7, 12), (21, 13), (5, 4), (12, 12), (9, 9), (9, 4), (22, 19), (28, 5), (12, 6), (2, 9), (4, 9), (9, 11), (11, 0), (17, 1), (5, 16), (13, 2), (7, 16), (4, 10), (13, 6), (27, 14), (25, 17), (7, 1), (24, 20), (4, 5), (4, 15), (8, 12), (15, 0), (15, 5), (11, 5), (4, 0), (27, 4), (9, 18), (20, 16), (10, 21), (4, 17), (15, 4), (13, 21), (11, 6), (25, 1), (22, 10), (5, 7), (5, 6), (8, 7), (15, 15), (28, 12), (12, 21), (12, 0), (18, 1), (21, 14), (15, 7), (9, 6), (27, 17), (24, 12), (11, 9), (19, 14), (9, 5), (25, 2), (22, 12), (17, 6), (10, 16), (10, 5), (25, 3), (22, 6), (17, 11), (23, 19), (1, 11), (24, 18), (19, 19), (25, 5), (18, 15), (16, 11), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634512", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 26), (18, 20), (2, 18), (24, 0), (23, 21), (11, 4), (5, 10), (1, 22), (20, 21), (23, 7), (3, 20), (8, 8), (0, 23), (26, 3), (19, 21), (19, 0), (7, 18), (11, 21), (13, 6), (14, 27), (25, 4), (4, 17), (21, 21), (1, 17), (12, 16), (6, 12), (9, 7), (7, 2), (13, 27), (15, 18), (8, 17), (22, 3), (26, 24), (1, 1), (1, 21), (24, 17), (8, 18), (13, 18), (23, 3), (8, 25), (11, 22), (4, 27), (17, 18), (10, 1), (27, 10), (18, 23), (28, 22), (5, 8), (15, 13), (5, 1), (17, 27), (28, 0), (17, 13), (1, 26), (12, 3), (21, 28), (15, 17), (10, 13), (20, 7), (20, 11), (27, 6), (23, 13), (13, 15), (16, 13), (16, 28), (18, 24), (16, 14), (14, 3), (18, 8), (5, 15), (1, 25), (16, 7), (6, 5), (17, 19), (7, 4), (6, 0), (6, 6), (17, 4), (25, 19), (28, 25), (16, 4), (26, 28), (11, 15), (12, 11), (2, 26), (11, 14), (0, 28), (26, 21), (6, 4), (25, 13), (18, 1), (23, 19), (22, 18), (26, 23), (5, 18), (14, 11), (24, 3), (10, 12), (14, 19), (23, 16), (18, 12), (21, 19), (14, 8), (26, 16), (12, 4), (6, 11), (24, 15), (2, 15), (24, 9), (6, 1), (2, 6), (22, 24), (9, 25), (5, 0), (0, 3), (12, 17), (14, 24), (28, 10), (10, 22), (25, 21), (13, 21), (28, 6), (2, 21), (12, 28), (20, 15), (19, 22), (10, 11), (19, 17), (21, 12), (19, 5), (17, 17), (0, 10), (3, 26), (19, 6), (5, 20), (8, 10), (27, 18), (6, 25), (4, 1), (3, 27), (0, 2), (10, 14), (28, 4), (6, 28), (4, 19), (19, 20), (3, 16), (26, 4), (6, 19), (14, 18), (23, 9), (28, 5), (14, 15), (27, 28), (2, 20), (0, 13), (21, 17), (19, 27), (24, 16), (8, 6), (22, 1), (12, 5), (8, 15), (15, 27), (0, 16), (11, 5), (8, 2), (14, 9), (7, 3), (20, 22), (2, 14), (18, 13), (16, 6), (8, 21), (4, 11), (4, 0), (13, 3), (18, 7), (2, 8), (24, 19), (26, 5), (28, 2), (27, 21), (9, 9), (19, 13), (27, 9), (4, 20), (24, 7), (19, 9), (22, 8), (7, 15), (5, 13), (16, 25), (27, 1), (25, 26), (8, 26), (7, 8), (7, 10), (27, 0), (26, 2), (21, 13), (10, 20), (24, 25), (21, 24), (0, 21), (20, 14), (14, 5), (21, 3), (21, 0), (4, 28), (7, 0), (23, 11), (1, 13), (16, 10), (1, 11), (16, 22), (8, 4), (12, 8), (25, 17), (11, 17), (5, 26), (17, 8), (7, 12), (0, 26), (12, 6), (14, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501450", "dataset": "MATH"}
{"messages": [{"content": "In a 29x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 22), (24, 0), (20, 2), (27, 21), (25, 20), (22, 7), (21, 6), (15, 20), (4, 4), (1, 1), (23, 21), (2, 21), (23, 6), (28, 1), (0, 2), (0, 15), (12, 21), (12, 2), (9, 6), (27, 4), (2, 12), (7, 10), (26, 8), (24, 8), (7, 17), (27, 19), (19, 15), (1, 12), (23, 0), (27, 5), (1, 22), (3, 20), (28, 0), (24, 14), (20, 20), (6, 7), (21, 17), (18, 1), (16, 8), (8, 7), (19, 6), (4, 0), (1, 8), (26, 19), (22, 9), (10, 13), (27, 17), (12, 17), (10, 14), (20, 4), (24, 15), (3, 17), (16, 4), (25, 12), (3, 7), (26, 13), (13, 5), (25, 2), (13, 16), (24, 7), (1, 10), (17, 1), (24, 19), (7, 6), (3, 13), (11, 13), (0, 6), (7, 11), (27, 7), (25, 6), (23, 9), (5, 8), (28, 13), (9, 8), (14, 11), (5, 0), (7, 1), (8, 22), (19, 13), (12, 9), (11, 5), (20, 3), (10, 5), (12, 7), (12, 6), (9, 14), (15, 21), (0, 17), (6, 22), (25, 14), (28, 11), (5, 2), (10, 2), (20, 8), (2, 22), (14, 16), (8, 3), (1, 19), (14, 22), (26, 16), (18, 13), (6, 8), (8, 17), (9, 21), (0, 19), (8, 16), (8, 8), (19, 2), (10, 3), (17, 20), (23, 15), (22, 0), (9, 19), (27, 3), (12, 5), (21, 19), (27, 11), (14, 19), (1, 3), (8, 9), (28, 16), (12, 15), (1, 20), (6, 11), (9, 11), (25, 11), (10, 1), (25, 0), (2, 9), (24, 16), (9, 7), (26, 10), (21, 0), (12, 10), (3, 4), (15, 14), (22, 12), (13, 8), (11, 2), (24, 17), (21, 14), (7, 22), (22, 19), (12, 18), (24, 20), (5, 14), (5, 18), (17, 2), (8, 0), (2, 5), (25, 13), (16, 2), (3, 19), (4, 22), (8, 19), (5, 22), (24, 22), (20, 17), (22, 21), (8, 1), (8, 20), (16, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997815", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), 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), (13, 15), (2, 21), (7, 5), (14, 11), (4, 26), (7, 21), (15, 22), (16, 5), (7, 12), (9, 16), (11, 26), (2, 24), (9, 21), (14, 19), (0, 24), (8, 25), (15, 20), (9, 13), (8, 2), (7, 15), (10, 20), (2, 14), (0, 20), (18, 16), (12, 6), (16, 9), (8, 20), (6, 25), (12, 11), (13, 26), (6, 17), (3, 15), (13, 9), (15, 21), (11, 18), (15, 16), (15, 24), (12, 15), (6, 2), (1, 24), (10, 26), (17, 27), (4, 25), (10, 19), (13, 10), (5, 26), (13, 12), (17, 13), (9, 2), (2, 19), (10, 25), (2, 5), (1, 0), (5, 15), (9, 26), (2, 2), (14, 3), (17, 17), (19, 20), (1, 25), (13, 13), (1, 23), (19, 5), (11, 16), (6, 11), (14, 6), (8, 19), (1, 8), (5, 16), (0, 15), (9, 23), (15, 19), (12, 18), (10, 12), (4, 18), (0, 4), (16, 2), (16, 11), (0, 8), (7, 19), (14, 8), (7, 2), (6, 7), (4, 2), (14, 1), (12, 27), (10, 14), (17, 9), (5, 22), (10, 27), (11, 25), (11, 7), (9, 5), (3, 17), (4, 12), (12, 19), (16, 10), (18, 2), (17, 25), (19, 13), (15, 0), (19, 22), (11, 14), (8, 4), (10, 15), (6, 24), (12, 26), (6, 13), (5, 17), (12, 10), (15, 23), (6, 15), (11, 20), (9, 0), (1, 12), (11, 11), (14, 20), (13, 20), (17, 19), (5, 6), (18, 4), (5, 4), (15, 13), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85580", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), 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), (23, 4), (3, 22), (14, 17), (27, 25), (4, 15), (24, 7), (21, 26), (1, 21), (12, 0), (15, 6), (20, 26), (22, 12), (8, 6), (4, 22), (20, 27), (25, 8), (15, 23), (22, 25), (11, 20), (7, 23), (27, 21), (25, 20), (2, 15), (13, 9), (17, 5), (4, 13), (4, 20), (0, 5), (3, 9), (22, 5), (1, 12), (20, 16), (19, 17), (25, 23), (9, 27), (26, 11), (26, 23), (13, 25), (25, 2), (25, 0), (14, 1), (13, 6), (15, 9), (19, 13), (19, 20), (22, 23), (24, 19), (20, 5), (9, 4), (3, 15), (14, 2), (11, 1), (25, 27), (4, 18), (21, 14), (23, 9), (21, 16), (16, 17), (26, 12), (17, 18), (6, 2), (12, 26), (25, 24), (7, 15), (17, 25), (12, 7), (3, 27), (1, 26), (19, 10), (23, 26), (4, 4), (26, 8), (11, 0), (21, 15), (25, 17), (1, 14), (14, 26), (0, 27), (2, 1), (26, 25), (17, 19), (15, 8), (22, 16), (6, 27), (0, 13), (10, 7), (3, 12), (17, 23), (7, 22), (21, 18), (3, 14), (14, 25), (16, 12), (14, 5), (1, 5), (18, 16), (5, 10), (7, 16), (24, 14), (6, 0), (24, 23), (2, 14), (10, 17), (6, 8), (11, 19), (1, 19), (26, 6), (27, 17), (2, 4), (15, 16), (6, 18), (6, 13), (11, 27), (1, 11), (9, 14), (26, 5), (12, 13), (11, 23), (7, 13), (26, 15), (19, 4), (6, 4), (13, 5), (10, 12), (25, 4), (14, 18), (2, 16), (2, 23), (27, 11), (17, 3), (21, 4), (22, 15), (11, 21), (17, 15), (15, 4), (17, 9), (27, 16), (9, 25), (23, 2), (18, 27), (20, 25), (13, 11), (1, 9), (24, 26), (0, 17), (3, 18), (4, 17), (20, 11), (24, 5), (0, 25), (18, 7), (10, 22), (12, 27), (1, 27), (15, 21), (0, 6), (4, 2), (7, 8), (12, 21), (18, 25), (27, 6), (25, 16), (17, 22), (11, 16), (26, 3), (26, 2), (14, 14), (9, 20), (18, 0), (21, 25), (25, 21), (18, 4), (27, 10), (1, 17), (7, 7), (13, 13), (23, 8), (1, 3), (11, 12), (10, 2), (10, 11), (12, 19), (23, 23), (21, 2), (15, 5), (5, 13), (20, 13), (27, 4), (5, 15), (0, 9), (8, 2), (19, 0), (13, 18), (3, 20), (27, 5), (13, 19), (13, 20), (13, 23), (20, 2), (12, 22), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34160", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), 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), (20, 7), (21, 16), (15, 18), (16, 20), (4, 22), (26, 18), (6, 26), (22, 22), (26, 19), (15, 12), (19, 7), (17, 22), (20, 25), (25, 23), (15, 7), (11, 21), (22, 20), (17, 15), (2, 22), (17, 3), (23, 26), (6, 17), (21, 12), (9, 20), (10, 16), (18, 21), (25, 15), (4, 24), (3, 22), (8, 14), (16, 8), (24, 9), (5, 24), (6, 1), (11, 2), (12, 15), (4, 17), (20, 10), (0, 18), (3, 18), (12, 24), (3, 12), (2, 17), (9, 8), (6, 6), (12, 21), (21, 20), (11, 18), (26, 2), (11, 9), (25, 25), (4, 0), (23, 1), (0, 9), (3, 7), (22, 26), (20, 1), (12, 0), (2, 16), (3, 8), (0, 12), (21, 19), (10, 17), (20, 5), (12, 4), (14, 0), (18, 16), (9, 26), (5, 9), (11, 5), (15, 1), (23, 6), (15, 26), (23, 22), (8, 20), (22, 9), (16, 1), (1, 9), (10, 25), (13, 16), (15, 25), (10, 15), (18, 19), (13, 1), (19, 1), (16, 21), (2, 8), (6, 14), (5, 2), (26, 6), (12, 22), (24, 18), (15, 5), (22, 11), (6, 4), (17, 14), (16, 4), (13, 7), (23, 14), (24, 15), (23, 2), (23, 20), (24, 21), (9, 13), (15, 14), (13, 4), (15, 22), (1, 7), (10, 20), (13, 0), (6, 13), (7, 16), (14, 2), (20, 26), (8, 1), (0, 5), (23, 3), (21, 21), (18, 9), (11, 16), (6, 10), (0, 15), (0, 20), (13, 20), (22, 10), (19, 10), (6, 9), (25, 5), (7, 14), (22, 1), (25, 1), (10, 5), (26, 20), (21, 9), (19, 21), (14, 24), (17, 11), (25, 11), (5, 12), (22, 12), (16, 5), (11, 6), (13, 5), (26, 1), (1, 25), (0, 3), (20, 8), (7, 8), (11, 15), (5, 4), (11, 17), (8, 18), (13, 11), (12, 5), (15, 16), (20, 17), (18, 8), (5, 22), (12, 13), (16, 12), (12, 9), (9, 23), (26, 11), (24, 11), (8, 19), (8, 21), (9, 1), (10, 0), (3, 0), (22, 24), (16, 25), (21, 13), (1, 13), (19, 14), (25, 19), (4, 18), (6, 0), (3, 21), (12, 10), (1, 15), (10, 26), (18, 13), (3, 3), (4, 20), (19, 23), (18, 22), (9, 19), (9, 22), (11, 19), (18, 0), (25, 26), (24, 7), (25, 2), (3, 14), (0, 24), (16, 24), (6, 23), (3, 11), (5, 15), (12, 25), (21, 23), (18, 12), (10, 23), (20, 22), (14, 13), (5, 25), (4, 1), (1, 22), (24, 13), (23, 13), (24, 22), (7, 4), (20, 21), (24, 25), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "652370", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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), (0, 16), (10, 9), (17, 1), (15, 16), (17, 18), (8, 16), (19, 15), (0, 5), (6, 7), (18, 8), (8, 9), (7, 10), (19, 6), (20, 11), (16, 6), (3, 11), (2, 4), (11, 0), (17, 13), (10, 13), (20, 10), (0, 2), (6, 13), (0, 11), (0, 8), (1, 7), (20, 7), (13, 14), (6, 20), (18, 3), (6, 2), (5, 1), (16, 0), (5, 19), (14, 9), (9, 0), (14, 4), (15, 5), (13, 16), (7, 4), (17, 20), (6, 16), (10, 5), (15, 8), (11, 20), (5, 15), (3, 18), (20, 3), (6, 14), (15, 19), (8, 3), (15, 10), (13, 7), (5, 18), (6, 17), (14, 6), (10, 4), (7, 3), (7, 13), (5, 12), (19, 8), (7, 12), (1, 8), (18, 2), (17, 3), (6, 19), (0, 3), (10, 7), (12, 0), (16, 4), (12, 18), (2, 20), (16, 13), (21, 1), (0, 7), (7, 18), (13, 3), (3, 10), (17, 15), (17, 14), (19, 16), (21, 7), (5, 4), (1, 18), (7, 17), (17, 6), (16, 2), (7, 20), (12, 19), (18, 15), (4, 7), (6, 1), (3, 9), (5, 3), (21, 8), (1, 5), (9, 6), (12, 8), (21, 10), (7, 0), (1, 14), (17, 7), (10, 20), (2, 2), (21, 18), (16, 9), (17, 8), (7, 9), (2, 12), (2, 17), (21, 11), (21, 12), (8, 11), (0, 10), (2, 19), (10, 11), (0, 4), (15, 12), (13, 17), (12, 12), (5, 0), (4, 11), (19, 10), (13, 8), (11, 18), (10, 3), (2, 0), (5, 9), (20, 12), (16, 7), (12, 14), (15, 17), (3, 20), (10, 0), (13, 9), (1, 20), (11, 19), (10, 8), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688128", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), 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), (15, 17), (16, 10), (23, 21), (20, 18), (1, 14), (4, 12), (9, 13), (8, 25), (5, 27), (25, 21), (0, 25), (14, 25), (8, 27), (6, 19), (10, 20), (25, 13), (21, 18), (1, 26), (10, 12), (12, 15), (0, 23), (0, 4), (19, 3), (7, 26), (24, 25), (2, 5), (9, 27), (2, 0), (21, 21), (9, 24), (23, 20), (23, 11), (6, 20), (13, 9), (4, 4), (0, 21), (4, 20), (2, 2), (25, 22), (16, 22), (21, 24), (8, 4), (15, 12), (23, 15), (13, 11), (19, 22), (22, 16), (1, 15), (0, 1), (16, 25), (7, 9), (13, 16), (16, 20), (25, 23), (16, 12), (4, 16), (8, 2), (11, 2), (6, 18), (24, 8), (6, 27), (4, 11), (5, 17), (17, 10), (14, 3), (11, 21), (16, 26), (8, 1), (3, 3), (19, 6), (19, 20), (24, 12), (15, 3), (17, 21), (6, 10), (25, 25), (3, 21), (23, 14), (22, 26), (4, 19), (11, 0), (18, 25), (3, 17), (23, 18), (16, 7), (17, 25), (12, 2), (12, 24), (25, 16), (13, 20), (20, 14), (0, 5), (8, 21), (22, 5), (17, 27), (19, 1), (9, 22), (15, 4), (4, 22), (16, 19), (2, 11), (11, 4), (20, 11), (13, 22), (5, 5), (9, 16), (16, 17), (17, 11), (19, 11), (10, 24), (9, 14), (5, 16), (2, 3), (19, 9), (25, 10), (14, 14), (24, 11), (17, 14), (5, 3), (12, 19), (0, 17), (22, 1), (25, 8), (7, 27), (10, 6), (12, 22), (15, 0), (3, 27), (21, 16), (7, 17), (25, 12), (1, 4), (3, 8), (10, 22), (24, 27), (12, 6), (9, 17), (23, 27), (23, 13), (1, 5), (1, 7), (1, 17), (0, 13), (18, 3), (24, 17), (13, 7), (2, 6), (5, 20), (23, 8), (8, 12), (23, 10), (13, 5), (5, 19), (0, 2), (18, 26), (14, 15), (6, 16), (19, 26), (3, 10), (16, 27), (0, 9), (10, 25), (20, 22), (3, 2), (20, 6), (13, 19), (20, 24), (19, 2), (25, 15), (24, 0), (4, 24), (13, 1), (19, 16), (4, 21), (18, 9), (17, 3), (13, 8), (13, 14), (25, 9), (0, 15), (6, 2), (20, 13), (19, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726396", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), 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), (24, 6), (4, 8), (20, 16), (23, 11), (19, 9), (14, 25), (25, 8), (24, 21), (16, 13), (25, 19), (22, 16), (3, 16), (23, 15), (17, 6), (11, 15), (21, 15), (14, 24), (10, 22), (4, 10), (7, 23), (12, 7), (16, 9), (2, 24), (25, 11), (6, 12), (6, 9), (11, 17), (23, 3), (17, 14), (17, 9), (10, 15), (10, 8), (12, 12), (8, 13), (5, 20), (9, 0), (17, 17), (22, 2), (14, 3), (0, 14), (4, 1), (23, 8), (14, 12), (8, 8), (0, 22), (17, 20), (15, 0), (24, 1), (9, 19), (1, 22), (1, 19), (1, 10), (9, 12), (1, 11), (9, 25), (16, 5), (7, 11), (7, 17), (23, 13), (11, 7), (15, 25), (13, 1), (16, 11), (19, 19), (2, 8), (9, 8), (8, 25), (25, 17), (7, 19), (25, 14), (20, 24), (23, 22), (17, 22), (2, 7), (17, 4), (20, 15), (5, 1), (14, 22), (8, 14), (14, 8), (16, 6), (15, 22), (21, 2), (20, 11), (18, 6), (17, 11), (0, 1), (12, 14), (1, 16), (14, 23), (15, 4), (7, 20), (2, 3), (20, 0), (16, 17), (6, 8), (23, 14), (1, 15), (24, 15), (23, 16), (13, 25), (11, 18), (17, 25), (16, 3), (11, 12), (16, 23), (4, 3), (1, 2), (8, 21), (24, 8), (6, 5), (13, 13), (0, 23), (7, 0), (19, 8), (8, 3), (12, 8), (8, 15), (15, 18), (21, 10), (22, 10), (20, 25), (16, 0), (1, 7), (20, 13), (0, 4), (17, 3), (9, 23), (3, 17), (20, 10), (20, 20), (6, 1), (8, 22), (8, 2), (3, 10), (10, 23), (23, 23), (23, 10), (10, 17), (13, 7), (6, 2), (0, 10), (7, 4), (11, 5), (12, 9), (24, 13), (18, 22), (1, 8), (18, 16), (4, 24), (21, 17), (25, 22), (4, 14), (20, 3), (24, 19), (3, 24), (16, 12), (6, 4), (5, 22), (10, 12), (20, 9), (13, 9), (25, 9), (2, 18), (4, 13), (13, 17), (19, 24), (12, 0), (11, 20), (13, 6), (5, 3), (15, 11), (12, 22), (16, 14), (4, 5), (14, 16), (14, 19), (0, 18), (16, 25), (15, 17), (24, 17), (6, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "921900", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 14), (13, 11), (20, 15), (25, 7), (18, 0), (13, 21), (9, 15), (20, 3), (17, 13), (10, 13), (12, 15), (6, 12), (7, 10), (4, 21), (9, 20), (23, 21), (5, 22), (21, 1), (4, 20), (25, 1), (3, 7), (25, 13), (10, 19), (1, 16), (9, 14), (18, 6), (11, 23), (17, 10), (7, 0), (4, 0), (5, 19), (10, 7), (13, 23), (18, 12), (1, 12), (2, 5), (17, 1), (28, 11), (0, 22), (10, 6), (10, 4), (18, 22), (19, 18), (20, 4), (17, 21), (7, 19), (16, 16), (24, 17), (17, 4), (0, 23), (13, 6), (27, 17), (6, 1), (21, 5), (1, 10), (12, 6), (6, 10), (5, 17), (8, 1), (10, 2), (17, 5), (26, 0), (5, 7), (27, 23), (14, 3), (25, 11), (10, 21), (28, 10), (20, 1), (20, 17), (26, 20), (0, 4), (10, 20), (28, 4), (8, 2), (19, 20), (1, 0), (11, 14), (6, 0), (17, 0), (25, 5), (16, 4), (2, 23), (4, 14), (21, 18), (18, 17), (22, 14), (5, 3), (19, 12), (18, 19), (22, 22), (12, 18), (6, 18), (18, 18), (5, 6), (9, 4), (5, 8), (19, 15), (22, 0), (13, 8), (14, 22), (14, 11), (6, 14), (4, 2), (23, 7), (28, 7), (3, 12), (2, 16), (13, 16), (5, 21), (3, 10), (4, 23), (17, 20), (25, 9), (26, 7), (1, 2), (15, 10), (17, 23), (0, 3), (22, 23), (27, 0), (9, 23), (15, 9), (15, 3), (20, 23), (17, 7), (18, 8), (18, 14), (7, 20), (9, 7), (15, 12), (26, 5), (8, 6), (24, 15), (24, 18), (27, 3), (7, 7), (15, 21), (7, 13), (7, 15), (12, 5), (24, 23), (2, 8), (5, 16), (16, 21), (5, 4), (4, 7), (13, 4), (18, 16), (7, 5), (9, 22), (0, 8), (24, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886431", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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), (20, 6), (23, 21), (27, 14), (9, 24), (24, 24), (8, 2), (12, 2), (23, 12), (19, 20), (22, 17), (3, 15), (26, 8), (21, 14), (22, 14), (26, 22), (4, 12), (11, 12), (14, 17), (27, 1), (20, 26), (10, 12), (11, 10), (24, 16), (3, 20), (3, 23), (18, 15), (23, 14), (1, 8), (27, 5), (17, 2), (14, 24), (18, 19), (22, 12), (10, 2), (23, 11), (16, 1), (16, 16), (2, 20), (4, 0), (12, 0), (21, 20), (10, 9), (6, 1), (22, 15), (4, 6), (3, 13), (20, 19), (21, 25), (26, 6), (17, 7), (27, 24), (14, 14), (19, 11), (15, 7), (23, 2), (7, 8), (3, 5), (0, 25), (19, 23), (21, 5), (7, 12), (17, 11), (15, 21), (0, 2), (11, 20), (26, 3), (27, 25), (4, 17), (13, 22), (21, 16), (19, 19), (22, 5), (6, 18), (10, 3), (16, 19), (12, 15), (4, 23), (19, 5), (19, 21), (3, 1), (22, 4), (16, 8), (25, 21), (2, 26), (1, 5), (23, 6), (25, 4), (27, 13), (16, 4), (8, 23), (12, 6), (7, 25), (13, 11), (16, 25), (12, 12), (1, 7), (26, 25), (11, 6), (0, 22), (6, 4), (25, 6), (2, 21), (15, 12), (26, 18), (24, 14), (11, 21), (21, 1), (19, 16), (12, 22), (26, 20), (13, 4), (11, 7), (25, 1), (23, 10), (0, 4), (25, 2), (5, 15), (25, 8), (8, 7), (4, 4), (21, 21), (5, 10), (6, 23), (6, 17), (8, 9), (18, 25), (18, 14), (24, 9), (2, 19), (14, 0), (17, 20), (5, 9), (26, 7), (2, 16), (21, 0), (6, 25), (18, 23), (26, 21), (15, 4), (8, 21), (21, 13), (8, 18), (9, 10), (23, 22), (0, 8), (20, 17), (0, 1), (10, 17), (8, 16), (24, 7), (19, 7), (7, 17), (7, 19), (12, 16), (8, 14), (4, 14), (19, 17), (24, 1), (25, 17), (5, 25), (0, 12), (6, 20), (23, 7), (9, 13), (11, 16), (11, 26), (21, 19), (4, 1), (11, 19), (7, 23), (2, 12), (13, 13), (18, 11), (1, 15), (8, 17), (6, 22), (18, 4), (1, 2), (0, 7), (3, 2), (0, 6), (9, 0), (23, 15), (17, 13), (11, 13), (17, 9), (25, 10), (25, 16), (1, 26), (15, 3), (9, 1), (11, 5), (7, 3), (1, 19), (4, 22), (12, 14), (24, 8), (13, 3), (24, 19), (22, 22), (17, 23), (23, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730228", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 25), (22, 2), (16, 0), (0, 2), (0, 15), (1, 17), (24, 1), (15, 3), (23, 20), (7, 16), (4, 23), (2, 17), (11, 16), (17, 19), (20, 4), (17, 14), (24, 11), (10, 7), (13, 10), (8, 5), (9, 18), (19, 21), (0, 5), (19, 2), (0, 17), (21, 17), (12, 24), (24, 9), (15, 17), (18, 17), (19, 1), (20, 10), (4, 22), (23, 6), (22, 12), (4, 19), (3, 5), (1, 18), (23, 19), (9, 24), (21, 8), (2, 4), (7, 8), (8, 26), (15, 21), (18, 3), (14, 12), (10, 22), (17, 20), (11, 23), (20, 11), (11, 8), (8, 8), (11, 9), (10, 23), (5, 9), (14, 17), (21, 21), (19, 9), (18, 10), (0, 9), (4, 0), (9, 13), (21, 5), (9, 16), (10, 14), (4, 26), (10, 11), (12, 16), (3, 19), (7, 7), (17, 12), (16, 3), (11, 12), (17, 4), (18, 18), (19, 23), (11, 4), (10, 26), (1, 12), (18, 8), (4, 5), (21, 9), (9, 25), (4, 3), (11, 14), (21, 3), (17, 5), (8, 6), (14, 24), (22, 3), (12, 26), (11, 17), (9, 23), (0, 22), (4, 25), (17, 3), (13, 4), (10, 0), (23, 23), (16, 23), (1, 14), (8, 9), (20, 13), (7, 5), (16, 21), (11, 3), (8, 11), (11, 5), (6, 15), (6, 25), (21, 20), (17, 0), (1, 22), (23, 15), (2, 0), (1, 8), (20, 9), (13, 23), (0, 4), (8, 21), (12, 20), (13, 15), (6, 13), (21, 14), (5, 16), (1, 9), (17, 7), (19, 4), (23, 3), (5, 25), (22, 18), (22, 0), (9, 9), (9, 17), (2, 19), (16, 25), (1, 13), (14, 3), (18, 22), (24, 13), (10, 25), (4, 6), (11, 25), (10, 2), (14, 11), (20, 7), (20, 0), (20, 8), (11, 19), (8, 0), (3, 11), (15, 19), (12, 17), (20, 15), (10, 4), (7, 9), (13, 1), (3, 13), (2, 18), (1, 0), (23, 9), (11, 1), (20, 3), (12, 8), (24, 23), (16, 2), (1, 2), (3, 0), (13, 14), (1, 5), (23, 11), (22, 5), (4, 12), (24, 25), (14, 22), (7, 15), (17, 22), (2, 11), (18, 14), (24, 12), (2, 13), (2, 16), (0, 10), (8, 10), (9, 7), (6, 7), (6, 5), (23, 24), (4, 11), (16, 4), (6, 12), (23, 2), (7, 18), (4, 24), (4, 10), (5, 24), (13, 21), (22, 4), (24, 5), (6, 8), (9, 20), (8, 25), (15, 0), (17, 16), (14, 4), (2, 24), (15, 5), (1, 19), (1, 6), (20, 22), (22, 11), (9, 21), (10, 15), (24, 20), (18, 25), (16, 8), (0, 16), (19, 12), (22, 14), (6, 26), (6, 17), (6, 1), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "642320", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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), (0, 1), (13, 6), (16, 15), (22, 2), (4, 3), (20, 16), (13, 2), (3, 3), (24, 0), (5, 1), (18, 19), (3, 16), (16, 20), (13, 9), (7, 2), (12, 5), (0, 3), (8, 18), (8, 9), (13, 17), (13, 1), (19, 15), (7, 5), (2, 18), (17, 3), (23, 10), (0, 19), (10, 7), (21, 6), (8, 13), (21, 11), (23, 13), (23, 6), (10, 13), (22, 3), (19, 9), (15, 8), (17, 14), (7, 10), (5, 13), (8, 20), (1, 17), (14, 17), (18, 8), (13, 20), (17, 1), (0, 4), (22, 6), (13, 3), (21, 2), (15, 0), (6, 5), (23, 5), (14, 8), (2, 10), (10, 2), (5, 7), (11, 14), (22, 14), (5, 6), (1, 8), (2, 19), (9, 14), (4, 20), (12, 0), (7, 17), (17, 17), (15, 9), (23, 1), (11, 12), (1, 6), (7, 6), (13, 12), (15, 2), (18, 3), (1, 11), (16, 18), (5, 10), (15, 10), (13, 11), (4, 14), (10, 1), (17, 0), (6, 10), (9, 20), (2, 14), (19, 6), (14, 11), (5, 4), (1, 7), (18, 7), (19, 16), (10, 20), (0, 12), (2, 12), (22, 15), (24, 11), (6, 6), (20, 0), (24, 12), (0, 2), (3, 12), (14, 12), (23, 20), (24, 18), (4, 7), (5, 8), (15, 17), (13, 10), (21, 14), (14, 9), (6, 11), (23, 2), (1, 18), (1, 4), (6, 7), (18, 13), (0, 15), (4, 4), (16, 6), (20, 13), (8, 17), (1, 16), (19, 19), (4, 16), (17, 15), (22, 19), (19, 20), (7, 20), (8, 19), (21, 8), (16, 1), (9, 2), (9, 8), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706956", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 22), (19, 6), (9, 2), (16, 23), (19, 14), (0, 5), (20, 9), (21, 11), (16, 10), (16, 12), (3, 21), (9, 13), (19, 9), (20, 23), (18, 20), (2, 3), (19, 8), (16, 8), (18, 6), (19, 4), (14, 10), (4, 17), (9, 21), (13, 10), (17, 4), (1, 20), (11, 23), (6, 3), (12, 10), (12, 18), (21, 17), (11, 12), (2, 7), (16, 5), (11, 21), (23, 20), (23, 14), (0, 12), (10, 2), (18, 17), (16, 2), (24, 24), (9, 24), (11, 19), (12, 15), (19, 18), (3, 9), (25, 3), (23, 10), (13, 14), (3, 15), (7, 4), (4, 20), (5, 8), (13, 3), (5, 2), (18, 24), (7, 18), (10, 7), (23, 16), (17, 18), (19, 15), (3, 8), (20, 19), (11, 5), (13, 6), (17, 15), (4, 18), (24, 7), (4, 6), (20, 2), (10, 20), (9, 5), (23, 9), (4, 4), (5, 0), (19, 22), (22, 20), (0, 23), (21, 9), (8, 8), (6, 20), (16, 9), (16, 17), (16, 19), (8, 17), (5, 5), (15, 0), (5, 18), (20, 1), (10, 18), (10, 6), (6, 19), (20, 5), (21, 7), (6, 12), (22, 12), (12, 3), (15, 4), (19, 1), (25, 6), (10, 5), (9, 22), (16, 15), (22, 1), (14, 18), (1, 18), (15, 19), (15, 16), (8, 0), (13, 19), (10, 0), (10, 16), (2, 13), (1, 16), (5, 4), (3, 11), (23, 12), (24, 8), (25, 12), (2, 20), (1, 4), (12, 22), (9, 16), (15, 2), (11, 18), (23, 3), (22, 2), (23, 18), (24, 5), (11, 15), (21, 4), (22, 5), (1, 21), (5, 19), (3, 23), (1, 14), (10, 21), (3, 19), (11, 1), (4, 9), (4, 0), (4, 5), (19, 13), (18, 21), (5, 7), (22, 13), (6, 7), (6, 16), (20, 21), (2, 5), (25, 0), (8, 18), (17, 14), (12, 19), (4, 16), (5, 11), (2, 9), (15, 7), (20, 14), (21, 5), (25, 17), (0, 17), (8, 24), (16, 0), (13, 11), (3, 10), (25, 20), (17, 13), (25, 14), (3, 7), (23, 21), (4, 3), (19, 7), (24, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "878160", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (17, 16), (12, 3), (22, 10), (15, 17), (16, 25), (8, 22), (3, 4), (21, 5), (6, 25), (17, 14), (1, 9), (11, 22), (10, 22), (3, 5), (19, 0), (15, 6), (8, 4), (2, 27), (15, 25), (16, 18), (8, 13), (23, 5), (8, 6), (19, 27), (16, 8), (6, 12), (18, 16), (1, 23), (25, 10), (18, 26), (7, 18), (5, 1), (9, 26), (22, 5), (25, 13), (17, 19), (0, 19), (18, 8), (11, 28), (12, 7), (21, 17), (0, 10), (17, 23), (0, 6), (16, 20), (16, 3), (3, 6), (25, 8), (17, 8), (9, 15), (14, 8), (22, 22), (14, 5), (1, 11), (10, 20), (22, 17), (2, 9), (14, 17), (6, 3), (18, 28), (24, 9), (12, 20), (20, 12), (24, 24), (7, 25), (20, 19), (15, 9), (3, 8), (24, 17), (4, 25), (5, 22), (19, 26), (13, 6), (0, 5), (16, 9), (5, 10), (25, 24), (22, 3), (7, 26), (0, 17), (23, 3), (15, 26), (3, 2), (24, 26), (22, 23), (2, 20), (19, 28), (3, 12), (22, 15), (5, 7), (21, 8), (15, 14), (6, 27), (21, 14), (20, 18), (11, 21), (19, 22), (16, 7), (18, 14), (4, 10), (25, 7), (18, 9), (14, 21), (4, 23), (12, 21), (3, 22), (7, 15), (11, 15), (25, 9), (23, 8), (20, 4), (0, 16), (13, 20), (7, 21), (21, 12), (15, 20), (12, 8), (17, 17), (0, 23), (19, 8), (10, 18), (11, 7), (15, 13), (0, 15), (10, 28), (3, 28), (1, 22), (11, 13), (22, 7), (25, 19), (23, 21), (20, 2), (12, 11), (17, 1), (16, 11), (16, 22), (4, 7), (11, 3), (24, 2), (1, 7), (13, 5), (13, 26), (5, 12), (14, 22), (10, 3), (4, 18), (13, 17), (10, 1), (9, 1), (24, 16), (23, 17), (2, 25), (3, 0), (14, 3), (6, 18), (8, 1), (12, 12), (13, 3), (4, 13), (17, 13), (8, 8), (14, 6), (2, 3), (13, 28), (8, 27), (13, 19), (14, 18), (13, 18), (10, 15), (8, 26), (21, 0), (7, 20), (17, 6), (13, 14), (6, 10), (6, 17), (2, 18), (22, 28), (25, 1), (7, 23), (6, 26), (0, 13), (21, 24), (2, 23), (2, 5), (15, 3), (6, 1), (13, 1), (1, 21), (10, 4), (22, 20), (8, 25), (13, 0), (20, 26), (14, 13), (3, 20), (20, 1), (11, 19), (14, 1), (1, 10), (18, 6), (16, 14), (18, 27), (11, 18), (1, 0), (13, 12), (18, 11), (1, 13), (7, 4), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "741570", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), 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), (18, 3), (14, 9), (9, 4), (7, 12), (3, 3), (12, 6), (18, 21), (1, 16), (2, 21), (1, 17), (7, 18), (12, 23), (19, 11), (16, 26), (6, 5), (15, 12), (6, 9), (18, 24), (17, 20), (1, 11), (10, 21), (13, 15), (4, 2), (3, 19), (12, 18), (2, 7), (5, 13), (18, 13), (15, 1), (11, 23), (5, 16), (6, 20), (9, 14), (18, 0), (16, 18), (4, 14), (19, 14), (16, 11), (10, 1), (1, 14), (15, 21), (16, 13), (11, 17), (9, 7), (5, 11), (7, 17), (10, 4), (6, 0), (5, 12), (13, 12), (17, 1), (18, 11), (15, 2), (19, 13), (0, 9), (7, 19), (11, 16), (0, 24), (5, 26), (6, 4), (12, 24), (4, 3), (4, 18), (2, 16), (17, 15), (15, 4), (7, 6), (1, 19), (17, 12), (19, 5), (7, 11), (17, 23), (16, 5), (14, 26), (6, 24), (7, 9), (11, 14), (9, 25), (19, 20), (9, 22), (1, 24), (14, 2), (17, 2), (8, 13), (4, 15), (3, 0), (16, 17), (12, 4), (12, 16), (9, 11), (7, 8), (5, 17), (0, 11), (15, 5), (7, 10), (0, 8), (13, 0), (3, 12), (3, 25), (11, 21), (4, 23), (16, 0), (19, 7), (2, 22), (2, 12), (9, 17), (4, 7), (17, 14), (13, 20), (0, 12), (4, 13), (9, 9), (3, 13), (12, 10), (12, 26), (18, 14), (2, 1), (0, 19), (1, 12), (14, 24), (14, 22), (14, 5), (18, 6), (6, 6), (7, 22), (6, 1), (15, 22), (4, 8), (14, 11), (9, 18), (0, 16), (15, 6), (19, 10), (12, 13), (14, 0), (5, 1), (16, 15), (6, 22), (1, 1), (3, 26), (12, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406152", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 8), (2, 18), (7, 21), (17, 9), (16, 19), (6, 13), (0, 4), (6, 27), (15, 1), (4, 2), (16, 8), (15, 24), (9, 6), (8, 14), (3, 16), (6, 16), (5, 26), (4, 26), (6, 23), (11, 18), (4, 3), (2, 21), (4, 11), (6, 14), (4, 0), (19, 23), (14, 16), (2, 17), (16, 1), (13, 23), (18, 26), (9, 10), (15, 11), (17, 26), (15, 25), (16, 16), (14, 12), (14, 10), (19, 25), (11, 1), (15, 6), (12, 10), (7, 19), (0, 27), (7, 17), (10, 1), (18, 1), (18, 8), (8, 27), (13, 13), (13, 2), (18, 7), (2, 10), (14, 13), (4, 12), (3, 12), (18, 16), (13, 19), (14, 20), (6, 11), (12, 16), (18, 6), (16, 25), (10, 17), (0, 20), (9, 20), (4, 7), (0, 18), (15, 22), (8, 7), (9, 27), (7, 9), (18, 20), (17, 4), (4, 17), (4, 20), (16, 9), (8, 26), (7, 23), (18, 17), (6, 3), (1, 24), (13, 4), (16, 7), (10, 13), (7, 6), (18, 18), (0, 5), (17, 11), (9, 23), (14, 22), (4, 13), (10, 20), (10, 10), (11, 6), (2, 19), (11, 22), (12, 15), (14, 9), (4, 22), (9, 15), (9, 25), (7, 15), (13, 21), (4, 18), (7, 16), (6, 17), (19, 0), (9, 22), (12, 13), (18, 23), (13, 14), (7, 25), (12, 9), (4, 27), (5, 8), (1, 17), (14, 18), (2, 6), (6, 10), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "983116", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 5), (1, 17), (10, 5), (3, 3), (18, 28), (19, 27), (14, 28), (5, 11), (13, 14), (6, 19), (5, 5), (4, 21), (12, 10), (6, 2), (13, 3), (18, 2), (17, 10), (13, 8), (9, 9), (5, 19), (19, 13), (20, 28), (6, 5), (16, 9), (19, 11), (17, 12), (4, 23), (12, 25), (1, 8), (6, 27), (4, 9), (13, 9), (1, 6), (7, 27), (21, 13), (11, 1), (0, 21), (8, 27), (20, 1), (15, 23), (5, 22), (0, 15), (11, 0), (14, 20), (17, 0), (16, 18), (8, 17), (7, 25), (16, 1), (16, 10), (12, 7), (5, 25), (7, 15), (5, 13), (7, 8), (0, 19), (11, 26), (15, 27), (1, 1), (7, 18), (19, 16), (12, 18), (4, 14), (18, 0), (19, 6), (4, 18), (5, 28), (16, 16), (7, 11), (3, 9), (8, 12), (15, 28), (0, 3), (15, 8), (11, 18), (13, 6), (13, 19), (12, 6), (2, 10), (1, 19), (20, 6), (10, 23), (13, 23), (19, 8), (1, 25), (16, 8), (21, 9), (0, 16), (6, 18), (2, 2), (10, 0), (6, 28), (7, 14), (18, 25), (2, 13), (15, 11), (12, 23), (14, 18), (13, 26), (17, 4), (10, 14), (3, 15), (2, 23), (16, 2), (8, 22), (17, 24), (21, 0), (14, 13), (4, 25), (17, 23), (3, 8), (19, 4), (21, 3), (7, 22), (21, 8), (1, 20), (2, 25), (13, 24), (16, 3), (6, 14), (14, 21), (0, 8), (1, 12), (5, 2), (8, 0), (8, 9), (5, 3), (9, 26), (12, 5), (9, 15), (16, 19), (6, 9), (16, 21), (19, 3), (2, 20), (11, 22), (20, 9), (14, 15), (10, 28), (1, 26), (17, 19), (14, 5), (7, 1), (19, 14), (10, 3), (10, 17), (11, 21), (5, 24), (5, 14), (18, 23), (12, 22), (4, 22), (10, 24), (12, 0), (4, 28), (8, 21), (13, 2), (10, 26), (4, 0), (8, 23), (4, 26), (17, 21), (16, 27), (13, 17), (10, 7), (11, 20), (5, 17), (8, 25), (19, 17), (5, 8), (3, 17), (11, 28), (7, 10), (20, 17), (11, 23), (20, 5), (17, 28), (9, 0), (15, 1), (9, 23), (7, 28), (11, 16), (15, 20), (18, 16), (15, 4), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179168", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 20), (2, 24), (11, 27), (18, 27), (25, 23), (26, 16), (15, 27), (24, 26), (7, 17), (12, 23), (6, 25), (7, 5), (19, 10), (15, 18), (12, 10), (7, 23), (19, 20), (20, 28), (25, 0), (19, 0), (24, 7), (3, 19), (19, 26), (14, 5), (6, 8), (24, 6), (2, 2), (1, 9), (11, 0), (27, 19), (12, 20), (4, 15), (0, 2), (3, 21), (21, 3), (22, 12), (13, 24), (12, 17), (12, 27), (17, 28), (19, 3), (1, 7), (2, 6), (13, 7), (17, 21), (1, 14), (18, 16), (25, 8), (15, 15), (0, 14), (19, 21), (26, 1), (16, 21), (19, 1), (4, 24), (3, 14), (8, 22), (12, 8), (17, 17), (10, 18), (4, 5), (20, 18), (3, 6), (21, 24), (18, 25), (23, 28), (3, 17), (17, 6), (1, 26), (6, 7), (11, 3), (22, 25), (15, 5), (9, 10), (27, 20), (25, 15), (8, 1), (13, 10), (15, 13), (7, 4), (20, 14), (0, 16), (12, 3), (22, 23), (17, 24), (23, 1), (16, 17), (25, 18), (17, 7), (18, 24), (23, 0), (14, 28), (14, 1), (19, 17), (24, 18), (20, 4), (4, 10), (2, 15), (6, 3), (20, 26), (15, 26), (11, 26), (13, 1), (22, 11), (21, 21), (16, 18), (12, 21), (10, 0), (6, 0), (19, 16), (7, 10), (16, 25), (6, 27), (0, 25), (3, 8), (13, 23), (12, 26), (4, 21), (26, 21), (0, 4), (7, 18), (6, 17), (2, 19), (1, 6), (12, 6), (1, 0), (7, 25), (11, 10), (19, 9), (9, 2), (25, 28), (19, 19), (4, 9), (10, 23), (2, 28), (1, 21), (3, 12), (12, 9), (21, 27), (1, 18), (10, 26), (5, 27), (22, 8), (18, 2), (8, 7), (4, 8), (10, 4), (10, 12), (8, 4), (7, 16), (1, 19), (21, 26), (2, 17), (19, 15), (5, 1), (27, 25), (17, 2), (5, 25), (26, 9), (22, 2), (26, 10), (22, 24), (11, 19), (0, 26), (8, 23), (24, 0), (13, 18), (5, 16), (1, 24), (13, 0), (25, 22), (23, 11), (8, 21), (27, 27), (20, 21), (13, 8), (14, 0), (9, 28), (11, 4), (16, 26), (11, 23), (16, 23), (12, 7), (13, 5), (3, 28), (3, 9), (13, 12), (14, 7), (26, 26), (21, 13), (27, 10), (25, 11), (1, 25), (27, 7), (3, 25), (23, 8), (13, 26), (11, 1), (20, 0), (17, 22), (9, 21), (13, 28), (22, 19), (14, 9), (20, 2), (13, 15), (0, 22), (10, 27), (14, 27), (15, 22), (20, 23), (23, 16), (15, 6), (2, 27), (21, 9), (13, 21), (11, 2), (9, 16), (26, 17), (25, 14), (25, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416660", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (18, 2), (2, 3), (21, 9), (11, 4), (2, 8), (14, 11), (3, 8), (0, 19), (10, 16), (5, 10), (0, 15), (8, 17), (3, 13), (5, 13), (14, 1), (17, 0), (20, 0), (0, 13), (18, 10), (4, 17), (6, 8), (1, 17), (11, 13), (8, 4), (2, 4), (5, 20), (22, 18), (17, 7), (10, 12), (22, 9), (14, 7), (15, 12), (13, 8), (20, 4), (19, 14), (16, 16), (9, 0), (11, 16), (10, 8), (19, 7), (13, 7), (21, 14), (9, 11), (1, 13), (5, 4), (0, 17), (17, 3), (14, 6), (12, 12), (18, 4), (11, 0), (18, 3), (2, 19), (19, 3), (13, 13), (22, 8), (19, 12), (22, 3), (19, 16), (6, 19), (12, 19), (0, 20), (6, 6), (20, 14), (11, 12), (20, 9), (8, 2), (1, 2), (4, 10), (7, 8), (14, 8), (7, 20), (9, 13), (13, 12), (11, 1), (22, 1), (9, 15), (11, 8), (7, 5), (17, 4), (13, 16), (4, 20), (22, 6), (15, 6), (1, 18), (4, 2), (17, 6), (7, 6), (12, 15), (4, 14), (14, 3), (13, 1), (22, 7), (12, 5), (19, 15), (12, 9), (18, 6), (13, 10), (16, 8), (1, 1), (3, 19), (4, 8), (11, 3), (18, 18), (14, 14), (9, 17), (12, 16), (8, 15), (18, 12), (11, 10), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758919", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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, 12), (17, 6), (11, 17), (1, 19), (5, 16), (15, 16), (4, 16), (5, 14), (6, 2), (7, 9), (8, 17), (19, 13), (9, 5), (16, 6), (11, 9), (1, 16), (19, 9), (9, 9), (4, 8), (19, 16), (1, 8), (25, 8), (9, 7), (10, 9), (10, 10), (12, 17), (12, 13), (0, 5), (4, 15), (17, 9), (23, 14), (16, 15), (14, 8), (25, 7), (8, 12), (10, 16), (0, 17), (9, 13), (18, 7), (18, 12), (24, 9), (7, 19), (23, 16), (12, 10), (8, 11), (5, 15), (13, 19), (22, 5), (6, 4), (5, 8), (13, 3), (26, 16), (7, 13), (17, 13), (26, 8), (22, 7), (23, 13), (12, 16), (11, 5), (6, 18), (2, 8), (20, 15), (17, 1), (4, 9), (21, 19), (6, 14), (3, 8), (25, 12), (23, 7), (3, 16), (24, 15), (2, 4), (26, 10), (11, 14), (6, 0), (24, 14), (7, 16), (25, 6), (23, 17), (22, 16), (14, 3), (6, 15), (11, 12), (8, 18), (18, 18), (25, 4), (23, 18), (26, 0), (11, 16), (17, 5), (15, 18), (6, 17), (6, 3), (4, 19), (24, 0), (20, 11), (18, 14), (24, 2), (1, 15), (13, 13), (17, 19), (17, 15), (13, 16), (9, 10), (17, 2), (3, 13), (23, 4), (1, 4), (8, 6), (12, 14), (10, 0), (22, 11), (15, 10), (2, 17), (15, 15), (10, 14), (21, 5), (11, 13), (22, 17), (0, 7), (4, 4), (7, 0), (18, 13), (13, 14), (15, 4), (24, 19), (0, 13), (25, 5), (24, 18), (2, 5), (2, 11), (26, 11), (14, 19), (6, 7), (4, 18), (16, 7), (19, 19), (19, 4), (8, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "958380", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 20), (9, 11), (14, 13), (17, 7), (9, 14), (10, 8), (5, 0), (0, 17), (17, 12), (8, 18), (18, 12), (3, 0), (19, 18), (8, 5), (12, 20), (11, 16), (14, 19), (1, 12), (6, 1), (18, 24), (4, 20), (21, 11), (11, 18), (17, 4), (19, 7), (19, 10), (19, 24), (0, 6), (9, 13), (18, 22), (12, 0), (14, 24), (5, 7), (19, 23), (0, 3), (1, 5), (11, 10), (10, 1), (11, 12), (5, 22), (2, 16), (9, 0), (16, 22), (16, 3), (6, 24), (13, 5), (0, 23), (16, 19), (15, 10), (8, 9), (9, 20), (11, 9), (12, 2), (1, 1), (4, 8), (11, 8), (12, 1), (6, 9), (10, 11), (4, 17), (1, 18), (7, 11), (8, 6), (16, 7), (18, 21), (1, 22), (19, 2), (10, 9), (10, 12), (21, 6), (19, 13), (14, 2), (17, 19), (5, 14), (6, 5), (19, 6), (10, 0), (14, 9), (1, 10), (12, 5), (2, 24), (19, 21), (17, 18), (9, 4), (0, 20), (15, 21), (3, 7), (18, 2), (16, 11), (5, 4), (11, 3), (20, 15), (14, 14), (18, 8), (18, 17), (12, 6), (1, 16), (1, 4), (1, 6), (20, 14), (4, 1), (4, 3), (15, 4), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923700", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), 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), (15, 17), (12, 17), (1, 10), (26, 13), (4, 7), (1, 5), (10, 12), (24, 1), (8, 3), (23, 5), (1, 0), (7, 21), (25, 9), (9, 0), (7, 12), (24, 21), (12, 10), (2, 11), (16, 11), (11, 7), (22, 3), (1, 14), (8, 10), (22, 9), (24, 18), (7, 20), (20, 17), (25, 5), (11, 23), (18, 1), (20, 11), (18, 19), (21, 2), (5, 20), (24, 8), (22, 18), (23, 4), (17, 13), (16, 25), (8, 14), (26, 18), (14, 2), (5, 10), (3, 15), (13, 4), (7, 25), (18, 9), (19, 6), (17, 23), (11, 3), (14, 3), (21, 17), (6, 19), (26, 15), (4, 19), (10, 15), (11, 13), (21, 23), (2, 9), (1, 19), (5, 3), (23, 25), (14, 23), (7, 16), (20, 24), (10, 17), (13, 11), (22, 6), (0, 5), (13, 2), (5, 6), (25, 8), (24, 20), (0, 22), (4, 14), (20, 14), (12, 21), (4, 26), (17, 18), (9, 2), (4, 16), (13, 6), (3, 16), (6, 25), (0, 3), (8, 6), (26, 8), (19, 4), (3, 19), (13, 21), (7, 26), (2, 25), (1, 21), (17, 4), (20, 19), (22, 0), (20, 4), (11, 18), (8, 12), (12, 16), (25, 16), (9, 14), (6, 15), (12, 11), (14, 21), (24, 16), (0, 9), (0, 8), (23, 14), (5, 25), (3, 22), (0, 13), (15, 8), (16, 23), (10, 4), (10, 11), (5, 24), (16, 19), (2, 14), (21, 9), (21, 18), (24, 22), (23, 18), (6, 12), (20, 0), (3, 2), (15, 10), (21, 24), (24, 25), (16, 21), (7, 4), (4, 1), (15, 12), (17, 16), (4, 20), (18, 5), (11, 11), (15, 7), (23, 21), (14, 13), (12, 15), (7, 10), (2, 6), (26, 6), (14, 18), (10, 18), (21, 22), (22, 7), (18, 18), (16, 14), (0, 10), (14, 16), (21, 11), (25, 18), (25, 13), (10, 24), (12, 1), (17, 20), (23, 13), (20, 1), (26, 5), (7, 6), (19, 3), (24, 2), (4, 8), (23, 26), (11, 16), (21, 21), (23, 10), (18, 3), (13, 8), (11, 17), (6, 22), (15, 15), (22, 10), (23, 6), (12, 3), (17, 15), (16, 5), (6, 16), (10, 19), (18, 23), (19, 9), (19, 21), (23, 15), (8, 1), (25, 10), (16, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202860", "dataset": "MATH"}
{"messages": [{"content": "In a 25x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 23), 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), (6, 22), (19, 16), (7, 18), (16, 23), (6, 8), (6, 16), (18, 14), (8, 5), (7, 17), (14, 3), (0, 12), (7, 20), (1, 4), (9, 21), (24, 0), (12, 17), (13, 21), (15, 4), (5, 23), (14, 16), (10, 1), (19, 13), (3, 13), (5, 10), (17, 12), (22, 17), (21, 8), (1, 7), (23, 12), (17, 10), (5, 20), (23, 9), (2, 5), (4, 1), (23, 14), (19, 22), (24, 1), (19, 0), (1, 16), (20, 17), (23, 3), (24, 2), (1, 23), (22, 22), (5, 3), (8, 9), (12, 12), (8, 7), (22, 1), (18, 4), (4, 20), (9, 3), (17, 19), (16, 1), (11, 17), (15, 10), (23, 10), (13, 19), (9, 13), (23, 15), (15, 2), (20, 11), (14, 22), (4, 23), (16, 18), (20, 0), (6, 2), (0, 2), (2, 14), (8, 4), (22, 5), (2, 13), (14, 2), (17, 23), (8, 0), (9, 4), (3, 15), (11, 2), (14, 11), (6, 21), (18, 3), (0, 16), (21, 2), (24, 8), (15, 9), (4, 11), (12, 9), (0, 21), (22, 20), (18, 13), (12, 5), (5, 4), (12, 3), (23, 16), (3, 17), (24, 10), (15, 11), (24, 3), (10, 13), (16, 10), (10, 12), (20, 4), (8, 17), (22, 15), (13, 1), (22, 4), (12, 0), (9, 5), (13, 9), (10, 0), (7, 12), (17, 4), (19, 6), (14, 17), (0, 23), (8, 22), (9, 19), (5, 18), (12, 10), (19, 5), (8, 6), (24, 14), (5, 8), (9, 1), (5, 11), (21, 21), (9, 16), (10, 5), (12, 6), (20, 13), (10, 9), (21, 19), (13, 13), (17, 9), (2, 23), (17, 13), (14, 4), (21, 0), (3, 22), (2, 21), (16, 22), (10, 8), (23, 17), (14, 12), (4, 19), (14, 10), (19, 19), (14, 13), (19, 10), (19, 21), (15, 0), (11, 18), (7, 7), (5, 21), (6, 18), (12, 19), (3, 14), (5, 16), (19, 3), (2, 15), (16, 3), (19, 11), (19, 18), (14, 15), (17, 5), (14, 1), (17, 8), (10, 2), (0, 18), (4, 13), (24, 20), (23, 1), (20, 10), (14, 9), (23, 4), (0, 7), (0, 4), (24, 19), (16, 4), (6, 12), (2, 0), (10, 21), (9, 2), (10, 10), (21, 17), (16, 0), (0, 15), (20, 18), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371808", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 15), (16, 3), (10, 0), (9, 10), (11, 1), (1, 1), (15, 17), (16, 10), (11, 14), (1, 19), (13, 15), (16, 18), (1, 16), (14, 5), (19, 7), (5, 1), (2, 7), (3, 12), (11, 15), (18, 5), (6, 9), (16, 7), (18, 1), (4, 10), (6, 16), (13, 5), (15, 2), (7, 7), (12, 9), (19, 17), (10, 6), (9, 4), (6, 2), (5, 13), (14, 20), (17, 2), (2, 4), (0, 20), (17, 8), (11, 16), (13, 6), (19, 12), (21, 7), (8, 8), (21, 19), (10, 10), (7, 19), (18, 3), (22, 1), (19, 11), (16, 20), (2, 11), (6, 17), (12, 4), (21, 17), (2, 8), (8, 5), (13, 17), (15, 11), (15, 12), (12, 3), (14, 19), (4, 20), (1, 9), (1, 15), (4, 11), (14, 6), (4, 19), (8, 17), (1, 3), (6, 7), (3, 18), (1, 11), (17, 14), (5, 0), (14, 2), (17, 15), (10, 14), (20, 15), (16, 19), (22, 14), (5, 9), (11, 2), (16, 12), (8, 3), (21, 4), (17, 3), (20, 3), (8, 14), (11, 20), (19, 0), (1, 13), (8, 7), (4, 18), (18, 20), (12, 8), (19, 6), (20, 4), (4, 15), (2, 18), (0, 6), (8, 16), (3, 6), (2, 9), (9, 7), (1, 4), (11, 3), (4, 12), (16, 2), (10, 13), (8, 6), (10, 18), (22, 17), (12, 17), (13, 18), (6, 3), (17, 13), (7, 1), (1, 0), (11, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695196", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (6, 19), (15, 20), (10, 13), (16, 20), (1, 16), (14, 19), (19, 7), (14, 25), (12, 2), (19, 19), (14, 22), (16, 13), (14, 23), (19, 27), (1, 4), (7, 5), (17, 13), (6, 18), (1, 20), (9, 16), (10, 21), (7, 7), (20, 5), (21, 3), (17, 26), (6, 10), (20, 10), (21, 6), (21, 13), (6, 26), (18, 20), (17, 1), (1, 2), (7, 23), (14, 0), (6, 0), (8, 18), (18, 8), (9, 3), (12, 20), (12, 24), (6, 9), (9, 11), (13, 12), (21, 2), (8, 1), (21, 12), (6, 24), (3, 21), (15, 14), (8, 23), (19, 11), (2, 23), (9, 15), (5, 4), (11, 6), (20, 0), (13, 21), (12, 25), (11, 10), (19, 5), (21, 19), (7, 18), (2, 15), (8, 25), (16, 21), (6, 13), (22, 21), (7, 4), (11, 2), (0, 10), (13, 8), (4, 21), (22, 8), (22, 10), (18, 2), (20, 28), (3, 3), (21, 16), (2, 13), (4, 28), (22, 3), (2, 0), (17, 21), (19, 17), (0, 7), (12, 0), (12, 26), (1, 8), (19, 24), (15, 16), (18, 4), (2, 9), (20, 15), (20, 22), (2, 11), (6, 8), (22, 26), (21, 24), (22, 23), (19, 14), (20, 16), (2, 8), (21, 8), (21, 9), (0, 21), (13, 16), (5, 13), (12, 9), (17, 2), (10, 0), (3, 12), (14, 11), (6, 12), (17, 20), (5, 10), (22, 4), (0, 28), (20, 6), (7, 21), (6, 21), (6, 22), (4, 18), (1, 21), (16, 22), (4, 10), (16, 0), (2, 3), (9, 26), (19, 10), (6, 25), (1, 27), (6, 28), (5, 7), (17, 14), (5, 2), (9, 14), (8, 14), (5, 23), (13, 5), (18, 11), (6, 20), (20, 4), (0, 23), (16, 18), (16, 10), (13, 0), (5, 27), (4, 26), (16, 11), (15, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241640", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), 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), (1, 15), (19, 18), (23, 6), (22, 2), (24, 19), (7, 19), (21, 6), (19, 2), (7, 8), (17, 4), (13, 10), (17, 15), (0, 3), (20, 16), (2, 2), (14, 7), (3, 13), (23, 5), (14, 5), (19, 13), (19, 5), (12, 19), (15, 12), (11, 14), (8, 2), (23, 2), (8, 18), (18, 3), (16, 19), (14, 15), (16, 21), (3, 14), (22, 7), (4, 19), (8, 14), (12, 3), (5, 15), (13, 0), (8, 3), (14, 0), (19, 4), (3, 2), (5, 10), (10, 14), (17, 6), (23, 0), (14, 1), (17, 13), (12, 4), (12, 9), (13, 21), (8, 0), (4, 11), (9, 12), (24, 18), (12, 11), (17, 9), (17, 20), (5, 8), (2, 19), (15, 13), (12, 15), (11, 19), (16, 16), (11, 6), (4, 16), (16, 2), (11, 20), (16, 7), (18, 6), (4, 13), (5, 20), (3, 6), (10, 9), (13, 12), (13, 9), (23, 4), (18, 7), (5, 2), (24, 3), (9, 15), (3, 12), (20, 11), (11, 1), (23, 19), (13, 5), (5, 12), (20, 3), (19, 0), (4, 6), (23, 14), (24, 17), (0, 5), (4, 2), (13, 16), (2, 10), (11, 2), (14, 11), (1, 9), (15, 10), (17, 19), (22, 0), (1, 10), (17, 7), (3, 9), (18, 18), (15, 8), (23, 11), (9, 11), (22, 16), (7, 0), (7, 12), (24, 9), (24, 12), (18, 11), (10, 20), (4, 15), (18, 16), (6, 15), (17, 11), (15, 4), (2, 14), (3, 0), (21, 14), (11, 8), (11, 9), (8, 8), (10, 8), (16, 11), (18, 2), (13, 19), (7, 9), (2, 17), (6, 17), (11, 18), (19, 17), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600054", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), 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), (1, 5), (6, 0), (2, 3), (4, 17), (12, 12), (1, 21), (21, 13), (12, 15), (19, 2), (3, 16), (20, 1), (5, 19), (4, 22), (16, 10), (9, 18), (19, 7), (6, 4), (14, 0), (9, 5), (17, 16), (4, 4), (11, 7), (14, 13), (21, 16), (2, 15), (11, 6), (21, 4), (14, 5), (18, 18), (0, 19), (9, 3), (5, 0), (2, 17), (18, 22), (8, 3), (6, 23), (12, 19), (21, 10), (15, 18), (10, 12), (20, 2), (22, 18), (17, 19), (1, 19), (9, 1), (0, 4), (3, 22), (6, 10), (2, 13), (0, 1), (1, 12), (20, 16), (12, 10), (15, 5), (9, 21), (14, 19), (20, 21), (19, 8), (17, 18), (3, 20), (20, 5), (13, 1), (15, 17), (23, 5), (12, 0), (5, 20), (11, 23), (3, 10), (22, 1), (3, 2), (8, 23), (9, 0), (12, 2), (9, 20), (20, 22), (1, 16), (4, 21), (2, 10), (10, 1), (13, 9), (6, 12), (15, 11), (1, 15), (7, 3), (15, 10), (14, 9), (18, 16), (19, 1), (3, 7), (17, 13), (1, 22), (3, 6), (17, 17), (22, 20), (18, 21), (9, 22), (23, 8), (4, 3), (3, 21), (5, 11), (9, 14), (17, 14), (13, 6), (17, 10), (1, 23), (15, 7), (18, 8), (18, 5), (4, 16), (7, 5), (21, 20), (11, 13), (4, 9), (19, 9), (8, 7), (20, 4), (21, 17), (16, 14), (5, 5), (16, 17), (4, 8), (10, 0), (5, 18), (23, 20), (23, 6), (15, 15), (17, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47036", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), 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), (21, 12), (18, 9), (11, 24), (16, 13), (16, 20), (10, 8), (12, 9), (1, 24), (18, 12), (4, 22), (18, 2), (1, 18), (0, 22), (1, 25), (1, 19), (12, 23), (3, 7), (3, 10), (1, 4), (19, 21), (1, 1), (12, 12), (21, 15), (20, 12), (0, 8), (8, 2), (3, 16), (13, 14), (10, 11), (11, 8), (11, 5), (16, 16), (5, 22), (6, 18), (15, 7), (15, 17), (10, 14), (22, 24), (9, 15), (22, 9), (6, 11), (2, 24), (0, 15), (21, 2), (16, 23), (16, 7), (2, 5), (18, 13), (4, 11), (22, 19), (14, 6), (13, 24), (12, 16), (20, 16), (4, 9), (2, 13), (11, 18), (8, 11), (12, 14), (13, 7), (22, 17), (12, 0), (22, 13), (9, 2), (12, 20), (6, 13), (4, 12), (15, 8), (5, 8), (17, 25), (10, 0), (7, 24), (11, 22), (12, 19), (13, 10), (11, 15), (19, 4), (14, 1), (10, 21), (4, 0), (6, 9), (3, 4), (18, 17), (4, 16), (4, 17), (16, 25), (21, 9), (10, 18), (19, 12), (22, 6), (8, 8), (18, 8), (11, 21), (6, 21), (15, 9), (5, 4), (21, 0), (1, 11), (0, 12), (14, 8), (15, 2), (7, 22), (9, 11), (16, 24), (17, 18), (7, 17), (14, 4), (1, 13), (8, 15), (4, 21), (22, 11), (16, 8), (13, 13), (21, 23), (14, 3), (21, 10), (15, 10), (6, 24), (11, 16), (16, 0), (12, 4), (16, 22), (11, 1), (9, 18), (3, 22), (14, 24), (8, 20), (3, 19), (5, 5), (2, 21), (6, 2), (17, 22), (7, 23), (9, 0), (16, 18), (2, 3), (12, 10), (8, 23), (1, 23), (9, 24), (21, 8), (13, 12), (14, 10), (13, 4), (18, 16), (13, 9), (17, 6), (22, 10), (2, 20), (12, 18), (10, 19), (16, 2), (17, 5), (8, 21), (4, 13), (1, 2), (10, 25), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784800", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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), (5, 9), (11, 19), (9, 19), (26, 8), (6, 20), (17, 11), (5, 19), (16, 16), (3, 12), (14, 12), (9, 4), (16, 21), (4, 13), (20, 12), (25, 14), (8, 21), (24, 3), (19, 10), (20, 5), (18, 18), (7, 9), (5, 12), (16, 4), (20, 16), (1, 11), (17, 3), (9, 17), (23, 7), (11, 15), (21, 12), (14, 13), (5, 16), (9, 7), (13, 4), (15, 9), (19, 15), (5, 7), (0, 3), (19, 13), (1, 17), (25, 20), (14, 14), (0, 13), (13, 12), (19, 11), (7, 10), (2, 11), (19, 0), (16, 18), (24, 1), (15, 3), (6, 2), (4, 12), (16, 8), (12, 12), (4, 2), (23, 14), (17, 19), (8, 5), (3, 18), (15, 14), (3, 14), (24, 9), (6, 10), (24, 10), (13, 1), (9, 8), (3, 3), (12, 4), (20, 4), (3, 6), (18, 13), (2, 0), (25, 15), (22, 16), (19, 18), (14, 7), (8, 10), (5, 20), (0, 9), (23, 12), (26, 5), (9, 0), (17, 20), (16, 6), (19, 5), (23, 6), (23, 16), (10, 1), (10, 2), (2, 6), (20, 3), (19, 16), (25, 11), (6, 5), (24, 15), (19, 17), (13, 5), (0, 10), (11, 17), (21, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195480", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), 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), (7, 21), (17, 18), (4, 4), (7, 14), (3, 18), (2, 11), (13, 21), (1, 22), (19, 19), (16, 19), (4, 6), (18, 7), (7, 8), (4, 13), (17, 11), (12, 16), (10, 2), (15, 12), (21, 3), (6, 8), (21, 9), (10, 19), (5, 11), (13, 1), (11, 7), (10, 6), (16, 11), (14, 2), (6, 19), (14, 18), (8, 16), (20, 12), (11, 16), (14, 10), (8, 21), (6, 12), (2, 19), (3, 22), (10, 11), (14, 19), (16, 7), (17, 0), (2, 13), (12, 18), (2, 9), (9, 1), (21, 12), (0, 13), (17, 16), (20, 1), (16, 21), (15, 17), (11, 21), (12, 17), (15, 21), (14, 13), (13, 19), (5, 0), (8, 3), (2, 0), (15, 16), (5, 4), (17, 3), (20, 22), (19, 17), (19, 21), (13, 3), (21, 17), (6, 17), (3, 17), (18, 1), (18, 2), (10, 14), (8, 18), (12, 2), (16, 20), (1, 12), (2, 2), (5, 10), (13, 22), (10, 20), (11, 15), (0, 16), (14, 11), (4, 19), (2, 22), (7, 19), (1, 2), (12, 12), (19, 7), (7, 18), (0, 5), (21, 2), (2, 15), (19, 20), (5, 7), (4, 22), (12, 13), (18, 21), (11, 17), (3, 6), (20, 8), (6, 16), (20, 10), (4, 11), (9, 21), (8, 2), (9, 8), (4, 9), (11, 18), (5, 19), (7, 10), (18, 9), (0, 3), (12, 4), (9, 22), (18, 22), (13, 12), (4, 12), (13, 2), (17, 8), (2, 7), (12, 6), (2, 5), (3, 12), (6, 6), (16, 9), (14, 21), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848440", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 22), (21, 16), (23, 9), (3, 14), (6, 23), (21, 24), (9, 5), (18, 2), (2, 20), (6, 0), (6, 16), (7, 3), (25, 23), (2, 3), (1, 3), (13, 12), (23, 17), (19, 13), (13, 15), (4, 4), (13, 24), (22, 10), (21, 1), (13, 14), (7, 4), (11, 2), (5, 24), (5, 10), (4, 9), (17, 17), (15, 4), (17, 26), (7, 10), (1, 2), (16, 8), (9, 26), (8, 19), (3, 17), (11, 7), (17, 3), (5, 3), (11, 23), (17, 13), (12, 15), (2, 19), (27, 0), (7, 26), (26, 26), (6, 12), (12, 9), (8, 25), (10, 3), (24, 3), (17, 16), (9, 2), (21, 23), (7, 21), (13, 6), (25, 13), (23, 16), (23, 18), (11, 5), (14, 10), (24, 0), (8, 18), (4, 18), (3, 2), (7, 19), (6, 26), (6, 22), (26, 11), (22, 0), (17, 23), (14, 4), (23, 23), (15, 14), (5, 25), (16, 14), (23, 7), (24, 16), (25, 9), (21, 22), (18, 16), (15, 23), (1, 24), (27, 3), (23, 5), (23, 15), (4, 25), (26, 17), (2, 0), (4, 6), (15, 22), (1, 14), (20, 23), (12, 8), (13, 13), (6, 9), (9, 16), (1, 16), (2, 10), (10, 18), (10, 21), (8, 21), (16, 7), (22, 9), (9, 6), (19, 12), (4, 11), (22, 5), (7, 14), (1, 19), (20, 7), (16, 2), (18, 17), (19, 26), (12, 14), (4, 19), (21, 6), (18, 18), (22, 6), (16, 0), (8, 23), (15, 9), (27, 23), (18, 3), (21, 13), (11, 14), (13, 17), (16, 4), (18, 1), (2, 14), (0, 16), (12, 24), (16, 12), (15, 1), (17, 2), (16, 24), (19, 11), (21, 5), (13, 26), (4, 5), (15, 3), (26, 13), (9, 7), (11, 11), (19, 23), (10, 15), (23, 6), (18, 8), (3, 19), (15, 15), (26, 18), (2, 2), (11, 20), (12, 25), (25, 25), (23, 26), (5, 16), (10, 24), (26, 0), (26, 22), (19, 17), (14, 13), (18, 14), (8, 7), (8, 8), (13, 25), (4, 0), (14, 3), (2, 24), (13, 7), (5, 7), (20, 11), (15, 7), (23, 14), (6, 17), (26, 3), (19, 15), (14, 19), (3, 15), (11, 6), (11, 0), (20, 0), (9, 9), (4, 8), (24, 5), (2, 4), (14, 11), (20, 3), (17, 10), (3, 0), (4, 26), (27, 13), (18, 9), (27, 6), (16, 17), (25, 19), (13, 3), (10, 23), (26, 23), (24, 8), (8, 24), (24, 23), (6, 6), (22, 16), (7, 5), (3, 21), (23, 12), (24, 2), (5, 23), (25, 22), (12, 1), (20, 10), (10, 4), (15, 11), (14, 0), (26, 8), (8, 2), (2, 23), (0, 21), (1, 21), (8, 3), (17, 19), (19, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690984", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), 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), (21, 13), (14, 20), (15, 16), (9, 15), (13, 11), (20, 10), (5, 7), (8, 21), (9, 20), (14, 18), (1, 13), (13, 18), (4, 1), (16, 2), (1, 6), (0, 5), (18, 16), (19, 6), (12, 4), (8, 6), (12, 15), (4, 9), (13, 16), (2, 4), (13, 21), (5, 12), (3, 2), (2, 17), (12, 20), (21, 0), (10, 5), (3, 14), (0, 18), (6, 14), (20, 20), (19, 9), (0, 17), (19, 14), (21, 4), (14, 9), (9, 10), (5, 3), (9, 3), (16, 16), (13, 1), (17, 11), (16, 3), (19, 16), (2, 0), (13, 7), (4, 6), (14, 11), (9, 5), (14, 6), (18, 20), (17, 12), (19, 5), (14, 1), (15, 12), (12, 13), (6, 5), (10, 6), (8, 18), (7, 21), (12, 14), (5, 10), (20, 15), (3, 13), (3, 3), (15, 19), (1, 14), (18, 13), (8, 13), (14, 17), (14, 15), (21, 18), (20, 2), (7, 0), (4, 10), (0, 20), (18, 14), (5, 18), (12, 7), (16, 20), (2, 10), (18, 21), (10, 10), (13, 6), (11, 6), (10, 8), (10, 20), (9, 8), (21, 17), (8, 8), (4, 21), (20, 3), (17, 19), (18, 9), (14, 16), (21, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441525", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), 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), (24, 17), (0, 8), (11, 13), (8, 8), (1, 17), (16, 14), (26, 19), (9, 8), (17, 2), (7, 11), (13, 8), (8, 10), (25, 7), (24, 12), (26, 1), (4, 11), (4, 9), (14, 1), (26, 12), (9, 10), (13, 15), (5, 9), (3, 20), (9, 20), (1, 7), (2, 6), (12, 13), (19, 5), (0, 13), (15, 0), (17, 9), (24, 16), (24, 6), (3, 7), (7, 3), (11, 7), (1, 16), (24, 0), (12, 5), (0, 11), (27, 6), (2, 5), (20, 2), (8, 2), (4, 17), (25, 15), (3, 18), (5, 15), (16, 18), (7, 10), (22, 1), (17, 5), (16, 2), (9, 19), (25, 3), (22, 6), (10, 7), (3, 4), (15, 11), (27, 9), (19, 14), (22, 8), (2, 3), (15, 15), (20, 9), (11, 6), (10, 15), (16, 9), (21, 15), (3, 13), (23, 16), (4, 3), (21, 0), (12, 16), (17, 8), (22, 13), (4, 14), (7, 8), (1, 3), (3, 8), (2, 1), (1, 18), (16, 1), (9, 2), (1, 13), (15, 19), (18, 7), (17, 16), (9, 13), (20, 3), (22, 9), (13, 18), (22, 7), (11, 20), (13, 19), (22, 20), (19, 19), (23, 19), (22, 4), (27, 14), (16, 0), (5, 16), (14, 8), (14, 17), (18, 5), (0, 16), (12, 11), (17, 18), (7, 17), (6, 18), (20, 19), (17, 15), (21, 4), (0, 18), (27, 16), (4, 19), (23, 9), (23, 17), (0, 9), (9, 12), (11, 3), (23, 18), (10, 2), (15, 2), (1, 2), (18, 19), (6, 3), (1, 11), (7, 7), (17, 7), (15, 16), (0, 20), (10, 8), (9, 5), (11, 19), (19, 4), (18, 8), (21, 20), (3, 5), (24, 20), (12, 20), (4, 15), (24, 15), (26, 5), (19, 12), (21, 17), (8, 5), (14, 0), (23, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943180", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 22), (12, 4), (20, 23), (22, 3), (20, 17), (4, 26), (6, 22), (1, 26), (16, 26), (3, 14), (22, 19), (0, 16), (24, 20), (6, 14), (5, 24), (19, 28), (16, 10), (18, 9), (15, 21), (14, 4), (12, 13), (15, 2), (10, 7), (17, 20), (2, 10), (18, 21), (6, 1), (10, 24), (11, 7), (22, 9), (17, 3), (0, 28), (15, 27), (1, 19), (13, 20), (20, 6), (19, 11), (5, 26), (15, 20), (23, 8), (3, 27), (1, 27), (4, 24), (6, 12), (20, 9), (22, 11), (2, 23), (22, 24), (19, 8), (5, 1), (12, 3), (20, 19), (17, 4), (11, 13), (0, 18), (23, 3), (12, 19), (22, 27), (9, 11), (10, 5), (13, 4), (22, 7), (24, 17), (13, 18), (14, 6), (11, 22), (6, 8), (23, 4), (11, 11), (14, 11), (7, 19), (0, 7), (8, 0), (14, 16), (22, 26), (18, 13), (16, 9), (14, 25), (16, 13), (5, 18), (17, 21), (2, 16), (23, 14), (10, 21), (3, 20), (19, 20), (15, 25), (3, 0), (12, 26), (15, 15), (18, 5), (2, 8), (16, 14), (23, 11), (6, 17), (19, 15), (1, 20), (1, 4), (23, 21), (10, 4), (15, 26), (19, 19), (20, 22), (18, 6), (1, 16), (13, 3), (9, 15), (4, 3), (7, 7), (1, 21), (23, 17), (14, 28), (5, 21), (3, 23), (21, 28), (3, 5), (7, 25), (19, 22), (9, 6), (2, 24), (15, 13), (10, 20), (18, 12), (20, 12), (2, 2), (18, 28), (20, 14), (14, 23), (13, 2), (13, 28), (22, 6), (7, 1), (9, 28), (18, 17), (0, 15), (12, 15), (22, 20), (17, 25), (0, 17), (7, 16), (1, 15), (6, 19), (0, 8), (9, 17), (18, 22), (2, 5), (0, 1), (5, 19), (16, 19), (18, 0), (10, 13), (21, 16), (10, 14), (11, 0), (21, 18), (22, 23), (7, 0), (24, 23), (11, 28), (12, 25), (0, 23), (23, 12), (1, 3), (11, 6), (3, 9), (11, 17), (3, 25), (6, 9), (16, 24), (19, 16), (22, 8), (23, 19), (20, 1), (24, 3), (6, 4), (20, 18), (2, 18), (9, 22), (16, 3), (9, 24), (16, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "935704", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 11), (13, 8), (24, 11), (10, 21), (1, 2), (17, 4), (18, 23), (19, 14), (8, 13), (14, 13), (27, 1), (4, 3), (19, 5), (5, 17), (16, 14), (5, 23), (26, 24), (5, 5), (21, 8), (26, 16), (11, 16), (3, 10), (9, 5), (8, 9), (0, 19), (10, 9), (4, 1), (19, 12), (11, 10), (1, 21), (26, 19), (19, 10), (18, 2), (12, 12), (1, 20), (2, 11), (23, 5), (27, 19), (25, 6), (12, 14), (7, 4), (3, 20), (23, 15), (24, 17), (22, 15), (27, 5), (25, 21), (8, 17), (0, 7), (12, 23), (7, 14), (28, 12), (23, 4), (26, 0), (15, 7), (27, 14), (21, 0), (16, 23), (24, 16), (14, 18), (24, 4), (1, 8), (0, 2), (10, 16), (25, 22), (4, 14), (15, 5), (24, 18), (5, 21), (13, 3), (12, 3), (25, 0), (11, 5), (9, 19), (1, 12), (18, 7), (5, 20), (26, 9), (20, 17), (26, 17), (5, 12), (17, 17), (9, 23), (2, 15), (27, 11), (11, 7), (3, 19), (17, 24), (6, 20), (22, 17), (20, 24), (4, 4), (23, 16), (0, 17), (10, 7), (24, 24), (26, 25), (11, 19), (22, 10), (18, 13), (0, 9), (15, 21), (21, 17), (6, 24), (17, 1), (14, 1), (13, 2), (8, 3), (21, 7), (7, 1), (8, 15), (5, 8), (28, 8), (10, 4), (20, 18), (22, 0), (25, 1), (26, 14), (15, 12), (13, 13), (13, 17), (16, 20), (15, 20), (20, 19), (2, 23), (24, 12), (15, 8), (17, 18), (7, 9), (20, 0), (14, 6), (6, 3), (2, 12), (16, 7), (22, 6), (11, 25), (23, 3), (19, 7), (0, 3), (25, 18), (22, 11), (18, 24), (7, 20), (1, 0), (16, 3), (12, 10), (24, 5), (8, 20), (3, 17), (2, 9), (9, 15), (7, 5), (2, 14), (18, 11), (1, 13), (19, 8), (8, 12), (7, 2), (17, 16), (8, 19), (10, 20), (20, 25), (19, 25), (21, 9), (15, 16), (21, 11), (26, 5), (28, 15), (13, 9), (22, 18), (17, 12), (7, 21), (26, 22), (21, 5), (16, 1), (28, 19), (4, 7), (25, 17), (10, 13), (24, 15), (10, 6), (4, 20), (18, 12), (8, 8), (20, 22), (28, 2), (21, 4), (15, 15), (15, 4), (26, 6), (16, 9), (3, 15), (25, 23), (19, 16), (27, 2), (1, 17), (22, 5), (27, 6), (0, 15), (27, 7), (28, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734280", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 11), (12, 18), (17, 17), (16, 4), (10, 11), (0, 14), (15, 21), (21, 7), (21, 15), (21, 21), (15, 6), (20, 12), (22, 3), (13, 15), (13, 13), (12, 10), (0, 5), (17, 12), (8, 14), (11, 4), (12, 2), (6, 6), (4, 13), (7, 18), (7, 1), (25, 9), (23, 19), (5, 1), (5, 4), (6, 3), (20, 20), (3, 8), (21, 12), (15, 3), (16, 16), (1, 18), (5, 14), (3, 19), (25, 12), (7, 4), (20, 21), (24, 13), (2, 12), (11, 19), (1, 1), (5, 19), (23, 4), (23, 5), (15, 5), (5, 3), (23, 0), (14, 2), (19, 10), (4, 8), (23, 6), (21, 20), (18, 5), (13, 5), (23, 11), (22, 2), (22, 9), (9, 7), (24, 3), (18, 14), (7, 11), (13, 14), (3, 18), (9, 5), (19, 18), (3, 13), (15, 9), (20, 6), (2, 10), (14, 10), (15, 1), (1, 11), (19, 13), (7, 13), (13, 21), (18, 11), (3, 16), (2, 14), (1, 8), (22, 15), (14, 20), (11, 18), (23, 1), (17, 1), (13, 7), (3, 1), (13, 11), (23, 9), (1, 21), (22, 21), (19, 4), (20, 11), (9, 9), (19, 21), (18, 20), (25, 20), (5, 2), (11, 15), (5, 13), (23, 3), (2, 3), (17, 9), (19, 15), (14, 3), (11, 5), (1, 4), (3, 17), (16, 14), (1, 2), (4, 3), (25, 4), (9, 17), (17, 3), (3, 7), (21, 17), (3, 15), (12, 20), (4, 20), (22, 18), (7, 14), (14, 16), (14, 7), (5, 11), (0, 1), (11, 0), (5, 12), (4, 14), (19, 14), (17, 10), (17, 11), (6, 19), (8, 16), (9, 19), (21, 1), (18, 10), (10, 6), (12, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784152", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 18), (3, 16), (14, 9), (17, 20), (9, 21), (7, 0), (12, 1), (2, 18), (18, 18), (15, 8), (21, 18), (3, 6), (10, 21), (10, 11), (5, 4), (14, 2), (10, 12), (9, 7), (6, 20), (10, 1), (1, 8), (17, 21), (3, 19), (4, 11), (9, 10), (2, 7), (2, 3), (14, 11), (14, 20), (6, 7), (3, 0), (17, 6), (11, 16), (15, 0), (6, 12), (21, 15), (9, 17), (5, 12), (21, 3), (0, 9), (13, 20), (17, 17), (7, 16), (18, 4), (3, 20), (6, 3), (3, 1), (7, 9), (4, 20), (2, 16), (12, 8), (5, 15), (17, 16), (12, 15), (18, 19), (20, 9), (16, 13), (20, 11), (18, 2), (21, 20), (5, 2), (6, 17), (2, 20), (4, 9), (14, 16), (12, 13), (14, 1), (11, 19), (16, 10), (20, 16), (21, 16), (11, 18), (10, 4), (4, 15), (21, 11), (7, 10), (20, 10), (16, 11), (3, 7), (20, 8), (17, 13), (13, 7), (9, 15), (22, 19), (0, 18), (11, 2), (8, 12), (20, 3), (14, 12), (16, 7), (13, 6), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "584550", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), 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), (8, 9), (23, 7), (18, 2), (23, 1), (2, 8), (5, 0), (26, 19), (9, 13), (9, 16), (27, 13), (12, 8), (25, 11), (15, 6), (21, 3), (9, 9), (20, 15), (15, 19), (26, 12), (5, 15), (10, 11), (22, 15), (1, 11), (24, 8), (10, 3), (7, 11), (5, 3), (20, 0), (14, 5), (4, 9), (8, 13), (19, 2), (5, 9), (19, 1), (25, 19), (20, 9), (14, 0), (24, 2), (2, 17), (7, 17), (22, 20), (9, 6), (4, 13), (19, 0), (22, 5), (21, 14), (6, 2), (8, 11), (19, 6), (18, 0), (14, 2), (26, 17), (22, 16), (9, 19), (1, 4), (19, 18), (7, 4), (18, 11), (6, 10), (19, 17), (3, 9), (5, 17), (14, 8), (0, 15), (4, 1), (12, 17), (27, 6), (5, 2), (3, 1), (17, 16), (10, 4), (15, 17), (2, 19), (14, 12), (26, 5), (25, 8), (14, 4), (11, 5), (21, 5), (6, 16), (27, 2), (9, 20), (3, 5), (2, 1), (25, 14), (27, 0), (22, 2), (0, 9), (9, 14), (7, 20), (24, 1), (7, 6), (10, 14), (14, 18), (22, 10), (9, 15), (5, 18), (8, 3), (11, 10), (20, 2), (22, 7), (15, 10), (24, 5), (5, 16), (25, 6), (8, 14), (13, 1), (15, 5), (22, 9), (5, 7), (16, 11), (13, 10), (26, 0), (22, 6), (8, 1), (16, 15), (26, 15), (17, 10), (1, 2), (5, 1), (8, 6), (10, 20), (16, 16), (26, 14), (18, 18), (3, 18), (22, 11), (21, 10), (12, 19), (11, 20), (8, 8), (22, 8), (25, 20), (7, 16), (21, 16), (16, 10), (15, 20), (12, 14), (19, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534026", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), 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), (21, 13), (15, 10), (7, 15), (0, 15), (6, 4), (1, 6), (19, 4), (19, 16), (5, 10), (10, 0), (7, 10), (19, 14), (16, 17), (14, 12), (7, 18), (5, 11), (5, 2), (7, 0), (9, 5), (5, 8), (13, 1), (18, 19), (6, 0), (3, 5), (22, 17), (22, 12), (2, 9), (15, 6), (20, 16), (10, 12), (1, 11), (22, 16), (8, 4), (6, 7), (11, 5), (18, 12), (14, 18), (11, 4), (4, 10), (13, 4), (0, 2), (21, 9), (0, 5), (16, 0), (4, 2), (6, 8), (3, 18), (1, 9), (1, 16), (8, 3), (12, 16), (16, 7), (19, 8), (8, 7), (16, 9), (7, 2), (12, 13), (11, 2), (21, 5), (2, 16), (8, 15), (8, 10), (22, 6), (2, 18), (17, 16), (3, 0), (20, 12), (7, 4), (14, 6), (22, 3), (4, 19), (21, 1), (12, 18), (11, 14), (8, 16), (8, 18), (3, 19), (20, 18), (21, 3), (5, 3), (7, 11), (5, 9), (22, 2), (12, 6), (12, 19), (11, 11), (13, 2), (16, 19), (9, 12), (14, 17), (12, 9), (22, 18), (15, 1), (11, 6), (17, 18), (20, 17), (1, 4), (20, 0), (12, 1), (21, 7), (17, 14), (9, 4), (5, 19), (18, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847561", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 20), (20, 0), (21, 20), (21, 14), (4, 14), (10, 10), (2, 13), (5, 21), (14, 17), (19, 15), (1, 15), (16, 17), (13, 19), (11, 14), (9, 23), (21, 24), (5, 1), (3, 6), (7, 6), (3, 5), (16, 15), (23, 10), (11, 12), (11, 3), (11, 10), (2, 22), (17, 12), (17, 25), (2, 1), (22, 3), (12, 1), (9, 14), (14, 2), (19, 19), (7, 22), (17, 14), (19, 14), (6, 15), (20, 16), (1, 1), (9, 5), (14, 0), (8, 4), (8, 19), (5, 7), (21, 16), (1, 2), (3, 8), (11, 9), (5, 16), (14, 20), (4, 25), (19, 13), (8, 25), (1, 19), (23, 12), (7, 14), (17, 22), (6, 9), (3, 0), (9, 22), (14, 18), (9, 16), (20, 1), (6, 3), (13, 17), (6, 7), (17, 2), (20, 6), (1, 3), (23, 21), (11, 8), (11, 20), (14, 6), (19, 3), (10, 11), (22, 6), (22, 8), (2, 7), (15, 23), (21, 13), (20, 15), (9, 13), (16, 22), (16, 11), (13, 8), (14, 21), (19, 24), (17, 21), (4, 18), (0, 6), (19, 6), (10, 22), (5, 14), (11, 5), (20, 17), (4, 16), (2, 24), (9, 17), (16, 2), (10, 13), (10, 4), (14, 8), (13, 2), (3, 20), (2, 25), (1, 22), (20, 2), (13, 11), (6, 1), (6, 2), (12, 24), (7, 12), (13, 7), (1, 20), (0, 23), (18, 21), (18, 12), (2, 23), (4, 13), (3, 19), (1, 14), (1, 25), (5, 8), (3, 24), (6, 23), (0, 7), (0, 5), (6, 4), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "921024", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 20), (0, 4), (7, 3), (13, 14), (18, 1), (21, 6), (21, 17), (22, 12), (6, 5), (6, 17), (5, 19), (1, 7), (19, 12), (25, 3), (13, 8), (24, 20), (3, 11), (12, 0), (23, 10), (10, 8), (24, 0), (16, 20), (18, 0), (18, 3), (1, 6), (14, 17), (4, 18), (20, 1), (1, 2), (0, 16), (9, 10), (12, 9), (12, 7), (17, 14), (10, 6), (11, 17), (22, 10), (13, 9), (5, 10), (20, 19), (12, 11), (25, 18), (14, 8), (1, 14), (9, 0), (13, 5), (13, 4), (15, 8), (9, 17), (3, 1), (15, 17), (16, 14), (12, 2), (7, 12), (2, 2), (23, 17), (23, 16), (12, 12), (7, 17), (8, 6), (17, 5), (20, 17), (3, 8), (1, 15), (16, 4), (21, 1), (17, 13), (20, 15), (24, 18), (13, 17), (21, 7), (22, 1), (17, 3), (15, 9), (4, 6), (13, 19), (2, 4), (22, 11), (11, 2), (8, 12), (4, 12), (12, 1), (9, 16), (24, 11), (24, 4), (22, 14), (3, 0), (18, 15), (5, 11), (16, 10), (11, 15), (9, 7), (2, 10), (19, 16), (20, 5), (0, 17), (8, 4), (6, 6), (24, 14), (13, 12), (11, 7), (25, 2), (14, 20), (19, 20), (6, 0), (22, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936601", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 16), (17, 7), (4, 23), (12, 20), (23, 24), (19, 0), (3, 15), (11, 25), (24, 19), (5, 5), (6, 25), (17, 25), (14, 4), (11, 2), (10, 9), (13, 21), (19, 16), (11, 6), (8, 10), (6, 6), (10, 12), (20, 24), (15, 13), (8, 17), (13, 3), (19, 24), (21, 24), (12, 11), (8, 11), (16, 24), (9, 11), (23, 9), (8, 3), (10, 14), (7, 8), (16, 22), (21, 14), (18, 4), (24, 21), (1, 17), (11, 17), (11, 11), (18, 19), (8, 19), (18, 26), (17, 19), (3, 13), (8, 23), (22, 12), (9, 3), (2, 19), (2, 0), (15, 14), (4, 6), (10, 17), (3, 2), (17, 10), (23, 0), (0, 8), (17, 1), (0, 22), (2, 3), (12, 4), (20, 12), (6, 26), (0, 21), (22, 21), (2, 17), (17, 22), (24, 14), (1, 23), (19, 4), (16, 25), (18, 0), (22, 23), (5, 16), (18, 13), (0, 13), (4, 0), (16, 21), (0, 6), (7, 15), (6, 13), (6, 11), (18, 8), (11, 19), (11, 4), (21, 6), (12, 16), (23, 10), (15, 18), (14, 21), (10, 25), (23, 2), (12, 1), (24, 15), (6, 20), (7, 13), (9, 0), (23, 1), (17, 20), (9, 1), (10, 1), (11, 14), (19, 19), (9, 2), (9, 4), (5, 23), (15, 8), (13, 5), (15, 3), (4, 19), (13, 25), (6, 18), (12, 0), (7, 23), (13, 23), (9, 6), (22, 24), (16, 19), (20, 8), (9, 12), (5, 26), (0, 2), (13, 0), (5, 11), (5, 3), (15, 15), (15, 2), (18, 2), (22, 14), (3, 11), (4, 7), (11, 3), (13, 16), (23, 5), (8, 16), (23, 12), (12, 15), (2, 15), (8, 1), (21, 1), (14, 14), (4, 16), (16, 23), (9, 22), (6, 5), (7, 7), (2, 11), (9, 21), (13, 2), (2, 13), (16, 7), (14, 15), (22, 3), (7, 14), (13, 20), (14, 17), (19, 5), (3, 18), (6, 22), (7, 18), (20, 14), (19, 8), (3, 14), (22, 25), (24, 4), (22, 19), (0, 19), (13, 15), (1, 21), (17, 18), (24, 11), (10, 3), (14, 16), (21, 23), (13, 6), (10, 23), (0, 10), (14, 9), (9, 13), (20, 2), (5, 21), (7, 3), (19, 3), (24, 10), (10, 26), (4, 4), (0, 3), (6, 17), (19, 18), (15, 9), (8, 4), (12, 22), (11, 8), (16, 20), (7, 22), (10, 8), (7, 17), (21, 22), (8, 15), (19, 13), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645696", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (24, 13), (17, 18), (4, 2), (25, 5), (16, 6), (4, 3), (17, 2), (15, 8), (18, 13), (9, 7), (16, 11), (12, 12), (26, 14), (2, 14), (6, 8), (12, 7), (17, 13), (10, 17), (19, 13), (7, 9), (22, 9), (18, 14), (23, 17), (24, 19), (0, 16), (26, 2), (18, 2), (14, 19), (5, 4), (16, 8), (13, 4), (5, 13), (19, 14), (13, 6), (27, 0), (22, 13), (18, 6), (5, 3), (22, 16), (9, 10), (15, 18), (1, 4), (25, 18), (1, 16), (21, 12), (23, 18), (11, 8), (1, 14), (17, 3), (7, 1), (20, 13), (13, 0), (9, 11), (18, 0), (8, 15), (21, 15), (6, 2), (18, 16), (25, 4), (24, 18), (6, 12), (12, 10), (14, 0), (27, 16), (5, 6), (0, 4), (8, 11), (26, 11), (4, 11), (17, 7), (11, 17), (7, 16), (16, 18), (5, 16), (0, 5), (23, 7), (11, 12), (8, 19), (20, 5), (17, 17), (6, 19), (2, 18), (17, 6), (17, 5), (14, 10), (9, 15), (21, 0), (20, 17), (20, 10), (25, 11), (19, 10), (25, 7), (6, 1), (19, 15), (2, 19), (17, 4), (1, 10), (19, 6), (5, 15), (17, 0), (2, 0), (24, 6), (10, 2), (13, 13), (18, 8), (24, 11), (22, 2), (19, 19), (16, 14), (20, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904365", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), 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), (0, 2), (11, 4), (6, 21), (22, 22), (12, 15), (5, 2), (6, 6), (4, 21), (1, 6), (9, 16), (2, 9), (4, 17), (0, 17), (6, 2), (14, 23), (6, 11), (16, 3), (17, 28), (19, 3), (0, 14), (16, 18), (12, 16), (9, 1), (16, 0), (3, 5), (1, 22), (9, 18), (19, 18), (7, 13), (6, 3), (8, 24), (21, 0), (0, 3), (3, 26), (9, 7), (19, 4), (19, 1), (21, 10), (0, 21), (20, 27), (10, 9), (10, 4), (21, 14), (16, 9), (15, 26), (5, 8), (0, 5), (16, 13), (8, 13), (19, 8), (0, 10), (4, 13), (7, 6), (20, 19), (1, 28), (7, 8), (14, 22), (20, 6), (20, 26), (7, 9), (0, 15), (15, 4), (20, 20), (14, 11), (8, 21), (16, 11), (9, 21), (20, 21), (9, 26), (7, 11), (4, 15), (2, 3), (20, 23), (0, 6), (21, 9), (19, 17), (3, 6), (3, 13), (15, 23), (11, 24), (21, 7), (5, 22), (15, 9), (6, 25), (2, 16), (16, 4), (2, 10), (9, 22), (11, 26), (13, 23), (13, 13), (18, 13), (14, 18), (19, 12), (10, 3), (14, 3), (19, 7), (2, 21), (15, 13), (14, 24), (3, 18), (1, 12), (16, 24), (15, 8), (20, 14), (5, 28), (22, 21), (4, 22), (3, 23), (0, 1), (11, 20), (8, 7), (18, 2), (2, 6), (2, 0), (14, 26), (19, 23), (18, 10), (3, 1), (13, 9), (3, 9), (6, 13), (7, 5), (10, 26), (4, 19), (15, 2), (21, 12), (20, 16), (22, 7), (9, 13), (22, 26), (18, 3), (0, 7), (17, 27), (18, 1), (20, 22), (4, 1), (16, 2), (17, 4), (19, 10), (21, 13), (12, 25), (5, 4), (21, 25), (13, 14), (22, 13), (14, 13), (7, 21), (7, 26), (16, 17), (18, 26), (11, 7), (17, 14), (4, 16), (18, 23), (7, 16), (6, 27), (11, 25), (1, 9), (18, 17), (15, 28), (4, 26), (18, 6), (6, 8), (18, 9), (0, 18), (12, 24), (2, 1), (7, 24), (20, 7), (6, 4), (12, 11), (4, 11), (10, 21), (22, 6), (2, 26), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877584", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), 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, 17), (11, 22), (16, 17), (9, 20), (19, 14), (16, 22), (5, 4), (11, 14), (17, 22), (18, 18), (14, 2), (11, 19), (20, 11), (8, 11), (7, 20), (17, 23), (14, 14), (20, 19), (2, 22), (9, 9), (20, 22), (14, 16), (2, 18), (10, 3), (8, 6), (3, 9), (8, 19), (11, 23), (17, 5), (15, 18), (17, 20), (3, 11), (8, 17), (16, 7), (19, 7), (10, 21), (9, 15), (5, 5), (16, 0), (14, 5), (4, 12), (14, 21), (11, 21), (7, 12), (2, 15), (18, 10), (4, 0), (3, 23), (10, 0), (10, 20), (11, 9), (11, 16), (12, 18), (3, 0), (10, 7), (1, 15), (5, 9), (10, 19), (15, 20), (4, 9), (17, 21), (1, 17), (11, 15), (7, 21), (20, 8), (13, 16), (19, 16), (8, 23), (3, 8), (12, 14), (0, 16), (2, 14), (9, 13), (13, 3), (14, 17), (1, 23), (12, 11), (16, 9), (7, 3), (10, 8), (20, 7), (15, 23), (9, 0), (5, 15), (20, 10), (17, 4), (14, 3), (6, 11), (0, 19), (8, 12), (14, 9), (11, 12), (5, 6), (17, 6), (18, 21), (4, 5), (6, 19), (6, 6), (11, 0), (11, 2), (15, 21), (1, 21), (5, 17), (9, 5), (0, 15), (1, 19), (12, 2), (20, 21), (20, 4), (12, 19), (16, 11), (4, 18), (16, 16), (13, 0), (1, 14), (13, 23), (15, 22), (6, 15), (5, 19), (4, 23), (18, 0), (12, 21), (8, 15), (14, 0), (8, 2), (0, 20), (3, 1), (18, 11), (15, 0), (9, 1), (16, 8), (2, 3), (20, 3), (3, 4), (15, 4), (0, 2), (12, 3), (16, 5), (17, 9), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499463", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 23), (16, 5), (9, 24), (7, 21), (3, 14), (17, 1), (6, 18), (12, 25), (8, 15), (5, 18), (9, 5), (7, 11), (9, 10), (16, 17), (19, 12), (0, 17), (14, 5), (7, 16), (2, 13), (18, 23), (16, 0), (20, 5), (4, 2), (20, 25), (20, 19), (8, 5), (13, 25), (0, 1), (1, 18), (9, 18), (20, 21), (9, 6), (22, 5), (21, 9), (16, 15), (0, 9), (7, 8), (3, 23), (11, 10), (5, 25), (11, 11), (19, 0), (8, 21), (10, 25), (22, 19), (17, 4), (6, 1), (16, 24), (9, 25), (21, 24), (5, 19), (4, 9), (2, 25), (2, 15), (12, 6), (13, 6), (11, 15), (18, 11), (20, 4), (14, 12), (5, 2), (0, 10), (1, 4), (1, 15), (12, 21), (5, 20), (13, 24), (11, 3), (15, 9), (21, 5), (19, 20), (9, 3), (10, 6), (21, 12), (12, 10), (15, 24), (22, 12), (22, 9), (5, 21), (7, 24), (20, 7), (5, 17), (14, 24), (22, 4), (12, 11), (13, 12), (5, 12), (12, 15), (10, 17), (12, 3), (19, 19), (20, 2), (8, 20), (11, 23), (21, 0), (18, 7), (14, 17), (19, 1), (2, 10), (11, 8), (21, 25), (21, 21), (10, 3), (1, 25), (1, 1), (12, 23), (15, 6), (4, 6), (13, 1), (14, 3), (3, 22), (10, 23), (21, 19), (18, 15), (11, 14), (20, 16), (7, 6), (15, 17), (20, 9), (2, 24), (1, 13), (18, 8), (4, 8), (11, 4), (0, 22), (15, 3), (8, 9), (10, 0), (2, 7), (6, 24), (13, 10), (13, 17), (9, 7), (0, 5), (13, 20), (14, 4), (7, 22), (13, 16), (19, 15), (15, 11), (21, 6), (19, 4), (7, 23), (3, 17), (9, 22), (1, 9), (22, 2), (18, 6), (17, 10), (10, 19), (9, 16), (16, 3), (4, 5), (6, 4), (1, 20), (14, 20), (12, 8), (6, 11), (20, 10), (7, 13), (14, 11), (16, 13), (3, 21), (19, 8), (15, 8), (3, 13), (2, 4), (14, 14), (18, 13), (8, 2), (17, 22), (10, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647424", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), 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, 7), (8, 0), (16, 11), (2, 1), (24, 14), (6, 0), (2, 15), (12, 17), (15, 20), (1, 19), (13, 19), (9, 8), (11, 0), (1, 9), (20, 5), (20, 2), (18, 9), (16, 21), (6, 12), (18, 12), (14, 7), (22, 17), (13, 4), (10, 18), (20, 6), (15, 12), (14, 10), (11, 8), (6, 19), (10, 12), (4, 11), (12, 20), (1, 6), (14, 5), (18, 21), (0, 6), (16, 17), (13, 20), (20, 18), (4, 8), (1, 14), (9, 6), (0, 1), (7, 12), (24, 19), (1, 18), (20, 21), (17, 3), (12, 9), (9, 11), (25, 11), (11, 16), (6, 15), (6, 1), (2, 19), (0, 21), (3, 10), (8, 6), (24, 7), (10, 21), (10, 4), (6, 2), (19, 13), (5, 19), (12, 0), (3, 3), (19, 16), (4, 17), (1, 10), (7, 8), (13, 10), (21, 21), (10, 7), (17, 12), (5, 2), (10, 10), (22, 10), (6, 13), (16, 5), (23, 12), (4, 0), (16, 3), (25, 14), (10, 2), (23, 7), (19, 18), (21, 15), (4, 14), (8, 1), (18, 17), (4, 4), (2, 4), (1, 4), (8, 13), (5, 0), (25, 3), (15, 18), (4, 21), (11, 12), (15, 6), (13, 1), (6, 17), (20, 13), (17, 8), (2, 9), (19, 17), (17, 1), (0, 8), (8, 7), (15, 17), (14, 17), (12, 21), (17, 4), (22, 4), (0, 17), (0, 12), (18, 14), (7, 6), (2, 11), (10, 11), (3, 19), (19, 19), (13, 3), (22, 21), (13, 2), (16, 20), (2, 3), (23, 17), (17, 19), (4, 16), (25, 2), (5, 17), (25, 13), (2, 21), (14, 19), (8, 12), (0, 19), (8, 5), (24, 4), (5, 4), (19, 2), (7, 9), (6, 20), (20, 15), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "722700", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), 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), (20, 9), (10, 0), (16, 5), (13, 0), (0, 11), (15, 1), (11, 18), (9, 18), (4, 16), (3, 18), (2, 11), (8, 18), (6, 5), (4, 9), (22, 18), (9, 21), (20, 3), (1, 10), (4, 20), (3, 20), (3, 11), (6, 4), (6, 1), (18, 21), (15, 9), (5, 5), (11, 21), (2, 22), (21, 22), (0, 16), (14, 4), (6, 7), (12, 11), (5, 18), (4, 15), (15, 16), (15, 17), (9, 8), (7, 3), (12, 14), (14, 18), (2, 6), (19, 11), (5, 2), (17, 21), (13, 14), (12, 2), (3, 2), (11, 10), (12, 0), (14, 11), (16, 13), (16, 10), (18, 18), (14, 5), (7, 8), (11, 0), (20, 14), (0, 6), (12, 13), (10, 19), (3, 7), (10, 13), (20, 18), (9, 5), (2, 0), (14, 9), (19, 3), (18, 8), (18, 4), (2, 2), (4, 1), (0, 21), (21, 15), (5, 21), (6, 2), (21, 14), (15, 10), (13, 6), (22, 17), (10, 10), (15, 13), (12, 1), (8, 22), (18, 1), (1, 1), (17, 19), (13, 22), (22, 11), (18, 0), (18, 6), (16, 3), (19, 7), (14, 14), (18, 2), (9, 2), (14, 16), (10, 6), (3, 9), (2, 12), (16, 14), (20, 12), (6, 0), (9, 16), (12, 20), (11, 17), (20, 7), (4, 18), (21, 17), (3, 12), (22, 6), (0, 13), (4, 7), (7, 13), (4, 6), (5, 9), (14, 13), (21, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726896", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 18), (26, 13), (9, 2), (6, 16), (24, 3), (25, 19), (15, 19), (10, 4), (26, 5), (28, 12), (1, 12), (22, 2), (5, 3), (12, 16), (17, 2), (16, 16), (18, 12), (9, 12), (20, 16), (13, 1), (9, 11), (27, 12), (20, 11), (28, 1), (16, 1), (3, 7), (13, 12), (26, 9), (0, 12), (7, 2), (22, 5), (4, 2), (9, 4), (8, 17), (18, 2), (3, 5), (21, 15), (24, 6), (16, 7), (6, 4), (14, 12), (19, 9), (14, 16), (15, 14), (19, 13), (5, 10), (20, 2), (8, 15), (23, 1), (7, 4), (21, 1), (2, 7), (13, 0), (13, 18), (5, 13), (19, 7), (25, 10), (14, 8), (11, 17), (3, 12), (3, 13), (1, 15), (11, 3), (7, 10), (26, 16), (11, 4), (11, 9), (16, 11), (2, 8), (15, 13), (16, 5), (2, 13), (22, 17), (10, 18), (21, 14), (19, 4), (24, 18), (27, 6), (20, 9), (1, 11), (10, 3), (11, 11), (25, 6), (11, 19), (4, 11), (19, 6), (24, 17), (20, 17), (26, 0), (0, 5), (5, 16), (19, 3), (22, 7), (3, 19), (20, 1), (6, 8), (15, 8), (9, 8), (9, 16), (4, 10), (16, 8), (6, 12), (4, 13), (6, 18), (15, 18), (1, 2), (26, 14), (7, 15), (28, 4), (12, 4), (13, 16), (26, 19), (0, 9), (23, 15), (4, 4), (18, 14), (15, 16), (15, 3), (8, 3), (28, 8), (12, 8), (16, 6), (10, 19), (22, 6), (7, 12), (17, 3), (7, 1), (0, 11), (7, 0), (24, 4), (12, 18), (19, 17), (21, 8), (26, 10), (18, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504990", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 23), (9, 3), (4, 2), (18, 1), (18, 9), (5, 0), (5, 23), (12, 15), (11, 1), (2, 17), (5, 7), (21, 7), (25, 12), (17, 5), (12, 12), (4, 7), (10, 23), (1, 19), (16, 16), (17, 14), (4, 12), (2, 6), (14, 2), (23, 20), (8, 12), (9, 9), (10, 7), (13, 7), (11, 17), (17, 16), (1, 11), (8, 10), (14, 4), (22, 0), (9, 14), (1, 16), (22, 12), (6, 0), (25, 21), (18, 11), (0, 6), (3, 16), (20, 1), (16, 12), (8, 2), (19, 23), (1, 17), (10, 9), (9, 17), (3, 11), (18, 21), (20, 6), (17, 23), (19, 22), (11, 18), (16, 1), (14, 10), (1, 6), (7, 9), (23, 2), (17, 17), (3, 1), (23, 18), (22, 8), (8, 20), (10, 22), (24, 8), (17, 13), (10, 1), (10, 3), (16, 9), (21, 8), (15, 14), (18, 3), (8, 0), (21, 1), (6, 15), (20, 23), (0, 18), (0, 19), (6, 11), (4, 0), (0, 12), (0, 7), (3, 22), (15, 10), (0, 23), (13, 24), (9, 18), (5, 2), (19, 2), (5, 8), (12, 17), (22, 10), (16, 22), (1, 10), (22, 14), (20, 22), (6, 12), (6, 8), (6, 1), (24, 23), (1, 0), (18, 18), (23, 13), (7, 8), (14, 15), (17, 1), (13, 5), (25, 10), (23, 14), (24, 12), (15, 18), (9, 15), (18, 8), (14, 18), (23, 10), (18, 4), (12, 21), (13, 15), (22, 13), (16, 0), (13, 23), (4, 16), (16, 3), (23, 6), (12, 16), (6, 18), (22, 18), (18, 24), (21, 19), (19, 1), (10, 11), (2, 11), (17, 9), (18, 12), (5, 11), (15, 20), (23, 7), (17, 21), (11, 14), (7, 15), (24, 6), (2, 23), (2, 5), (21, 22), (10, 16), (25, 15), (4, 4), (6, 23), (8, 14), (23, 22), (15, 22), (1, 4), (18, 7), (7, 22), (3, 10), (5, 14), (15, 11), (25, 23), (6, 6), (24, 21), (0, 24), (24, 18), (21, 20), (21, 15), (6, 10), (9, 1), (1, 13), (8, 18), (16, 18), (22, 4), (16, 19), (0, 13), (10, 12), (18, 0), (3, 18), (6, 21), (16, 2), (24, 19), (8, 16), (3, 5), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12960", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 22), (11, 4), (12, 18), (6, 15), (8, 24), (9, 7), (14, 15), (19, 0), (12, 1), (18, 8), (17, 3), (17, 24), (2, 6), (4, 16), (10, 15), (9, 8), (1, 9), (12, 5), (19, 24), (0, 3), (10, 10), (17, 9), (14, 14), (8, 21), (17, 20), (8, 6), (4, 12), (8, 19), (5, 8), (10, 7), (5, 11), (11, 24), (6, 8), (12, 7), (14, 5), (20, 17), (10, 23), (7, 0), (6, 3), (15, 15), (3, 19), (5, 12), (18, 18), (4, 1), (20, 16), (3, 18), (17, 13), (4, 18), (13, 3), (6, 4), (11, 8), (2, 17), (6, 12), (3, 3), (10, 14), (1, 10), (7, 6), (11, 20), (2, 19), (3, 16), (12, 17), (4, 17), (1, 0), (9, 21), (0, 14), (16, 8), (10, 22), (5, 10), (2, 1), (18, 21), (3, 15), (6, 18), (6, 0), (20, 8), (15, 3), (11, 11), (7, 17), (5, 23), (11, 23), (13, 16), (19, 20), (19, 19), (8, 20), (7, 5), (13, 4), (2, 8), (9, 16), (11, 15), (2, 4), (20, 22), (20, 21), (5, 20), (3, 24), (9, 11), (12, 9), (16, 18), (13, 8), (16, 11), (12, 12), (7, 18), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775314", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 25), (6, 11), (23, 16), (18, 24), (6, 10), (0, 27), (5, 22), (2, 19), (19, 25), (6, 19), (11, 26), (15, 15), (3, 11), (2, 17), (0, 17), (6, 4), (10, 28), (17, 9), (11, 19), (10, 27), (16, 12), (4, 7), (11, 21), (8, 18), (4, 21), (5, 17), (22, 24), (21, 22), (20, 28), (0, 12), (5, 3), (2, 10), (17, 20), (21, 9), (0, 25), (20, 8), (15, 27), (13, 10), (22, 17), (22, 9), (11, 8), (20, 11), (14, 26), (11, 23), (18, 27), (4, 4), (14, 20), (5, 15), (13, 0), (20, 2), (18, 14), (10, 21), (12, 19), (9, 3), (9, 11), (20, 12), (23, 20), (14, 0), (10, 24), (15, 28), (14, 5), (7, 26), (12, 9), (9, 4), (14, 17), (15, 7), (21, 15), (6, 3), (18, 2), (8, 7), (8, 10), (20, 22), (17, 17), (0, 28), (1, 5), (20, 3), (19, 17), (2, 26), (16, 21), (2, 24), (7, 9), (18, 7), (1, 12), (16, 3), (2, 7), (6, 17), (15, 10), (6, 6), (21, 5), (23, 25), (23, 24), (19, 1), (15, 17), (19, 10), (7, 16), (8, 24), (16, 7), (9, 21), (24, 1), (9, 7), (14, 27), (12, 22), (17, 25), (17, 6), (11, 2), (4, 10), (22, 6), (10, 4), (1, 21), (2, 28), (1, 0), (14, 10), (23, 18), (13, 13), (18, 11), (14, 23), (16, 18), (1, 10), (3, 4), (19, 12), (22, 25), (14, 24), (6, 25), (9, 25), (5, 5), (21, 21), (4, 13), (12, 20), (9, 19), (17, 23), (3, 23), (16, 6), (23, 27), (12, 17), (7, 14), (24, 16), (19, 15), (17, 19), (19, 24), (22, 16), (24, 3), (23, 22), (22, 11), (24, 23), (9, 27), (24, 20), (3, 5), (3, 14), (9, 5), (13, 25), (21, 17), (13, 2), (15, 9), (9, 9), (0, 13), (11, 25), (18, 23), (22, 28), (17, 28), (8, 14), (23, 13), (21, 6), (19, 9), (1, 4), (22, 8), (20, 24), (6, 9), (6, 13), (22, 4), (15, 2), (9, 22), (13, 1), (2, 12), (13, 27), (19, 3), (13, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658264", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (10, 10), (6, 23), (13, 6), (6, 13), (1, 11), (20, 3), (6, 0), (10, 17), (18, 24), (9, 14), (10, 27), (13, 14), (3, 19), (9, 3), (11, 1), (21, 24), (25, 24), (19, 18), (4, 19), (24, 17), (0, 22), (12, 11), (14, 27), (8, 20), (18, 4), (2, 12), (1, 8), (4, 2), (8, 6), (11, 5), (5, 4), (5, 6), (22, 4), (12, 24), (20, 10), (9, 19), (5, 15), (22, 22), (13, 3), (16, 18), (7, 8), (23, 15), (5, 21), (11, 17), (2, 24), (17, 10), (18, 2), (2, 7), (17, 16), (13, 17), (16, 6), (4, 20), (24, 7), (22, 15), (4, 22), (25, 15), (22, 26), (14, 13), (23, 0), (16, 1), (12, 16), (23, 18), (18, 15), (24, 12), (10, 15), (3, 18), (11, 26), (9, 10), (5, 1), (17, 24), (0, 13), (16, 17), (13, 9), (19, 28), (11, 23), (10, 23), (14, 15), (11, 28), (7, 22), (9, 2), (12, 3), (4, 5), (16, 10), (23, 23), (12, 25), (24, 20), (15, 14), (16, 27), (3, 8), (25, 11), (12, 1), (14, 14), (0, 10), (3, 5), (11, 13), (5, 20), (11, 16), (16, 16), (9, 12), (14, 18), (21, 28), (13, 8), (6, 3), (12, 13), (2, 19), (10, 28), (23, 8), (20, 12), (2, 14), (4, 28), (10, 20), (6, 8), (1, 16), (2, 15), (20, 28), (6, 19), (20, 11), (16, 25), (18, 9), (14, 17), (21, 5), (10, 22), (0, 15), (1, 10), (17, 12), (10, 13), (0, 21), (3, 0), (19, 24), (15, 21), (18, 18), (18, 14), (0, 1), (6, 28), (7, 3), (20, 23), (18, 0), (12, 15), (3, 4), (10, 3), (24, 3), (11, 25), (19, 9), (24, 18), (13, 20), (13, 24), (9, 28), (11, 0), (3, 10), (17, 21), (8, 8), (23, 11), (24, 2), (6, 10), (25, 14), (5, 24), (20, 14), (10, 8), (15, 12), (7, 16), (6, 9), (9, 27), (12, 7), (15, 13), (15, 5), (9, 9), (19, 3), (14, 24), (17, 17), (23, 26), (14, 4), (17, 4), (19, 5), (10, 0), (24, 19), (7, 17), (8, 16), (9, 21), (24, 14), (22, 9), (23, 27), (11, 15), (24, 0), (18, 26), (23, 12), (13, 18), (8, 2), (7, 6), (13, 15), (22, 25), (7, 19), (11, 19), (0, 12), (8, 3), (11, 7), (20, 13), (7, 26), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177772", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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), (27, 15), (26, 1), (12, 4), (15, 23), (17, 23), (8, 16), (19, 13), (9, 23), (8, 24), (7, 8), (7, 7), (12, 22), (14, 14), (22, 14), (3, 0), (24, 15), (20, 5), (18, 22), (15, 17), (17, 21), (14, 4), (18, 20), (4, 21), (16, 11), (19, 17), (26, 23), (20, 20), (27, 22), (11, 1), (3, 7), (25, 11), (11, 22), (15, 8), (20, 13), (23, 9), (21, 7), (8, 17), (7, 13), (27, 1), (24, 20), (11, 9), (8, 10), (13, 0), (3, 17), (26, 20), (23, 25), (0, 9), (2, 13), (9, 11), (27, 7), (7, 23), (19, 10), (15, 13), (22, 13), (6, 7), (21, 1), (10, 26), (23, 22), (19, 21), (14, 6), (1, 5), (25, 13), (23, 26), (0, 21), (19, 14), (27, 23), (1, 6), (15, 4), (9, 4), (9, 15), (4, 7), (6, 23), (11, 11), (21, 5), (5, 11), (24, 23), (11, 8), (12, 11), (10, 3), (15, 10), (19, 8), (27, 25), (11, 3), (22, 22), (4, 19), (20, 18), (4, 8), (7, 14), (16, 20), (23, 14), (11, 19), (17, 20), (18, 23), (23, 17), (6, 16), (20, 14), (10, 12), (26, 25), (9, 14), (24, 21), (9, 3), (27, 24), (10, 2), (2, 24), (24, 26), (11, 18), (25, 9), (21, 17), (20, 19), (8, 23), (23, 16), (6, 8), (0, 7), (16, 8), (26, 19), (7, 10), (27, 2), (21, 20), (1, 20), (15, 1), (19, 16), (18, 5), (21, 13), (24, 4), (22, 17), (25, 4), (12, 21), (11, 2), (16, 26), (1, 24), (19, 20), (26, 10), (16, 14), (0, 13), (24, 11), (25, 15), (15, 22), (1, 3), (10, 19), (3, 12), (4, 2), (11, 20), (16, 19), (14, 23), (11, 0), (12, 2), (6, 19), (16, 13), (6, 25), (5, 21), (14, 18), (18, 9), (9, 25), (7, 24), (19, 5), (11, 5), (4, 23), (2, 23), (1, 16), (14, 15), (1, 10), (21, 2), (21, 21), (2, 11), (27, 4), (15, 21), (22, 12), (2, 12), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968326", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 11), (17, 11), (10, 2), (11, 22), (7, 13), (11, 7), (18, 20), (20, 8), (0, 7), (8, 4), (15, 0), (21, 24), (3, 9), (20, 22), (4, 2), (10, 11), (5, 14), (0, 11), (13, 23), (24, 2), (22, 24), (12, 14), (23, 20), (11, 9), (20, 0), (8, 19), (5, 5), (18, 3), (13, 18), (1, 15), (7, 24), (0, 14), (20, 7), (12, 3), (14, 18), (15, 13), (2, 21), (16, 16), (23, 0), (14, 7), (11, 13), (24, 9), (23, 1), (19, 22), (20, 13), (1, 10), (0, 21), (12, 24), (19, 7), (11, 15), (7, 23), (6, 21), (4, 0), (5, 9), (25, 18), (10, 17), (19, 5), (4, 24), (18, 23), (6, 9), (8, 16), (16, 13), (7, 3), (15, 14), (19, 23), (17, 19), (24, 18), (8, 14), (15, 1), (15, 5), (19, 17), (10, 12), (14, 0), (25, 0), (13, 12), (14, 14), (19, 12), (16, 6), (20, 4), (8, 7), (16, 14), (11, 20), (3, 0), (1, 14), (3, 14), (6, 5), (25, 10), (24, 20), (15, 15), (20, 3), (9, 5), (22, 19), (10, 3), (8, 17), (17, 17), (0, 8), (13, 15), (19, 9), (2, 11), (8, 20), (6, 19), (24, 6), (14, 10), (11, 21), (17, 22), (6, 3), (4, 1), (1, 2), (21, 18), (0, 24), (4, 18), (20, 17), (1, 20), (16, 12), (7, 4), (1, 6), (1, 8), (7, 5), (10, 16), (25, 19), (23, 21), (2, 19), (23, 4), (10, 14), (13, 17), (5, 12), (10, 23), (25, 2), (3, 24), (13, 14), (2, 6), (0, 22), (2, 22), (6, 22), (6, 12), (2, 18), (13, 8), (18, 24), (21, 0), (25, 8), (13, 20), (14, 16), (2, 0), (11, 12), (21, 2), (0, 4), (15, 8), (8, 2), (9, 8), (16, 22), (12, 15), (3, 19), (5, 7), (18, 6), (17, 4), (4, 3), (23, 14), (15, 19), (24, 3), (7, 2), (2, 5), (24, 11), (3, 6), (25, 11), (4, 11), (8, 5), (21, 16), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677796", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 10), (19, 3), (16, 6), (18, 11), (10, 16), (14, 17), (17, 7), (6, 14), (12, 7), (5, 12), (17, 0), (14, 0), (12, 11), (8, 18), (16, 7), (13, 11), (3, 0), (0, 16), (12, 2), (8, 19), (9, 7), (6, 9), (4, 8), (15, 12), (4, 15), (14, 16), (13, 17), (16, 0), (15, 17), (2, 16), (18, 15), (2, 3), (6, 18), (18, 9), (16, 8), (16, 13), (11, 19), (7, 8), (15, 18), (5, 8), (16, 12), (15, 1), (12, 5), (4, 6), (6, 5), (17, 8), (5, 17), (19, 14), (2, 0), (8, 11), (12, 0), (7, 9), (9, 3), (8, 4), (8, 14), (1, 8), (12, 19), (12, 3), (15, 0), (2, 5), (15, 6), (2, 17), (16, 10), (17, 18), (3, 19), (17, 4), (1, 4), (14, 19), (5, 10), (15, 3), (16, 17), (6, 12), (5, 14), (9, 13), (16, 19), (13, 18), (16, 14), (3, 7), (14, 8), (10, 3), (19, 15), (15, 9), (10, 8), (4, 13), (9, 14), (9, 10), (6, 0), (7, 3), (7, 16), (16, 1), (17, 2), (11, 14), (19, 8), (19, 5), (14, 6), (15, 8), (12, 9), (18, 3), (0, 1), (2, 18), (3, 18), (7, 2), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759696", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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), (8, 7), (1, 4), (1, 15), (1, 26), (14, 13), (17, 13), (9, 25), (12, 12), (9, 16), (7, 23), (10, 18), (8, 20), (18, 13), (11, 16), (3, 6), (17, 10), (6, 4), (6, 20), (13, 3), (21, 2), (22, 22), (2, 15), (16, 3), (11, 5), (9, 5), (10, 2), (17, 16), (3, 19), (0, 11), (21, 20), (16, 25), (2, 21), (20, 14), (0, 21), (6, 2), (1, 18), (19, 5), (9, 7), (7, 3), (19, 21), (1, 23), (3, 15), (19, 15), (14, 21), (22, 25), (12, 18), (11, 18), (5, 20), (21, 22), (2, 8), (2, 24), (5, 15), (14, 12), (14, 15), (14, 4), (16, 22), (21, 8), (12, 26), (6, 15), (18, 5), (0, 7), (19, 2), (1, 6), (1, 3), (0, 14), (13, 22), (0, 2), (14, 3), (15, 1), (7, 0), (9, 4), (21, 25), (0, 3), (12, 9), (2, 14), (10, 3), (8, 0), (4, 13), (13, 18), (17, 6), (4, 12), (3, 13), (22, 15), (0, 20), (18, 14), (11, 2), (4, 10), (2, 11), (6, 16), (8, 15), (2, 12), (12, 23), (15, 13), (19, 11), (15, 15), (1, 1), (10, 6), (21, 9), (16, 14), (11, 17), (7, 11), (22, 11), (5, 24), (9, 22), (22, 14), (9, 11), (3, 17), (2, 9), (17, 21), (9, 26), (14, 22), (21, 19), (21, 12), (1, 10), (8, 19), (5, 0), (20, 20), (6, 17), (1, 20), (15, 16), (22, 18), (19, 3), (4, 9), (14, 23), (22, 1), (10, 24), (17, 0), (18, 11), (11, 20), (10, 15), (1, 12), (11, 11), (10, 26), (10, 9), (18, 22), (19, 18), (15, 12), (19, 8), (21, 5), (9, 15), (15, 8), (11, 12), (4, 16), (21, 24), (15, 18), (22, 9), (18, 23), (15, 7), (22, 5), (20, 8), (4, 4), (18, 19), (2, 2), (15, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643500", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 12), (1, 1), (13, 6), (0, 17), (10, 8), (14, 0), (13, 22), (20, 20), (2, 22), (11, 2), (10, 4), (7, 19), (7, 18), (16, 20), (2, 1), (21, 7), (17, 17), (17, 11), (14, 5), (23, 7), (4, 6), (7, 15), (9, 8), (8, 20), (19, 19), (0, 2), (1, 14), (20, 2), (13, 16), (15, 5), (11, 22), (7, 3), (0, 22), (8, 9), (6, 6), (1, 7), (14, 8), (2, 9), (14, 7), (10, 14), (22, 11), (22, 16), (14, 13), (0, 15), (5, 21), (17, 20), (19, 14), (1, 3), (23, 0), (9, 2), (2, 3), (14, 21), (17, 16), (8, 4), (0, 10), (10, 16), (7, 1), (18, 19), (13, 14), (6, 11), (18, 0), (22, 5), (12, 17), (1, 21), (11, 8), (14, 11), (19, 20), (10, 7), (12, 11), (5, 14), (23, 1), (3, 16), (16, 9), (12, 9), (22, 18), (11, 13), (3, 20), (4, 9), (18, 17), (13, 13), (15, 17), (5, 12), (12, 20), (2, 8), (20, 6), (12, 12), (18, 4), (13, 21), (10, 20), (9, 19), (2, 2), (12, 22), (18, 14), (10, 10), (13, 2), (5, 1), (6, 13), (22, 22), (13, 18), (10, 18), (21, 17), (13, 17), (4, 15), (15, 15), (11, 19), (5, 15), (3, 5), (9, 3), (8, 22), (7, 21), (1, 11), (13, 19), (10, 15), (3, 2), (1, 12), (12, 16), (5, 3), (15, 21), (23, 17), (8, 21), (4, 5), (0, 4), (18, 1), (3, 17), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789276", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (3, 0), (14, 20), (4, 16), (4, 18), (1, 4), (3, 19), (18, 2), (1, 11), (11, 13), (16, 2), (6, 0), (5, 8), (3, 14), (10, 0), (21, 5), (14, 8), (6, 13), (0, 15), (13, 14), (9, 18), (21, 6), (15, 16), (13, 18), (10, 6), (20, 13), (6, 16), (14, 17), (13, 19), (21, 13), (0, 1), (17, 20), (17, 12), (19, 16), (5, 12), (17, 0), (16, 5), (15, 13), (6, 12), (8, 20), (17, 15), (5, 14), (7, 2), (14, 10), (21, 11), (11, 18), (20, 2), (12, 18), (15, 9), (2, 1), (4, 11), (8, 8), (14, 14), (10, 12), (20, 6), (13, 1), (14, 18), (0, 20), (14, 0), (9, 10), (5, 18), (10, 7), (2, 15), (17, 9), (11, 7), (1, 12), (17, 3), (18, 17), (20, 10), (1, 5), (3, 18), (15, 18), (20, 3), (11, 6), (0, 7), (13, 0), (13, 6), (2, 20), (0, 11), (8, 11), (12, 17), (21, 7), (4, 5), (19, 9), (18, 15), (8, 13), (3, 13), (10, 13), (19, 7), (5, 6), (15, 14), (5, 10), (13, 7), (9, 3), (13, 5), (13, 17), (7, 10), (11, 19), (17, 1), (1, 15), (12, 6), (14, 7), (7, 5), (2, 5), (10, 14), (8, 2), (9, 14), (7, 18), (17, 7), (11, 15), (16, 19), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643682", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 0), (12, 3), (19, 11), (11, 4), (5, 2), (19, 0), (23, 21), (24, 15), (23, 4), (18, 6), (17, 19), (13, 2), (2, 17), (21, 6), (25, 2), (21, 13), (5, 16), (12, 2), (25, 19), (6, 22), (8, 11), (13, 13), (23, 15), (17, 4), (6, 19), (9, 14), (16, 22), (15, 21), (21, 7), (0, 13), (24, 8), (12, 18), (8, 5), (8, 8), (1, 12), (23, 18), (9, 0), (13, 10), (0, 18), (9, 22), (14, 20), (12, 13), (14, 10), (2, 18), (9, 18), (21, 14), (25, 3), (22, 8), (16, 9), (2, 6), (19, 9), (1, 5), (18, 16), (9, 19), (1, 16), (1, 6), (17, 9), (6, 8), (18, 7), (2, 14), (6, 16), (2, 13), (24, 13), (3, 19), (21, 15), (1, 10), (4, 19), (24, 19), (19, 16), (23, 2), (11, 1), (24, 6), (19, 8), (3, 21), (7, 10), (0, 17), (22, 20), (6, 13), (14, 3), (6, 15), (14, 0), (13, 15), (24, 18), (6, 18), (14, 6), (19, 20), (0, 4), (21, 11), (25, 9), (14, 7), (8, 3), (23, 12), (9, 1), (20, 9), (22, 6), (4, 14), (5, 12), (7, 16), (16, 3), (10, 14), (20, 2), (15, 18), (24, 10), (15, 9), (12, 1), (10, 15), (23, 11), (15, 3), (14, 1), (1, 17), (12, 20), (10, 16), (13, 18), (15, 6), (14, 17), (14, 16), (25, 12), (15, 19), (12, 16), (7, 22), (7, 7), (12, 6), (0, 14), (8, 15), (7, 20), (2, 11), (12, 8), (20, 19), (0, 5), (10, 6), (7, 19), (11, 15), (18, 9), (2, 7), (7, 6), (11, 11), (8, 14), (4, 4), (17, 17), (20, 1), (11, 5), (23, 20), (21, 5), (16, 1), (18, 17), (1, 18), (2, 5), (1, 7), (12, 9), (5, 20), (8, 2), (11, 16), (25, 5), (21, 4), (5, 11), (17, 21), (17, 11), (25, 17), (12, 5), (20, 21), (4, 17), (1, 2), (2, 10), (7, 4), (0, 22), (6, 1), (13, 22), (15, 22), (16, 5), (21, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770792", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 17), (16, 14), (5, 27), (7, 10), (4, 20), (8, 23), (7, 7), (14, 3), (8, 10), (13, 1), (16, 12), (8, 4), (14, 14), (4, 9), (6, 18), (14, 26), (4, 15), (18, 8), (6, 15), (8, 21), (10, 1), (2, 8), (15, 6), (6, 17), (0, 8), (13, 2), (18, 24), (13, 7), (15, 25), (17, 15), (15, 17), (5, 8), (11, 13), (5, 17), (17, 8), (15, 24), (11, 16), (4, 13), (6, 11), (13, 5), (1, 24), (14, 0), (3, 6), (8, 7), (19, 6), (13, 26), (1, 7), (8, 18), (4, 8), (9, 8), (6, 16), (5, 10), (1, 16), (3, 8), (6, 6), (6, 14), (16, 3), (9, 18), (19, 3), (7, 8), (5, 19), (2, 21), (7, 16), (4, 0), (18, 12), (14, 4), (10, 3), (19, 1), (15, 27), (15, 26), (10, 17), (4, 25), (11, 15), (12, 11), (7, 4), (17, 23), (13, 25), (18, 11), (11, 14), (0, 17), (16, 8), (16, 5), (12, 14), (16, 25), (11, 12), (1, 5), (16, 23), (0, 16), (14, 11), (0, 27), (2, 6), (16, 19), (3, 18), (8, 5), (4, 14), (18, 3), (5, 24), (4, 23), (13, 0), (17, 24), (1, 20), (2, 0), (19, 4), (16, 16), (6, 25), (14, 25), (6, 4), (3, 5), (12, 23), (17, 18), (16, 10), (7, 9), (17, 0), (17, 2), (19, 10), (12, 25), (9, 20), (7, 20), (13, 21), (9, 3), (0, 23), (3, 11), (7, 17), (5, 21), (14, 19), (2, 12), (19, 9), (13, 4), (9, 15), (14, 1), (10, 8), (3, 7), (0, 15), (0, 11), (3, 24), (7, 12), (10, 23), (1, 26), (5, 1), (12, 6), (18, 2), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "939330", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), 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), (2, 4), (24, 20), (14, 11), (11, 13), (24, 9), (0, 12), (4, 1), (1, 15), (20, 4), (15, 12), (7, 8), (4, 15), (0, 15), (0, 16), (12, 15), (16, 23), (1, 13), (5, 6), (13, 10), (21, 21), (13, 6), (10, 2), (12, 3), (6, 0), (10, 22), (11, 19), (28, 8), (24, 8), (2, 15), (1, 9), (17, 9), (3, 20), (24, 3), (6, 6), (18, 19), (19, 9), (25, 5), (26, 1), (16, 8), (15, 7), (3, 12), (22, 16), (19, 4), (3, 16), (6, 5), (26, 10), (28, 12), (18, 10), (10, 3), (11, 11), (21, 16), (19, 11), (22, 22), (19, 3), (18, 2), (23, 6), (15, 11), (18, 3), (27, 0), (20, 6), (9, 11), (23, 15), (25, 0), (25, 2), (17, 15), (24, 17), (5, 12), (9, 21), (17, 8), (12, 16), (15, 1), (4, 20), (11, 18), (15, 19), (24, 7), (16, 6), (6, 13), (25, 6), (22, 15), (21, 1), (15, 10), (5, 17), (7, 10), (16, 10), (15, 3), (28, 4), (18, 16), (7, 19), (25, 13), (11, 23), (22, 7), (20, 3), (19, 21), (13, 16), (13, 18), (16, 16), (6, 7), (16, 20), (9, 20), (24, 14), (3, 7), (5, 22), (11, 6), (10, 19), (17, 21), (4, 23), (1, 20), (9, 17), (12, 20), (17, 5), (6, 16), (27, 16), (22, 20), (23, 11), (2, 3), (8, 1), (26, 13), (14, 15), (10, 20), (7, 17), (3, 8), (7, 6), (16, 22), (18, 9), (1, 18), (18, 15), (25, 16), (14, 0), (24, 2), (4, 6), (19, 13), (9, 8), (23, 13), (25, 22), (11, 8), (7, 18), (11, 14), (24, 13), (16, 11), (24, 11), (26, 9), (19, 17), (22, 6), (8, 11), (0, 5), (25, 4), (6, 14), (26, 11), (4, 9), (7, 11), (6, 2), (28, 5), (12, 23), (12, 1), (15, 15), (19, 23), (23, 21), (10, 8), (22, 5), (20, 5), (23, 7), (7, 16), (1, 2), (5, 8), (25, 17), (8, 3), (3, 6), (28, 10), (18, 1), (10, 13), (10, 0), (9, 10), (0, 20), (2, 6), (15, 2), (8, 22), (28, 16), (17, 6), (14, 1), (2, 16), (17, 7), (26, 16), (20, 7), (0, 19), (5, 2), (28, 20), (9, 1), (25, 14), (23, 17), (7, 23), (26, 23), (3, 5), (11, 7), (27, 11), (8, 21), (8, 18), (24, 16), (4, 2), (13, 22), (25, 9), (25, 7), (5, 11), (24, 15), (0, 7), (11, 10), (20, 13), (2, 23), (13, 23), (2, 1), (17, 16), (27, 5), (10, 6), (28, 6), (11, 20), (18, 20), (26, 6), (16, 19), (8, 16), (13, 15), (10, 1), (23, 14), (4, 18), (21, 5), (18, 5), (11, 3), (21, 11), (0, 22), (28, 1), (21, 13), (12, 7), (1, 10), (0, 8), (13, 8), (24, 4), (25, 1), (20, 21), (12, 22), (12, 0), (22, 21), (20, 10), (2, 17), (11, 9), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799216", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 21), (24, 16), (18, 0), (24, 1), (21, 4), (1, 8), (7, 9), (22, 12), (5, 0), (7, 19), (19, 12), (4, 7), (11, 10), (6, 2), (0, 5), (4, 10), (22, 15), (8, 11), (3, 11), (17, 21), (22, 0), (15, 15), (8, 10), (19, 9), (2, 14), (11, 17), (16, 11), (6, 5), (21, 5), (24, 14), (5, 7), (8, 7), (23, 19), (15, 16), (13, 12), (10, 7), (15, 0), (3, 13), (19, 17), (11, 8), (13, 20), (7, 1), (13, 3), (0, 12), (10, 10), (13, 15), (13, 5), (7, 5), (23, 17), (20, 12), (19, 14), (17, 8), (6, 11), (3, 3), (15, 10), (1, 16), (24, 2), (5, 14), (6, 7), (12, 17), (10, 15), (12, 13), (20, 17), (9, 21), (1, 13), (0, 18), (14, 1), (24, 6), (10, 2), (22, 5), (0, 14), (12, 21), (5, 3), (14, 0), (12, 16), (4, 18), (3, 7), (6, 17), (18, 20), (6, 19), (24, 19), (12, 20), (17, 10), (20, 14), (20, 11), (0, 10), (15, 3), (22, 20), (6, 14), (12, 2), (11, 19), (8, 9), (8, 3), (2, 8), (20, 16), (23, 6), (9, 2), (2, 10), (16, 6), (20, 20), (12, 11), (5, 8), (18, 4), (4, 14), (7, 6), (13, 9), (8, 5), (11, 11), (12, 4), (15, 14), (15, 20), (20, 18), (14, 4), (11, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "868080", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (4, 12), (21, 2), (6, 9), (14, 13), (9, 13), (19, 17), (3, 7), (7, 20), (14, 7), (4, 3), (13, 9), (11, 2), (12, 23), (19, 22), (14, 5), (5, 15), (1, 9), (10, 0), (6, 5), (16, 2), (19, 15), (2, 20), (1, 14), (14, 1), (1, 19), (17, 0), (7, 18), (4, 9), (19, 21), (21, 15), (18, 4), (21, 4), (6, 11), (18, 10), (19, 19), (18, 22), (2, 4), (20, 7), (13, 19), (16, 14), (15, 3), (2, 9), (4, 7), (21, 14), (7, 17), (9, 24), (20, 11), (14, 8), (18, 6), (3, 8), (18, 5), (1, 8), (12, 8), (21, 7), (21, 22), (17, 2), (7, 24), (5, 17), (10, 19), (20, 3), (11, 24), (21, 23), (19, 6), (0, 24), (4, 22), (0, 19), (18, 24), (3, 18), (8, 9), (7, 5), (3, 23), (15, 13), (18, 3), (18, 19), (14, 6), (11, 19), (8, 7), (16, 22), (20, 4), (14, 3), (21, 0), (9, 3), (15, 9), (2, 8), (5, 19), (21, 12), (16, 7), (21, 20), (9, 16), (16, 24), (16, 11), (21, 16), (12, 14), (6, 0), (6, 17), (16, 18), (4, 6), (9, 12), (20, 19), (19, 10), (21, 21), (14, 12), (15, 20), (13, 24), (19, 18), (6, 4), (20, 6), (20, 20), (8, 12), (8, 1), (1, 7), (11, 14), (5, 0), (10, 14), (20, 23), (17, 19), (9, 15), (14, 19), (8, 15), (6, 23), (19, 7), (16, 1), (17, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "837741", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 20), (5, 0), (12, 20), (15, 9), (22, 11), (12, 10), (25, 11), (7, 1), (14, 11), (7, 19), (0, 1), (12, 8), (7, 9), (16, 12), (16, 10), (16, 7), (11, 21), (8, 10), (11, 0), (8, 13), (16, 8), (28, 11), (10, 10), (25, 0), (23, 17), (1, 18), (14, 17), (6, 17), (14, 22), (28, 12), (17, 4), (23, 4), (26, 0), (15, 13), (27, 15), (16, 0), (22, 0), (20, 17), (6, 7), (3, 8), (6, 12), (1, 12), (25, 18), (21, 1), (28, 21), (16, 17), (28, 9), (7, 16), (3, 15), (24, 15), (10, 14), (5, 13), (7, 22), (15, 20), (9, 23), (7, 7), (2, 7), (4, 22), (6, 21), (0, 15), (17, 5), (4, 17), (23, 21), (18, 10), (23, 19), (12, 18), (24, 7), (4, 14), (1, 9), (4, 18), (10, 7), (12, 17), (25, 19), (3, 4), (2, 10), (11, 6), (20, 23), (12, 9), (10, 4), (16, 2), (3, 10), (13, 23), (22, 18), (22, 15), (21, 18), (23, 18), (24, 4), (19, 2), (2, 11), (28, 16), (0, 2), (18, 12), (21, 17), (15, 15), (26, 1), (12, 6), (7, 5), (4, 15), (23, 6), (14, 6), (7, 17), (22, 3), (27, 1), (25, 1), (18, 20), (3, 5), (14, 23), (2, 6), (9, 16), (6, 10), (10, 3), (18, 18), (26, 8), (2, 4), (8, 19), (27, 16), (23, 16), (23, 3), (4, 4), (25, 2), (11, 10), (13, 17), (28, 19), (28, 6), (28, 5), (1, 13), (2, 3), (11, 9), (22, 10), (26, 16), (11, 12), (26, 3), (13, 15), (22, 1), (13, 3), (8, 12), (1, 5), (15, 18), (11, 18), (22, 19), (9, 13), (27, 9), (24, 14), (6, 8), (8, 4), (20, 13), (21, 5), (23, 20), (27, 5), (27, 3), (6, 15), (9, 18), (27, 12), (1, 20), (24, 1), (2, 19), (11, 3), (14, 15), (15, 22), (27, 21), (16, 13), (16, 14), (25, 8), (20, 5), (12, 1), (15, 17), (13, 6), (21, 7), (19, 16), (3, 13), (6, 2), (0, 14), (17, 9), (18, 14), (22, 21), (25, 5), (15, 19), (4, 1), (12, 7), (27, 8), (23, 2), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853200", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), 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), (6, 6), (14, 7), (15, 0), (15, 2), (18, 7), (9, 17), (9, 8), (1, 3), (1, 4), (6, 15), (16, 5), (5, 12), (8, 8), (9, 9), (4, 12), (19, 6), (11, 9), (2, 17), (17, 1), (18, 15), (2, 12), (19, 3), (16, 15), (14, 5), (10, 8), (16, 2), (11, 1), (4, 3), (15, 14), (19, 18), (18, 1), (3, 0), (7, 13), (13, 7), (0, 10), (18, 6), (19, 14), (10, 10), (4, 18), (17, 18), (20, 15), (7, 3), (17, 19), (15, 4), (5, 2), (11, 3), (0, 1), (12, 16), (12, 15), (3, 7), (15, 6), (4, 2), (12, 3), (9, 14), (14, 18), (16, 8), (11, 13), (8, 13), (9, 4), (0, 3), (1, 6), (13, 3), (20, 5), (6, 2), (19, 12), (7, 15), (14, 9), (14, 2), (18, 11), (12, 1), (17, 3), (16, 14), (19, 5), (10, 7), (7, 8), (12, 11), (10, 15), (11, 12), (3, 1), (4, 11), (6, 17), (13, 18), (8, 1), (6, 16), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853464", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 27), (24, 1), (1, 25), (5, 7), (24, 20), (1, 12), (6, 18), (17, 8), (20, 19), (18, 26), (3, 20), (10, 18), (17, 24), (9, 14), (17, 21), (15, 20), (13, 3), (12, 9), (3, 10), (7, 13), (19, 23), (22, 3), (13, 26), (5, 23), (6, 11), (3, 3), (22, 9), (7, 11), (11, 2), (9, 26), (15, 10), (9, 6), (18, 7), (19, 4), (20, 11), (6, 24), (17, 5), (15, 15), (14, 8), (9, 11), (7, 3), (13, 15), (0, 16), (19, 25), (5, 3), (5, 19), (21, 5), (16, 9), (21, 1), (11, 14), (19, 22), (11, 1), (18, 17), (13, 4), (19, 6), (13, 0), (23, 8), (5, 16), (9, 15), (17, 4), (13, 13), (20, 22), (22, 10), (15, 27), (14, 19), (0, 18), (14, 1), (8, 12), (17, 0), (17, 1), (14, 25), (5, 10), (1, 27), (1, 13), (23, 3), (9, 1), (13, 24), (3, 16), (20, 6), (10, 14), (22, 2), (22, 8), (10, 3), (1, 14), (3, 0), (12, 26), (12, 18), (10, 22), (2, 23), (21, 25), (1, 1), (4, 26), (22, 5), (14, 12), (21, 21), (24, 19), (12, 22), (9, 12), (17, 27), (1, 3), (16, 25), (12, 7), (0, 9), (15, 17), (0, 12), (20, 14), (24, 4), (9, 4), (5, 11), (18, 12), (23, 10), (21, 23), (24, 22), (13, 17), (23, 0), (14, 6), (11, 25), (13, 1), (11, 15), (22, 14), (13, 10), (6, 6), (18, 6), (22, 19), (22, 6), (7, 26), (22, 25), (14, 22), (4, 23), (15, 11), (12, 14), (8, 9), (4, 12), (7, 1), (17, 18), (5, 24), (4, 16), (4, 25), (10, 2), (1, 5), (20, 25), (2, 5), (12, 23), (21, 9), (13, 21), (16, 16), (10, 10), (18, 4), (1, 11), (17, 23), (7, 7), (24, 11), (23, 7), (2, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366720", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), 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, 16), (21, 11), (5, 23), (17, 22), (2, 4), (10, 21), (5, 5), (17, 14), (20, 16), (0, 9), (23, 21), (8, 13), (12, 14), (6, 4), (14, 21), (1, 14), (1, 20), (19, 22), (21, 9), (3, 8), (22, 8), (5, 15), (0, 6), (16, 16), (22, 6), (4, 6), (20, 1), (20, 8), (17, 17), (0, 17), (6, 8), (14, 14), (10, 5), (23, 22), (13, 13), (9, 20), (4, 20), (22, 15), (3, 15), (13, 19), (3, 14), (5, 25), (7, 4), (21, 8), (5, 7), (12, 9), (21, 4), (11, 6), (19, 1), (5, 9), (6, 9), (7, 9), (2, 14), (20, 4), (18, 13), (10, 17), (4, 1), (3, 0), (19, 16), (8, 20), (19, 15), (1, 19), (12, 3), (21, 1), (23, 3), (12, 21), (10, 0), (12, 24), (22, 3), (1, 18), (13, 5), (15, 19), (21, 5), (16, 7), (13, 4), (10, 12), (14, 23), (2, 9), (5, 17), (22, 17), (1, 25), (15, 22), (16, 20), (10, 9), (18, 14), (9, 2), (19, 20), (2, 16), (21, 7), (12, 23), (18, 8), (6, 25), (19, 10), (4, 19), (19, 7), (5, 11), (10, 16), (7, 6), (12, 20), (21, 25), (17, 12), (0, 11), (2, 20), (12, 2), (23, 10), (11, 21), (8, 5), (5, 19), (15, 15), (10, 18), (14, 7), (2, 0), (9, 13), (8, 16), (0, 19), (3, 17), (20, 5), (9, 9), (23, 14), (3, 23), (19, 4), (6, 11), (16, 3), (4, 4), (9, 8), (0, 18), (2, 25), (11, 9), (20, 10), (19, 25), (7, 15), (18, 22), (11, 15), (4, 0), (17, 5), (23, 17), (14, 15), (2, 12), (5, 4), (0, 8), (18, 25), (7, 20), (5, 0), (20, 9), (17, 20), (22, 20), (5, 8), (12, 7), (4, 22), (0, 5), (5, 2), (15, 18), (19, 6), (0, 21), (9, 25), (20, 3), (3, 24), (11, 1), (17, 11), (5, 10), (18, 24), (7, 21), (12, 18), (7, 23), (7, 7), (0, 16), (22, 19), (7, 19), (18, 5), (23, 8), (8, 9), (15, 6), (12, 19), (4, 18), (4, 7), (9, 5), (2, 15), (23, 4), (23, 1), (9, 23), (23, 24), (22, 7), (16, 22), (17, 23), (18, 7), (7, 2), (17, 3), (6, 23), (6, 17), (11, 14), (8, 0), (21, 0), (16, 10), (18, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161920", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), 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, 6), (19, 23), (15, 20), (16, 21), (17, 1), (8, 11), (3, 16), (20, 24), (12, 24), (9, 19), (2, 15), (12, 20), (19, 9), (19, 13), (20, 13), (16, 12), (13, 12), (21, 21), (15, 6), (19, 10), (22, 18), (2, 18), (7, 0), (13, 5), (8, 1), (18, 9), (20, 10), (19, 0), (10, 12), (0, 1), (18, 1), (14, 13), (12, 12), (22, 21), (21, 2), (7, 15), (21, 22), (2, 11), (8, 23), (14, 11), (15, 10), (17, 4), (1, 4), (11, 7), (3, 10), (2, 4), (10, 0), (14, 9), (4, 21), (15, 24), (5, 7), (0, 2), (5, 24), (3, 23), (1, 14), (3, 2), (17, 24), (12, 13), (0, 15), (8, 14), (8, 15), (9, 15), (12, 8), (12, 18), (7, 9), (5, 4), (12, 21), (16, 0), (22, 3), (11, 19), (17, 16), (20, 12), (20, 19), (14, 22), (7, 7), (4, 17), (11, 24), (5, 13), (14, 4), (1, 23), (13, 3), (19, 17), (22, 0), (17, 18), (5, 20), (4, 15), (2, 23), (5, 21), (17, 23), (15, 15), (10, 6), (15, 12), (13, 10), (10, 5), (22, 1), (19, 12), (16, 4), (6, 24), (5, 12), (8, 18), (17, 11), (12, 14), (3, 20), (22, 10), (1, 12), (2, 2), (0, 10), (9, 20), (15, 2), (15, 23), (1, 2), (1, 3), (14, 8), (15, 17), (7, 2), (15, 9), (15, 11), (20, 3), (10, 3), (11, 6), (1, 8), (5, 16), (11, 15), (6, 2), (4, 3), (13, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289386", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 18), (11, 8), (17, 13), (21, 7), (15, 0), (8, 1), (11, 13), (8, 8), (21, 1), (16, 5), (1, 24), (14, 11), (3, 9), (10, 9), (20, 23), (4, 9), (14, 12), (10, 4), (18, 19), (2, 13), (15, 12), (11, 17), (10, 26), (5, 10), (10, 13), (8, 4), (20, 16), (2, 4), (9, 13), (4, 7), (15, 18), (19, 21), (20, 10), (9, 23), (11, 6), (21, 11), (4, 19), (7, 18), (2, 7), (16, 19), (8, 22), (10, 11), (1, 19), (18, 12), (7, 19), (11, 20), (1, 11), (20, 26), (0, 6), (10, 0), (9, 5), (6, 6), (8, 16), (2, 10), (2, 1), (17, 16), (12, 18), (14, 22), (0, 1), (0, 19), (11, 18), (21, 4), (1, 6), (7, 23), (3, 18), (8, 23), (6, 1), (8, 7), (14, 13), (0, 9), (9, 25), (5, 9), (19, 22), (1, 15), (9, 10), (9, 24), (17, 10), (6, 14), (6, 10), (11, 10), (12, 6), (13, 24), (4, 21), (0, 21), (21, 5), (19, 10), (19, 18), (5, 20), (16, 22), (10, 22), (7, 1), (6, 8), (18, 7), (8, 18), (5, 21), (4, 17), (18, 8), (20, 12), (1, 22), (6, 16), (3, 13), (7, 4), (8, 19), (10, 21), (3, 11), (12, 3), (2, 14), (8, 14), (20, 1), (20, 2), (5, 19), (10, 12), (19, 20), (11, 21), (18, 18), (10, 5), (20, 21), (16, 4), (19, 6), (17, 26), (16, 10), (21, 3), (21, 17), (0, 15), (14, 24), (15, 23), (12, 16), (0, 5), (2, 11), (21, 2), (13, 19), (6, 23), (13, 16), (16, 7), (2, 8), (4, 5), (3, 2), (0, 13), (12, 25), (8, 25), (3, 16), (12, 22), (3, 23), (10, 10), (15, 1), (8, 26), (17, 1), (8, 9), (10, 14), (10, 17), (16, 17), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792243", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), 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, 19), (7, 7), (4, 11), (10, 18), (2, 9), (3, 14), (4, 18), (6, 4), (15, 12), (9, 7), (4, 14), (9, 4), (7, 6), (2, 6), (19, 1), (0, 20), (0, 19), (19, 13), (3, 21), (0, 14), (7, 18), (13, 14), (11, 9), (11, 1), (17, 20), (14, 7), (12, 4), (18, 10), (4, 15), (18, 15), (16, 12), (15, 14), (12, 10), (14, 15), (4, 3), (15, 10), (3, 4), (14, 5), (3, 5), (8, 13), (16, 6), (14, 17), (8, 20), (17, 2), (11, 0), (15, 17), (18, 3), (18, 2), (17, 9), (7, 11), (9, 6), (1, 11), (1, 12), (10, 12), (6, 21), (16, 9), (10, 1), (14, 8), (5, 6), (10, 3), (12, 23), (12, 12), (8, 16), (1, 16), (3, 18), (5, 10), (12, 6), (5, 7), (18, 17), (11, 23), (3, 23), (9, 16), (14, 22), (14, 3), (14, 0), (4, 9), (18, 23), (18, 21), (13, 16), (16, 11), (1, 8), (2, 1), (15, 7), (17, 13), (15, 21), (2, 15), (18, 16), (19, 5), (17, 17), (11, 14), (18, 8), (13, 18), (4, 12), (17, 14), (18, 1), (19, 7), (16, 23), (10, 23), (2, 2), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "831930", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 25), (11, 12), (16, 8), (18, 7), (16, 25), (19, 27), (23, 17), (3, 16), (22, 25), (3, 14), (26, 20), (22, 13), (20, 12), (8, 11), (23, 15), (8, 12), (2, 16), (1, 7), (6, 15), (6, 16), (26, 9), (17, 4), (15, 26), (8, 2), (12, 27), (17, 26), (8, 8), (16, 5), (6, 11), (1, 24), (20, 19), (9, 5), (16, 27), (15, 4), (25, 16), (2, 0), (18, 24), (10, 19), (7, 0), (22, 6), (12, 28), (10, 6), (8, 10), (18, 21), (5, 26), (24, 22), (15, 3), (8, 0), (18, 4), (21, 1), (8, 3), (6, 12), (1, 13), (17, 3), (0, 6), (12, 20), (0, 13), (4, 22), (17, 2), (24, 4), (24, 28), (2, 22), (12, 17), (21, 11), (13, 25), (6, 14), (19, 1), (26, 12), (16, 26), (5, 23), (8, 19), (6, 5), (10, 16), (12, 11), (7, 18), (4, 26), (26, 18), (24, 25), (26, 7), (5, 14), (25, 19), (24, 3), (25, 10), (3, 26), (19, 4), (26, 19), (13, 19), (18, 13), (7, 17), (10, 20), (0, 28), (10, 21), (13, 8), (16, 11), (7, 20), (0, 3), (12, 24), (18, 3), (13, 16), (21, 16), (19, 23), (21, 2), (9, 0), (11, 13), (26, 21), (10, 11), (26, 8), (14, 26), (10, 13), (24, 13), (0, 9), (9, 27), (2, 23), (4, 3), (5, 12), (0, 8), (9, 6), (26, 11), (5, 24), (19, 20), (9, 2), (10, 23), (8, 5), (22, 10), (2, 24), (3, 2), (0, 14), (11, 8), (5, 18), (5, 9), (13, 3), (20, 10), (21, 24), (19, 22), (24, 10), (4, 6), (23, 13), (2, 12), (24, 5), (8, 26), (5, 15), (9, 23), (23, 5), (20, 15), (0, 7), (26, 22), (7, 6), (8, 9), (19, 5), (24, 27), (1, 6), (18, 5), (22, 17), (7, 21), (15, 5), (22, 1), (12, 23), (26, 6), (12, 3), (22, 15), (25, 12), (19, 12), (5, 17), (21, 4), (14, 11), (22, 0), (21, 12), (7, 16), (17, 21), (24, 1), (26, 10), (19, 21), (15, 16), (13, 11), (10, 7), (14, 3), (14, 6), (7, 26), (8, 13), (26, 13), (11, 11), (3, 5), (8, 4), (11, 19), (25, 5), (23, 7), (10, 9), (8, 1), (23, 19), (22, 23), (13, 14), (21, 5), (5, 6), (17, 17), (21, 21), (22, 27), (18, 26), (3, 4), (16, 18), (10, 15), (14, 19), (3, 0), (6, 28), (22, 11), (15, 14), (19, 3), (17, 1), (21, 27), (19, 28), (19, 11), (23, 23), (16, 0), (11, 5), (3, 19), (3, 21), (26, 14), (9, 19), (25, 3), (15, 9), (2, 3), (18, 18), (10, 14), (2, 21), (3, 3), (22, 16), (11, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528480", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 10), (19, 3), (15, 15), (1, 18), (27, 18), (2, 16), (26, 10), (7, 18), (2, 14), (22, 2), (7, 11), (19, 6), (26, 4), (12, 5), (9, 2), (15, 0), (13, 0), (15, 4), (1, 6), (12, 16), (0, 3), (12, 9), (3, 7), (0, 11), (6, 15), (8, 12), (22, 1), (24, 8), (4, 10), (2, 1), (1, 11), (26, 15), (26, 11), (13, 2), (7, 1), (14, 14), (26, 16), (13, 10), (13, 5), (8, 10), (18, 4), (27, 6), (1, 19), (28, 2), (14, 11), (4, 18), (25, 1), (15, 17), (14, 17), (11, 3), (28, 0), (18, 3), (0, 18), (10, 3), (1, 7), (13, 19), (6, 6), (11, 9), (19, 16), (5, 17), (22, 7), (4, 12), (27, 1), (2, 8), (4, 2), (4, 14), (17, 4), (15, 9), (19, 19), (7, 6), (26, 9), (16, 3), (5, 18), (11, 13), (6, 4), (15, 3), (24, 18), (28, 1), (5, 1), (0, 4), (2, 18), (13, 1), (17, 2), (7, 20), (12, 15), (3, 4), (14, 9), (5, 4), (16, 11), (11, 19), (4, 9), (28, 16), (16, 4), (15, 2), (22, 17), (14, 7), (12, 11), (23, 19), (18, 5), (21, 12), (21, 11), (1, 2), (17, 8), (6, 17), (27, 2), (26, 2), (3, 11), (8, 9), (24, 14), (6, 5), (14, 16), (0, 8), (28, 11), (16, 10), (5, 13), (25, 20), (20, 4), (27, 5), (16, 8), (16, 17), (0, 17), (25, 10), (1, 9), (15, 19), (14, 4), (1, 12), (0, 9), (28, 3), (26, 1), (1, 20), (5, 10), (21, 0), (11, 5), (17, 9), (28, 7), (18, 18), (4, 5), (7, 9), (25, 13), (14, 20), (12, 7), (10, 12), (7, 10), (9, 19), (16, 1), (18, 9), (2, 13), (15, 8), (27, 7), (6, 0), (0, 14), (13, 15), (10, 1), (23, 9), (2, 17), (3, 13), (12, 3), (25, 12), (10, 10), (16, 5), (18, 10), (12, 8), (15, 1), (8, 20), (17, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "916200", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (1, 20), (16, 12), (1, 10), (9, 14), (3, 7), (13, 5), (10, 19), (5, 0), (5, 19), (17, 13), (0, 19), (3, 9), (15, 19), (3, 12), (11, 10), (5, 8), (3, 5), (7, 18), (9, 4), (9, 21), (18, 14), (7, 4), (13, 11), (14, 19), (18, 8), (14, 14), (7, 11), (19, 5), (6, 9), (16, 21), (19, 0), (14, 7), (6, 16), (0, 12), (5, 10), (4, 12), (0, 21), (18, 15), (3, 15), (3, 16), (5, 18), (6, 18), (12, 20), (2, 11), (9, 1), (15, 6), (1, 12), (3, 14), (19, 10), (7, 6), (9, 19), (5, 9), (3, 11), (13, 9), (19, 20), (13, 6), (17, 18), (8, 15), (11, 17), (18, 7), (11, 16), (19, 14), (12, 21), (4, 6), (4, 8), (18, 2), (6, 14), (13, 14), (5, 11), (19, 7), (0, 18), (2, 21), (14, 5), (6, 7), (0, 4), (2, 6), (8, 5), (11, 1), (17, 1), (13, 12), (3, 20), (16, 17), (7, 2), (19, 16), (1, 18), (3, 18), (2, 20), (4, 5), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565475", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 25), (7, 9), (19, 17), (8, 26), (1, 26), (10, 18), (10, 8), (11, 20), (21, 6), (8, 6), (10, 12), (2, 8), (13, 24), (16, 6), (21, 14), (4, 5), (19, 1), (13, 22), (18, 18), (5, 6), (4, 3), (4, 23), (13, 6), (12, 17), (6, 22), (2, 18), (15, 16), (1, 16), (3, 7), (15, 19), (20, 14), (14, 10), (2, 2), (4, 8), (4, 26), (7, 17), (13, 26), (15, 13), (15, 10), (20, 9), (17, 21), (13, 14), (3, 8), (3, 23), (11, 6), (6, 1), (19, 19), (6, 20), (7, 24), (17, 5), (2, 13), (12, 4), (6, 14), (19, 0), (7, 18), (9, 11), (9, 16), (19, 12), (3, 19), (6, 18), (4, 15), (3, 10), (7, 7), (19, 23), (5, 27), (16, 24), (17, 26), (14, 8), (10, 23), (3, 24), (3, 13), (14, 5), (1, 14), (12, 7), (11, 8), (16, 22), (14, 17), (9, 25), (17, 11), (9, 0), (20, 25), (21, 24), (6, 8), (20, 26), (13, 9), (14, 1), (16, 8), (15, 27), (14, 21), (11, 21), (7, 1), (9, 9), (0, 12), (19, 11), (15, 25), (3, 2), (2, 14), (5, 11), (10, 3), (12, 24), (14, 20), (18, 6), (4, 4), (18, 24), (1, 2), (1, 15), (10, 27), (0, 11), (19, 16), (18, 23), (13, 11), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964692", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 9), (18, 7), (21, 10), (18, 2), (5, 18), (2, 8), (7, 17), (0, 6), (18, 18), (6, 13), (13, 4), (11, 2), (13, 9), (2, 18), (10, 1), (24, 5), (23, 6), (2, 12), (11, 12), (2, 13), (24, 14), (5, 13), (18, 1), (10, 18), (24, 8), (25, 12), (24, 11), (15, 3), (8, 17), (9, 3), (14, 13), (25, 13), (0, 5), (15, 4), (17, 3), (26, 8), (9, 16), (19, 14), (23, 11), (17, 19), (9, 14), (7, 12), (11, 18), (4, 1), (11, 1), (23, 10), (17, 0), (14, 11), (5, 14), (19, 18), (12, 16), (16, 13), (14, 6), (18, 0), (14, 12), (6, 3), (20, 1), (22, 17), (23, 3), (4, 11), (1, 5), (17, 7), (9, 4), (24, 15), (14, 9), (14, 18), (23, 4), (21, 14), (13, 6), (2, 10), (13, 16), (18, 9), (15, 6), (19, 11), (12, 5), (22, 3), (16, 19), (9, 12), (0, 8), (13, 0), (16, 10), (0, 9), (9, 6), (12, 6), (12, 14), (1, 1), (16, 0), (15, 0), (2, 3), (24, 6), (26, 12), (14, 10), (16, 8), (16, 7), (15, 11), (16, 17), (17, 12), (5, 11), (19, 19), (14, 1), (22, 13), (10, 14), (19, 5), (8, 11), (7, 11), (1, 11), (1, 2), (3, 3), (9, 8), (8, 9), (18, 4), (12, 2), (4, 6), (5, 0), (3, 2), (1, 3), (6, 19), (0, 14), (15, 15), (10, 9), (16, 18), (15, 16), (9, 2), (1, 16), (9, 7), (26, 1), (6, 18), (20, 0), (2, 0), (15, 5), (1, 14), (21, 11), (18, 16), (22, 10), (21, 17), (3, 15), (5, 9), (2, 1), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865808", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (23, 15), (17, 19), (1, 1), (14, 15), (3, 9), (0, 4), (24, 13), (22, 18), (13, 9), (4, 4), (0, 15), (24, 4), (25, 15), (17, 16), (10, 7), (12, 7), (23, 13), (13, 15), (16, 0), (1, 7), (26, 18), (0, 18), (10, 12), (24, 9), (14, 5), (14, 7), (25, 4), (0, 3), (14, 9), (7, 5), (23, 16), (19, 7), (7, 16), (4, 11), (23, 3), (19, 0), (9, 11), (9, 9), (12, 13), (25, 0), (2, 13), (4, 18), (19, 19), (10, 17), (15, 14), (22, 1), (8, 4), (26, 3), (8, 13), (11, 17), (7, 7), (10, 3), (20, 19), (7, 9), (5, 20), (19, 12), (6, 12), (13, 10), (5, 14), (9, 4), (3, 4), (21, 17), (14, 20), (19, 5), (18, 3), (8, 20), (25, 7), (16, 1), (11, 15), (21, 4), (20, 6), (21, 20), (18, 19), (18, 10), (25, 12), (0, 6), (18, 5), (7, 3), (21, 12), (22, 6), (1, 8), (0, 14), (5, 12), (7, 10), (22, 17), (25, 18), (14, 2), (12, 5), (7, 4), (7, 11), (15, 15), (1, 12), (18, 15), (6, 7), (23, 20), (6, 11), (12, 17), (18, 16), (23, 8), (19, 10), (21, 1), (10, 19), (6, 20), (22, 13), (11, 13), (23, 14), (3, 12), (20, 2), (3, 15), (23, 6), (8, 14), (12, 18), (25, 5), (22, 9), (6, 10), (6, 13), (16, 7), (6, 2), (12, 11), (12, 6), (9, 16), (24, 16), (16, 4), (10, 10), (18, 18), (18, 1), (11, 5), (13, 6), (24, 12), (1, 2), (21, 5), (2, 20), (3, 14), (8, 18), (25, 14), (4, 6), (1, 10), (15, 16), (25, 6), (24, 8), (12, 16), (14, 19), (25, 16), (11, 19), (8, 17), (22, 7), (23, 9), (10, 1), (7, 12), (6, 3), (17, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545163", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 1), (15, 10), (0, 23), (2, 25), (2, 4), (16, 10), (5, 26), (26, 23), (6, 0), (14, 3), (11, 26), (25, 21), (3, 18), (20, 16), (19, 18), (14, 4), (21, 19), (16, 8), (23, 20), (4, 16), (25, 8), (22, 11), (9, 18), (26, 17), (20, 0), (18, 2), (6, 10), (8, 17), (12, 14), (22, 15), (21, 12), (25, 26), (19, 0), (13, 9), (14, 7), (21, 3), (22, 16), (16, 11), (2, 10), (26, 21), (7, 13), (6, 11), (22, 2), (1, 18), (22, 19), (4, 24), (9, 2), (26, 5), (6, 1), (26, 0), (4, 14), (14, 17), (15, 17), (17, 14), (15, 9), (17, 3), (17, 18), (16, 20), (5, 11), (11, 2), (10, 19), (19, 19), (12, 23), (3, 5), (2, 12), (21, 0), (25, 4), (13, 23), (14, 20), (8, 8), (5, 17), (14, 26), (6, 7), (20, 10), (26, 24), (1, 16), (3, 9), (9, 5), (8, 1), (6, 5), (21, 17), (4, 0), (9, 6), (10, 9), (23, 16), (10, 23), (26, 8), (20, 7), (17, 26), (20, 23), (2, 2), (18, 18), (18, 14), (16, 14), (24, 0), (8, 16), (10, 0), (25, 6), (6, 24), (14, 16), (13, 16), (15, 7), (24, 9), (24, 8), (1, 15), (1, 12), (24, 10), (4, 13), (24, 7), (23, 19), (10, 7), (14, 13), (17, 23), (16, 19), (24, 18), (12, 18), (4, 7), (23, 12), (4, 19), (19, 21), (13, 25), (17, 19), (1, 5), (22, 1), (7, 19), (9, 21), (1, 8), (1, 2), (17, 22), (6, 17), (3, 20), (19, 24), (20, 5), (11, 4), (8, 9), (1, 24), (8, 19), (16, 15), (5, 22), (21, 7), (13, 11), (23, 18), (5, 16), (26, 11), (11, 15), (21, 1), (1, 19), (0, 8), (25, 22), (1, 25), (5, 10), (7, 10), (15, 24), (10, 8), (3, 1), (4, 22), (6, 19), (10, 5), (24, 15), (8, 11), (15, 26), (25, 13), (4, 20), (8, 10), (15, 23), (11, 12), (2, 13), (16, 5), (2, 5), (15, 0), (19, 13), (8, 21), (3, 14), (10, 4), (11, 1), (22, 6), (4, 11), (17, 1), (23, 8), (3, 2), (22, 9), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535680", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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), (7, 16), (21, 8), (28, 9), (23, 4), (16, 5), (3, 25), (5, 17), (27, 26), (16, 3), (10, 16), (14, 18), (21, 23), (26, 7), (3, 10), (28, 18), (9, 2), (12, 14), (23, 0), (23, 26), (10, 0), (19, 0), (8, 12), (17, 18), (28, 0), (10, 26), (11, 12), (26, 4), (6, 0), (8, 4), (1, 7), (4, 24), (13, 12), (5, 10), (21, 4), (2, 0), (17, 26), (22, 10), (15, 23), (10, 8), (27, 0), (24, 13), (15, 8), (1, 21), (23, 7), (2, 8), (26, 9), (11, 20), (3, 3), (21, 11), (9, 26), (27, 20), (9, 8), (27, 11), (17, 3), (24, 12), (18, 1), (15, 18), (7, 8), (24, 21), (6, 22), (16, 0), (15, 4), (5, 5), (22, 22), (20, 26), (9, 21), (12, 25), (13, 11), (1, 22), (18, 13), (6, 17), (18, 9), (24, 2), (8, 11), (6, 3), (18, 18), (19, 10), (3, 2), (6, 15), (23, 20), (13, 25), (17, 25), (12, 1), (24, 6), (14, 10), (16, 15), (5, 19), (8, 19), (23, 13), (0, 7), (8, 7), (13, 26), (14, 25), (11, 25), (26, 23), (17, 10), (27, 15), (17, 5), (22, 17), (14, 11), (0, 15), (8, 5), (5, 21), (0, 18), (21, 24), (19, 8), (25, 3), (3, 1), (17, 6), (15, 7), (26, 19), (16, 11), (23, 16), (21, 25), (10, 2), (11, 14), (14, 23), (25, 23), (19, 9), (10, 17), (3, 20), (8, 23), (21, 10), (22, 18), (10, 25), (28, 21), (10, 20), (23, 25), (24, 7), (7, 18), (11, 15), (22, 19), (24, 5), (27, 16), (27, 23), (1, 10), (17, 23), (0, 25), (17, 19), (8, 1), (21, 19), (10, 14), (6, 1), (5, 18), (2, 6), (22, 1), (5, 15), (3, 7), (20, 1), (24, 18), (9, 25), (28, 8), (22, 24), (25, 14), (4, 4), (9, 7), (4, 14), (20, 19), (19, 3), (23, 14), (5, 2), (24, 25), (5, 24), (14, 20), (22, 23), (4, 16), (6, 9), (22, 0), (21, 5), (23, 18), (20, 18), (25, 5), (5, 1), (14, 3), (11, 19), (25, 8), (15, 13), (20, 9), (26, 0), (6, 19), (6, 11), (13, 18), (22, 21), (17, 20), (13, 19), (21, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430440", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (22, 13), (10, 7), (1, 18), (10, 20), (21, 6), (6, 20), (5, 8), (8, 1), (26, 8), (20, 11), (15, 7), (23, 20), (8, 12), (9, 1), (17, 19), (10, 16), (17, 16), (0, 14), (25, 10), (4, 5), (23, 5), (24, 1), (24, 10), (5, 2), (2, 17), (19, 8), (20, 17), (10, 10), (11, 3), (0, 19), (20, 0), (18, 1), (21, 9), (26, 6), (10, 9), (21, 3), (19, 6), (18, 14), (10, 6), (17, 9), (20, 19), (9, 14), (14, 20), (8, 6), (18, 19), (21, 1), (1, 12), (25, 7), (2, 14), (11, 15), (9, 12), (24, 5), (14, 14), (19, 18), (25, 19), (4, 6), (6, 12), (12, 20), (0, 16), (21, 7), (14, 4), (4, 2), (16, 20), (15, 20), (6, 0), (0, 8), (20, 1), (0, 20), (23, 7), (15, 14), (6, 8), (22, 2), (18, 5), (22, 20), (14, 8), (6, 1), (19, 19), (22, 12), (19, 9), (5, 12), (14, 16), (25, 8), (12, 19), (12, 11), (13, 20), (1, 4), (26, 4), (21, 0), (6, 5), (7, 12), (23, 2), (10, 18), (9, 13), (19, 4), (22, 0), (14, 17), (20, 13), (7, 5), (18, 9), (6, 14), (8, 13), (4, 7), (12, 0), (1, 11), (19, 2), (2, 7), (7, 15), (7, 9), (14, 0), (8, 20), (7, 18), (23, 1), (15, 4), (6, 18), (14, 7), (25, 18), (2, 18), (23, 17), (2, 1), (17, 17), (20, 5), (1, 6), (10, 1), (7, 2), (25, 11), (13, 19), (13, 5), (9, 18), (17, 2), (20, 15), (7, 17), (2, 0), (21, 18), (12, 4), (9, 7), (15, 11), (19, 13), (5, 1), (16, 6), (11, 0), (11, 13), (13, 9), (17, 4), (26, 11), (13, 17), (13, 16), (20, 3), (1, 5), (10, 3), (24, 7), (10, 11), (10, 15), (15, 18), (23, 18), (17, 5), (6, 13), (24, 14), (7, 6), (11, 8), (10, 17), (17, 20), (8, 10), (15, 6), (12, 16), (14, 18), (20, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574842", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), 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), (18, 21), (18, 23), (22, 25), (24, 1), (18, 8), (19, 10), (3, 12), (22, 22), (20, 0), (6, 3), (21, 3), (13, 4), (7, 23), (15, 21), (11, 13), (8, 4), (7, 7), (1, 27), (13, 19), (25, 22), (21, 4), (16, 17), (18, 19), (12, 15), (11, 3), (23, 7), (13, 16), (14, 20), (19, 18), (17, 9), (0, 13), (15, 11), (20, 5), (14, 22), (8, 22), (18, 17), (16, 24), (18, 14), (19, 25), (21, 24), (7, 20), (24, 20), (25, 6), (8, 20), (17, 25), (17, 6), (4, 26), (2, 20), (16, 2), (17, 10), (6, 1), (1, 23), (11, 23), (23, 20), (6, 2), (6, 25), (10, 15), (25, 3), (15, 9), (22, 13), (24, 11), (19, 11), (2, 0), (12, 2), (13, 17), (3, 14), (17, 5), (8, 19), (3, 0), (22, 17), (22, 19), (15, 24), (25, 2), (16, 1), (4, 22), (8, 6), (25, 23), (22, 18), (20, 7), (12, 5), (17, 26), (21, 12), (25, 16), (9, 3), (0, 25), (19, 19), (3, 23), (6, 19), (8, 2), (11, 5), (1, 4), (9, 22), (19, 3), (12, 9), (25, 24), (3, 4), (8, 10), (16, 22), (10, 8), (3, 22), (21, 20), (1, 0), (19, 17), (14, 9), (12, 20), (4, 9), (4, 27), (20, 15), (7, 13), (1, 21), (16, 8), (19, 9), (9, 16), (17, 27), (10, 11), (14, 13), (17, 2), (15, 22), (4, 15), (0, 12), (18, 10), (9, 2), (23, 13), (5, 3), (4, 25), (12, 22), (20, 27), (24, 16), (23, 3), (22, 24), (1, 2), (18, 13), (25, 15), (6, 12), (25, 9), (23, 25), (0, 6), (1, 8), (16, 27), (20, 16), (17, 22), (10, 17), (7, 0), (2, 5), (17, 8), (12, 4), (18, 1), (6, 4), (13, 1), (20, 14), (15, 17), (18, 7), (14, 10), (12, 24), (12, 11), (21, 2), (0, 2), (21, 22), (16, 19), (19, 23), (4, 5), (11, 15), (24, 0), (2, 21), (2, 18), (17, 11), (5, 6), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511920", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 17), (18, 17), (10, 22), (0, 5), (7, 11), (10, 11), (14, 1), (9, 21), (3, 11), (4, 22), (16, 10), (25, 17), (2, 0), (13, 6), (1, 23), (4, 13), (24, 3), (1, 18), (25, 19), (21, 10), (17, 19), (15, 11), (13, 20), (11, 10), (9, 2), (21, 14), (4, 19), (21, 2), (16, 7), (4, 15), (22, 4), (13, 9), (14, 4), (4, 6), (13, 23), (6, 4), (1, 20), (20, 14), (6, 16), (18, 22), (11, 5), (19, 6), (3, 21), (8, 15), (5, 21), (17, 23), (2, 19), (8, 9), (6, 5), (0, 3), (25, 9), (16, 12), (20, 6), (18, 16), (5, 19), (19, 0), (22, 14), (20, 19), (3, 13), (9, 15), (1, 4), (7, 21), (21, 6), (8, 3), (3, 2), (19, 8), (18, 14), (6, 15), (16, 19), (4, 17), (19, 14), (8, 6), (14, 17), (4, 10), (10, 8), (7, 3), (11, 9), (25, 12), (16, 23), (5, 15), (2, 17), (2, 23), (10, 0), (1, 9), (10, 19), (1, 5), (15, 14), (0, 7), (17, 2), (23, 13), (5, 8), (21, 18), (23, 12), (6, 7), (23, 7), (20, 2), (4, 18), (1, 1), (15, 9), (5, 13), (2, 8), (3, 17), (4, 0), (0, 8), (14, 19), (13, 4), (7, 18), (24, 1), (10, 13), (24, 19), (25, 10), (25, 21), (22, 10), (4, 12), (19, 16), (11, 0), (24, 18), (8, 11), (11, 13), (0, 18), (5, 12), (7, 7), (0, 6), (23, 3), (19, 23), (4, 16), (3, 5), (7, 9), (13, 12), (15, 20), (22, 17), (12, 8), (16, 15), (3, 6), (24, 17), (15, 13), (20, 20), (25, 4), (0, 4), (23, 4), (3, 15), (14, 11), (23, 2), (18, 4), (18, 2), (17, 13), (18, 19), (20, 13), (16, 22), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587574", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (27, 15), (10, 7), (12, 0), (8, 9), (4, 5), (26, 15), (21, 16), (27, 8), (1, 16), (5, 3), (19, 16), (4, 10), (7, 1), (6, 3), (13, 9), (16, 2), (6, 1), (23, 12), (26, 12), (23, 10), (11, 4), (3, 16), (11, 0), (19, 21), (6, 5), (22, 18), (24, 21), (10, 6), (13, 16), (10, 0), (20, 20), (7, 8), (8, 12), (24, 14), (3, 9), (6, 14), (11, 11), (1, 7), (23, 5), (16, 17), (20, 16), (8, 21), (19, 5), (20, 12), (25, 4), (1, 20), (21, 10), (15, 8), (21, 15), (23, 9), (3, 5), (26, 1), (4, 19), (0, 21), (5, 16), (9, 13), (5, 7), (0, 3), (17, 2), (8, 10), (12, 4), (11, 10), (15, 18), (21, 18), (17, 17), (22, 19), (2, 4), (7, 15), (26, 10), (7, 4), (3, 11), (15, 19), (13, 19), (20, 18), (0, 9), (3, 20), (21, 20), (21, 21), (15, 5), (25, 9), (4, 7), (11, 8), (8, 2), (27, 19), (11, 3), (27, 11), (25, 1), (24, 18), (8, 7), (17, 1), (27, 10), (16, 7), (0, 17), (11, 7), (23, 2), (2, 20), (9, 14), (14, 14), (26, 13), (25, 19), (2, 3), (27, 0), (16, 14), (16, 9), (6, 9), (3, 10), (15, 6), (21, 9), (14, 2), (9, 8), (23, 8), (8, 6), (8, 4), (27, 2), (25, 13), (23, 4), (14, 17), (24, 5), (15, 14), (25, 5), (9, 20), (24, 4), (0, 15), (16, 4), (19, 14), (20, 1), (10, 2), (27, 14), (21, 5), (19, 10), (24, 9), (5, 9), (12, 8), (15, 10), (24, 13), (2, 2), (13, 15), (27, 9), (16, 8), (4, 2), (13, 12), (10, 8), (13, 20), (17, 0), (6, 16), (18, 8), (17, 11), (0, 6), (8, 17), (16, 11), (10, 14), (25, 6), (6, 0), (12, 17), (1, 14), (1, 12), (25, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394632", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), 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, 11), (3, 1), (19, 2), (8, 13), (18, 5), (13, 5), (8, 18), (11, 8), (13, 2), (9, 1), (11, 1), (13, 1), (1, 23), (6, 11), (1, 10), (6, 8), (15, 10), (8, 8), (13, 20), (9, 21), (2, 19), (18, 6), (5, 6), (13, 0), (21, 2), (11, 9), (12, 16), (12, 13), (19, 0), (7, 1), (3, 4), (21, 1), (19, 22), (4, 0), (13, 6), (9, 12), (17, 15), (11, 21), (16, 21), (3, 8), (18, 18), (7, 13), (10, 13), (20, 2), (2, 6), (22, 8), (12, 7), (13, 7), (16, 7), (20, 12), (19, 5), (18, 13), (10, 14), (11, 13), (11, 17), (8, 4), (1, 17), (21, 11), (4, 5), (8, 20), (2, 17), (9, 14), (9, 9), (0, 19), (8, 22), (19, 17), (4, 23), (20, 8), (10, 9), (5, 23), (0, 2), (6, 9), (1, 15), (20, 10), (6, 12), (19, 14), (5, 3), (5, 0), (11, 12), (6, 0), (8, 9), (11, 4), (11, 2), (21, 16), (20, 15), (8, 2), (20, 19), (0, 15), (14, 13), (3, 21), (9, 22), (6, 19), (13, 15), (3, 9), (17, 13), (1, 2), (21, 0), (2, 7), (20, 18), (12, 2), (11, 14), (5, 18), (19, 12), (12, 5), (7, 11), (21, 14), (15, 21), (21, 5), (2, 4), (16, 1), (19, 19), (14, 12), (5, 9), (22, 1), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769158", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 15), (24, 8), (18, 1), (18, 5), (13, 14), (27, 8), (25, 1), (11, 22), (6, 8), (14, 0), (3, 7), (13, 2), (16, 15), (27, 1), (13, 16), (17, 1), (5, 5), (21, 12), (7, 20), (1, 8), (25, 7), (7, 11), (17, 14), (4, 16), (11, 14), (25, 26), (25, 24), (27, 2), (0, 2), (6, 12), (20, 9), (26, 5), (24, 9), (27, 18), (13, 12), (22, 10), (1, 18), (0, 25), (14, 19), (22, 23), (14, 4), (18, 26), (20, 4), (1, 6), (9, 14), (19, 3), (15, 17), (11, 1), (1, 26), (16, 5), (7, 17), (16, 16), (15, 9), (16, 21), (9, 6), (3, 23), (13, 19), (20, 20), (23, 9), (0, 5), (17, 19), (16, 17), (21, 11), (0, 24), (15, 15), (22, 14), (12, 6), (15, 2), (1, 14), (0, 8), (17, 12), (4, 19), (0, 20), (13, 8), (22, 21), (22, 15), (20, 15), (19, 9), (21, 22), (13, 3), (22, 1), (11, 10), (20, 25), (10, 7), (20, 23), (1, 24), (14, 24), (24, 22), (8, 21), (16, 6), (5, 1), (3, 22), (8, 24), (12, 14), (24, 19), (23, 19), (2, 12), (6, 11), (1, 25), (8, 14), (4, 18), (27, 5), (18, 3), (11, 9), (5, 11), (25, 25), (26, 6), (6, 25), (27, 3), (11, 25), (1, 5), (6, 1), (19, 15), (23, 10), (7, 6), (21, 6), (5, 7), (11, 2), (6, 7), (27, 16), (8, 26), (7, 18), (21, 9), (4, 8), (7, 14), (27, 6), (6, 3), (17, 20), (5, 9), (15, 22), (15, 21), (9, 22), (12, 7), (26, 3), (13, 26), (15, 0), (25, 20), (21, 26), (14, 14), (24, 13), (10, 4), (8, 9), (23, 12), (9, 24), (4, 17), (21, 18), (2, 26), (14, 10), (11, 26), (16, 8), (6, 14), (10, 18), (4, 7), (0, 7), (16, 2), (25, 6), (0, 10), (7, 2), (24, 14), (11, 5), (13, 10), (21, 7), (25, 21), (1, 15), (14, 21), (21, 20), (2, 7), (10, 12), (9, 5), (22, 7), (26, 23), (21, 0), (10, 9), (12, 0), (11, 6), (7, 26), (8, 3), (4, 0), (17, 23), (2, 1), (17, 0), (2, 13), (10, 2), (12, 26), (0, 21), (17, 21), (4, 25), (21, 16), (26, 14), (18, 24), (11, 20), (18, 6), (0, 6), (3, 26), (3, 9), (19, 4), (26, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492102", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), 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), (13, 9), (20, 12), (0, 13), (22, 7), (2, 9), (6, 8), (21, 17), (7, 10), (22, 5), (22, 1), (14, 1), (8, 4), (10, 0), (17, 23), (2, 16), (1, 8), (14, 10), (10, 24), (15, 0), (2, 22), (14, 23), (7, 24), (22, 13), (4, 23), (10, 14), (20, 15), (7, 1), (14, 16), (21, 19), (7, 15), (5, 25), (7, 13), (0, 23), (19, 25), (18, 20), (17, 12), (15, 12), (4, 19), (8, 23), (12, 14), (17, 2), (21, 11), (20, 24), (19, 22), (4, 24), (7, 5), (21, 24), (18, 24), (14, 3), (16, 16), (6, 18), (19, 11), (2, 5), (9, 0), (14, 8), (1, 21), (10, 8), (17, 3), (0, 18), (21, 25), (16, 23), (5, 23), (3, 14), (16, 25), (11, 19), (20, 1), (15, 20), (6, 16), (15, 11), (7, 21), (18, 0), (17, 15), (20, 23), (9, 13), (10, 9), (10, 7), (12, 2), (18, 19), (17, 0), (12, 8), (3, 13), (1, 17), (20, 21), (11, 13), (2, 21), (3, 15), (4, 12), (21, 18), (14, 6), (1, 10), (16, 8), (2, 25), (8, 15), (8, 2), (0, 14), (0, 6), (9, 19), (14, 0), (10, 17), (0, 7), (12, 15), (5, 8), (4, 1), (3, 21), (2, 2), (15, 24), (19, 23), (3, 20), (8, 21), (4, 2), (11, 25), (1, 24), (1, 13), (1, 14), (9, 11), (1, 5), (0, 9), (18, 10), (10, 25), (19, 18), (0, 24), (19, 6), (8, 7), (19, 19), (14, 19), (6, 2), (4, 8), (8, 6), (9, 1), (11, 21), (14, 22), (12, 10), (12, 17), (8, 16), (3, 7), (22, 19), (16, 24), (16, 14), (19, 9), (22, 8), (2, 10), (14, 2), (19, 13), (1, 9), (5, 7), (11, 14), (17, 22), (15, 17), (3, 16), (6, 12), (18, 2), (9, 4), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385350", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 27), (23, 27), (1, 21), (11, 12), (21, 4), (24, 11), (25, 5), (9, 7), (7, 23), (17, 4), (5, 23), (0, 5), (5, 18), (20, 21), (18, 12), (3, 0), (24, 7), (24, 12), (14, 12), (11, 22), (0, 24), (14, 8), (6, 2), (5, 16), (0, 7), (9, 10), (2, 9), (21, 17), (20, 23), (10, 10), (5, 1), (14, 25), (7, 10), (1, 7), (15, 23), (22, 26), (1, 2), (20, 12), (4, 7), (13, 23), (18, 15), (7, 17), (4, 14), (6, 13), (22, 13), (9, 17), (17, 13), (11, 15), (19, 9), (13, 12), (4, 6), (23, 7), (13, 6), (3, 19), (16, 22), (22, 4), (15, 16), (9, 6), (23, 3), (9, 9), (17, 9), (11, 19), (24, 23), (11, 3), (2, 26), (14, 22), (9, 13), (22, 24), (7, 6), (10, 25), (2, 1), (0, 13), (15, 1), (24, 8), (7, 9), (1, 16), (16, 4), (10, 5), (14, 4), (22, 23), (20, 6), (0, 10), (1, 15), (4, 25), (15, 4), (9, 27), (25, 19), (5, 13), (7, 0), (1, 3), (5, 0), (4, 13), (13, 17), (11, 27), (18, 25), (0, 9), (17, 17), (21, 19), (0, 11), (16, 2), (18, 21), (5, 14), (15, 15), (14, 27), (3, 2), (20, 25), (20, 13), (22, 19), (15, 18), (8, 0), (24, 4), (0, 20), (3, 10), (19, 15), (0, 15), (2, 0), (2, 27), (15, 13), (11, 18), (2, 24), (13, 21), (0, 18), (12, 25), (3, 26), (12, 11), (23, 14), (19, 14), (24, 25), (9, 11), (2, 15), (3, 25), (24, 19), (25, 24), (3, 13), (16, 19), (21, 8), (4, 2), (24, 17), (3, 23), (2, 19), (18, 16), (12, 24), (6, 6), (12, 14), (6, 11), (8, 19), (14, 9), (8, 22), (3, 3), (12, 3), (8, 1), (5, 26), (17, 19), (1, 27), (15, 8), (5, 6), (25, 14), (21, 16), (13, 7), (10, 26), (8, 24), (22, 18), (14, 23), (14, 20), (5, 3), (9, 25), (2, 23), (22, 5), (8, 25), (10, 3), (10, 8), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581348", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 20), (6, 0), (10, 16), (13, 16), (20, 0), (17, 25), (4, 7), (8, 16), (7, 0), (9, 14), (3, 6), (3, 22), (14, 7), (0, 8), (10, 26), (13, 19), (13, 4), (13, 7), (6, 17), (22, 25), (23, 7), (24, 15), (23, 4), (13, 10), (1, 26), (14, 12), (4, 9), (4, 10), (19, 6), (10, 0), (13, 1), (3, 26), (22, 21), (10, 27), (6, 27), (3, 14), (8, 8), (19, 13), (13, 21), (17, 23), (5, 19), (12, 16), (3, 2), (10, 8), (22, 1), (3, 3), (15, 1), (12, 23), (12, 0), (0, 12), (21, 13), (14, 1), (3, 20), (12, 27), (6, 12), (4, 13), (20, 8), (10, 21), (16, 15), (8, 5), (9, 1), (6, 16), (0, 1), (10, 10), (12, 17), (22, 17), (18, 19), (5, 1), (3, 21), (5, 4), (0, 23), (5, 17), (21, 26), (9, 6), (9, 12), (11, 21), (1, 22), (14, 19), (16, 11), (2, 18), (23, 20), (2, 19), (2, 5), (2, 20), (23, 17), (12, 13), (21, 10), (13, 0), (13, 8), (11, 18), (1, 8), (1, 12), (20, 22), (11, 9), (10, 14), (1, 20), (16, 26), (17, 22), (3, 11), (14, 0), (24, 11), (18, 11), (6, 4), (0, 10), (11, 5), (9, 9), (2, 8), (3, 7), (14, 26), (4, 24), (13, 26), (13, 2), (9, 7), (24, 6), (20, 9), (10, 7), (7, 7), (14, 4), (1, 16), (17, 20), (17, 17), (4, 23), (9, 23), (15, 24), (8, 17), (3, 19), (14, 8), (6, 14), (3, 8), (18, 7), (1, 18), (23, 15), (14, 10), (18, 5), (7, 11), (18, 21), (1, 25), (14, 11), (7, 13), (2, 22), (2, 15), (15, 4), (0, 22), (1, 7), (5, 22), (8, 24), (5, 21), (9, 17), (24, 24), (18, 10), (2, 27), (0, 13), (23, 8), (24, 1), (3, 25), (10, 11), (0, 4), (21, 18), (10, 2), (23, 16), (15, 17), (9, 13), (20, 12), (4, 11), (22, 20), (4, 6), (16, 4), (14, 3), (17, 6), (7, 4), (19, 10), (4, 20), (13, 18), (2, 10), (7, 23), (7, 5), (19, 11), (6, 26), (16, 21), (5, 7), (15, 14), (5, 25), (10, 19), (19, 21), (16, 8), (16, 6), (12, 6), (17, 19), (22, 13), (11, 19), (22, 26), (7, 21), (2, 11), (7, 22), (20, 19), (19, 16), (22, 10), (8, 20), (23, 3), (0, 18), (12, 4), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448840", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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, 10), (14, 16), (13, 10), (16, 9), (3, 4), (7, 20), (19, 15), (9, 12), (18, 14), (3, 5), (2, 7), (11, 17), (5, 12), (17, 9), (10, 18), (17, 0), (12, 18), (2, 10), (18, 17), (19, 10), (19, 1), (5, 2), (6, 2), (8, 15), (15, 14), (11, 21), (8, 11), (0, 5), (0, 14), (20, 4), (19, 4), (11, 16), (3, 1), (1, 5), (16, 21), (14, 17), (3, 0), (1, 2), (15, 15), (14, 19), (10, 2), (6, 0), (16, 18), (11, 19), (2, 4), (9, 10), (9, 17), (16, 14), (3, 11), (0, 1), (16, 16), (0, 16), (2, 13), (4, 15), (11, 15), (7, 4), (9, 20), (3, 8), (1, 13), (11, 8), (12, 20), (13, 14), (0, 13), (15, 6), (20, 3), (2, 14), (11, 4), (13, 11), (19, 0), (19, 6), (1, 21), (1, 17), (4, 7), (10, 19), (8, 1), (6, 3), (12, 7), (14, 8), (4, 0), (1, 18), (15, 4), (2, 18), (8, 12), (15, 16), (15, 7), (5, 8), (14, 1), (12, 17), (9, 1), (6, 15), (13, 15), (6, 5), (7, 11), (10, 1), (8, 18), (20, 17), (15, 12), (10, 4), (20, 13), (18, 11), (5, 1), (19, 13), (19, 2), (18, 0), (9, 11), (20, 1), (15, 1), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590928", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), 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), (22, 19), (9, 0), (14, 22), (5, 19), (21, 12), (27, 12), (17, 0), (10, 19), (17, 1), (11, 12), (8, 1), (1, 0), (4, 18), (2, 22), (24, 24), (20, 8), (17, 10), (14, 15), (24, 20), (26, 13), (23, 22), (26, 22), (4, 23), (17, 17), (11, 9), (22, 22), (12, 0), (14, 0), (20, 3), (3, 12), (22, 25), (25, 10), (23, 24), (13, 25), (18, 21), (4, 21), (4, 0), (16, 15), (23, 23), (3, 21), (15, 12), (23, 15), (5, 21), (8, 15), (11, 21), (0, 15), (8, 14), (24, 23), (8, 10), (2, 0), (11, 0), (21, 3), (8, 16), (14, 25), (16, 10), (11, 7), (4, 9), (15, 10), (14, 19), (9, 17), (20, 15), (27, 13), (16, 22), (4, 20), (22, 7), (25, 9), (7, 3), (19, 15), (11, 5), (27, 17), (11, 22), (20, 23), (6, 11), (21, 4), (1, 3), (15, 20), (10, 10), (1, 9), (9, 6), (5, 7), (24, 0), (1, 12), (12, 11), (5, 5), (26, 21), (25, 15), (20, 5), (0, 18), (17, 16), (21, 9), (18, 8), (7, 18), (0, 3), (15, 2), (14, 21), (11, 20), (20, 6), (19, 9), (24, 3), (8, 0), (1, 22), (8, 8), (26, 12), (12, 2), (10, 0), (14, 9), (27, 16), (4, 5), (10, 17), (1, 17), (19, 11), (22, 24), (6, 20), (22, 0), (1, 10), (15, 17), (3, 24), (22, 9), (24, 9), (17, 4), (22, 5), (2, 25), (12, 16), (17, 24), (13, 5), (15, 23), (23, 21), (3, 0), (19, 1), (16, 7), (3, 19), (9, 1), (25, 16), (12, 20), (12, 15), (21, 25), (25, 5), (18, 12), (1, 20), (18, 17), (20, 20), (3, 5), (18, 24), (15, 21), (24, 2), (3, 9), (19, 6), (13, 17), (7, 21), (16, 20), (11, 19), (2, 20), (5, 9), (21, 23), (2, 17), (7, 11), (9, 16), (13, 14), (7, 7), (11, 15), (10, 21), (10, 2), (26, 17), (18, 0), (1, 15), (21, 18), (2, 8), (4, 19), (18, 22), (7, 15), (19, 21), (24, 17), (7, 0), (14, 10), (2, 7), (8, 20), (26, 15), (18, 25), (11, 2), (5, 17), (9, 18), (10, 5), (17, 8), (23, 13), (21, 14), (20, 0), (23, 9), (25, 17), (21, 13), (1, 23), (5, 10), (21, 0), (25, 6), (23, 25), (4, 3), (7, 20), (26, 24), (8, 17), (27, 19), (17, 22), (16, 14), (24, 21), (20, 4), (0, 10), (10, 4), (9, 13), (23, 2), (25, 21), (2, 24), (23, 14), (22, 1), (27, 2), (17, 20), (21, 7), (26, 8), (19, 10), (17, 21), (18, 2), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934794", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 19), (19, 5), (12, 19), (9, 19), (4, 10), (18, 5), (13, 0), (8, 21), (9, 6), (16, 14), (4, 2), (19, 14), (1, 7), (14, 21), (17, 9), (12, 8), (2, 4), (5, 11), (17, 7), (2, 3), (11, 4), (15, 17), (9, 13), (0, 12), (5, 4), (11, 15), (18, 8), (17, 23), (1, 23), (9, 14), (3, 19), (7, 13), (15, 5), (19, 6), (14, 23), (10, 11), (2, 16), (1, 8), (17, 8), (9, 8), (3, 16), (5, 9), (13, 23), (1, 12), (0, 5), (11, 7), (17, 22), (4, 5), (12, 16), (10, 9), (8, 6), (0, 4), (6, 18), (18, 4), (18, 3), (13, 12), (19, 3), (13, 19), (17, 4), (14, 10), (9, 12), (1, 14), (19, 7), (6, 10), (2, 6), (6, 12), (19, 1), (10, 13), (19, 11), (12, 14), (16, 10), (12, 12), (19, 15), (7, 1), (11, 16), (6, 3), (12, 1), (7, 5), (9, 22), (7, 9), (8, 11), (7, 0), (5, 0), (7, 14), (2, 7), (0, 11), (0, 3), (7, 12), (8, 18), (3, 21), (15, 7), (8, 5), (7, 21), (9, 5), (1, 1), (6, 22), (13, 5), (6, 2), (8, 0), (6, 14), (0, 10), (9, 0), (15, 22), (12, 0), (6, 21), (1, 9), (9, 2), (13, 18), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941390", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 24), (1, 14), (3, 19), (10, 12), (4, 24), (4, 4), (16, 20), (6, 8), (0, 23), (4, 10), (9, 20), (5, 2), (19, 22), (0, 12), (4, 21), (8, 18), (16, 2), (7, 5), (4, 12), (17, 4), (4, 6), (3, 23), (6, 4), (13, 3), (10, 25), (0, 5), (6, 5), (5, 8), (12, 16), (12, 22), (16, 11), (5, 7), (7, 11), (10, 23), (3, 13), (6, 20), (8, 14), (10, 22), (0, 13), (0, 2), (3, 15), (17, 2), (19, 11), (5, 20), (12, 2), (7, 18), (4, 9), (18, 5), (14, 12), (14, 19), (7, 25), (7, 14), (12, 26), (2, 7), (15, 12), (0, 25), (18, 7), (15, 24), (1, 12), (7, 23), (16, 22), (3, 8), (19, 20), (9, 11), (7, 9), (11, 2), (6, 12), (10, 16), (4, 25), (10, 15), (12, 4), (17, 13), (15, 14), (2, 16), (10, 21), (7, 6), (2, 15), (5, 10), (1, 18), (3, 11), (10, 17), (2, 3), (1, 25), (0, 11), (5, 0), (15, 19), (5, 13), (4, 2), (11, 10), (11, 3), (14, 25), (3, 5), (9, 6), (2, 1), (19, 1), (7, 24), (10, 2), (8, 6), (7, 4), (17, 17), (5, 5), (5, 21), (1, 3), (18, 1), (15, 15), (15, 10), (13, 25), (4, 0), (17, 24), (13, 23), (13, 22), (14, 14), (10, 0), (11, 19), (11, 4), (13, 20), (2, 20), (0, 10), (8, 10), (1, 24), (12, 25), (16, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "790452", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (25, 6), (8, 2), (8, 8), (15, 11), (12, 17), (11, 4), (7, 17), (17, 14), (24, 3), (4, 8), (0, 4), (6, 8), (8, 11), (8, 14), (5, 0), (24, 4), (26, 14), (26, 3), (14, 10), (15, 20), (14, 12), (1, 14), (23, 14), (5, 17), (14, 13), (1, 11), (3, 7), (9, 11), (3, 6), (26, 16), (9, 10), (21, 3), (6, 13), (20, 12), (4, 9), (14, 18), (1, 17), (13, 17), (11, 10), (0, 11), (9, 19), (7, 9), (9, 15), (9, 2), (10, 8), (25, 7), (17, 3), (22, 13), (16, 20), (1, 10), (13, 14), (16, 3), (23, 10), (25, 12), (24, 6), (2, 6), (2, 4), (1, 12), (26, 5), (8, 3), (15, 14), (2, 15), (21, 12), (4, 3), (19, 18), (10, 2), (0, 2), (25, 5), (6, 14), (14, 11), (7, 5), (24, 16), (9, 5), (18, 1), (8, 5), (15, 9), (17, 10), (7, 1), (20, 19), (26, 19), (11, 16), (23, 13), (0, 19), (23, 4), (6, 3), (5, 20), (16, 8), (8, 7), (20, 18), (23, 19), (12, 0), (2, 16), (17, 2), (21, 9), (14, 19), (11, 19), (18, 16), (3, 0), (3, 13), (9, 18), (1, 6), (10, 6), (17, 12), (4, 4), (22, 5), (19, 19), (25, 17), (3, 20), (12, 8), (15, 16), (19, 9), (12, 11), (7, 11), (23, 12), (5, 13), (15, 0), (12, 7), (19, 5), (25, 9), (1, 1), (19, 0), (14, 3), (14, 5), (26, 7), (22, 15), (5, 19), (21, 10), (5, 1), (20, 4), (18, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978540", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 17), (21, 22), (9, 16), (4, 25), (4, 13), (2, 24), (1, 5), (16, 8), (6, 10), (12, 7), (24, 9), (1, 1), (22, 21), (16, 6), (17, 27), (25, 26), (2, 4), (22, 11), (12, 26), (27, 14), (10, 12), (27, 3), (11, 3), (12, 20), (11, 20), (19, 27), (2, 16), (18, 6), (5, 2), (22, 16), (5, 8), (12, 0), (27, 12), (17, 24), (24, 0), (20, 10), (17, 26), (21, 16), (4, 16), (3, 9), (19, 10), (10, 3), (27, 13), (1, 8), (23, 12), (10, 4), (8, 23), (9, 26), (7, 6), (23, 22), (1, 6), (0, 26), (0, 25), (11, 19), (8, 18), (2, 25), (24, 1), (23, 10), (4, 26), (6, 20), (24, 21), (3, 27), (8, 13), (15, 0), (21, 4), (10, 23), (12, 1), (4, 22), (21, 11), (24, 10), (20, 22), (7, 25), (20, 24), (7, 4), (7, 27), (13, 24), (20, 9), (1, 18), (9, 22), (4, 4), (9, 11), (11, 11), (5, 5), (6, 18), (20, 12), (10, 21), (16, 18), (11, 0), (7, 19), (10, 16), (18, 24), (3, 17), (20, 5), (24, 17), (21, 8), (8, 8), (11, 23), (10, 7), (11, 2), (19, 4), (10, 18), (14, 13), (7, 9), (9, 5), (13, 20), (21, 10), (25, 23), (20, 3), (21, 12), (6, 26), (6, 2), (25, 27), (15, 15), (4, 18), (21, 25), (24, 8), (6, 23), (25, 8), (10, 13), (16, 11), (22, 8), (12, 25), (13, 5), (4, 6), (15, 11), (7, 1), (15, 7), (16, 12), (22, 23), (1, 17), (9, 1), (2, 9), (4, 24), (12, 13), (9, 19), (5, 12), (11, 26), (22, 2), (0, 13), (9, 20), (12, 12), (17, 18), (0, 22), (26, 8), (24, 14), (22, 18), (11, 22), (24, 5), (13, 3), (9, 13), (9, 25), (12, 14), (13, 19), (19, 1), (1, 15), (11, 12), (6, 1), (12, 8), (8, 20), (3, 2), (18, 11), (25, 2), (1, 12), (5, 20), (13, 2), (15, 13), (3, 25), (27, 9), (1, 16), (16, 7), (13, 1), (8, 19), (12, 15), (15, 3), (27, 21), (17, 14), (21, 23), (12, 21), (23, 16), (8, 2), (14, 27), (24, 16), (9, 27), (17, 5), (2, 18), (4, 15), (10, 27), (6, 15), (10, 19), (16, 21), (27, 18), (2, 1), (4, 12), (10, 8), (13, 27), (3, 12), (19, 7), (16, 2), (22, 1), (5, 16), (19, 17), (13, 17), (23, 4), (15, 5), (24, 7), (22, 3), (14, 23), (19, 25), (7, 8), (20, 14), (20, 2), (3, 8), (3, 22), (0, 14), (8, 7), (9, 15), (13, 8), (22, 9), (2, 22), (10, 20), (5, 3), (16, 27), (2, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966816", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), 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), (7, 3), (26, 20), (3, 4), (7, 9), (20, 22), (19, 3), (25, 1), (21, 19), (11, 18), (8, 22), (0, 7), (16, 15), (22, 0), (13, 3), (13, 5), (19, 0), (10, 5), (17, 12), (8, 12), (17, 9), (11, 17), (4, 4), (6, 15), (19, 2), (15, 19), (20, 7), (1, 2), (9, 14), (13, 15), (20, 17), (16, 16), (26, 21), (24, 23), (14, 21), (16, 20), (12, 21), (17, 17), (24, 1), (22, 16), (3, 13), (16, 4), (9, 23), (3, 0), (25, 15), (11, 12), (27, 5), (1, 4), (25, 19), (3, 11), (12, 13), (13, 14), (6, 0), (21, 23), (6, 4), (4, 9), (24, 17), (13, 1), (23, 14), (8, 10), (6, 8), (13, 6), (5, 23), (26, 5), (23, 10), (17, 20), (10, 2), (14, 6), (1, 3), (10, 17), (19, 8), (2, 6), (2, 18), (3, 8), (2, 21), (13, 13), (23, 2), (11, 20), (11, 19), (19, 4), (6, 6), (22, 15), (8, 15), (7, 18), (10, 9), (7, 10), (14, 3), (27, 4), (19, 7), (7, 12), (18, 16), (5, 2), (6, 7), (9, 18), (24, 6), (13, 18), (17, 8), (21, 4), (11, 5), (25, 17), (24, 4), (7, 5), (10, 6), (15, 3), (12, 22), (19, 22), (18, 11), (26, 16), (3, 9), (25, 8), (2, 23), (17, 15), (23, 8), (24, 8), (22, 2), (3, 7), (17, 22), (0, 14), (25, 23), (6, 22), (19, 13), (15, 22), (21, 6), (0, 18), (11, 15), (16, 7), (4, 12), (15, 0), (6, 2), (26, 12), (21, 14), (19, 12), (7, 0), (21, 10), (23, 9), (12, 10), (27, 8), (8, 4), (8, 6), (25, 18), (21, 20), (20, 14), (15, 1), (18, 17), (18, 21), (18, 2), (12, 12), (16, 23), (20, 13), (1, 14), (26, 15), (3, 2), (24, 11), (16, 9), (5, 3), (18, 19), (18, 12), (18, 15), (5, 14), (23, 20), (13, 11), (15, 16), (27, 0), (3, 15), (10, 0), (18, 9), (25, 12), (6, 19), (6, 1), (11, 3), (20, 15), (22, 9), (8, 3), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394812", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), 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), (10, 15), (11, 2), (21, 14), (24, 0), (22, 15), (24, 19), (22, 4), (25, 3), (4, 0), (16, 7), (25, 14), (12, 11), (12, 13), (19, 5), (16, 16), (15, 13), (14, 1), (18, 11), (22, 18), (17, 5), (19, 7), (7, 14), (10, 20), (18, 16), (2, 13), (25, 15), (16, 17), (14, 22), (2, 9), (23, 19), (8, 20), (0, 4), (21, 17), (13, 11), (12, 22), (21, 2), (11, 12), (25, 10), (4, 5), (7, 1), (1, 13), (22, 7), (6, 19), (3, 13), (19, 16), (17, 4), (4, 11), (6, 21), (3, 15), (23, 10), (17, 9), (23, 14), (13, 9), (20, 1), (25, 6), (20, 8), (16, 21), (16, 10), (2, 20), (23, 18), (6, 5), (25, 19), (10, 22), (5, 19), (7, 22), (2, 17), (2, 2), (12, 3), (24, 18), (10, 10), (21, 1), (25, 5), (14, 16), (20, 21), (24, 9), (20, 17), (2, 18), (23, 13), (15, 20), (14, 7), (1, 9), (18, 1), (18, 14), (2, 12), (6, 16), (23, 17), (3, 18), (2, 0), (12, 20), (24, 2), (15, 6), (22, 22), (18, 17), (17, 3), (16, 15), (2, 5), (21, 16), (8, 3), (24, 16), (12, 12), (10, 14), (16, 13), (4, 1), (25, 11), (15, 10), (23, 6), (4, 22), (18, 2), (6, 13), (17, 1), (25, 9), (24, 15), (6, 4), (19, 20), (14, 3), (2, 11), (24, 1), (2, 19), (6, 2), (8, 18), (3, 5), (4, 6), (25, 16), (19, 3), (19, 9), (12, 16), (3, 1), (22, 12), (11, 4), (6, 6), (5, 3), (5, 21), (1, 10), (21, 9), (5, 20), (4, 8), (15, 11), (7, 16), (17, 12), (22, 2), (16, 19), (8, 22), (5, 18), (12, 15), (14, 20), (20, 13), (20, 9), (11, 20), (0, 15), (1, 8), (20, 2), (10, 7), (23, 11), (5, 11), (0, 22), (20, 5), (5, 0), (17, 20), (25, 4), (1, 17), (14, 9), (18, 3), (10, 19), (18, 21), (11, 22), (22, 3), (7, 21), (11, 18), (22, 21), (25, 18), (8, 16), (13, 22), (14, 6), (23, 16), (9, 9), (14, 18), (17, 13), (21, 21), (6, 3), (5, 2), (15, 22), (16, 18), (7, 19), (7, 15), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "639408", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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), (0, 5), (11, 16), (6, 6), (17, 19), (10, 12), (10, 20), (8, 17), (1, 15), (3, 13), (11, 21), (15, 7), (15, 1), (6, 20), (0, 15), (12, 5), (8, 1), (11, 17), (17, 6), (9, 6), (20, 13), (0, 4), (9, 15), (11, 10), (8, 2), (3, 0), (14, 8), (4, 9), (5, 17), (8, 15), (11, 1), (0, 1), (0, 3), (18, 13), (12, 17), (17, 11), (5, 10), (18, 7), (2, 1), (16, 0), (5, 13), (2, 19), (4, 1), (14, 2), (7, 5), (15, 2), (11, 15), (13, 12), (9, 20), (18, 0), (20, 15), (16, 16), (9, 12), (7, 3), (20, 3), (1, 10), (5, 2), (7, 20), (13, 5), (4, 8), (8, 13), (16, 13), (12, 14), (4, 2), (12, 3), (8, 12), (2, 0), (8, 8), (11, 8), (7, 14), (19, 4), (9, 21), (6, 11), (0, 20), (13, 18), (20, 6), (15, 11), (15, 13), (11, 4), (5, 8), (19, 15), (14, 21), (17, 18), (3, 19), (14, 15), (19, 8), (3, 20), (19, 13), (20, 10), (1, 6), (0, 13), (8, 19), (4, 18), (12, 15), (2, 11), (14, 19), (14, 12), (7, 1), (15, 4), (10, 13), (16, 21), (6, 13), (19, 21), (10, 2), (3, 2), (16, 10), (16, 3), (2, 16), (13, 15), (5, 21), (10, 10), (5, 16), (2, 12), (2, 13), (9, 17), (2, 6), (3, 15), (3, 21), (1, 13), (12, 21), (17, 17), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865524", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (16, 11), (16, 17), (10, 14), (6, 13), (20, 2), (21, 20), (6, 0), (1, 11), (16, 6), (10, 16), (21, 10), (0, 20), (11, 7), (7, 4), (6, 5), (14, 20), (4, 5), (19, 0), (12, 20), (19, 18), (22, 7), (0, 4), (16, 10), (0, 9), (11, 9), (4, 19), (19, 2), (21, 6), (11, 19), (10, 19), (18, 20), (11, 3), (5, 20), (22, 15), (4, 15), (22, 18), (2, 15), (6, 3), (14, 2), (17, 15), (15, 2), (21, 16), (11, 18), (14, 19), (22, 9), (18, 19), (3, 9), (8, 6), (14, 4), (10, 7), (12, 0), (6, 18), (3, 5), (10, 15), (4, 8), (19, 12), (9, 16), (18, 3), (22, 4), (1, 7), (13, 3), (19, 19), (7, 7), (9, 5), (15, 19), (2, 10), (7, 9), (20, 8), (15, 4), (21, 15), (4, 9), (14, 15), (16, 0), (11, 14), (9, 19), (14, 10), (5, 6), (22, 0), (1, 5), (15, 0), (17, 14), (2, 18), (12, 5), (1, 13), (12, 9), (1, 19), (11, 17), (1, 1), (3, 6), (18, 17), (20, 7), (11, 10), (6, 2), (21, 17), (19, 9), (18, 2), (8, 9), (20, 9), (2, 19), (13, 13), (5, 2), (8, 19), (12, 6), (13, 10), (1, 9), (22, 10), (16, 16), (14, 17), (0, 1), (2, 6), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "582712", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 25), (9, 16), (7, 5), (14, 10), (25, 18), (5, 23), (24, 17), (3, 3), (12, 7), (16, 26), (3, 26), (4, 2), (26, 3), (0, 21), (24, 9), (25, 25), (15, 22), (4, 20), (7, 26), (13, 4), (5, 2), (12, 26), (8, 6), (10, 4), (9, 12), (22, 26), (5, 12), (8, 26), (11, 13), (23, 10), (0, 27), (15, 8), (18, 9), (20, 0), (2, 5), (15, 28), (10, 0), (18, 3), (1, 25), (19, 22), (8, 15), (22, 24), (21, 24), (19, 25), (2, 24), (15, 4), (11, 27), (6, 0), (15, 13), (4, 14), (5, 18), (9, 24), (6, 2), (24, 15), (12, 0), (24, 23), (21, 11), (25, 14), (3, 16), (25, 19), (18, 19), (14, 20), (5, 28), (20, 26), (7, 8), (22, 16), (17, 0), (13, 10), (8, 23), (17, 26), (7, 2), (19, 5), (9, 11), (1, 8), (13, 6), (15, 23), (26, 14), (20, 11), (19, 15), (11, 17), (18, 17), (8, 17), (26, 15), (9, 22), (6, 23), (25, 1), (16, 17), (22, 9), (5, 17), (12, 23), (1, 21), (10, 12), (15, 10), (7, 18), (14, 13), (3, 25), (18, 8), (1, 16), (12, 24), (4, 19), (17, 13), (13, 17), (8, 12), (5, 15), (2, 6), (17, 19), (14, 28), (15, 17), (13, 26), (9, 13), (13, 11), (15, 20), (6, 26), (23, 3), (22, 17), (21, 1), (0, 22), (5, 14), (3, 5), (16, 19), (11, 2), (25, 21), (6, 22), (19, 13), (16, 21), (1, 14), (12, 10), (22, 28), (13, 23), (7, 28), (6, 24), (24, 28), (9, 9), (15, 5), (23, 22), (5, 9), (24, 4), (15, 27), (4, 13), (26, 13), (24, 11), (14, 8), (10, 9), (7, 19), (8, 13), (11, 6), (21, 27), (14, 27), (15, 9), (8, 25), (6, 3), (11, 25), (0, 1), (24, 0), (15, 26), (19, 1), (1, 22), (5, 26), (17, 10), (4, 21), (14, 23), (2, 27), (1, 27), (2, 4), (5, 20), (8, 3), (24, 14), (23, 18), (8, 1), (19, 26), (6, 28), (14, 7), (18, 15), (25, 5), (19, 21), (17, 11), (6, 6), (3, 4), (15, 14), (15, 25), (4, 4), (2, 15), (23, 15), (5, 10), (3, 22), (15, 6), (8, 18), (3, 10), (15, 19), (10, 14), (3, 28), (17, 23), (5, 3), (3, 12), (2, 22), (20, 7), (4, 17), (23, 2), (6, 8), (19, 20), (4, 10), (25, 13), (4, 23), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587716", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 26), (21, 1), (13, 1), (1, 13), (5, 27), (8, 11), (13, 24), (0, 19), (18, 28), (17, 12), (15, 19), (11, 21), (4, 28), (10, 26), (0, 13), (12, 9), (1, 3), (10, 27), (19, 5), (20, 19), (19, 3), (8, 5), (16, 23), (10, 18), (14, 19), (13, 28), (11, 27), (11, 5), (7, 24), (16, 7), (1, 15), (1, 22), (3, 28), (14, 22), (13, 0), (17, 2), (21, 18), (9, 23), (15, 10), (17, 19), (13, 27), (4, 21), (16, 27), (21, 26), (5, 26), (6, 13), (17, 6), (17, 26), (1, 27), (6, 24), (0, 3), (4, 27), (1, 20), (15, 13), (8, 8), (8, 3), (12, 14), (20, 27), (13, 25), (3, 3), (19, 12), (14, 10), (10, 14), (0, 14), (14, 17), (8, 6), (16, 3), (8, 16), (2, 14), (2, 11), (5, 24), (21, 27), (10, 23), (2, 2), (10, 22), (4, 16), (21, 14), (8, 24), (3, 1), (5, 6), (12, 4), (19, 15), (8, 9), (16, 20), (1, 6), (0, 8), (5, 21), (2, 18), (7, 16), (19, 23), (13, 7), (9, 8), (9, 25), (14, 26), (1, 28), (1, 11), (3, 17), (11, 14), (18, 4), (3, 15), (9, 14), (11, 2), (18, 15), (10, 3), (4, 6), (12, 8), (9, 15), (17, 25), (21, 3), (10, 21), (9, 11), (2, 19), (17, 1), (3, 23), (0, 15), (20, 22), (5, 15), (3, 5), (16, 24), (18, 7), (17, 3), (16, 0), (9, 6), (1, 14), (13, 23), (15, 7), (3, 6), (19, 10), (17, 10), (3, 19), (11, 6), (8, 25), (7, 23), (12, 15), (16, 8), (8, 4), (19, 25), (1, 7), (10, 6), (15, 18), (6, 1), (17, 15), (12, 18), (15, 12), (2, 12), (9, 18), (4, 20), (4, 8), (4, 15), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "652650", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (6, 8), (1, 8), (5, 14), (9, 23), (4, 4), (14, 7), (9, 24), (11, 19), (2, 15), (9, 20), (2, 10), (3, 7), (16, 12), (4, 5), (14, 22), (15, 8), (8, 13), (3, 22), (0, 8), (3, 19), (15, 20), (19, 6), (10, 7), (8, 1), (0, 13), (8, 16), (11, 20), (19, 0), (7, 10), (15, 18), (4, 19), (13, 8), (12, 13), (13, 17), (10, 23), (2, 0), (11, 16), (15, 2), (8, 20), (10, 22), (16, 4), (16, 23), (6, 9), (20, 21), (13, 22), (17, 14), (12, 5), (18, 22), (13, 11), (13, 16), (14, 23), (5, 22), (18, 12), (20, 10), (8, 5), (12, 20), (20, 0), (17, 5), (14, 24), (18, 5), (0, 14), (13, 4), (2, 9), (11, 15), (2, 3), (7, 1), (12, 18), (16, 3), (9, 7), (12, 19), (17, 24), (17, 0), (10, 12), (7, 11), (7, 21), (19, 20), (9, 10), (10, 2), (11, 6), (9, 2), (5, 2), (3, 8), (12, 6), (7, 13), (20, 14), (6, 13), (13, 10), (4, 20), (9, 25), (11, 8), (14, 20), (6, 4), (5, 5), (14, 17), (0, 5), (20, 18), (4, 2), (9, 4), (19, 23), (16, 24), (4, 18), (13, 9), (1, 21), (15, 19), (7, 14), (19, 22), (8, 14), (9, 9), (11, 22), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553729", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), 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), (6, 6), (5, 6), (10, 2), (14, 8), (20, 14), (15, 15), (25, 18), (14, 15), (20, 17), (21, 14), (22, 17), (11, 7), (19, 1), (18, 21), (20, 12), (27, 3), (14, 20), (0, 13), (9, 3), (22, 12), (27, 0), (26, 20), (15, 9), (1, 0), (13, 2), (25, 3), (11, 21), (11, 13), (11, 4), (22, 1), (17, 2), (19, 7), (3, 21), (3, 13), (19, 10), (10, 23), (27, 17), (11, 6), (24, 0), (8, 23), (4, 11), (25, 13), (1, 19), (0, 10), (11, 23), (1, 13), (1, 5), (13, 18), (4, 17), (12, 9), (13, 19), (12, 7), (27, 11), (6, 14), (23, 10), (21, 11), (21, 9), (21, 20), (8, 19), (14, 21), (7, 11), (20, 2), (22, 15), (6, 13), (1, 10), (19, 23), (17, 1), (27, 16), (21, 7), (13, 20), (15, 21), (26, 13), (27, 23), (27, 20), (13, 5), (20, 9), (27, 15), (12, 21), (2, 23), (27, 10), (23, 5), (19, 22), (10, 18), (24, 22), (20, 15), (0, 21), (6, 5), (13, 10), (18, 10), (21, 21), (14, 7), (7, 24), (18, 12), (15, 17), (25, 20), (13, 15), (8, 17), (4, 6), (25, 10), (23, 7), (7, 21), (8, 20), (15, 10), (21, 4), (4, 20), (17, 6), (5, 14), (9, 10), (17, 22), (18, 7), (4, 12), (1, 24), (3, 3), (18, 1), (21, 18), (13, 22), (25, 0), (4, 10), (25, 1), (7, 14), (11, 24), (5, 3), (5, 9), (9, 2), (9, 4), (14, 22), (27, 1), (17, 18), (12, 11), (19, 4), (21, 10), (7, 18), (22, 16), (24, 7), (20, 18), (14, 12), (11, 11), (26, 12), (1, 8), (21, 17), (4, 2), (26, 16), (10, 14), (27, 5), (9, 24), (18, 11), (3, 1), (22, 8), (1, 7), (6, 17), (6, 7), (24, 12), (12, 17), (10, 19), (5, 22), (15, 0), (21, 5), (0, 4), (22, 13), (24, 21), (27, 14), (13, 9), (4, 7), (15, 20), (18, 18), (24, 16), (10, 11), (23, 11), (7, 12), (9, 20), (20, 21), (26, 6), (16, 18), (26, 2), (5, 16), (26, 10), (26, 15), (16, 14), (25, 6), (22, 24), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884880", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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, 14), (9, 1), (8, 1), (6, 5), (18, 0), (15, 20), (13, 17), (15, 17), (13, 16), (1, 12), (5, 18), (3, 14), (11, 12), (12, 5), (19, 4), (2, 13), (12, 3), (9, 15), (16, 19), (14, 5), (14, 3), (17, 13), (1, 8), (13, 18), (5, 7), (12, 19), (10, 14), (19, 5), (18, 8), (0, 5), (0, 13), (14, 15), (12, 12), (11, 14), (9, 16), (4, 6), (15, 2), (1, 14), (1, 11), (11, 5), (2, 8), (4, 5), (5, 14), (9, 10), (18, 11), (1, 2), (0, 11), (14, 11), (10, 15), (19, 10), (14, 8), (16, 11), (2, 20), (3, 0), (5, 8), (8, 15), (7, 13), (6, 18), (13, 7), (5, 10), (3, 7), (3, 9), (9, 17), (18, 5), (3, 11), (8, 5), (15, 4), (16, 20), (10, 3), (14, 6), (6, 6), (7, 12), (15, 9), (1, 5), (13, 5), (2, 19), (7, 7), (16, 9), (5, 6), (9, 3), (18, 4), (17, 4), (6, 11), (8, 16), (11, 3), (2, 1), (6, 17), (9, 13), (4, 19), (12, 7), (17, 15), (1, 20), (1, 4), (10, 2), (7, 18), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980838", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 13), (9, 2), (15, 7), (15, 4), (4, 4), (9, 24), (2, 23), (13, 13), (8, 25), (9, 18), (13, 23), (17, 10), (13, 21), (17, 16), (6, 19), (14, 16), (5, 6), (16, 0), (2, 24), (17, 2), (9, 14), (10, 14), (7, 7), (10, 6), (0, 14), (17, 9), (13, 0), (18, 7), (17, 18), (12, 15), (17, 3), (15, 11), (4, 13), (3, 7), (10, 15), (19, 16), (11, 25), (18, 2), (13, 15), (2, 12), (15, 14), (15, 21), (11, 0), (1, 13), (2, 22), (18, 0), (2, 15), (17, 14), (1, 10), (2, 20), (3, 3), (9, 10), (1, 7), (16, 22), (9, 6), (3, 9), (0, 2), (7, 4), (18, 20), (12, 17), (13, 8), (18, 8), (7, 23), (4, 17), (9, 22), (11, 3), (19, 20), (0, 23), (17, 5), (0, 12), (4, 3), (11, 5), (15, 24), (0, 6), (12, 3), (0, 8), (5, 10), (13, 19), (16, 9), (15, 0), (8, 9), (0, 16), (11, 12), (16, 2), (7, 6), (2, 2), (4, 23), (17, 13), (3, 11), (5, 2), (3, 17), (6, 20), (18, 13), (12, 6), (19, 7), (12, 2), (2, 14), (10, 4), (1, 21), (4, 24), (12, 8), (4, 25), (6, 4), (13, 6), (9, 0), (10, 1), (15, 12), (6, 13), (11, 10), (16, 17), (1, 19), (10, 17), (4, 10), (19, 3), (10, 20), (7, 20), (8, 13), (18, 19), (15, 9), (1, 8), (14, 1), (8, 15), (12, 14), (12, 24), (8, 24), (17, 22), (14, 20), (19, 0), (2, 8), (7, 5), (10, 5), (15, 20), (11, 6), (11, 18), (13, 24), (13, 4), (7, 18), (17, 8), (3, 14), (1, 5), (19, 17), (18, 3), (19, 10), (14, 6), (19, 5), (8, 17), (19, 18), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "938280", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 17), (2, 18), (27, 16), (6, 14), (1, 28), (19, 7), (21, 3), (12, 28), (25, 26), (18, 17), (2, 11), (3, 10), (12, 7), (26, 20), (0, 18), (14, 1), (7, 23), (19, 2), (1, 9), (12, 16), (24, 4), (0, 4), (1, 2), (0, 16), (14, 18), (6, 9), (11, 18), (2, 9), (15, 24), (9, 21), (22, 27), (11, 3), (13, 25), (14, 24), (17, 2), (26, 27), (17, 11), (23, 6), (26, 1), (9, 24), (10, 14), (26, 18), (12, 12), (3, 8), (11, 1), (22, 4), (8, 16), (16, 23), (18, 9), (17, 24), (7, 4), (23, 0), (15, 11), (11, 25), (8, 21), (18, 25), (14, 26), (1, 10), (12, 9), (24, 17), (26, 6), (15, 10), (25, 16), (11, 11), (19, 1), (6, 20), (19, 10), (2, 4), (5, 28), (20, 7), (14, 27), (26, 23), (19, 16), (14, 15), (27, 21), (11, 21), (25, 6), (18, 1), (20, 3), (25, 12), (10, 22), (6, 2), (5, 23), (18, 24), (8, 9), (20, 2), (4, 19), (18, 0), (27, 13), (16, 7), (22, 15), (6, 24), (10, 15), (24, 0), (11, 15), (20, 4), (25, 11), (0, 3), (14, 6), (2, 15), (20, 22), (8, 14), (1, 26), (4, 4), (6, 17), (7, 25), (5, 5), (8, 18), (17, 3), (19, 8), (16, 28), (9, 4), (7, 26), (15, 9), (1, 14), (2, 0), (18, 13), (0, 22), (9, 26), (22, 0), (27, 15), (3, 16), (21, 14), (14, 28), (23, 8), (25, 22), (5, 25), (10, 17), (24, 19), (16, 13), (6, 13), (26, 13), (0, 10), (27, 27), (2, 7), (0, 14), (6, 11), (4, 0), (14, 4), (7, 7), (8, 15), (21, 24), (2, 27), (24, 14), (1, 20), (3, 11), (23, 11), (4, 3), (9, 10), (12, 17), (2, 16), (6, 18), (16, 20), (9, 18), (26, 4), (12, 23), (23, 9), (13, 23), (14, 22), (4, 6), (22, 2), (17, 23), (5, 17), (16, 19), (13, 20), (25, 0), (8, 27), (17, 6), (0, 15), (4, 5), (10, 3), (16, 24), (1, 7), (21, 27), (5, 19), (1, 21), (4, 10), (3, 0), (10, 12), (17, 8), (10, 16), (1, 24), (27, 25), (12, 2), (25, 10), (22, 23), (21, 16), (16, 26), (3, 17), (18, 14), (21, 19), (15, 14), (12, 24), (20, 21), (17, 5), (13, 1), (27, 8), (23, 4), (27, 1), (20, 0), (2, 6), (10, 8), (19, 26), (12, 22), (27, 14), (10, 6), (19, 24), (26, 17), (10, 5), (3, 15), (25, 9), (27, 18), (20, 18), (17, 9), (4, 9), (3, 12), (0, 5), (3, 19), (7, 1), (23, 16), (0, 7), (12, 20), (6, 8), (12, 15), (8, 12), (11, 27), (12, 13), (2, 3), (8, 23), (25, 20), (17, 22), (17, 26), (19, 3), (4, 16), (13, 11), (2, 5), (12, 6), (18, 16), (27, 2), (9, 5), (26, 7), (22, 24), (12, 4), (8, 13), (15, 22), (11, 22), (25, 19), (1, 4), (8, 0), (0, 28), (7, 17), (10, 28), (0, 17), (13, 2), (23, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904320", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), 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), (16, 6), (10, 13), (1, 4), (15, 18), (14, 12), (9, 0), (21, 8), (2, 2), (7, 3), (20, 18), (6, 13), (17, 1), (3, 9), (22, 9), (1, 19), (13, 11), (13, 6), (9, 12), (10, 10), (16, 13), (7, 11), (10, 2), (25, 18), (6, 20), (5, 3), (5, 19), (1, 8), (10, 0), (10, 11), (18, 17), (2, 20), (11, 15), (20, 14), (1, 10), (10, 9), (9, 4), (14, 18), (22, 17), (11, 20), (16, 5), (13, 9), (12, 7), (14, 3), (24, 18), (7, 9), (10, 19), (0, 5), (18, 3), (14, 14), (20, 6), (2, 17), (2, 1), (16, 17), (3, 14), (9, 7), (0, 13), (4, 7), (23, 3), (10, 14), (0, 20), (3, 2), (24, 15), (7, 1), (19, 5), (2, 9), (14, 8), (23, 17), (8, 19), (6, 16), (10, 20), (16, 9), (4, 18), (0, 10), (13, 16), (2, 19), (8, 3), (10, 4), (12, 17), (0, 12), (2, 8), (9, 1), (4, 2), (14, 6), (6, 10), (11, 9), (7, 6), (3, 19), (14, 10), (14, 2), (10, 16), (22, 0), (18, 5), (18, 16), (4, 10), (18, 1), (12, 14), (18, 11), (14, 1), (25, 14), (24, 0), (23, 6), (7, 16), (14, 0), (9, 19), (21, 19), (5, 10), (25, 19), (17, 18), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648264", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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), (18, 11), (13, 0), (4, 11), (6, 0), (8, 17), (9, 11), (16, 3), (19, 10), (19, 15), (23, 1), (22, 13), (12, 16), (6, 2), (3, 19), (19, 4), (4, 7), (8, 7), (24, 5), (19, 7), (24, 19), (19, 1), (22, 5), (2, 17), (15, 6), (5, 15), (2, 9), (22, 15), (13, 15), (2, 13), (3, 8), (4, 9), (21, 0), (8, 3), (11, 10), (2, 11), (0, 7), (0, 13), (13, 12), (0, 17), (7, 4), (18, 20), (23, 11), (5, 9), (15, 14), (13, 3), (3, 11), (9, 4), (15, 5), (15, 17), (7, 8), (10, 6), (11, 6), (23, 19), (9, 14), (24, 13), (4, 4), (10, 15), (24, 18), (23, 2), (21, 15), (3, 6), (13, 20), (16, 13), (2, 10), (21, 8), (15, 8), (24, 12), (20, 19), (15, 12), (22, 0), (10, 19), (9, 17), (17, 0), (17, 4), (15, 2), (20, 3), (6, 4), (12, 18), (10, 11), (17, 8), (18, 12), (16, 19), (14, 12), (9, 3), (2, 7), (6, 9), (21, 16), (3, 13), (11, 19), (20, 12), (18, 0), (3, 1), (9, 19), (2, 15), (21, 2), (10, 0), (10, 12), (6, 11), (8, 14), (24, 17), (21, 19), (2, 2), (2, 16), (10, 18), (7, 18), (10, 13), (4, 20), (17, 20), (18, 16), (14, 15), (15, 13), (13, 5), (4, 3), (20, 16), (8, 13), (22, 6), (10, 14), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992352", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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), (21, 15), (13, 13), (10, 2), (8, 6), (23, 15), (2, 2), (10, 10), (17, 20), (19, 17), (6, 2), (10, 6), (3, 17), (23, 7), (20, 17), (16, 2), (7, 12), (23, 6), (6, 13), (4, 3), (1, 2), (3, 11), (0, 3), (22, 20), (1, 19), (15, 8), (14, 6), (17, 10), (13, 0), (23, 16), (13, 19), (2, 9), (5, 13), (6, 7), (14, 1), (5, 14), (21, 13), (19, 13), (21, 12), (4, 14), (22, 16), (22, 8), (5, 20), (16, 20), (15, 4), (19, 9), (12, 11), (10, 0), (14, 17), (17, 0), (0, 8), (5, 4), (8, 8), (21, 5), (13, 3), (0, 14), (4, 15), (23, 17), (11, 11), (9, 19), (11, 0), (3, 5), (17, 4), (1, 12), (8, 2), (13, 6), (1, 6), (6, 12), (5, 15), (9, 15), (13, 17), (12, 2), (14, 11), (3, 18), (2, 0), (7, 2), (11, 1), (16, 5), (21, 18), (5, 9), (18, 10), (19, 15), (3, 2), (10, 17), (15, 11), (21, 6), (10, 7), (10, 14), (10, 12), (15, 16), (20, 10), (2, 6), (7, 17), (19, 7), (2, 18), (6, 8), (9, 6), (8, 1), (21, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "957232", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 17), (20, 15), (3, 1), (9, 9), (14, 14), (17, 3), (19, 15), (21, 6), (25, 9), (14, 16), (22, 3), (11, 5), (25, 7), (0, 11), (22, 10), (4, 13), (27, 19), (12, 6), (10, 13), (5, 3), (4, 19), (4, 6), (9, 7), (25, 2), (13, 8), (26, 16), (26, 10), (21, 19), (9, 19), (28, 19), (6, 13), (25, 3), (0, 17), (21, 1), (28, 18), (10, 16), (12, 1), (13, 5), (3, 16), (4, 11), (24, 7), (3, 11), (15, 10), (22, 1), (15, 14), (14, 4), (24, 20), (14, 5), (28, 6), (11, 11), (8, 12), (18, 11), (25, 19), (8, 8), (11, 1), (4, 4), (22, 11), (17, 20), (13, 10), (17, 5), (14, 20), (23, 17), (8, 1), (6, 14), (5, 17), (7, 7), (2, 19), (23, 2), (9, 18), (2, 15), (22, 19), (11, 8), (12, 4), (22, 9), (13, 14), (7, 18), (16, 21), (12, 17), (22, 16), (0, 3), (28, 12), (23, 6), (12, 16), (14, 0), (6, 18), (10, 11), (10, 21), (19, 19), (7, 19), (8, 3), (20, 18), (17, 12), (23, 7), (16, 14), (5, 21), (23, 12), (7, 8), (26, 0), (8, 5), (27, 6), (24, 2), (27, 8), (20, 13), (23, 4), (13, 15), (15, 2), (12, 14), (23, 18), (20, 20), (20, 10), (6, 5), (14, 7), (20, 12), (25, 15), (16, 4), (10, 20), (16, 13), (8, 13), (25, 13), (27, 10), (9, 0), (0, 18), (5, 18), (5, 10), (3, 2), (3, 18), (2, 12), (7, 15), (10, 4), (0, 20), (3, 15), (17, 17), (7, 20), (25, 6), (22, 17), (5, 14), (11, 7), (4, 5), (5, 6), (28, 15), (14, 3), (8, 2), (12, 2), (1, 21), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362028", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), 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, 19), (26, 10), (4, 23), (20, 22), (22, 19), (6, 4), (24, 12), (22, 17), (14, 18), (22, 13), (19, 8), (8, 11), (10, 7), (9, 23), (12, 14), (9, 9), (20, 15), (25, 6), (18, 17), (24, 19), (2, 4), (20, 9), (19, 22), (17, 19), (7, 21), (25, 0), (15, 0), (19, 12), (13, 5), (4, 1), (10, 11), (14, 13), (17, 1), (13, 10), (5, 9), (18, 5), (13, 6), (9, 8), (5, 1), (8, 13), (0, 16), (21, 12), (11, 17), (21, 7), (17, 17), (27, 22), (27, 23), (4, 7), (27, 2), (9, 16), (15, 7), (20, 16), (26, 19), (12, 8), (20, 14), (8, 18), (15, 19), (4, 15), (28, 19), (22, 4), (10, 22), (2, 22), (28, 9), (5, 23), (16, 19), (1, 5), (27, 3), (2, 7), (20, 1), (12, 6), (11, 2), (0, 12), (1, 4), (19, 7), (25, 1), (7, 20), (7, 18), (5, 8), (24, 20), (27, 11), (8, 2), (24, 1), (14, 23), (20, 6), (28, 10), (2, 11), (17, 2), (14, 7), (20, 20), (23, 19), (3, 23), (26, 23), (14, 14), (13, 21), (11, 0), (18, 3), (4, 9), (2, 10), (22, 6), (0, 17), (4, 21), (28, 16), (27, 9), (26, 9), (7, 22), (11, 12), (1, 15), (22, 21), (13, 0), (15, 18), (8, 10), (12, 10), (4, 16), (24, 11), (3, 12), (25, 5), (19, 5), (24, 18), (5, 13), (18, 20), (13, 20), (11, 8), (23, 5), (5, 21), (17, 13), (20, 5), (28, 11), (23, 17), (3, 3), (16, 4), (24, 15), (5, 7), (18, 2), (6, 12), (21, 14), (8, 1), (2, 2), (4, 17), (21, 9), (6, 13), (12, 9), (19, 10), (13, 17), (25, 16), (3, 2), (19, 14), (7, 5), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185372", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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), (6, 9), (2, 7), (17, 3), (9, 21), (16, 4), (20, 0), (7, 20), (8, 2), (0, 9), (18, 2), (3, 21), (10, 0), (2, 4), (18, 10), (4, 15), (14, 17), (18, 7), (10, 7), (2, 14), (11, 16), (16, 19), (6, 0), (16, 21), (17, 6), (4, 12), (0, 2), (1, 9), (1, 3), (11, 19), (12, 13), (6, 21), (17, 12), (18, 8), (7, 12), (15, 3), (14, 10), (9, 0), (12, 7), (2, 13), (3, 2), (15, 8), (16, 12), (2, 20), (9, 9), (16, 20), (15, 20), (8, 9), (11, 17), (6, 15), (15, 18), (12, 19), (14, 14), (16, 17), (1, 4), (10, 3), (4, 7), (5, 11), (4, 9), (2, 15), (20, 5), (10, 16), (14, 0), (6, 8), (6, 4), (17, 7), (13, 17), (1, 11), (2, 12), (14, 9), (9, 14), (17, 1), (7, 19), (4, 20), (5, 7), (20, 11), (8, 12), (5, 4), (18, 20), (5, 9), (19, 10), (0, 17), (2, 17), (2, 16), (16, 7), (5, 15), (0, 7), (4, 11), (12, 21), (6, 6), (17, 15), (11, 13), (10, 18), (18, 19), (0, 1), (19, 17), (7, 1), (14, 2), (20, 9), (5, 14), (19, 19), (5, 3), (7, 11), (19, 15), (5, 18), (11, 2), (20, 4), (10, 8), (20, 16), (12, 10), (18, 0), (3, 15), (8, 17), (10, 17), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766902", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 11), (21, 10), (12, 17), (4, 14), (0, 4), (14, 0), (6, 9), (20, 10), (11, 0), (17, 8), (13, 0), (24, 12), (6, 19), (22, 3), (22, 11), (17, 15), (12, 3), (8, 13), (1, 22), (19, 11), (3, 4), (17, 6), (9, 9), (12, 12), (11, 14), (4, 23), (6, 17), (7, 16), (20, 20), (6, 11), (10, 5), (22, 13), (22, 24), (24, 20), (21, 1), (10, 14), (4, 20), (13, 17), (13, 2), (3, 15), (19, 21), (11, 21), (14, 14), (16, 16), (19, 1), (3, 10), (20, 17), (9, 8), (2, 22), (2, 5), (16, 4), (1, 0), (17, 22), (18, 18), (9, 4), (22, 15), (8, 1), (19, 8), (20, 2), (15, 12), (11, 8), (5, 5), (16, 11), (19, 7), (6, 0), (18, 10), (1, 5), (18, 23), (10, 19), (17, 13), (12, 20), (16, 23), (14, 9), (4, 10), (13, 24), (13, 19), (25, 21), (19, 10), (19, 0), (1, 17), (14, 3), (1, 19), (14, 10), (21, 12), (22, 19), (25, 18), (7, 24), (5, 20), (10, 4), (24, 6), (10, 16), (9, 0), (1, 23), (5, 3), (24, 16), (4, 8), (1, 24), (17, 18), (20, 21), (21, 15), (2, 18), (5, 16), (2, 14), (23, 24), (0, 11), (25, 22), (23, 18), (7, 22), (12, 0), (19, 2), (19, 15), (14, 15), (19, 5), (9, 1), (5, 11), (23, 17), (4, 2), (18, 4), (18, 14), (17, 5), (25, 12), (12, 9), (8, 5), (5, 18), (5, 4), (0, 10), (8, 0), (14, 20), (2, 17), (8, 3), (5, 6), (5, 2), (24, 7), (2, 10), (14, 24), (18, 17), (13, 21), (21, 24), (14, 4), (21, 17), (0, 24), (24, 8), (6, 8), (21, 0), (13, 16), (20, 19), (4, 13), (25, 9), (18, 19), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708852", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 10), (7, 17), (12, 15), (3, 23), (2, 17), (13, 9), (26, 8), (8, 14), (17, 6), (15, 11), (11, 12), (8, 15), (11, 16), (11, 9), (18, 23), (15, 19), (3, 0), (18, 0), (23, 12), (7, 13), (17, 0), (16, 4), (5, 3), (8, 23), (11, 13), (9, 11), (4, 16), (23, 2), (5, 21), (5, 11), (9, 19), (24, 13), (20, 14), (17, 21), (0, 12), (0, 21), (15, 5), (26, 12), (16, 18), (4, 2), (16, 7), (0, 11), (23, 3), (25, 15), (24, 8), (26, 21), (18, 2), (23, 22), (8, 6), (19, 20), (24, 6), (20, 15), (4, 5), (3, 12), (4, 3), (19, 8), (2, 14), (26, 3), (8, 12), (5, 4), (25, 16), (21, 14), (18, 21), (11, 17), (10, 1), (25, 12), (14, 20), (24, 15), (8, 11), (16, 16), (23, 18), (15, 6), (15, 7), (9, 22), (18, 14), (10, 11), (1, 19), (21, 8), (11, 11), (22, 14), (14, 1), (17, 13), (16, 5), (5, 12), (22, 0), (25, 13), (14, 3), (15, 10), (2, 16), (22, 22), (21, 20), (4, 22), (13, 6), (18, 12), (14, 23), (12, 16), (17, 7), (22, 9), (15, 15), (23, 4), (0, 8), (24, 9), (5, 8), (14, 11), (21, 10), (21, 11), (13, 2), (9, 20), (19, 10), (6, 15), (26, 16), (23, 1), (21, 18), (3, 16), (5, 2), (6, 6), (11, 22), (19, 19), (24, 17), (26, 13), (2, 20), (6, 7), (25, 0), (19, 0), (16, 15), (22, 1), (3, 5), (18, 13), (9, 2), (17, 5), (15, 18), (6, 5), (14, 7), (9, 8), (2, 13), (26, 10), (15, 16), (24, 3), (7, 3), (13, 11), (0, 23), (24, 16), (6, 9), (11, 2), (7, 2), (6, 3), (8, 9), (9, 15), (16, 0), (6, 2), (10, 2), (19, 9), (5, 16), (25, 18), (20, 0), (16, 6), (9, 16), (9, 21), (18, 4), (16, 8), (19, 5), (19, 21), (14, 16), (24, 7), (16, 23), (15, 20), (26, 22), (1, 10), (15, 23), (7, 15), (1, 22), (7, 21), (2, 10), (21, 2), (17, 1), (10, 5), (4, 6), (19, 4), (9, 6), (3, 9), (8, 18), (23, 21), (13, 4), (13, 23), (2, 7), (1, 17), (3, 4), (24, 0), (6, 17), (21, 1), (14, 17), (25, 11), (14, 21), (24, 18), (13, 10), (15, 21), (21, 7), (25, 7), (18, 18), (16, 22), (3, 11), (26, 4), (14, 2), (9, 5), (10, 15), (22, 5), (24, 10), (17, 8), (1, 11), (4, 7), (4, 18), (22, 4), (3, 20), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647055", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), 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), (3, 4), (11, 1), (1, 20), (11, 20), (4, 6), (5, 2), (5, 21), (5, 9), (14, 9), (14, 8), (9, 7), (12, 19), (11, 5), (19, 5), (1, 19), (15, 20), (4, 3), (15, 9), (13, 9), (6, 10), (9, 14), (21, 19), (3, 20), (4, 7), (17, 1), (14, 6), (18, 0), (1, 12), (9, 20), (12, 1), (15, 11), (8, 18), (15, 14), (6, 19), (4, 12), (8, 2), (8, 12), (4, 1), (14, 15), (0, 16), (21, 14), (8, 17), (12, 15), (20, 19), (13, 6), (1, 10), (17, 6), (9, 0), (14, 17), (18, 19), (7, 5), (15, 13), (4, 14), (14, 13), (11, 8), (7, 10), (14, 11), (20, 20), (3, 16), (10, 0), (0, 11), (19, 1), (1, 4), (21, 0), (13, 15), (18, 15), (15, 16), (15, 18), (8, 6), (0, 21), (3, 8), (16, 6), (20, 17), (21, 20), (16, 2), (7, 9), (2, 0), (1, 7), (15, 4), (17, 21), (17, 3), (7, 13), (10, 10), (15, 17), (12, 0), (10, 18), (12, 21), (12, 18), (7, 18), (16, 1), (11, 10), (5, 4), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "788770", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (21, 6), (17, 15), (0, 9), (8, 5), (16, 7), (8, 3), (14, 16), (20, 3), (4, 9), (20, 5), (14, 18), (0, 12), (6, 12), (3, 3), (0, 19), (23, 14), (6, 2), (21, 13), (1, 3), (6, 4), (3, 7), (17, 14), (0, 11), (24, 0), (23, 20), (4, 1), (16, 6), (5, 5), (14, 2), (10, 12), (16, 16), (16, 5), (11, 5), (2, 17), (17, 6), (22, 17), (15, 16), (16, 18), (16, 12), (15, 10), (13, 1), (25, 5), (9, 11), (19, 7), (9, 1), (20, 6), (26, 8), (5, 1), (20, 10), (24, 5), (5, 12), (24, 11), (12, 16), (11, 11), (21, 1), (13, 18), (11, 9), (26, 16), (6, 7), (7, 16), (1, 0), (20, 16), (7, 12), (7, 19), (6, 14), (9, 5), (18, 20), (19, 20), (14, 1), (16, 14), (15, 0), (25, 10), (18, 17), (13, 3), (3, 10), (13, 16), (3, 18), (0, 4), (3, 6), (17, 3), (26, 4), (11, 12), (13, 6), (9, 16), (19, 15), (17, 10), (1, 13), (5, 2), (22, 1), (23, 2), (15, 12), (17, 18), (13, 11), (4, 16), (2, 10), (14, 7), (20, 1), (0, 10), (8, 1), (17, 17), (17, 16), (20, 20), (10, 0), (6, 5), (17, 2), (11, 1), (1, 18), (6, 8), (11, 19), (4, 10), (12, 0), (25, 4), (7, 3), (18, 5), (23, 3), (11, 13), (2, 20), (1, 15), (0, 7), (1, 9), (17, 1), (15, 18), (8, 2), (23, 19), (16, 20), (22, 3), (0, 18), (12, 6), (18, 11), (8, 14), (22, 2), (11, 6), (24, 6), (9, 9), (20, 2), (8, 18), (24, 15), (5, 20), (20, 13), (10, 7), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41664", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 21), (20, 7), (20, 5), (19, 20), (12, 24), (12, 12), (19, 27), (11, 3), (8, 27), (11, 18), (3, 10), (11, 8), (10, 19), (20, 27), (2, 14), (19, 1), (9, 14), (14, 24), (9, 22), (0, 3), (4, 23), (4, 26), (6, 22), (13, 27), (20, 8), (13, 3), (20, 26), (19, 10), (17, 5), (9, 24), (3, 16), (13, 19), (18, 17), (5, 18), (4, 22), (16, 0), (6, 2), (15, 22), (13, 5), (12, 0), (1, 24), (12, 9), (3, 20), (17, 4), (6, 14), (9, 18), (9, 5), (7, 15), (2, 24), (3, 15), (8, 20), (1, 13), (18, 16), (3, 25), (18, 11), (17, 10), (3, 27), (13, 25), (13, 17), (11, 25), (9, 11), (18, 10), (10, 18), (14, 23), (4, 2), (11, 19), (0, 25), (17, 26), (1, 18), (13, 9), (1, 2), (17, 0), (6, 28), (8, 3), (13, 26), (10, 17), (18, 5), (11, 12), (21, 20), (21, 23), (8, 13), (4, 11), (14, 3), (15, 17), (19, 21), (0, 21), (11, 20), (6, 23), (12, 10), (10, 11), (17, 13), (1, 28), (21, 19), (2, 27), (4, 14), (16, 15), (1, 8), (5, 24), (13, 18), (13, 8), (18, 7), (0, 11), (12, 8), (18, 21), (12, 19), (7, 21), (8, 12), (3, 3), (14, 11), (1, 26), (16, 25), (10, 5), (2, 28), (1, 10), (18, 15), (11, 6), (6, 24), (5, 23), (21, 11), (8, 6), (21, 9), (18, 6), (16, 21), (17, 8), (10, 2), (14, 4), (1, 17), (18, 13), (9, 4), (5, 4), (0, 15), (21, 24), (12, 7), (13, 6), (17, 3), (19, 12), (11, 22), (13, 22), (11, 11), (6, 17), (17, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78144", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 16), (2, 21), (11, 25), (13, 5), (11, 28), (12, 1), (17, 26), (6, 23), (10, 25), (5, 26), (0, 9), (7, 28), (10, 13), (9, 17), (14, 4), (7, 10), (11, 11), (6, 3), (3, 12), (6, 8), (19, 27), (14, 14), (8, 2), (12, 19), (11, 16), (4, 26), (13, 9), (0, 14), (15, 7), (4, 0), (16, 25), (15, 12), (17, 27), (12, 3), (0, 28), (16, 19), (7, 20), (7, 13), (8, 27), (2, 26), (17, 25), (15, 8), (13, 12), (13, 24), (4, 3), (9, 25), (13, 11), (11, 5), (11, 26), (19, 2), (12, 23), (16, 1), (1, 8), (12, 28), (11, 19), (11, 22), (16, 21), (16, 0), (6, 12), (0, 6), (14, 24), (8, 16), (9, 24), (1, 18), (10, 10), (8, 8), (17, 0), (6, 2), (15, 10), (19, 8), (1, 24), (0, 5), (13, 17), (13, 25), (11, 24), (10, 7), (17, 12), (3, 16), (1, 1), (10, 22), (8, 1), (14, 0), (18, 14), (2, 25), (6, 6), (9, 10), (15, 21), (3, 20), (2, 19), (3, 7), (2, 4), (15, 14), (5, 14), (9, 19), (10, 17), (13, 19), (1, 19), (19, 5), (12, 5), (18, 18), (1, 28), (18, 23), (18, 24), (2, 15), (4, 2), (15, 4), (1, 6), (12, 6), (14, 26), (5, 0), (3, 13), (2, 11), (8, 11), (18, 13), (7, 5), (9, 23), (18, 9), (5, 6), (17, 16), (8, 22), (7, 15), (5, 28), (12, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780384", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 22), (3, 25), (1, 15), (22, 13), (11, 12), (14, 6), (3, 9), (7, 1), (10, 8), (11, 3), (11, 10), (23, 13), (1, 13), (14, 4), (10, 24), (10, 13), (14, 11), (9, 10), (18, 8), (2, 28), (11, 20), (13, 21), (5, 21), (11, 0), (16, 5), (17, 25), (14, 24), (8, 4), (11, 2), (12, 4), (14, 23), (16, 12), (16, 15), (12, 27), (3, 21), (9, 28), (21, 28), (23, 16), (22, 27), (21, 17), (22, 17), (19, 2), (0, 10), (16, 10), (18, 9), (1, 24), (4, 16), (2, 26), (21, 10), (3, 1), (19, 14), (19, 16), (0, 20), (10, 6), (5, 23), (20, 19), (15, 8), (9, 11), (14, 28), (5, 10), (4, 1), (0, 28), (11, 23), (11, 19), (6, 5), (1, 1), (9, 14), (11, 1), (4, 21), (20, 14), (13, 28), (20, 4), (8, 2), (10, 11), (17, 26), (12, 26), (14, 21), (18, 7), (18, 2), (22, 0), (15, 5), (16, 26), (16, 1), (21, 25), (0, 13), (14, 10), (7, 24), (18, 22), (23, 17), (15, 3), (7, 26), (1, 20), (0, 6), (20, 26), (8, 24), (21, 27), (0, 14), (4, 7), (8, 19), (12, 7), (20, 0), (22, 19), (16, 6), (3, 10), (18, 14), (13, 22), (18, 3), (13, 25), (5, 14), (0, 8), (3, 23), (21, 6), (15, 27), (4, 9), (5, 12), (8, 11), (16, 0), (21, 3), (13, 19), (8, 15), (1, 19), (4, 20), (2, 11), (21, 22), (6, 4), (7, 0), (20, 28), (14, 27), (17, 21), (13, 16), (9, 19), (11, 25), (4, 11), (6, 28), (9, 0), (22, 11), (21, 9), (10, 0), (19, 5), (23, 11), (22, 2), (23, 15), (1, 14), (12, 19), (13, 27), (22, 5), (15, 17), (22, 7), (8, 21), (18, 13), (21, 12), (23, 19), (8, 20), (17, 28), (1, 3), (21, 23), (11, 8), (0, 11), (23, 14), (15, 28), (9, 9), (9, 24), (9, 23), (7, 4), (1, 5), (19, 25), (16, 20), (14, 13), (16, 28), (6, 26), (6, 17), (15, 10), (17, 4), (23, 1), (17, 27), (5, 28), (6, 27), (20, 7), (19, 11), (8, 9), (7, 19), (16, 2), (7, 11), (15, 25), (22, 22), (8, 1), (4, 28), (19, 0), (16, 3), (21, 24), (13, 14), (6, 15), (16, 23), (9, 17), (19, 12), (20, 1), (3, 17), (1, 7), (14, 3), (10, 5), (8, 3), (16, 11), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696870", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 10), (10, 10), (16, 18), (3, 11), (4, 2), (12, 4), (12, 2), (4, 19), (2, 10), (0, 10), (17, 5), (6, 12), (10, 18), (21, 2), (19, 6), (9, 15), (3, 16), (19, 3), (7, 17), (4, 1), (5, 12), (12, 0), (22, 8), (7, 10), (18, 12), (22, 14), (11, 15), (16, 14), (7, 18), (12, 7), (15, 2), (18, 0), (9, 16), (17, 4), (10, 8), (14, 10), (16, 7), (3, 13), (2, 14), (19, 18), (4, 4), (8, 0), (18, 16), (21, 12), (3, 19), (0, 16), (13, 6), (1, 19), (13, 5), (11, 2), (2, 19), (18, 9), (11, 3), (20, 7), (3, 18), (14, 17), (14, 18), (5, 10), (14, 2), (3, 10), (20, 8), (15, 13), (1, 16), (12, 13), (16, 11), (3, 2), (7, 1), (5, 3), (13, 3), (18, 11), (19, 5), (7, 3), (2, 9), (22, 2), (18, 10), (20, 5), (17, 1), (10, 9), (3, 8), (13, 7), (19, 13), (22, 13), (10, 3), (0, 19), (22, 17), (15, 4), (17, 12), (14, 13), (22, 18), (4, 6), (0, 6), (15, 17), (11, 14), (1, 0), (19, 7), (12, 5), (18, 5), (22, 12), (14, 8), (9, 5), (10, 13), (8, 14), (20, 12), (18, 19), (22, 9), (13, 12), (0, 17), (12, 17), (5, 9), (7, 9), (4, 10), (16, 9), (19, 19), (20, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570318", "dataset": "MATH"}
{"messages": [{"content": "In a 25x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 9), (13, 16), (10, 15), (3, 8), (8, 16), (19, 20), (22, 21), (3, 5), (9, 5), (6, 5), (3, 11), (7, 7), (10, 12), (10, 20), (3, 20), (23, 17), (16, 3), (22, 19), (12, 21), (23, 10), (12, 19), (7, 14), (9, 12), (21, 6), (6, 22), (6, 21), (21, 12), (17, 0), (16, 11), (24, 6), (19, 6), (5, 1), (8, 12), (18, 6), (2, 3), (14, 10), (9, 1), (15, 2), (0, 10), (15, 20), (23, 4), (3, 21), (17, 21), (19, 9), (17, 16), (10, 16), (8, 18), (5, 19), (18, 11), (0, 1), (19, 3), (24, 4), (21, 22), (14, 21), (14, 16), (7, 22), (12, 12), (22, 18), (23, 9), (18, 19), (16, 19), (22, 2), (4, 14), (14, 8), (7, 15), (0, 15), (2, 19), (10, 5), (21, 0), (15, 7), (20, 19), (14, 18), (21, 5), (11, 3), (3, 14), (10, 10), (12, 7), (14, 5), (13, 17), (14, 12), (13, 1), (5, 8), (2, 8), (17, 1), (17, 2), (8, 17), (22, 13), (17, 14), (16, 10), (23, 7), (7, 20), (13, 21), (6, 3), (12, 14), (7, 5), (21, 2), (8, 22), (9, 10), (9, 15), (17, 7), (11, 16), (0, 13), (0, 5), (20, 10), (24, 11), (7, 17), (7, 12), (18, 8), (1, 18), (13, 20), (3, 18), (24, 16), (13, 11), (24, 21), (6, 20), (0, 6), (2, 22), (14, 7), (2, 14), (4, 12), (13, 7), (12, 9), (5, 14), (18, 17), (2, 0), (21, 11), (15, 8), (24, 0), (16, 12), (14, 13), (16, 20), (20, 11), (18, 5), (16, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616359", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 15), (2, 20), (11, 9), (7, 4), (9, 20), (18, 14), (17, 14), (8, 9), (1, 17), (10, 5), (4, 17), (0, 12), (21, 0), (21, 4), (0, 7), (16, 14), (5, 3), (11, 13), (19, 15), (21, 3), (20, 21), (4, 14), (5, 20), (15, 22), (21, 19), (18, 20), (10, 1), (13, 17), (12, 6), (1, 15), (3, 7), (13, 5), (17, 11), (11, 4), (17, 3), (10, 17), (20, 9), (22, 9), (9, 0), (6, 4), (10, 9), (10, 18), (5, 10), (11, 16), (4, 20), (6, 3), (21, 12), (10, 20), (23, 14), (1, 8), (21, 17), (7, 12), (16, 19), (7, 18), (4, 8), (11, 17), (19, 11), (19, 8), (5, 9), (21, 20), (12, 22), (0, 14), (6, 22), (15, 5), (4, 10), (19, 19), (11, 1), (14, 2), (0, 4), (6, 20), (1, 20), (12, 19), (9, 12), (15, 12), (15, 21), (21, 15), (14, 18), (1, 7), (9, 14), (2, 1), (21, 9), (14, 7), (8, 13), (21, 21), (3, 22), (9, 1), (18, 4), (0, 20), (17, 18), (10, 0), (11, 7), (10, 8), (13, 4), (5, 1), (6, 5), (7, 14), (4, 21), (6, 9), (6, 21), (10, 14), (22, 16), (12, 20), (6, 11), (20, 17), (23, 10), (14, 16), (16, 13), (13, 2), (8, 0), (5, 5), (22, 20), (9, 15), (15, 16), (15, 7), (9, 17), (1, 12), (15, 18), (19, 22), (7, 13), (0, 15), (10, 10), (2, 6), (15, 4), (19, 20), (18, 10), (23, 7), (11, 5), (8, 21), (1, 22), (20, 4), (4, 7), (22, 1), (18, 8), (13, 9), (2, 4), (15, 14), (22, 3), (16, 20), (22, 10), (18, 3), (15, 11), (16, 6), (6, 15), (9, 13), (12, 0), (8, 2), (2, 19), (16, 0), (2, 13), (23, 13), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590400", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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), (14, 8), (7, 5), (18, 5), (10, 5), (13, 12), (13, 18), (0, 19), (20, 12), (4, 2), (18, 20), (10, 11), (17, 8), (16, 1), (20, 11), (19, 15), (7, 16), (0, 7), (5, 6), (2, 3), (2, 18), (20, 3), (2, 19), (6, 18), (21, 19), (0, 13), (21, 14), (1, 0), (2, 10), (11, 10), (19, 4), (4, 10), (5, 20), (1, 5), (5, 9), (5, 5), (19, 11), (15, 16), (13, 4), (13, 17), (7, 19), (6, 3), (16, 7), (7, 3), (10, 14), (18, 15), (21, 17), (4, 5), (12, 4), (15, 19), (11, 15), (9, 6), (9, 17), (18, 9), (17, 12), (14, 19), (0, 17), (10, 16), (18, 10), (21, 9), (6, 12), (3, 3), (6, 6), (5, 2), (3, 6), (11, 12), (2, 0), (4, 3), (21, 15), (7, 9), (8, 17), (2, 6), (9, 3), (10, 1), (21, 4), (16, 3), (18, 7), (13, 13), (20, 0), (14, 3), (4, 0), (7, 14), (10, 4), (17, 4), (21, 1), (20, 18), (0, 18), (19, 8), (0, 12), (20, 8), (15, 2), (19, 2), (19, 20), (7, 13), (7, 20), (16, 8), (5, 16), (18, 1), (13, 1), (18, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814477", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), 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), (25, 11), (9, 0), (6, 0), (10, 3), (14, 26), (5, 23), (17, 26), (12, 18), (8, 2), (25, 6), (24, 20), (3, 6), (8, 17), (7, 21), (0, 6), (8, 9), (11, 16), (25, 22), (1, 16), (13, 8), (13, 14), (25, 0), (4, 18), (14, 13), (7, 17), (8, 24), (15, 1), (8, 11), (16, 20), (5, 13), (3, 5), (23, 13), (11, 1), (22, 19), (3, 1), (16, 5), (12, 15), (10, 1), (12, 22), (20, 2), (1, 13), (1, 2), (23, 15), (16, 1), (16, 17), (16, 3), (12, 3), (5, 24), (12, 7), (25, 13), (11, 17), (21, 14), (18, 15), (9, 6), (13, 9), (5, 3), (8, 5), (3, 19), (21, 23), (15, 17), (18, 10), (23, 20), (7, 3), (17, 6), (3, 24), (14, 0), (14, 25), (25, 8), (24, 15), (19, 24), (22, 26), (7, 18), (10, 24), (9, 15), (7, 19), (25, 17), (11, 11), (7, 13), (5, 6), (14, 18), (4, 24), (2, 18), (14, 22), (18, 9), (13, 12), (23, 14), (6, 14), (10, 4), (22, 5), (16, 7), (10, 13), (22, 4), (19, 25), (2, 10), (23, 21), (16, 0), (2, 14), (15, 24), (16, 19), (16, 6), (2, 3), (25, 25), (23, 6), (6, 13), (9, 26), (9, 19), (14, 15), (1, 25), (4, 14), (2, 9), (19, 9), (2, 8), (19, 7), (4, 8), (8, 25), (12, 10), (7, 10), (9, 7), (23, 3), (16, 18), (6, 6), (21, 19), (24, 12), (0, 25), (20, 9), (13, 1), (21, 2), (5, 10), (15, 8), (3, 16), (24, 18), (10, 6), (13, 21), (9, 22), (3, 11), (8, 13), (16, 12), (13, 20), (3, 17), (8, 14), (8, 18), (20, 3), (21, 18), (10, 12), (18, 25), (3, 25), (24, 19), (7, 4), (17, 10), (4, 4), (3, 7), (4, 6), (8, 12), (16, 10), (3, 12), (8, 0), (22, 24), (3, 2), (9, 5), (15, 23), (25, 15), (1, 26), (20, 7), (25, 21), (10, 22), (22, 18), (15, 22), (2, 26), (14, 12), (17, 4), (7, 14), (22, 0), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77490", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), 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, 19), (9, 6), (23, 3), (7, 18), (21, 16), (6, 19), (1, 4), (12, 21), (15, 10), (17, 22), (2, 21), (23, 15), (16, 20), (0, 17), (23, 19), (16, 15), (8, 19), (9, 10), (4, 12), (5, 19), (16, 2), (20, 15), (9, 11), (23, 5), (13, 20), (19, 1), (6, 9), (0, 5), (4, 16), (15, 22), (11, 13), (23, 0), (13, 17), (12, 18), (19, 13), (8, 17), (12, 3), (11, 10), (23, 11), (11, 2), (18, 12), (9, 4), (9, 21), (5, 3), (11, 16), (13, 0), (3, 1), (3, 2), (10, 16), (10, 4), (14, 22), (4, 18), (19, 20), (0, 14), (17, 3), (15, 11), (17, 2), (9, 1), (13, 6), (1, 15), (5, 1), (19, 8), (1, 1), (20, 12), (4, 9), (21, 12), (5, 15), (21, 19), (12, 8), (13, 9), (17, 13), (18, 14), (17, 8), (6, 3), (23, 16), (4, 15), (4, 11), (3, 22), (18, 18), (17, 1), (18, 16), (6, 18), (21, 18), (12, 1), (12, 4), (3, 5), (16, 22), (22, 9), (7, 9), (11, 9), (14, 1), (5, 8), (12, 22), (0, 1), (9, 5), (12, 5), (12, 6), (22, 22), (5, 11), (14, 4), (1, 10), (15, 20), (4, 14), (19, 5), (19, 0), (17, 19), (12, 15), (8, 21), (13, 3), (15, 19), (18, 6), (8, 6), (20, 17), (12, 20), (0, 12), (0, 11), (17, 14), (18, 10), (13, 15), (17, 20), (14, 9), (21, 10), (20, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825132", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 8), (5, 6), (8, 4), (10, 0), (17, 14), (6, 11), (8, 16), (16, 5), (16, 11), (2, 4), (16, 15), (12, 7), (13, 9), (2, 17), (9, 19), (6, 4), (5, 9), (1, 8), (14, 8), (15, 17), (17, 9), (14, 11), (18, 10), (0, 14), (4, 15), (4, 19), (1, 13), (18, 1), (10, 2), (3, 0), (2, 0), (14, 3), (3, 6), (14, 17), (5, 14), (3, 8), (14, 16), (10, 19), (20, 12), (8, 14), (6, 8), (16, 19), (4, 3), (11, 3), (13, 4), (11, 0), (11, 19), (17, 8), (14, 20), (21, 4), (1, 5), (21, 15), (20, 13), (8, 2), (8, 20), (1, 20), (9, 0), (7, 6), (5, 10), (14, 7), (16, 8), (16, 4), (7, 5), (5, 3), (18, 20), (3, 17), (14, 4), (20, 8), (16, 13), (12, 14), (1, 3), (21, 7), (20, 2), (1, 18), (18, 11), (18, 5), (9, 16), (8, 15), (9, 1), (5, 15), (19, 13), (15, 8), (4, 16), (11, 17), (6, 18), (17, 16), (0, 6), (0, 2), (16, 12), (18, 3), (12, 9), (13, 6), (20, 20), (11, 2), (11, 14), (15, 7), (21, 5), (4, 11), (19, 14), (1, 10), (17, 4), (12, 4), (17, 19), (17, 10), (0, 10), (2, 1), (15, 5), (3, 20), (7, 11), (19, 10), (7, 18), (0, 12), (20, 18), (10, 6), (14, 9), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711328", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 24), (1, 17), (24, 8), (28, 15), (22, 2), (12, 13), (0, 22), (6, 18), (14, 26), (20, 13), (1, 0), (14, 12), (3, 1), (10, 12), (21, 13), (27, 3), (25, 27), (0, 14), (16, 9), (9, 0), (25, 17), (28, 21), (24, 23), (5, 2), (25, 3), (6, 16), (4, 12), (17, 16), (2, 10), (5, 8), (22, 1), (26, 17), (28, 26), (23, 23), (7, 26), (5, 23), (8, 10), (19, 20), (16, 5), (4, 17), (0, 11), (16, 17), (18, 25), (25, 6), (5, 7), (26, 23), (11, 5), (21, 15), (10, 3), (3, 24), (5, 11), (21, 23), (5, 3), (5, 4), (5, 15), (4, 18), (4, 4), (20, 26), (24, 4), (13, 5), (1, 15), (27, 11), (5, 22), (24, 14), (0, 13), (17, 24), (16, 26), (4, 23), (21, 17), (21, 14), (3, 23), (18, 13), (25, 7), (1, 21), (21, 20), (9, 6), (20, 10), (7, 0), (3, 19), (16, 2), (4, 2), (19, 1), (23, 9), (28, 3), (12, 21), (9, 8), (25, 0), (25, 2), (17, 7), (6, 15), (9, 20), (10, 24), (23, 2), (15, 16), (15, 5), (28, 11), (13, 10), (10, 20), (14, 21), (12, 27), (13, 24), (8, 26), (6, 0), (15, 25), (9, 26), (11, 11), (13, 6), (5, 12), (22, 13), (7, 20), (18, 26), (27, 15), (22, 21), (24, 26), (26, 6), (6, 13), (1, 5), (23, 12), (24, 17), (21, 16), (8, 0), (7, 22), (17, 21), (16, 16), (6, 20), (0, 8), (19, 8), (15, 11), (11, 15), (23, 10), (8, 20), (22, 10), (26, 1), (26, 12), (26, 27), (2, 25), (26, 3), (4, 25), (5, 20), (27, 17), (20, 8), (7, 3), (20, 5), (14, 15), (21, 27), (26, 4), (21, 8), (6, 9), (13, 3), (23, 24), (22, 14), (6, 17), (22, 15), (8, 27), (2, 7), (21, 26), (15, 20), (17, 2), (12, 20), (23, 16), (10, 9), (2, 26), (15, 18), (11, 10), (10, 4), (11, 9), (7, 27), (19, 7), (23, 22), (13, 20), (14, 0), (6, 1), (10, 0), (8, 13), (21, 1), (20, 0), (24, 22), (9, 3), (17, 15), (5, 0), (9, 11), (24, 10), (6, 7), (15, 2), (2, 11), (24, 9), (0, 18), (5, 21), (3, 22), (6, 6), (2, 17), (15, 7), (0, 3), (21, 7), (5, 10), (19, 15), (18, 27), (1, 7), (20, 18), (21, 0), (11, 17), (6, 22), (24, 13), (23, 1), (13, 14), (24, 27), (23, 14), (22, 6), (6, 2), (17, 27), (11, 22), (14, 25), (5, 9), (13, 22), (23, 17), (2, 0), (1, 24), (18, 19), (4, 5), (10, 23), (1, 10), (8, 25), (1, 12), (6, 12), (2, 15), (25, 16), (3, 14), (6, 5), (20, 1), (14, 13), (2, 24), (2, 23), (9, 25), (23, 20), (5, 13), (6, 8), (23, 27), (14, 24), (26, 24), (13, 19), (11, 2), (8, 24), (28, 0), (28, 25), (7, 7), (13, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365400", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 16), (12, 22), (19, 17), (10, 8), (4, 19), (17, 10), (5, 17), (0, 3), (5, 21), (3, 11), (7, 2), (26, 6), (20, 10), (11, 1), (26, 19), (3, 14), (5, 3), (1, 20), (17, 3), (12, 11), (17, 23), (8, 20), (15, 15), (2, 1), (9, 20), (6, 21), (2, 23), (23, 12), (24, 18), (13, 11), (22, 17), (16, 20), (7, 9), (24, 14), (15, 22), (15, 6), (2, 19), (2, 12), (23, 19), (3, 5), (17, 16), (23, 18), (5, 9), (11, 7), (0, 14), (19, 5), (21, 16), (19, 7), (25, 6), (25, 14), (3, 0), (12, 5), (6, 11), (22, 18), (6, 9), (13, 12), (8, 18), (13, 17), (11, 3), (14, 5), (0, 22), (17, 22), (16, 12), (19, 9), (14, 19), (21, 19), (8, 22), (20, 4), (21, 10), (8, 11), (15, 11), (2, 3), (24, 12), (6, 6), (17, 20), (1, 0), (15, 8), (3, 16), (20, 18), (8, 12), (11, 4), (12, 18), (26, 2), (15, 17), (23, 2), (23, 23), (6, 7), (18, 2), (23, 21), (18, 10), (0, 13), (22, 13), (21, 6), (12, 23), (20, 19), (7, 18), (5, 6), (25, 10), (0, 18), (18, 3), (5, 4), (21, 11), (7, 4), (5, 20), (5, 15), (10, 4), (16, 4), (1, 19), (11, 10), (23, 4), (6, 12), (13, 23), (12, 13), (11, 6), (13, 21), (14, 11), (9, 18), (14, 13), (23, 14), (20, 12), (3, 3), (16, 21), (16, 10), (0, 4), (4, 16), (26, 8), (19, 23), (26, 13), (6, 3), (14, 12), (10, 15), (8, 13), (21, 1), (10, 14), (8, 16), (21, 0), (20, 23), (13, 8), (7, 10), (4, 7), (4, 12), (4, 2), (18, 8), (10, 1), (7, 5), (6, 4), (23, 11), (5, 12), (0, 17), (13, 18), (24, 22), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "434448", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (4, 3), (12, 1), (15, 8), (15, 19), (10, 6), (8, 16), (7, 9), (6, 19), (8, 6), (9, 5), (3, 17), (17, 21), (15, 13), (2, 12), (14, 13), (4, 17), (13, 20), (15, 0), (4, 22), (3, 4), (15, 14), (3, 22), (9, 13), (16, 21), (7, 4), (15, 10), (10, 0), (6, 5), (21, 21), (15, 3), (6, 24), (12, 16), (6, 16), (1, 15), (16, 15), (4, 6), (10, 10), (20, 4), (7, 16), (8, 3), (16, 13), (11, 1), (19, 23), (12, 15), (4, 0), (21, 18), (18, 22), (3, 8), (16, 18), (15, 24), (6, 21), (16, 5), (21, 19), (7, 0), (1, 1), (11, 23), (1, 6), (7, 11), (9, 15), (8, 12), (18, 24), (9, 17), (7, 3), (10, 14), (17, 7), (17, 13), (20, 1), (11, 7), (10, 7), (12, 5), (1, 8), (20, 0), (14, 22), (9, 7), (3, 1), (0, 11), (13, 8), (14, 15), (9, 11), (7, 2), (9, 16), (6, 0), (13, 16), (13, 14), (17, 0), (16, 10), (4, 2), (11, 0), (20, 7), (7, 13), (0, 16), (14, 17), (13, 5), (7, 22), (13, 4), (7, 15), (19, 1), (4, 13), (8, 11), (17, 19), (7, 24), (18, 1), (17, 17), (16, 17), (5, 18), (18, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914676", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (17, 18), (17, 26), (23, 5), (15, 19), (19, 22), (17, 12), (21, 13), (12, 14), (13, 7), (4, 21), (9, 14), (14, 22), (11, 9), (3, 1), (22, 27), (19, 28), (11, 17), (3, 13), (2, 0), (6, 27), (23, 22), (19, 17), (0, 12), (5, 10), (0, 28), (5, 25), (20, 3), (19, 25), (20, 9), (5, 26), (2, 10), (21, 16), (0, 25), (17, 17), (0, 23), (13, 15), (3, 20), (21, 6), (16, 14), (4, 8), (20, 6), (21, 23), (21, 25), (8, 22), (10, 14), (7, 18), (1, 5), (9, 1), (20, 1), (11, 15), (12, 22), (12, 13), (16, 7), (17, 8), (22, 6), (18, 15), (2, 27), (11, 23), (23, 12), (12, 16), (17, 10), (1, 20), (10, 23), (22, 17), (22, 26), (12, 27), (9, 25), (1, 1), (11, 11), (22, 1), (22, 19), (13, 9), (8, 13), (8, 11), (22, 13), (2, 18), (5, 2), (22, 18), (21, 4), (20, 11), (21, 1), (18, 0), (4, 1), (15, 24), (15, 15), (4, 17), (3, 7), (0, 16), (22, 21), (16, 22), (10, 16), (21, 5), (8, 12), (20, 5), (12, 4), (16, 21), (1, 23), (12, 10), (18, 4), (6, 6), (6, 13), (9, 17), (0, 14), (17, 16), (8, 27), (16, 11), (1, 13), (11, 19), (3, 28), (23, 3), (6, 14), (16, 1), (9, 21), (14, 13), (20, 7), (14, 20), (17, 9), (21, 28), (17, 19), (11, 10), (21, 14), (19, 26), (8, 0), (19, 23), (3, 0), (19, 2), (11, 22), (14, 28), (7, 15), (23, 9), (13, 16), (0, 4), (6, 9), (12, 26), (7, 25), (12, 21), (7, 4), (18, 12), (8, 7), (4, 27), (10, 20), (10, 17), (1, 11), (7, 11), (18, 25), (17, 2), (17, 11), (1, 28), (13, 10), (1, 26), (12, 9), (5, 18), (3, 12), (13, 3), (6, 21), (21, 21), (13, 27), (16, 2), (22, 16), (4, 2), (8, 9), (12, 12), (19, 24), (18, 23), (13, 6), (9, 12), (12, 3), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25200", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), 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), (15, 18), (8, 12), (8, 5), (24, 0), (5, 5), (10, 15), (10, 11), (1, 8), (7, 8), (6, 18), (21, 18), (11, 19), (7, 0), (11, 7), (23, 4), (20, 2), (5, 2), (4, 12), (17, 15), (19, 7), (12, 9), (6, 16), (0, 10), (9, 8), (6, 10), (16, 5), (2, 5), (1, 16), (10, 4), (18, 3), (21, 4), (17, 2), (9, 7), (20, 16), (24, 1), (10, 1), (1, 12), (15, 4), (12, 12), (6, 13), (15, 17), (24, 10), (14, 17), (7, 1), (10, 17), (23, 14), (6, 4), (10, 13), (23, 18), (12, 3), (19, 17), (3, 0), (13, 2), (14, 14), (2, 9), (21, 10), (23, 17), (24, 13), (3, 4), (12, 10), (11, 5), (12, 19), (11, 4), (23, 0), (3, 15), (19, 5), (15, 0), (19, 10), (21, 1), (6, 7), (9, 0), (17, 0), (16, 7), (1, 7), (24, 14), (15, 8), (1, 5), (3, 13), (8, 10), (4, 15), (15, 2), (19, 8), (9, 12), (7, 13), (11, 18), (23, 7), (17, 8), (6, 8), (4, 0), (18, 5), (18, 0), (16, 12), (1, 14), (23, 2), (2, 17), (11, 17), (16, 14), (4, 14), (8, 19), (2, 6), (24, 9), (9, 3), (2, 2), (11, 13), (16, 18), (5, 4), (4, 10), (12, 6), (0, 16), (21, 2), (17, 6), (7, 6), (23, 10), (22, 11), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304617", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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, 17), (20, 21), (16, 11), (16, 0), (17, 12), (19, 17), (14, 12), (5, 20), (9, 22), (3, 9), (12, 4), (10, 24), (20, 8), (7, 17), (15, 8), (15, 16), (11, 18), (14, 22), (14, 24), (15, 13), (19, 24), (20, 10), (14, 11), (17, 1), (21, 20), (18, 15), (4, 7), (13, 0), (3, 2), (7, 10), (13, 10), (14, 21), (12, 14), (11, 9), (5, 2), (5, 16), (2, 4), (8, 14), (0, 7), (12, 15), (19, 10), (16, 6), (18, 1), (13, 17), (10, 1), (8, 0), (14, 16), (13, 1), (17, 3), (17, 21), (9, 19), (15, 15), (13, 21), (20, 5), (19, 23), (6, 20), (16, 2), (5, 8), (0, 24), (21, 13), (8, 15), (10, 16), (18, 7), (17, 5), (7, 22), (17, 9), (16, 3), (6, 12), (3, 4), (5, 14), (17, 2), (2, 21), (10, 10), (4, 19), (15, 4), (8, 24), (1, 21), (20, 2), (9, 11), (8, 19), (13, 5), (15, 10), (15, 0), (15, 14), (0, 4), (18, 6), (21, 11), (1, 8), (12, 2), (17, 18), (3, 13), (6, 24), (6, 8), (3, 23), (5, 11), (10, 6), (5, 19), (7, 1), (5, 22), (11, 6), (2, 16), (21, 3), (21, 21), (8, 4), (8, 23), (7, 23), (4, 4), (16, 17), (13, 13), (6, 1), (16, 18), (8, 6), (4, 15), (13, 4), (1, 23), (17, 22), (6, 10), (10, 15), (5, 7), (7, 21), (20, 14), (7, 5), (7, 2), (9, 3), (15, 24), (18, 13), (0, 21), (9, 23), (1, 4), (11, 20), (21, 10), (11, 0), (2, 14), (12, 20), (0, 9), (18, 5), (20, 17), (14, 0), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917568", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (17, 9), (8, 17), (16, 12), (0, 4), (1, 17), (3, 2), (21, 16), (22, 12), (0, 18), (12, 16), (15, 17), (0, 16), (4, 16), (21, 11), (23, 9), (18, 13), (23, 17), (23, 4), (19, 1), (4, 5), (10, 0), (18, 15), (17, 7), (3, 9), (9, 19), (15, 16), (8, 12), (19, 12), (5, 19), (23, 13), (3, 13), (5, 4), (6, 10), (14, 0), (22, 16), (22, 18), (13, 7), (8, 19), (0, 3), (20, 3), (16, 13), (19, 7), (19, 15), (15, 3), (18, 19), (7, 13), (7, 8), (17, 3), (2, 5), (9, 14), (11, 16), (11, 7), (22, 6), (1, 3), (5, 18), (5, 15), (10, 9), (21, 7), (17, 8), (11, 19), (7, 1), (17, 1), (14, 10), (18, 11), (3, 18), (8, 6), (17, 13), (1, 18), (17, 0), (22, 4), (20, 10), (10, 8), (22, 5), (18, 6), (18, 4), (2, 7), (20, 15), (15, 13), (20, 1), (20, 7), (9, 11), (8, 3), (5, 12), (0, 17), (3, 8), (20, 14), (5, 7), (14, 8), (15, 5), (2, 1), (21, 18), (12, 19), (1, 12), (23, 14), (11, 0), (15, 2), (23, 11), (14, 6), (23, 3), (6, 2), (22, 9), (7, 3), (0, 1), (6, 8), (15, 11), (3, 11), (13, 16), (10, 2), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917749", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 11), (9, 26), (18, 6), (3, 22), (1, 5), (19, 0), (13, 5), (15, 1), (0, 25), (14, 3), (20, 12), (3, 6), (4, 3), (1, 22), (6, 5), (15, 14), (10, 12), (3, 11), (6, 4), (9, 22), (15, 2), (3, 4), (12, 11), (1, 2), (21, 0), (7, 11), (12, 3), (13, 14), (7, 19), (12, 14), (2, 11), (1, 3), (16, 23), (5, 14), (20, 4), (14, 22), (21, 3), (0, 13), (15, 15), (9, 12), (9, 4), (4, 17), (6, 6), (8, 7), (20, 23), (13, 20), (4, 12), (8, 21), (12, 16), (14, 24), (10, 3), (18, 26), (4, 15), (10, 16), (3, 13), (17, 11), (14, 9), (13, 7), (10, 18), (0, 3), (15, 5), (11, 3), (4, 19), (10, 23), (16, 25), (8, 3), (9, 18), (1, 1), (12, 24), (14, 10), (9, 15), (8, 0), (8, 14), (0, 2), (0, 14), (10, 11), (19, 26), (7, 12), (3, 24), (0, 20), (18, 24), (16, 20), (21, 10), (17, 3), (4, 0), (13, 11), (8, 6), (1, 20), (14, 6), (5, 17), (0, 9), (18, 19), (12, 9), (13, 23), (5, 0), (18, 9), (7, 15), (4, 21), (11, 18), (18, 21), (19, 13), (7, 16), (19, 2), (3, 15), (7, 18), (16, 16), (11, 26), (3, 8), (8, 17), (5, 5), (21, 24), (19, 16), (8, 23), (13, 22), (21, 25), (10, 15), (4, 23), (19, 24), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986158", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 1), (13, 17), (14, 5), (6, 17), (14, 3), (2, 2), (17, 21), (2, 5), (20, 5), (11, 3), (0, 4), (2, 20), (14, 19), (6, 9), (6, 21), (9, 18), (18, 16), (4, 12), (19, 12), (1, 8), (4, 13), (17, 10), (15, 7), (21, 4), (2, 13), (18, 4), (1, 11), (22, 18), (0, 10), (15, 19), (11, 19), (6, 8), (20, 12), (5, 10), (16, 21), (11, 18), (12, 14), (19, 2), (12, 11), (10, 8), (5, 18), (1, 7), (7, 16), (14, 15), (4, 8), (22, 6), (4, 15), (22, 15), (16, 14), (7, 6), (13, 15), (5, 21), (6, 19), (17, 7), (1, 21), (0, 18), (16, 10), (19, 0), (4, 6), (10, 1), (0, 15), (4, 21), (0, 17), (19, 7), (14, 13), (21, 1), (12, 16), (11, 13), (22, 14), (3, 20), (3, 17), (1, 6), (15, 2), (8, 0), (3, 2), (0, 20), (15, 0), (15, 21), (16, 19), (17, 2), (16, 4), (9, 19), (2, 10), (22, 10), (5, 16), (2, 15), (8, 11), (6, 3), (19, 3), (15, 9), (11, 10), (5, 13), (17, 19), (9, 17), (16, 9), (14, 10), (16, 2), (19, 19), (21, 7), (3, 6), (4, 2), (18, 15), (5, 15), (11, 16), (8, 13), (8, 15), (11, 5), (16, 8), (18, 7), (0, 11), (19, 16), (16, 7), (10, 9), (2, 16), (17, 20), (1, 3), (8, 2), (22, 17), (14, 16), (3, 12), (21, 13), (22, 11), (19, 4), (6, 4), (0, 8), (13, 18), (16, 20), (21, 20), (13, 19), (18, 6), (8, 14), (20, 16), (21, 0), (3, 1), (17, 17), (6, 20), (12, 13), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824425", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 18), (14, 27), (15, 22), (6, 17), (23, 18), (8, 13), (14, 3), (3, 14), (21, 14), (6, 8), (10, 22), (18, 8), (12, 27), (10, 8), (4, 16), (23, 12), (18, 14), (23, 0), (21, 17), (13, 7), (24, 5), (11, 2), (6, 9), (7, 24), (14, 5), (16, 17), (8, 7), (1, 13), (4, 2), (18, 10), (19, 21), (6, 14), (16, 20), (5, 27), (14, 4), (16, 14), (25, 10), (3, 12), (2, 21), (12, 13), (23, 14), (7, 9), (25, 0), (10, 12), (13, 12), (4, 17), (2, 7), (22, 25), (8, 18), (19, 13), (6, 10), (0, 17), (13, 27), (6, 19), (24, 23), (13, 15), (10, 19), (15, 6), (3, 8), (2, 16), (15, 16), (6, 7), (19, 25), (17, 5), (9, 21), (8, 11), (22, 12), (19, 16), (1, 22), (5, 14), (2, 22), (18, 4), (19, 27), (14, 20), (12, 7), (12, 5), (2, 17), (13, 23), (2, 15), (20, 0), (6, 12), (9, 4), (10, 3), (3, 15), (21, 2), (17, 12), (10, 25), (1, 25), (3, 23), (1, 27), (23, 3), (15, 20), (2, 3), (1, 2), (3, 7), (17, 18), (18, 17), (14, 26), (5, 9), (23, 26), (10, 0), (13, 1), (8, 0), (2, 11), (24, 2), (4, 23), (19, 8), (13, 24), (25, 3), (8, 19), (12, 18), (8, 26), (17, 15), (23, 25), (9, 5), (17, 7), (11, 18), (21, 23), (6, 0), (21, 1), (4, 1), (22, 13), (21, 0), (9, 3), (18, 11), (4, 22), (23, 6), (17, 16), (16, 0), (21, 18), (5, 20), (10, 18), (8, 21), (18, 22), (12, 24), (16, 5), (15, 19), (21, 8), (20, 20), (5, 24), (11, 17), (1, 15), (3, 26), (17, 8), (17, 11), (5, 3), (1, 7), (8, 9), (11, 11), (4, 21), (11, 15), (25, 1), (12, 25), (15, 12), (0, 5), (1, 26), (21, 7), (17, 25), (17, 10), (14, 8), (25, 7), (16, 6), (13, 20), (20, 21), (19, 18), (20, 16), (10, 6), (3, 19), (0, 10), (12, 3), (9, 23), (1, 9), (3, 0), (3, 21), (18, 16), (14, 19), (2, 0), (5, 7), (23, 22), (10, 13), (0, 6), (10, 20), (7, 10), (19, 14), (9, 17), (25, 9), (0, 2), (0, 21), (9, 20), (10, 24), (14, 1), (23, 23), (8, 4), (12, 17), (3, 18), (14, 0), (3, 22), (23, 21), (22, 23), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876848", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (16, 20), (2, 11), (11, 5), (0, 3), (6, 11), (11, 15), (14, 20), (22, 10), (15, 14), (19, 12), (15, 2), (3, 2), (22, 11), (4, 14), (21, 10), (17, 5), (0, 19), (22, 6), (13, 19), (5, 5), (13, 14), (20, 14), (8, 16), (18, 19), (12, 18), (20, 18), (6, 12), (12, 9), (21, 1), (12, 6), (2, 0), (12, 17), (12, 0), (17, 3), (2, 6), (8, 20), (4, 13), (4, 16), (17, 7), (19, 8), (3, 4), (17, 17), (16, 14), (5, 10), (2, 19), (11, 8), (12, 20), (19, 18), (15, 15), (4, 19), (1, 14), (8, 17), (1, 2), (4, 6), (17, 20), (13, 0), (22, 3), (1, 5), (5, 1), (22, 16), (6, 3), (6, 18), (7, 7), (13, 10), (10, 7), (10, 3), (13, 1), (14, 6), (15, 13), (16, 10), (15, 0), (7, 14), (17, 8), (22, 4), (8, 5), (3, 13), (5, 0), (3, 20), (18, 9), (19, 5), (0, 17), (22, 8), (20, 16), (8, 8), (2, 3), (9, 11), (10, 18), (9, 20), (2, 5), (16, 16), (6, 10), (14, 10), (22, 13), (8, 10), (11, 2), (6, 8), (11, 13), (10, 4), (6, 14), (2, 12), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999216", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), 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), (19, 7), (6, 5), (15, 27), (6, 1), (26, 13), (5, 23), (27, 14), (12, 2), (10, 0), (27, 2), (21, 0), (4, 4), (25, 10), (26, 3), (17, 16), (25, 4), (6, 6), (12, 11), (3, 18), (7, 11), (12, 25), (27, 20), (24, 6), (20, 4), (15, 16), (4, 14), (10, 6), (6, 7), (3, 21), (25, 2), (23, 3), (10, 13), (10, 1), (24, 12), (6, 0), (6, 26), (8, 18), (13, 16), (1, 13), (4, 22), (1, 16), (17, 23), (1, 27), (6, 2), (0, 4), (15, 10), (9, 4), (15, 19), (21, 22), (17, 9), (7, 1), (8, 13), (22, 1), (10, 20), (17, 24), (13, 27), (0, 20), (4, 6), (4, 13), (13, 1), (16, 18), (15, 5), (3, 27), (3, 11), (23, 12), (9, 26), (18, 0), (23, 18), (11, 7), (5, 5), (23, 20), (13, 15), (0, 5), (16, 6), (3, 17), (22, 13), (16, 19), (15, 26), (1, 21), (27, 15), (28, 21), (7, 9), (25, 14), (18, 23), (18, 9), (9, 7), (20, 27), (14, 17), (10, 18), (21, 18), (21, 16), (11, 3), (2, 13), (15, 11), (3, 15), (12, 23), (15, 15), (21, 4), (1, 18), (14, 3), (12, 0), (21, 12), (27, 26), (10, 26), (13, 5), (24, 21), (3, 4), (6, 15), (16, 16), (13, 17), (2, 15), (1, 17), (12, 8), (27, 1), (23, 11), (5, 18), (3, 25), (14, 16), (0, 1), (2, 7), (11, 8), (16, 26), (14, 22), (4, 0), (1, 8), (5, 14), (25, 16), (19, 17), (8, 15), (10, 15), (13, 3), (13, 18), (25, 19), (6, 22), (27, 18), (2, 2), (23, 0), (3, 12), (4, 24), (9, 15), (14, 0), (5, 2), (21, 2), (24, 14), (22, 21), (27, 5), (20, 2), (14, 24), (23, 14), (8, 10), (12, 20), (1, 10), (18, 5), (14, 5), (11, 4), (17, 15), (28, 15), (13, 4), (15, 13), (5, 20), (26, 27), (23, 1), (19, 24), (16, 1), (15, 17), (19, 1), (5, 0), (21, 21), (7, 21), (20, 1), (10, 5), (16, 21), (28, 19), (19, 8), (22, 11), (2, 8), (5, 6), (24, 3), (19, 11), (15, 3), (25, 15), (8, 2), (11, 0), (21, 6), (1, 12), (7, 8), (19, 14), (18, 19), (14, 21), (26, 26), (0, 22), (24, 11), (25, 11), (12, 4), (4, 15), (18, 7), (19, 10), (27, 22), (20, 13), (25, 23), (9, 13), (23, 10), (10, 24), (3, 6), (2, 1), (22, 22), (8, 24), (16, 7), (17, 1), (5, 26), (3, 1), (24, 9), (18, 11), (1, 4), (28, 4), (1, 26), (7, 18), (7, 5), (27, 17), (27, 7), (15, 14), (0, 24), (25, 24), (18, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425184", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), 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), (2, 12), (6, 6), (8, 17), (14, 15), (0, 5), (5, 6), (20, 21), (13, 1), (1, 7), (5, 21), (12, 3), (12, 8), (12, 9), (20, 7), (1, 17), (15, 2), (14, 8), (1, 5), (10, 14), (17, 7), (13, 11), (0, 10), (5, 18), (12, 19), (14, 17), (19, 16), (0, 6), (17, 5), (17, 11), (2, 14), (17, 14), (8, 9), (16, 8), (3, 21), (14, 2), (11, 22), (14, 16), (17, 22), (2, 8), (8, 18), (16, 14), (3, 15), (1, 20), (21, 11), (9, 12), (19, 21), (13, 9), (5, 19), (9, 10), (8, 4), (9, 8), (7, 21), (4, 17), (21, 14), (3, 10), (21, 17), (10, 15), (11, 23), (20, 5), (15, 6), (10, 17), (4, 22), (6, 8), (13, 8), (14, 9), (9, 15), (17, 19), (2, 9), (12, 10), (0, 7), (2, 7), (15, 8), (13, 16), (9, 21), (17, 17), (13, 12), (10, 8), (20, 20), (19, 1), (5, 10), (13, 20), (8, 14), (4, 15), (10, 3), (7, 16), (7, 18), (0, 13), (18, 11), (15, 13), (7, 12), (11, 13), (18, 21), (9, 17), (1, 21), (21, 8), (3, 6), (8, 2), (5, 14), (1, 8), (18, 3), (2, 10), (3, 1), (16, 2), (18, 22), (4, 20), (13, 10), (11, 17), (0, 12), (16, 12), (12, 20), (3, 2), (17, 15), (15, 19), (16, 13), (9, 9), (2, 22), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "312710", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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), (15, 24), (14, 17), (12, 18), (4, 5), (1, 13), (2, 15), (15, 12), (11, 19), (19, 22), (15, 10), (7, 7), (8, 21), (3, 23), (1, 2), (15, 0), (8, 11), (17, 4), (17, 17), (13, 0), (18, 21), (15, 18), (3, 20), (7, 3), (13, 9), (13, 15), (4, 17), (3, 4), (15, 4), (17, 19), (10, 2), (4, 16), (19, 11), (12, 24), (4, 23), (13, 16), (2, 5), (0, 20), (18, 1), (11, 3), (1, 24), (8, 7), (18, 12), (9, 19), (0, 2), (13, 8), (8, 9), (1, 15), (15, 5), (10, 22), (2, 11), (10, 15), (8, 12), (3, 1), (9, 20), (15, 17), (10, 19), (10, 7), (10, 0), (2, 19), (8, 19), (1, 11), (14, 20), (4, 1), (12, 4), (3, 15), (12, 9), (19, 8), (4, 8), (16, 12), (15, 7), (12, 14), (1, 10), (9, 0), (8, 23), (5, 6), (5, 13), (1, 5), (6, 3), (17, 6), (14, 23), (7, 18), (3, 6), (16, 6), (3, 16), (7, 10), (17, 14), (14, 10), (18, 13), (10, 4), (5, 10), (16, 22), (11, 17), (12, 0), (16, 3), (0, 21), (9, 9), (7, 23), (0, 15), (13, 22), (5, 0), (15, 20), (2, 0), (17, 8), (12, 19), (3, 7), (15, 22), (6, 17), (3, 3), (2, 22), (8, 22), (14, 6), (5, 20), (17, 1), (17, 7), (2, 13), (14, 5), (15, 1), (5, 16), (7, 14), (3, 9), (8, 0), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890760", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 18), (12, 20), (15, 12), (27, 15), (15, 3), (28, 16), (2, 5), (17, 7), (19, 2), (13, 25), (4, 25), (22, 4), (0, 5), (0, 4), (27, 12), (2, 10), (0, 24), (8, 10), (0, 17), (18, 17), (13, 20), (13, 0), (16, 17), (7, 7), (25, 12), (16, 7), (6, 23), (12, 1), (14, 15), (12, 0), (23, 15), (15, 2), (14, 16), (19, 21), (0, 11), (10, 10), (11, 21), (14, 9), (19, 25), (24, 14), (15, 24), (26, 12), (13, 1), (14, 23), (23, 3), (16, 3), (8, 16), (13, 22), (19, 11), (26, 2), (5, 9), (7, 22), (21, 7), (26, 10), (26, 25), (4, 17), (26, 3), (18, 14), (13, 9), (8, 6), (12, 5), (22, 7), (23, 17), (25, 19), (7, 11), (14, 20), (22, 8), (10, 8), (23, 2), (6, 8), (10, 12), (25, 16), (24, 17), (0, 6), (20, 18), (2, 23), (5, 13), (21, 5), (14, 7), (18, 9), (27, 2), (18, 22), (24, 24), (22, 22), (24, 6), (5, 19), (13, 24), (20, 16), (1, 16), (2, 20), (18, 8), (6, 14), (23, 11), (23, 16), (8, 11), (11, 17), (4, 3), (8, 18), (24, 10), (6, 19), (0, 25), (23, 14), (5, 2), (21, 1), (10, 18), (7, 10), (19, 3), (7, 23), (3, 6), (6, 2), (0, 21), (21, 17), (9, 7), (11, 0), (0, 22), (21, 8), (10, 0), (0, 13), (23, 12), (4, 4), (11, 16), (9, 4), (27, 25), (23, 7), (10, 15), (6, 7), (5, 3), (17, 13), (16, 0), (6, 9), (17, 16), (19, 22), (20, 21), (0, 12), (1, 7), (8, 24), (3, 5), (8, 9), (23, 20), (22, 18), (11, 8), (10, 14), (21, 14), (7, 1), (18, 25), (20, 3), (7, 25), (22, 19), (15, 6), (9, 0), (0, 18), (18, 23), (14, 24), (17, 23), (5, 0), (26, 22), (8, 19), (21, 13), (9, 25), (15, 7), (3, 4), (24, 1), (26, 19), (17, 25), (2, 12), (18, 10), (20, 6), (9, 15), (1, 12), (16, 19), (11, 15), (7, 5), (16, 4), (17, 17), (27, 11), (20, 25), (5, 11), (20, 12), (1, 8), (8, 7), (25, 15), (28, 15), (9, 14), (13, 19), (26, 24), (1, 20), (8, 0), (2, 8), (22, 3), (4, 18), (1, 19), (25, 24), (12, 15), (2, 9), (26, 7), (3, 14), (6, 24), (3, 2), (20, 17), (26, 18), (26, 14), (0, 8), (5, 7), (2, 14), (27, 17), (18, 18), (20, 15), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "783360", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), 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), (8, 6), (6, 14), (2, 0), (19, 1), (3, 12), (13, 3), (18, 6), (21, 20), (2, 3), (0, 17), (7, 22), (15, 21), (1, 11), (17, 15), (12, 16), (18, 19), (8, 2), (24, 21), (1, 5), (4, 17), (19, 15), (24, 9), (10, 7), (0, 9), (5, 7), (11, 5), (10, 22), (20, 6), (16, 16), (12, 9), (21, 22), (6, 2), (11, 0), (23, 6), (7, 4), (0, 8), (12, 4), (8, 20), (1, 4), (13, 21), (10, 16), (10, 20), (13, 17), (13, 1), (12, 19), (24, 19), (13, 14), (9, 10), (16, 12), (14, 21), (8, 0), (25, 20), (21, 19), (19, 9), (18, 20), (24, 8), (10, 8), (18, 11), (0, 12), (17, 21), (13, 15), (6, 18), (20, 5), (11, 17), (4, 22), (22, 2), (8, 19), (18, 13), (0, 20), (3, 9), (16, 7), (10, 3), (15, 5), (14, 11), (11, 22), (11, 4), (17, 13), (22, 9), (10, 18), (3, 18), (25, 0), (16, 22), (13, 10), (13, 9), (16, 19), (3, 5), (13, 7), (7, 7), (17, 1), (7, 5), (5, 0), (22, 17), (6, 11), (4, 7), (11, 2), (24, 16), (15, 0), (8, 10), (13, 8), (5, 20), (23, 10), (7, 14), (22, 7), (3, 16), (10, 1), (10, 2), (0, 10), (16, 9), (10, 6), (13, 16), (18, 4), (0, 15), (2, 16), (3, 13), (8, 12), (4, 12), (11, 11), (22, 21), (18, 8), (17, 3), (8, 9), (23, 4), (3, 10), (12, 8), (7, 20), (7, 10), (5, 14), (2, 20), (4, 5), (24, 5), (25, 9), (14, 18), (14, 8), (23, 5), (19, 12), (20, 1), (21, 2), (12, 1), (8, 1), (20, 4), (20, 22), (6, 17), (4, 15), (13, 18), (1, 18), (14, 15), (0, 4), (17, 0), (9, 13), (9, 22), (16, 5), (2, 8), (22, 0), (14, 7), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "737880", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (7, 16), (0, 20), (22, 9), (6, 4), (9, 19), (18, 10), (8, 8), (0, 2), (24, 0), (19, 11), (15, 14), (14, 17), (27, 13), (0, 18), (23, 9), (3, 15), (7, 11), (2, 16), (23, 17), (9, 4), (10, 15), (24, 8), (2, 12), (12, 9), (4, 0), (20, 14), (10, 4), (21, 16), (14, 10), (1, 8), (4, 17), (13, 0), (24, 5), (24, 18), (15, 4), (13, 18), (23, 10), (9, 1), (11, 9), (15, 18), (11, 4), (1, 9), (26, 13), (13, 1), (21, 17), (11, 12), (6, 10), (0, 14), (16, 20), (16, 12), (18, 4), (1, 13), (19, 8), (5, 19), (7, 15), (16, 16), (27, 8), (19, 7), (3, 1), (23, 6), (14, 8), (19, 1), (9, 13), (5, 12), (22, 7), (21, 10), (20, 8), (23, 13), (9, 20), (17, 7), (18, 9), (3, 6), (3, 18), (11, 14), (25, 5), (21, 11), (23, 4), (7, 19), (13, 17), (25, 4), (7, 4), (9, 6), (1, 15), (11, 10), (24, 17), (0, 11), (9, 2), (18, 7), (22, 4), (0, 16), (25, 15), (8, 0), (20, 6), (4, 10), (20, 16), (14, 7), (19, 17), (20, 4), (8, 1), (24, 11), (4, 3), (15, 2), (16, 1), (4, 20), (21, 19), (13, 11), (17, 8), (11, 0), (18, 12), (16, 17), (26, 11), (0, 7), (15, 16), (23, 19), (2, 9), (11, 16), (13, 8), (14, 14), (7, 2), (24, 15), (19, 2), (20, 9), (12, 20), (7, 13), (23, 16), (7, 10), (9, 17), (13, 9), (21, 7), (15, 6), (20, 13), (16, 4), (12, 12), (25, 0), (15, 11), (25, 19), (3, 0), (22, 3), (2, 4), (18, 19), (13, 5), (10, 0), (11, 3), (16, 7), (1, 18), (26, 19), (16, 8), (11, 7), (26, 7), (23, 11), (2, 6), (6, 1), (6, 16), (18, 8), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897683", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), 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), (25, 8), (27, 4), (0, 12), (28, 0), (16, 15), (14, 10), (8, 2), (20, 18), (13, 14), (15, 19), (16, 18), (10, 9), (16, 12), (10, 17), (7, 2), (13, 9), (24, 4), (7, 19), (4, 5), (11, 15), (11, 2), (19, 2), (10, 8), (6, 19), (16, 3), (11, 17), (28, 14), (23, 5), (28, 4), (21, 7), (14, 12), (23, 17), (15, 10), (2, 11), (18, 11), (25, 6), (16, 9), (8, 0), (15, 12), (2, 13), (2, 12), (27, 14), (15, 2), (8, 7), (24, 11), (0, 3), (23, 4), (4, 0), (1, 8), (7, 16), (21, 3), (15, 6), (6, 1), (27, 5), (1, 3), (11, 12), (3, 8), (20, 2), (5, 14), (16, 6), (0, 1), (22, 18), (4, 18), (24, 0), (3, 3), (28, 12), (17, 4), (27, 12), (11, 10), (24, 9), (18, 15), (21, 5), (9, 14), (20, 14), (2, 1), (24, 8), (27, 1), (9, 9), (22, 13), (8, 4), (18, 8), (0, 17), (28, 15), (13, 0), (7, 9), (4, 12), (19, 11), (26, 6), (12, 17), (22, 12), (20, 3), (6, 8), (28, 8), (24, 19), (22, 1), (2, 14), (0, 10), (8, 12), (15, 16), (23, 18), (25, 4), (10, 14), (7, 3), (17, 5), (6, 10), (3, 1), (21, 9), (25, 5), (11, 19), (27, 11), (2, 5), (10, 7), (26, 1), (9, 7), (27, 2), (6, 12), (17, 3), (10, 12), (15, 4), (27, 16), (10, 4), (19, 15), (6, 3), (16, 0), (2, 15), (27, 19), (0, 9), (14, 17), (13, 2), (3, 2), (5, 7), (21, 4), (12, 16), (25, 17), (17, 10), (26, 7), (11, 3), (17, 2), (20, 5), (9, 19), (23, 13), (4, 1), (6, 0), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770366", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 2), (19, 6), (2, 5), (23, 12), (18, 14), (17, 17), (9, 2), (9, 16), (11, 6), (10, 16), (23, 10), (22, 12), (9, 5), (15, 9), (20, 15), (10, 8), (2, 16), (17, 14), (9, 14), (12, 9), (6, 15), (15, 3), (13, 0), (21, 8), (8, 3), (16, 9), (14, 14), (22, 13), (18, 11), (5, 2), (16, 18), (16, 14), (10, 10), (12, 3), (15, 14), (21, 10), (1, 8), (9, 13), (4, 4), (23, 3), (8, 2), (21, 0), (1, 19), (5, 9), (7, 14), (16, 19), (10, 5), (4, 17), (16, 1), (13, 5), (21, 17), (16, 11), (16, 4), (8, 14), (8, 12), (16, 3), (6, 11), (2, 13), (19, 8), (3, 19), (17, 13), (23, 11), (15, 10), (14, 5), (9, 12), (22, 19), (21, 12), (22, 3), (4, 12), (23, 16), (11, 15), (18, 17), (2, 17), (7, 15), (8, 8), (0, 15), (1, 3), (16, 8), (20, 2), (3, 11), (10, 2), (0, 18), (1, 13), (12, 5), (11, 3), (18, 15), (10, 11), (23, 9), (22, 5), (13, 13), (18, 5), (11, 19), (3, 4), (17, 6), (2, 2), (4, 2), (8, 17), (3, 5), (20, 0), (18, 1), (3, 3), (14, 12), (17, 0), (20, 18), (21, 19), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778858", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 27), (6, 3), (13, 9), (12, 7), (26, 1), (21, 8), (22, 15), (10, 26), (13, 17), (22, 19), (19, 2), (13, 13), (22, 16), (7, 28), (1, 6), (17, 19), (7, 6), (21, 1), (12, 13), (1, 5), (19, 28), (1, 17), (19, 21), (19, 5), (4, 7), (16, 22), (8, 13), (21, 14), (2, 2), (23, 12), (6, 14), (7, 24), (8, 18), (6, 4), (2, 15), (24, 10), (15, 19), (20, 18), (18, 25), (3, 8), (18, 18), (12, 0), (7, 16), (25, 4), (5, 2), (18, 7), (23, 2), (20, 22), (6, 20), (5, 13), (26, 4), (14, 9), (6, 27), (12, 23), (23, 28), (23, 16), (25, 28), (5, 20), (3, 23), (24, 18), (13, 15), (24, 5), (1, 9), (2, 12), (11, 27), (14, 24), (8, 26), (13, 5), (4, 2), (2, 9), (17, 28), (22, 28), (4, 15), (8, 7), (2, 20), (3, 11), (8, 20), (0, 1), (12, 21), (21, 24), (12, 28), (22, 5), (25, 0), (26, 20), (13, 20), (10, 17), (10, 23), (20, 23), (0, 20), (21, 20), (24, 14), (10, 16), (26, 15), (0, 8), (18, 5), (1, 7), (18, 22), (16, 21), (1, 22), (20, 24), (1, 1), (19, 11), (2, 28), (8, 24), (20, 21), (24, 19), (0, 19), (11, 22), (4, 16), (3, 14), (8, 4), (6, 13), (4, 17), (18, 26), (10, 22), (22, 22), (10, 25), (6, 5), (26, 7), (24, 22), (6, 16), (2, 11), (5, 16), (12, 25), (17, 6), (11, 20), (7, 18), (13, 10), (20, 19), (13, 1), (1, 3), (4, 25), (21, 17), (6, 2), (10, 20), (18, 24), (26, 3), (4, 21), (21, 15), (13, 22), (8, 2), (16, 9), (24, 8), (5, 7), (19, 26), (2, 25), (21, 4), (5, 23), (22, 6), (14, 10), (23, 19), (1, 14), (22, 20), (24, 12), (13, 21), (12, 17), (2, 23), (19, 14), (5, 0), (3, 26), (21, 25), (17, 24), (12, 12), (5, 27), (13, 4), (24, 11), (21, 19), (6, 7), (22, 21), (22, 1), (12, 1), (0, 6), (22, 13), (25, 14), (11, 28), (0, 3), (3, 19), (3, 25), (9, 8), (15, 24), (23, 11), (26, 14), (22, 12), (22, 9), (26, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "929538", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 22), (21, 16), (6, 11), (9, 4), (3, 14), (8, 17), (14, 22), (14, 0), (21, 21), (0, 19), (3, 0), (2, 2), (2, 22), (13, 9), (4, 1), (11, 20), (18, 8), (8, 20), (1, 15), (16, 5), (4, 18), (6, 3), (3, 7), (19, 24), (5, 2), (22, 9), (12, 12), (16, 7), (0, 15), (7, 15), (22, 2), (3, 3), (5, 22), (13, 4), (14, 24), (3, 22), (12, 16), (6, 23), (16, 25), (17, 18), (2, 7), (16, 12), (15, 8), (7, 4), (12, 4), (22, 14), (19, 22), (9, 13), (15, 15), (10, 6), (12, 13), (15, 24), (9, 25), (19, 2), (13, 22), (19, 15), (17, 10), (2, 24), (5, 15), (12, 21), (7, 14), (15, 21), (18, 16), (19, 13), (10, 0), (16, 10), (2, 23), (14, 15), (18, 9), (12, 17), (3, 18), (15, 9), (11, 8), (22, 21), (0, 20), (10, 3), (21, 8), (13, 20), (5, 7), (7, 22), (10, 25), (14, 8), (10, 14), (19, 23), (4, 19), (1, 0), (15, 25), (18, 4), (9, 8), (18, 21), (16, 15), (12, 23), (12, 19), (6, 6), (6, 7), (9, 16), (18, 19), (19, 14), (4, 0), (16, 18), (5, 5), (5, 3), (3, 21), (19, 19), (15, 22), (15, 23), (14, 7), (20, 12), (11, 19), (14, 18), (7, 10), (16, 11), (19, 1), (19, 11), (4, 2), (11, 23), (5, 17), (14, 25), (0, 21), (10, 4), (14, 14), (12, 10), (16, 16), (2, 10), (7, 23), (18, 2), (16, 9), (4, 9), (0, 6), (8, 7), (1, 2), (21, 22), (0, 4), (13, 2), (10, 20), (7, 24), (1, 25), (8, 0), (7, 7), (20, 22), (9, 17), (5, 24), (21, 1), (9, 6), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780320", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 3), (21, 15), (17, 17), (7, 19), (22, 13), (10, 2), (5, 13), (16, 0), (18, 1), (21, 7), (17, 0), (13, 14), (3, 19), (17, 3), (6, 2), (15, 4), (19, 12), (19, 14), (18, 15), (3, 18), (4, 2), (9, 3), (6, 19), (20, 19), (2, 6), (10, 14), (0, 11), (14, 1), (15, 17), (19, 15), (1, 1), (8, 15), (17, 18), (18, 14), (15, 13), (6, 3), (17, 12), (3, 16), (16, 12), (20, 1), (4, 16), (10, 15), (16, 11), (11, 18), (15, 7), (5, 14), (10, 16), (17, 14), (19, 10), (10, 1), (21, 11), (5, 9), (0, 15), (15, 3), (12, 15), (4, 13), (2, 14), (4, 7), (21, 9), (20, 17), (0, 9), (5, 4), (6, 10), (20, 7), (16, 13), (22, 6), (16, 9), (11, 5), (1, 18), (16, 5), (0, 17), (21, 3), (22, 7), (1, 12), (10, 17), (10, 19), (7, 11), (3, 10), (8, 17), (13, 3), (11, 1), (0, 6), (9, 9), (13, 16), (6, 16), (19, 7), (12, 13), (8, 11), (10, 6), (12, 18), (0, 18), (13, 6), (5, 19), (10, 9), (7, 12), (17, 7), (4, 15), (11, 9), (11, 4), (9, 17), (9, 13), (8, 3), (15, 1), (16, 1), (14, 17), (7, 8), (12, 16), (7, 14), (19, 18), (20, 2), (22, 8), (1, 17), (14, 9), (16, 17), (0, 2), (22, 5), (15, 0), (2, 16), (14, 11), (21, 5), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926168", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 17), (12, 17), (1, 10), (25, 5), (13, 24), (21, 4), (9, 23), (18, 10), (6, 27), (18, 24), (20, 7), (17, 16), (25, 15), (15, 0), (4, 8), (26, 24), (24, 1), (11, 3), (18, 8), (13, 6), (5, 11), (22, 7), (12, 21), (17, 14), (24, 16), (5, 9), (7, 5), (17, 3), (4, 25), (12, 1), (24, 12), (24, 3), (2, 21), (4, 16), (10, 27), (21, 22), (19, 6), (0, 13), (22, 27), (10, 28), (6, 0), (11, 5), (19, 22), (17, 0), (21, 0), (3, 2), (25, 24), (15, 25), (2, 7), (22, 13), (0, 25), (5, 1), (12, 6), (11, 26), (8, 19), (13, 21), (6, 19), (0, 20), (22, 6), (13, 27), (23, 7), (11, 4), (7, 28), (13, 3), (6, 26), (1, 5), (2, 3), (21, 3), (14, 13), (8, 22), (23, 24), (11, 25), (13, 25), (12, 14), (12, 22), (4, 11), (21, 5), (14, 8), (18, 12), (21, 18), (23, 15), (0, 24), (5, 6), (14, 6), (18, 9), (5, 3), (2, 12), (25, 13), (11, 17), (7, 3), (20, 0), (8, 27), (12, 4), (13, 16), (17, 28), (21, 28), (22, 8), (16, 24), (22, 24), (13, 20), (15, 20), (25, 23), (24, 20), (2, 23), (0, 1), (14, 20), (20, 26), (1, 8), (0, 9), (5, 24), (26, 10), (11, 22), (8, 5), (0, 27), (24, 14), (24, 10), (3, 4), (11, 14), (4, 7), (21, 1), (8, 0), (24, 11), (20, 4), (15, 8), (2, 15), (16, 4), (11, 23), (5, 4), (13, 14), (24, 18), (8, 20), (14, 0), (26, 14), (7, 21), (7, 4), (19, 0), (16, 13), (14, 16), (10, 24), (1, 4), (3, 23), (16, 7), (16, 17), (11, 16), (8, 7), (15, 17), (18, 17), (26, 16), (20, 6), (18, 5), (5, 12), (23, 18), (22, 14), (10, 10), (17, 20), (4, 12), (17, 2), (3, 19), (3, 9), (14, 5), (6, 11), (17, 22), (25, 4), (26, 7), (24, 25), (21, 21), (22, 10), (22, 11), (23, 0), (26, 6), (11, 2), (20, 21), (9, 1), (16, 22), (11, 18), (3, 8), (2, 25), (3, 10), (18, 14), (16, 2), (2, 27), (3, 13), (19, 19), (12, 12), (17, 26), (5, 15), (6, 10), (22, 5), (3, 18), (26, 26), (3, 0), (26, 18), (3, 15), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17496", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), 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), (1, 22), (4, 6), (20, 16), (19, 9), (5, 24), (20, 28), (11, 18), (5, 28), (18, 7), (20, 11), (0, 22), (3, 1), (6, 28), (11, 21), (11, 13), (21, 25), (17, 27), (19, 11), (6, 22), (19, 26), (7, 25), (4, 1), (20, 24), (12, 2), (2, 3), (8, 28), (24, 11), (7, 9), (12, 0), (20, 13), (9, 19), (14, 1), (10, 3), (11, 1), (4, 10), (14, 0), (6, 4), (14, 18), (7, 14), (0, 17), (13, 4), (23, 14), (8, 26), (10, 17), (9, 0), (5, 18), (14, 23), (1, 27), (23, 4), (18, 11), (21, 19), (9, 11), (1, 7), (24, 8), (11, 7), (9, 7), (24, 19), (3, 14), (2, 0), (11, 25), (8, 11), (18, 18), (16, 13), (3, 5), (2, 27), (18, 13), (23, 0), (7, 3), (13, 19), (23, 27), (1, 2), (12, 14), (6, 9), (22, 6), (23, 28), (6, 11), (22, 7), (5, 10), (17, 11), (18, 23), (9, 21), (15, 12), (3, 23), (20, 1), (18, 17), (3, 12), (9, 4), (13, 16), (1, 6), (10, 15), (15, 19), (13, 22), (11, 15), (7, 5), (7, 26), (5, 20), (0, 7), (14, 6), (11, 20), (6, 25), (2, 11), (3, 13), (5, 11), (24, 20), (17, 7), (21, 12), (15, 8), (18, 5), (4, 16), (19, 20), (9, 2), (22, 28), (11, 27), (7, 4), (5, 19), (5, 12), (16, 24), (3, 16), (23, 18), (6, 17), (9, 8), (11, 26), (17, 21), (0, 14), (22, 22), (2, 24), (4, 24), (16, 18), (23, 22), (8, 24), (21, 6), (16, 0), (9, 12), (20, 5), (21, 8), (17, 24), (7, 22), (2, 18), (22, 25), (19, 12), (2, 25), (1, 1), (12, 21), (6, 3), (8, 12), (23, 25), (8, 5), (0, 20), (6, 24), (22, 15), (9, 25), (17, 9), (1, 21), (18, 14), (10, 22), (21, 23), (20, 22), (1, 8), (19, 24), (24, 3), (21, 10), (1, 10), (6, 7), (7, 28), (22, 19), (1, 18), (22, 18), (15, 17), (2, 6), (18, 15), (13, 26), (11, 10), (18, 4), (3, 9), (9, 28), (21, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390108", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (14, 19), (11, 4), (12, 5), (9, 17), (10, 21), (12, 8), (9, 7), (25, 6), (8, 5), (23, 5), (22, 15), (25, 14), (27, 0), (20, 15), (18, 4), (13, 13), (25, 8), (8, 15), (6, 19), (5, 12), (18, 5), (11, 16), (19, 20), (2, 17), (8, 19), (1, 15), (17, 11), (16, 4), (25, 21), (17, 20), (10, 8), (19, 21), (18, 21), (22, 6), (6, 9), (25, 1), (8, 7), (27, 6), (5, 14), (13, 12), (25, 19), (14, 0), (19, 10), (10, 9), (14, 8), (4, 8), (0, 15), (10, 14), (16, 3), (12, 11), (20, 0), (10, 20), (20, 9), (27, 7), (15, 9), (20, 4), (1, 19), (26, 20), (18, 1), (13, 5), (11, 0), (17, 10), (13, 14), (8, 0), (4, 18), (15, 11), (13, 7), (8, 9), (22, 9), (4, 14), (0, 16), (1, 21), (1, 8), (23, 6), (14, 16), (15, 16), (27, 12), (2, 9), (18, 14), (11, 9), (15, 12), (7, 2), (25, 7), (19, 19), (4, 19), (5, 10), (17, 5), (24, 8), (20, 16), (27, 9), (12, 16), (1, 6), (6, 8), (17, 1), (16, 12), (3, 12), (1, 1), (4, 13), (11, 7), (4, 7), (3, 4), (5, 16), (8, 17), (20, 8), (16, 9), (16, 6), (16, 17), (10, 2), (0, 13), (16, 14), (22, 20), (21, 13), (22, 19), (12, 9), (7, 15), (1, 5), (14, 14), (22, 5), (1, 11), (1, 20), (23, 15), (25, 12), (4, 2), (16, 13), (5, 11), (0, 18), (9, 14), (15, 13), (22, 16), (1, 9), (8, 3), (20, 10), (26, 9), (16, 1), (16, 21), (22, 4), (10, 1), (5, 3), (20, 1), (26, 3), (8, 10), (14, 20), (20, 20), (22, 11), (1, 14), (3, 9), (26, 16), (20, 18), (8, 16), (11, 21), (1, 18), (17, 4), (4, 12), (9, 12), (9, 21), (2, 6), (12, 1), (0, 5), (8, 1), (6, 21), (21, 16), (6, 10), (27, 2), (10, 15), (7, 0), (18, 6), (14, 5), (21, 21), (10, 0), (6, 18), (7, 17), (21, 1), (26, 8), (21, 7), (9, 4), (13, 9), (24, 0), (3, 15), (7, 19), (17, 19), (2, 19), (22, 0), (23, 7), (20, 5), (0, 6), (15, 20), (5, 2), (25, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708750", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 19), (10, 23), (23, 18), (20, 3), (18, 3), (15, 16), (12, 24), (12, 12), (4, 19), (0, 13), (7, 0), (1, 9), (20, 20), (0, 6), (23, 0), (11, 11), (3, 2), (0, 23), (24, 2), (6, 5), (4, 0), (16, 18), (12, 8), (9, 3), (18, 21), (20, 5), (13, 2), (13, 6), (8, 20), (16, 5), (6, 25), (14, 26), (2, 22), (0, 5), (13, 16), (22, 11), (17, 24), (0, 24), (2, 26), (12, 5), (18, 12), (4, 9), (4, 26), (20, 2), (6, 1), (18, 9), (22, 23), (12, 10), (4, 23), (5, 0), (1, 18), (13, 14), (4, 12), (20, 15), (0, 17), (22, 14), (22, 15), (14, 17), (15, 11), (19, 10), (13, 13), (1, 16), (21, 20), (21, 1), (20, 25), (8, 3), (18, 14), (20, 13), (21, 14), (10, 13), (5, 2), (8, 14), (9, 14), (16, 11), (15, 17), (7, 10), (5, 5), (12, 26), (8, 23), (4, 14), (10, 17), (7, 16), (8, 7), (5, 11), (9, 22), (6, 23), (13, 10), (9, 10), (18, 6), (7, 21), (17, 17), (13, 24), (23, 7), (18, 23), (15, 12), (15, 6), (17, 1), (1, 13), (0, 21), (19, 8), (10, 9), (7, 12), (6, 11), (11, 24), (12, 21), (11, 20), (12, 6), (23, 15), (16, 26), (18, 1), (6, 12), (4, 16), (18, 5), (0, 14), (24, 17), (11, 3), (1, 21), (19, 5), (23, 4), (20, 0), (12, 11), (6, 0), (6, 7), (4, 1), (3, 9), (13, 23), (24, 8), (9, 18), (7, 23), (12, 22), (9, 26), (17, 5), (24, 13), (15, 14), (11, 26), (10, 24), (9, 7), (2, 23), (23, 12), (8, 26), (13, 12), (23, 25), (0, 26), (24, 24), (6, 2), (15, 25), (16, 21), (23, 16), (15, 5), (1, 5), (18, 20), (14, 3), (19, 0), (17, 8), (14, 18), (9, 16), (24, 10), (3, 4), (21, 3), (19, 9), (15, 0), (12, 16), (13, 1), (6, 17), (18, 19), (5, 3), (21, 12), (22, 25), (23, 6), (8, 19), (8, 15), (10, 3), (16, 15), (13, 17), (8, 24), (4, 3), (1, 8), (3, 0), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612975", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 9), (20, 12), (6, 7), (13, 2), (20, 10), (2, 3), (11, 20), (4, 4), (14, 0), (11, 1), (8, 18), (11, 17), (9, 23), (12, 19), (5, 19), (16, 11), (8, 4), (14, 3), (15, 9), (7, 17), (11, 11), (1, 20), (11, 10), (16, 10), (16, 14), (8, 14), (4, 23), (13, 4), (6, 13), (3, 20), (17, 25), (20, 4), (9, 14), (13, 12), (3, 17), (15, 14), (16, 17), (10, 2), (11, 12), (13, 22), (20, 8), (8, 9), (8, 24), (8, 7), (10, 11), (4, 6), (20, 11), (6, 20), (8, 0), (18, 0), (19, 17), (9, 19), (18, 22), (18, 10), (8, 11), (4, 7), (14, 21), (5, 6), (12, 12), (18, 3), (10, 4), (20, 13), (19, 15), (20, 18), (12, 17), (5, 3), (18, 4), (6, 10), (17, 22), (0, 15), (7, 18), (20, 16), (2, 24), (15, 21), (10, 15), (11, 16), (13, 23), (8, 6), (15, 23), (13, 19), (12, 25), (20, 24), (18, 21), (4, 16), (0, 10), (5, 17), (14, 24), (18, 15), (18, 5), (12, 24), (19, 19), (15, 16), (12, 4), (6, 21), (3, 21), (10, 24), (9, 15), (15, 19), (9, 10), (2, 4), (7, 13), (12, 0), (10, 6), (3, 22), (9, 21), (13, 24), (1, 13), (3, 0), (7, 15), (7, 23), (10, 21), (19, 12), (5, 4), (1, 11), (3, 10), (9, 4), (0, 20), (3, 19), (5, 25), (13, 10), (6, 11), (0, 23), (3, 23), (13, 3), (13, 20), (14, 16), (15, 6), (8, 3), (4, 11), (4, 15), (17, 17), (5, 13), (2, 20), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "261800", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), 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), (6, 20), (1, 8), (9, 3), (2, 9), (2, 3), (5, 3), (12, 7), (8, 11), (10, 18), (2, 23), (2, 21), (8, 19), (15, 17), (3, 22), (6, 18), (18, 0), (20, 8), (16, 18), (6, 2), (1, 10), (15, 21), (16, 3), (6, 4), (14, 17), (10, 14), (14, 9), (15, 4), (9, 16), (2, 20), (16, 1), (14, 7), (17, 17), (2, 7), (10, 4), (12, 8), (5, 14), (16, 11), (12, 13), (18, 13), (12, 2), (13, 12), (4, 3), (4, 17), (13, 7), (19, 13), (16, 21), (6, 8), (4, 11), (11, 20), (1, 1), (12, 16), (14, 15), (14, 21), (4, 10), (9, 21), (5, 8), (7, 14), (13, 5), (17, 21), (5, 19), (20, 14), (1, 3), (18, 11), (6, 17), (7, 11), (18, 6), (3, 16), (18, 18), (19, 21), (6, 0), (19, 18), (17, 20), (20, 22), (7, 15), (5, 11), (2, 14), (7, 19), (7, 4), (10, 12), (8, 15), (5, 6), (3, 4), (3, 20), (8, 3), (1, 2), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574081", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 26), (0, 3), (10, 0), (17, 7), (5, 19), (12, 8), (3, 10), (12, 22), (4, 1), (0, 26), (7, 3), (17, 18), (14, 6), (24, 26), (12, 15), (2, 16), (22, 23), (3, 8), (20, 12), (0, 19), (12, 4), (17, 3), (10, 10), (22, 9), (22, 13), (24, 14), (5, 3), (3, 2), (11, 17), (18, 15), (2, 24), (1, 11), (26, 0), (1, 26), (10, 14), (22, 15), (7, 2), (15, 5), (3, 26), (7, 6), (23, 19), (18, 9), (26, 10), (25, 9), (10, 22), (6, 2), (22, 8), (21, 2), (14, 26), (24, 3), (9, 3), (21, 6), (12, 20), (7, 8), (11, 20), (0, 11), (23, 12), (8, 21), (6, 18), (25, 26), (17, 13), (7, 23), (22, 1), (17, 1), (0, 5), (20, 20), (13, 16), (4, 12), (3, 13), (9, 18), (6, 17), (22, 12), (7, 15), (14, 3), (13, 12), (23, 22), (0, 12), (21, 1), (4, 10), (12, 12), (5, 21), (1, 22), (10, 3), (21, 10), (17, 12), (21, 7), (3, 22), (1, 12), (23, 15), (9, 26), (10, 20), (6, 11), (16, 0), (5, 4), (7, 19), (11, 13), (1, 15), (0, 15), (19, 6), (19, 5), (4, 17), (11, 10), (25, 25), (20, 18), (15, 13), (13, 11), (9, 20), (23, 8), (14, 20), (25, 3), (12, 3), (8, 14), (26, 19), (18, 22), (14, 15), (13, 10), (12, 5), (2, 17), (11, 25), (15, 2), (2, 23), (14, 9), (25, 1), (13, 8), (9, 24), (21, 22), (15, 12), (11, 6), (9, 7), (8, 3), (15, 19), (0, 1), (24, 12), (23, 7), (3, 7), (2, 4), (23, 10), (16, 15), (12, 13), (8, 23), (6, 0), (13, 4), (1, 8), (1, 25), (10, 18), (20, 7), (12, 9), (19, 20), (11, 9), (1, 2), (0, 10), (10, 17), (15, 14), (24, 19), (16, 19), (13, 15), (11, 16), (20, 24), (20, 26), (19, 7), (17, 24), (6, 4), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163291", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 16), (24, 13), (12, 17), (22, 11), (9, 21), (13, 11), (3, 2), (24, 8), (24, 17), (5, 9), (1, 13), (18, 17), (6, 11), (1, 20), (23, 11), (9, 12), (9, 3), (17, 14), (20, 16), (9, 20), (5, 23), (4, 18), (8, 8), (23, 7), (8, 10), (7, 0), (27, 6), (14, 22), (0, 20), (17, 5), (2, 14), (23, 4), (13, 9), (13, 8), (21, 15), (6, 19), (24, 9), (1, 2), (18, 4), (13, 2), (25, 11), (26, 8), (9, 11), (26, 12), (9, 2), (0, 1), (7, 13), (22, 19), (7, 12), (16, 18), (15, 15), (2, 19), (9, 18), (25, 5), (10, 20), (4, 9), (17, 4), (5, 16), (14, 13), (21, 7), (6, 5), (21, 9), (5, 22), (0, 11), (9, 7), (4, 14), (27, 1), (25, 9), (0, 17), (27, 11), (17, 10), (21, 4), (16, 23), (0, 21), (10, 15), (19, 0), (7, 6), (9, 19), (18, 22), (25, 7), (14, 5), (8, 5), (22, 5), (1, 15), (2, 21), (17, 13), (11, 9), (19, 9), (24, 4), (20, 4), (15, 4), (22, 14), (1, 16), (16, 8), (7, 20), (7, 3), (5, 11), (13, 1), (16, 17), (7, 23), (12, 10), (20, 5), (10, 7), (16, 15), (20, 14), (2, 0), (3, 10), (19, 6), (10, 17), (3, 17), (20, 13), (14, 14), (0, 12), (13, 7), (7, 5), (12, 4), (16, 5), (4, 12), (10, 21), (24, 2), (2, 2), (21, 11), (2, 13), (24, 3), (9, 10), (21, 10), (2, 22), (7, 14), (19, 22), (3, 21), (10, 6), (16, 11), (16, 2), (10, 11), (8, 3), (14, 21), (19, 3), (1, 17), (13, 17), (17, 1), (27, 7), (18, 11), (22, 1), (12, 3), (21, 21), (17, 6), (19, 20), (14, 17), (0, 8), (2, 8), (20, 17), (7, 1), (15, 14), (17, 17), (24, 5), (15, 2), (4, 3), (11, 11), (15, 5), (26, 15), (10, 3), (21, 16), (24, 6), (0, 13), (22, 16), (10, 16), (21, 19), (12, 0), (9, 16), (27, 8), (25, 6), (0, 22), (5, 1), (21, 3), (15, 22), (1, 6), (11, 4), (4, 16), (13, 23), (24, 10), (19, 8), (4, 0), (25, 2), (17, 15), (16, 1), (3, 18), (27, 3), (11, 19), (26, 9), (2, 11), (23, 1), (12, 2), (11, 12), (23, 23), (18, 3), (25, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730974", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (5, 0), (12, 10), (5, 13), (11, 23), (21, 9), (13, 24), (17, 23), (12, 15), (11, 4), (8, 2), (16, 17), (16, 11), (21, 0), (1, 10), (5, 9), (15, 19), (19, 2), (15, 11), (10, 16), (7, 18), (15, 7), (4, 11), (8, 6), (0, 22), (1, 14), (10, 1), (16, 15), (12, 0), (20, 24), (19, 14), (8, 9), (18, 22), (17, 21), (3, 8), (14, 24), (7, 12), (6, 21), (16, 12), (6, 23), (5, 12), (13, 15), (20, 6), (17, 19), (20, 19), (4, 6), (3, 3), (11, 10), (20, 8), (9, 16), (20, 15), (2, 19), (7, 0), (2, 3), (6, 17), (12, 7), (11, 18), (6, 5), (15, 20), (14, 15), (5, 22), (12, 23), (11, 15), (14, 3), (8, 13), (1, 24), (5, 8), (1, 12), (21, 10), (17, 6), (9, 4), (20, 16), (2, 15), (0, 9), (13, 9), (0, 12), (8, 8), (17, 4), (4, 20), (9, 1), (18, 11), (1, 11), (19, 4), (13, 20), (1, 22), (2, 14), (11, 3), (9, 7), (6, 8), (3, 2), (18, 19), (1, 20), (20, 4), (18, 7), (2, 9), (9, 5), (1, 4), (8, 12), (9, 9), (19, 0), (10, 21), (15, 9), (11, 16), (14, 1), (15, 0), (11, 17), (2, 11), (0, 17), (8, 24), (13, 16), (16, 23), (7, 17), (4, 9), (18, 21), (1, 13), (3, 24), (5, 3), (15, 10), (16, 24), (18, 16), (19, 3), (2, 23), (10, 14), (18, 13), (8, 17), (3, 9), (0, 20), (16, 13), (1, 15), (12, 11), (13, 8), (2, 13), (16, 2), (19, 23), (12, 14), (10, 18), (0, 6), (3, 17), (9, 13), (20, 9), (17, 9), (20, 2), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914444", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 26), (1, 16), (14, 25), (18, 26), (22, 4), (19, 13), (18, 9), (3, 28), (8, 11), (25, 10), (1, 5), (23, 0), (15, 12), (5, 18), (0, 5), (2, 27), (3, 14), (19, 8), (25, 7), (7, 3), (11, 2), (18, 3), (0, 15), (22, 5), (14, 1), (15, 0), (24, 2), (4, 18), (3, 26), (0, 9), (5, 2), (13, 8), (17, 8), (2, 23), (24, 21), (18, 19), (9, 16), (2, 3), (9, 9), (25, 0), (19, 3), (21, 22), (0, 13), (22, 15), (12, 15), (9, 5), (1, 18), (7, 5), (6, 11), (24, 27), (5, 20), (7, 18), (23, 7), (13, 24), (25, 13), (18, 27), (24, 23), (7, 14), (9, 1), (6, 0), (9, 20), (25, 9), (17, 24), (2, 17), (2, 14), (6, 25), (1, 22), (0, 3), (9, 22), (16, 12), (21, 11), (14, 19), (12, 28), (2, 10), (20, 26), (3, 6), (4, 22), (20, 11), (16, 4), (20, 8), (10, 16), (11, 8), (25, 16), (22, 22), (14, 3), (8, 5), (0, 10), (17, 13), (4, 19), (8, 23), (18, 10), (4, 16), (24, 12), (9, 19), (9, 24), (23, 23), (4, 0), (20, 28), (11, 25), (24, 6), (5, 26), (0, 27), (12, 20), (17, 1), (18, 25), (2, 24), (0, 11), (13, 28), (12, 18), (16, 26), (20, 9), (7, 6), (9, 2), (12, 19), (21, 10), (18, 23), (17, 6), (25, 18), (10, 24), (1, 10), (25, 5), (1, 20), (3, 20), (13, 5), (1, 28), (4, 25), (22, 21), (25, 27), (10, 13), (13, 26), (10, 17), (6, 23), (7, 17), (0, 4), (1, 6), (11, 4), (4, 10), (16, 7), (23, 19), (5, 7), (21, 21), (13, 13), (0, 17), (5, 3), (4, 23), (19, 22), (0, 12), (3, 8), (13, 14), (1, 19), (7, 23), (20, 13), (1, 1), (11, 17), (17, 25), (1, 13), (4, 15), (23, 24), (2, 11), (3, 1), (7, 10), (5, 8), (6, 4), (19, 17), (7, 22), (12, 1), (5, 23), (4, 3), (12, 25), (3, 5), (21, 6), (0, 21), (21, 12), (2, 21), (18, 21), (11, 22), (25, 20), (17, 28), (11, 23), (22, 7), (16, 19), (15, 13), (3, 0), (14, 26), (10, 21), (15, 25), (19, 10), (8, 20), (8, 18), (5, 9), (3, 11), (1, 9), (22, 0), (4, 24), (9, 26), (3, 16), (8, 17), (23, 5), (0, 2), (6, 2), (10, 8), (4, 21), (16, 15), (15, 18), (11, 13), (21, 20), (24, 8), (7, 11), (13, 11), (18, 24), (13, 9), (11, 24), (17, 17), (20, 5), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631890", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 19), (11, 1), (23, 16), (8, 1), (4, 16), (4, 5), (1, 12), (9, 10), (7, 16), (16, 4), (14, 16), (17, 17), (24, 4), (0, 19), (14, 13), (15, 17), (21, 3), (9, 4), (24, 13), (3, 12), (18, 16), (20, 8), (12, 10), (4, 10), (0, 1), (2, 11), (10, 17), (6, 15), (14, 17), (8, 17), (3, 11), (10, 4), (7, 1), (3, 16), (15, 5), (14, 12), (21, 19), (27, 16), (14, 8), (25, 19), (23, 15), (19, 0), (4, 9), (24, 12), (15, 19), (14, 5), (19, 2), (11, 0), (8, 0), (13, 5), (20, 16), (10, 10), (16, 17), (26, 12), (5, 3), (11, 9), (10, 6), (28, 12), (19, 13), (22, 17), (1, 5), (9, 12), (21, 7), (2, 3), (25, 10), (26, 2), (0, 10), (5, 19), (20, 12), (12, 11), (0, 16), (28, 17), (18, 7), (7, 11), (20, 14), (1, 17), (17, 4), (15, 3), (27, 7), (19, 15), (2, 6), (11, 10), (16, 14), (2, 12), (13, 0), (0, 3), (19, 3), (27, 18), (28, 8), (18, 11), (0, 17), (6, 14), (23, 0), (5, 0), (1, 14), (14, 11), (25, 9), (3, 1), (17, 8), (12, 7), (9, 8), (20, 7), (5, 16), (15, 4), (5, 18), (28, 18), (9, 17), (0, 8), (0, 9), (28, 5), (28, 15), (11, 4), (26, 17), (6, 5), (25, 14), (12, 6), (23, 2), (14, 6), (8, 10), (19, 17), (11, 18), (18, 19), (4, 11), (9, 16), (26, 11), (6, 6), (26, 9), (4, 3), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791750", "dataset": "MATH"}
{"messages": [{"content": "In a 27x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 16), (11, 5), (2, 24), (8, 21), (16, 0), (23, 14), (20, 12), (14, 20), (22, 2), (23, 22), (1, 20), (26, 0), (4, 5), (25, 11), (14, 21), (17, 22), (15, 20), (10, 16), (4, 23), (24, 12), (9, 0), (4, 7), (23, 24), (3, 24), (2, 19), (4, 24), (12, 14), (10, 12), (18, 5), (6, 16), (14, 3), (24, 0), (7, 20), (8, 8), (9, 13), (17, 4), (16, 23), (12, 6), (5, 6), (12, 24), (7, 10), (19, 0), (20, 13), (19, 22), (26, 5), (2, 0), (10, 1), (21, 12), (22, 17), (11, 8), (22, 0), (24, 9), (1, 24), (19, 24), (8, 9), (15, 5), (12, 22), (12, 15), (18, 6), (4, 10), (2, 1), (24, 10), (18, 2), (9, 17), (26, 17), (20, 14), (5, 14), (17, 6), (9, 10), (24, 16), (7, 3), (7, 2), (20, 17), (21, 24), (18, 17), (1, 16), (2, 9), (7, 12), (20, 7), (25, 8), (13, 8), (26, 22), (10, 13), (14, 16), (6, 12), (24, 17), (16, 2), (9, 3), (17, 18), (14, 15), (10, 17), (25, 19), (0, 21), (17, 19), (6, 14), (10, 14), (25, 21), (14, 8), (17, 11), (4, 15), (6, 8), (6, 18), (6, 1), (8, 5), (11, 17), (23, 0), (21, 21), (6, 15), (9, 11), (14, 9), (20, 23), (15, 23), (16, 5), (24, 8), (10, 8), (14, 23), (26, 20), (20, 9), (3, 5), (20, 22), (6, 0), (17, 13), (25, 2), (8, 20), (19, 6), (0, 24), (12, 3), (13, 20), (14, 24), (12, 20), (20, 5), (20, 1), (3, 2), (17, 7), (2, 15), (20, 3), (0, 7), (3, 10), (9, 22), (10, 2), (24, 18), (23, 13), (0, 9), (17, 15), (18, 12), (17, 10), (21, 14), (23, 7), (18, 11), (18, 23), (21, 8), (13, 3), (12, 8), (0, 4), (19, 1), (0, 17), (12, 0), (4, 17), (13, 24), (26, 21), (14, 6), (3, 19), (4, 20), (22, 24), (19, 18), (18, 20), (17, 5), (18, 14), (0, 23), (26, 12), (5, 23), (20, 8), (3, 9), (23, 16), (2, 21), (13, 16), (9, 5), (3, 11), (15, 17), (13, 2), (25, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380352", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 20), (9, 4), (14, 17), (17, 0), (19, 11), (11, 5), (18, 13), (7, 11), (4, 14), (2, 1), (3, 15), (10, 2), (12, 12), (9, 22), (13, 1), (9, 23), (19, 3), (16, 18), (21, 13), (7, 3), (18, 23), (6, 4), (4, 11), (14, 6), (7, 9), (12, 2), (8, 21), (10, 14), (17, 22), (9, 21), (10, 19), (21, 5), (18, 6), (14, 20), (9, 19), (3, 4), (18, 9), (21, 21), (6, 10), (16, 1), (14, 3), (18, 7), (2, 15), (8, 11), (15, 9), (11, 17), (2, 13), (4, 2), (10, 21), (20, 12), (4, 0), (17, 12), (4, 4), (20, 21), (9, 6), (2, 12), (18, 20), (16, 0), (1, 12), (12, 23), (10, 23), (16, 9), (16, 2), (11, 12), (18, 19), (10, 15), (12, 4), (7, 6), (9, 1), (13, 5), (10, 0), (20, 22), (15, 19), (8, 5), (14, 11), (14, 21), (21, 15), (6, 14), (2, 23), (5, 22), (20, 10), (19, 15), (9, 7), (3, 14), (14, 9), (6, 20), (16, 21), (3, 10), (16, 3), (3, 5), (11, 4), (1, 16), (18, 8), (1, 18), (4, 19), (2, 11), (14, 23), (4, 23), (10, 20), (7, 12), (0, 14), (13, 10), (6, 9), (8, 0), (3, 0), (15, 8), (13, 20), (6, 3), (10, 10), (20, 3), (5, 0), (7, 18), (5, 2), (19, 2), (6, 5), (9, 15), (0, 22), (11, 2), (8, 15), (2, 22), (9, 14), (19, 1), (1, 14), (17, 17), (12, 11), (10, 7), (14, 0), (15, 13), (11, 19), (9, 3), (15, 12), (16, 14), (17, 9), (15, 6), (14, 12), (9, 13), (12, 8), (3, 16), (8, 3), (3, 13), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "644508", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), 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), (6, 1), (10, 7), (1, 27), (13, 1), (7, 15), (15, 19), (11, 10), (20, 3), (13, 22), (8, 26), (7, 17), (13, 19), (12, 28), (7, 22), (11, 15), (0, 25), (2, 4), (1, 6), (2, 11), (20, 24), (12, 0), (4, 7), (17, 4), (3, 14), (17, 2), (4, 0), (21, 25), (15, 2), (15, 3), (15, 14), (10, 28), (10, 6), (9, 3), (3, 0), (2, 24), (20, 16), (9, 10), (19, 28), (0, 2), (21, 15), (15, 12), (16, 9), (3, 17), (3, 28), (7, 9), (10, 11), (3, 18), (16, 6), (4, 28), (21, 22), (16, 3), (11, 25), (3, 22), (17, 26), (13, 24), (13, 9), (17, 27), (18, 0), (8, 7), (1, 7), (6, 17), (19, 16), (16, 4), (18, 5), (21, 24), (1, 23), (14, 10), (21, 1), (20, 18), (20, 5), (20, 25), (10, 18), (0, 22), (12, 22), (10, 20), (10, 1), (17, 22), (0, 9), (0, 4), (9, 11), (3, 8), (2, 3), (2, 23), (14, 14), (17, 7), (11, 0), (11, 2), (18, 26), (2, 28), (9, 23), (15, 10), (2, 27), (20, 20), (4, 2), (20, 6), (2, 1), (12, 24), (5, 25), (14, 27), (6, 3), (6, 26), (14, 11), (13, 26), (15, 26), (19, 24), (14, 5), (10, 19), (8, 25), (1, 10), (5, 18), (6, 28), (11, 6), (16, 1), (19, 23), (6, 10), (16, 17), (5, 15), (12, 18), (10, 14), (7, 0), (21, 10), (3, 1), (15, 7), (4, 4), (4, 8), (14, 16), (5, 13), (10, 21), (19, 3), (19, 21), (7, 8), (12, 7), (13, 23), (19, 17), (14, 15), (4, 19), (20, 4), (4, 12), (4, 20), (3, 25), (3, 21), (6, 15), (13, 15), (8, 22), (0, 19), (4, 13), (13, 18), (11, 4), (3, 20), (5, 12), (14, 17), (12, 14), (5, 10), (11, 8), (11, 26), (2, 10), (12, 5), (3, 7), (10, 8), (7, 21), (17, 8), (10, 0), (20, 19), (16, 12), (9, 28), (7, 6), (2, 19), (2, 22), (15, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579000", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), 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), (6, 25), (4, 3), (23, 15), (13, 2), (16, 11), (9, 25), (11, 0), (19, 12), (18, 20), (6, 9), (8, 24), (20, 13), (1, 0), (17, 14), (22, 11), (1, 15), (3, 11), (10, 23), (6, 8), (12, 9), (4, 8), (12, 22), (25, 15), (12, 12), (22, 21), (8, 0), (14, 6), (4, 16), (17, 2), (0, 18), (21, 24), (12, 14), (11, 4), (25, 14), (24, 24), (4, 9), (14, 8), (25, 11), (22, 9), (2, 21), (5, 23), (16, 19), (24, 0), (24, 8), (10, 6), (12, 8), (1, 5), (3, 3), (16, 25), (6, 4), (3, 2), (5, 12), (19, 18), (0, 16), (9, 8), (1, 14), (15, 6), (19, 5), (6, 2), (24, 10), (13, 14), (10, 4), (2, 24), (13, 11), (25, 12), (11, 20), (5, 24), (10, 7), (24, 15), (9, 6), (23, 6), (12, 2), (21, 16), (3, 21), (20, 3), (13, 21), (0, 24), (16, 4), (13, 10), (17, 1), (2, 11), (7, 12), (3, 12), (18, 25), (21, 8), (4, 21), (19, 11), (13, 24), (22, 14), (11, 25), (11, 2), (19, 19), (21, 12), (7, 0), (17, 25), (11, 17), (0, 7), (22, 17), (5, 3), (13, 3), (2, 2), (8, 19), (22, 12), (13, 19), (6, 3), (16, 18), (18, 11), (18, 0), (20, 20), (15, 18), (20, 0), (25, 4), (20, 4), (10, 2), (25, 10), (0, 21), (25, 17), (18, 9), (11, 24), (7, 1), (18, 1), (7, 15), (8, 10), (20, 10), (9, 23), (6, 14), (23, 9), (2, 25), (12, 25), (13, 12), (9, 11), (8, 8), (3, 9), (12, 1), (22, 24), (25, 7), (20, 9), (14, 22), (14, 5), (13, 22), (14, 18), (16, 0), (18, 5), (10, 9), (21, 6), (15, 1), (5, 0), (10, 8), (23, 20), (8, 5), (5, 15), (15, 13), (19, 3), (1, 17), (8, 14), (19, 17), (11, 7), (21, 9), (24, 21), (14, 11), (19, 2), (23, 5), (8, 7), (5, 11), (5, 1), (23, 17), (21, 13), (23, 4), (3, 0), (18, 17), (14, 4), (21, 18), (17, 4), (14, 12), (8, 3), (17, 18), (6, 17), (13, 20), (21, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922821", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 20), (14, 15), (17, 9), (8, 2), (15, 6), (0, 5), (2, 23), (18, 3), (13, 10), (20, 8), (13, 6), (0, 8), (7, 3), (19, 21), (1, 6), (20, 4), (3, 19), (7, 0), (7, 10), (8, 19), (11, 16), (7, 22), (10, 0), (13, 8), (9, 20), (5, 9), (22, 10), (0, 12), (12, 2), (4, 8), (22, 13), (10, 17), (10, 14), (14, 0), (10, 1), (20, 12), (12, 3), (13, 21), (16, 2), (5, 18), (20, 6), (4, 17), (3, 23), (10, 6), (2, 17), (9, 10), (20, 20), (8, 20), (23, 7), (10, 20), (6, 19), (14, 2), (20, 17), (13, 19), (22, 17), (22, 18), (2, 9), (0, 4), (23, 3), (5, 20), (17, 19), (20, 23), (17, 0), (19, 6), (9, 2), (7, 17), (22, 21), (10, 13), (1, 9), (13, 15), (4, 3), (19, 11), (4, 2), (14, 4), (6, 14), (15, 22), (3, 16), (21, 23), (3, 12), (22, 22), (13, 22), (1, 23), (9, 8), (18, 18), (17, 23), (2, 13), (5, 23), (0, 21), (8, 13), (20, 21), (12, 15), (21, 13), (16, 0), (14, 23), (19, 7), (19, 2), (8, 8), (2, 18), (13, 9), (21, 7), (16, 15), (5, 3), (16, 13), (6, 9), (13, 7), (9, 6), (21, 21), (7, 19), (12, 4), (13, 18), (13, 4), (17, 6), (11, 14), (11, 10), (2, 10), (1, 22), (15, 23), (6, 0), (21, 4), (6, 6), (16, 21), (5, 22), (15, 16), (3, 21), (8, 23), (21, 9), (12, 11), (13, 23), (23, 2), (14, 11), (21, 6), (14, 8), (2, 14), (22, 23), (0, 18), (14, 3), (1, 12), (1, 19), (18, 10), (7, 4), (4, 0), (7, 20), (9, 9), (21, 18), (16, 7), (21, 17), (13, 3), (11, 20), (5, 13), (13, 16), (23, 0), (6, 5), (12, 20), (6, 7), (18, 21), (23, 17), (13, 11), (2, 22), (14, 19), (22, 15), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "929880", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 21), (7, 3), (17, 20), (17, 10), (14, 20), (5, 21), (5, 12), (23, 3), (3, 15), (22, 1), (10, 10), (3, 0), (2, 9), (15, 19), (8, 3), (6, 18), (6, 15), (18, 8), (13, 17), (5, 22), (2, 15), (19, 16), (9, 16), (15, 12), (5, 7), (21, 19), (18, 11), (13, 22), (15, 4), (1, 22), (1, 3), (3, 20), (4, 0), (22, 18), (19, 3), (15, 13), (19, 5), (5, 19), (5, 9), (23, 4), (3, 12), (2, 0), (22, 21), (5, 0), (6, 9), (18, 7), (5, 3), (18, 22), (9, 7), (1, 18), (8, 22), (10, 11), (4, 1), (2, 7), (0, 1), (12, 8), (18, 4), (2, 16), (23, 12), (18, 19), (17, 7), (13, 11), (16, 14), (20, 2), (23, 13), (0, 7), (9, 0), (13, 18), (13, 15), (22, 14), (0, 13), (1, 4), (16, 18), (2, 13), (13, 4), (5, 15), (7, 8), (3, 21), (22, 16), (17, 3), (8, 14), (18, 14), (9, 12), (5, 17), (6, 5), (13, 20), (2, 14), (16, 10), (9, 14), (1, 12), (3, 8), (10, 16), (17, 21), (0, 16), (0, 3), (7, 14), (13, 5), (22, 2), (20, 6), (17, 16), (12, 1), (19, 8), (10, 18), (5, 4), (22, 9), (21, 2), (11, 15), (23, 18), (4, 20), (5, 13), (17, 6), (20, 20), (9, 21), (18, 0), (12, 15), (10, 6), (19, 9), (3, 18), (8, 5), (22, 11), (16, 6), (17, 22), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "782079", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), 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), (1, 18), (28, 8), (13, 9), (5, 18), (1, 4), (19, 13), (1, 16), (20, 17), (3, 7), (26, 4), (27, 15), (28, 19), (5, 6), (12, 17), (28, 3), (19, 18), (6, 6), (0, 13), (2, 14), (16, 7), (20, 3), (13, 6), (19, 14), (14, 4), (16, 1), (11, 5), (18, 0), (3, 16), (9, 10), (17, 12), (11, 11), (25, 7), (6, 19), (26, 10), (24, 17), (18, 12), (26, 14), (18, 10), (4, 8), (6, 3), (25, 20), (1, 9), (21, 1), (28, 6), (27, 5), (8, 17), (13, 8), (21, 4), (14, 8), (17, 6), (15, 16), (17, 0), (8, 20), (5, 11), (20, 12), (7, 1), (21, 8), (13, 20), (16, 15), (22, 0), (27, 4), (15, 4), (13, 19), (0, 18), (15, 17), (6, 18), (22, 7), (1, 1), (10, 5), (19, 20), (13, 0), (5, 17), (18, 7), (9, 8), (24, 4), (2, 19), (4, 2), (11, 0), (6, 10), (20, 2), (1, 7), (20, 1), (16, 9), (22, 11), (17, 13), (24, 7), (11, 12), (18, 6), (15, 8), (28, 5), (23, 1), (28, 0), (3, 18), (27, 11), (24, 15), (21, 15), (13, 13), (4, 15), (26, 13), (0, 12), (26, 17), (15, 7), (0, 17), (8, 0), (24, 3), (3, 0), (25, 10), (20, 6), (15, 9), (22, 5), (12, 19), (3, 13), (1, 20), (12, 8), (22, 10), (27, 7), (21, 17), (13, 11), (26, 20), (13, 4), (23, 14), (21, 5), (4, 14), (4, 7), (8, 11), (19, 7), (9, 18), (16, 4), (24, 13), (5, 0), (20, 18), (12, 13), (4, 10), (12, 4), (12, 14), (6, 11), (12, 16), (9, 20), (2, 15), (11, 17), (8, 2), (21, 7), (13, 1), (22, 16), (10, 14), (15, 2), (5, 1), (7, 20), (1, 0), (12, 20), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730800", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 8), (15, 17), (1, 11), (0, 8), (21, 20), (17, 4), (7, 19), (2, 12), (18, 22), (14, 9), (7, 7), (12, 10), (2, 1), (20, 17), (11, 23), (12, 13), (18, 13), (5, 2), (17, 20), (0, 11), (3, 15), (4, 3), (9, 6), (15, 7), (14, 19), (18, 14), (4, 22), (18, 18), (2, 2), (20, 7), (8, 7), (9, 8), (5, 0), (14, 15), (18, 11), (9, 11), (3, 6), (20, 12), (3, 0), (7, 13), (3, 21), (17, 16), (11, 20), (16, 14), (21, 17), (21, 9), (19, 19), (21, 22), (11, 18), (20, 21), (3, 2), (10, 21), (18, 23), (4, 6), (11, 21), (10, 20), (12, 2), (18, 21), (2, 13), (19, 1), (20, 11), (20, 3), (13, 0), (14, 10), (0, 17), (17, 12), (13, 8), (10, 4), (13, 11), (20, 0), (14, 18), (5, 7), (11, 2), (11, 22), (5, 16), (0, 3), (19, 4), (19, 9), (15, 14), (18, 16), (12, 12), (4, 13), (9, 2), (18, 2), (7, 0), (14, 7), (7, 20), (4, 23), (0, 10), (13, 4), (1, 22), (6, 9), (15, 4), (16, 21), (0, 1), (1, 8), (19, 12), (3, 12), (21, 4), (12, 1), (2, 0), (8, 6), (10, 7), (9, 18), (6, 17), (5, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695478", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 15), (21, 16), (19, 7), (22, 7), (20, 7), (0, 1), (7, 8), (9, 7), (4, 13), (12, 0), (7, 17), (16, 6), (1, 16), (5, 14), (16, 18), (3, 13), (16, 1), (19, 1), (3, 15), (3, 8), (13, 8), (9, 1), (9, 11), (19, 11), (0, 14), (14, 7), (21, 11), (22, 2), (22, 14), (6, 2), (19, 3), (6, 10), (14, 13), (22, 3), (5, 16), (22, 1), (18, 9), (16, 3), (2, 4), (10, 7), (19, 14), (8, 6), (16, 13), (3, 9), (22, 4), (6, 15), (4, 6), (6, 8), (1, 15), (19, 8), (2, 10), (3, 5), (16, 19), (13, 9), (21, 19), (11, 10), (5, 9), (4, 17), (19, 10), (6, 14), (3, 2), (20, 1), (14, 16), (4, 9), (10, 18), (6, 19), (16, 8), (1, 9), (17, 11), (13, 15), (7, 10), (12, 11), (16, 9), (5, 10), (14, 10), (13, 0), (9, 9), (10, 5), (11, 14), (18, 11), (10, 0), (20, 8), (1, 1), (15, 11), (19, 13), (17, 1), (11, 19), (3, 11), (20, 12), (12, 16), (17, 4), (9, 13), (19, 4), (10, 12), (1, 18), (14, 11), (15, 2), (1, 3), (21, 10), (9, 12), (1, 12), (12, 18), (4, 0), (8, 0), (10, 6), (10, 19), (21, 6), (1, 6), (0, 18), (10, 4), (4, 12), (6, 18), (20, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367273", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (19, 7), (12, 8), (5, 15), (0, 4), (0, 9), (0, 12), (11, 19), (11, 20), (6, 22), (3, 14), (17, 22), (11, 13), (4, 2), (15, 7), (11, 3), (12, 4), (12, 0), (17, 19), (18, 22), (11, 1), (11, 21), (4, 10), (15, 22), (2, 21), (8, 16), (19, 13), (2, 1), (12, 18), (3, 15), (10, 6), (5, 5), (2, 20), (0, 3), (19, 10), (5, 3), (5, 21), (11, 0), (2, 13), (13, 10), (17, 0), (14, 4), (12, 13), (18, 5), (13, 13), (17, 16), (0, 8), (8, 13), (2, 17), (12, 21), (8, 7), (15, 17), (6, 11), (9, 3), (0, 1), (15, 18), (7, 14), (13, 20), (5, 4), (15, 10), (19, 9), (7, 18), (15, 12), (7, 12), (13, 18), (14, 2), (8, 18), (6, 10), (14, 1), (18, 2), (4, 15), (1, 19), (11, 11), (11, 22), (0, 21), (16, 4), (6, 14), (5, 16), (4, 5), (10, 9), (16, 17), (5, 0), (12, 15), (2, 18), (2, 15), (16, 8), (10, 17), (13, 7), (16, 19), (9, 9), (19, 0), (15, 16), (6, 16), (13, 3), (16, 11), (18, 18), (9, 0), (6, 1), (18, 9), (16, 16), (1, 14), (3, 2), (1, 5), (14, 16), (12, 6), (15, 13), (0, 19), (4, 16), (14, 20), (0, 11), (18, 6), (13, 2), (6, 5), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755433", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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), (19, 0), (18, 15), (5, 0), (16, 3), (2, 4), (19, 6), (20, 15), (17, 16), (2, 10), (17, 7), (2, 6), (4, 14), (18, 16), (1, 2), (7, 10), (9, 11), (14, 11), (15, 1), (20, 6), (5, 12), (8, 15), (19, 12), (8, 6), (4, 11), (2, 15), (6, 4), (6, 1), (9, 5), (5, 9), (10, 3), (20, 5), (9, 3), (15, 17), (10, 14), (2, 5), (0, 14), (17, 6), (20, 16), (17, 3), (12, 6), (10, 20), (13, 11), (1, 1), (10, 7), (13, 10), (1, 12), (14, 15), (7, 6), (0, 19), (18, 6), (14, 18), (3, 16), (5, 1), (15, 12), (14, 10), (14, 6), (12, 0), (10, 16), (8, 20), (8, 18), (8, 9), (19, 7), (4, 16), (0, 2), (10, 4), (19, 2), (18, 3), (1, 7), (9, 14), (16, 15), (11, 13), (15, 6), (6, 5), (7, 8), (0, 8), (20, 11), (13, 15), (8, 17), (12, 16), (11, 4), (19, 14), (14, 8), (4, 15), (7, 14), (1, 5), (20, 20), (6, 17), (13, 19), (16, 7), (9, 6), (1, 8), (8, 19), (19, 4), (6, 8), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31605", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 1), (13, 20), (24, 25), (24, 14), (12, 22), (12, 24), (14, 18), (20, 9), (19, 14), (8, 27), (21, 0), (27, 16), (22, 11), (26, 12), (6, 22), (18, 19), (13, 26), (5, 25), (8, 21), (21, 9), (16, 9), (22, 23), (12, 12), (11, 18), (22, 2), (23, 22), (12, 26), (2, 3), (15, 23), (2, 24), (1, 0), (10, 14), (20, 1), (6, 13), (4, 22), (22, 18), (5, 26), (17, 17), (16, 3), (18, 16), (16, 18), (14, 3), (9, 5), (22, 0), (20, 11), (17, 24), (17, 8), (27, 26), (9, 23), (3, 11), (2, 19), (24, 16), (3, 7), (3, 21), (12, 15), (22, 14), (19, 11), (8, 26), (16, 8), (13, 10), (14, 8), (11, 11), (2, 2), (1, 13), (24, 13), (22, 16), (7, 21), (18, 12), (6, 21), (24, 26), (23, 16), (6, 7), (8, 25), (15, 16), (2, 25), (15, 15), (9, 3), (11, 27), (1, 9), (3, 16), (26, 8), (10, 25), (22, 3), (6, 1), (8, 0), (12, 18), (14, 1), (22, 13), (20, 4), (2, 6), (13, 2), (11, 12), (6, 19), (23, 23), (14, 2), (0, 14), (14, 7), (26, 22), (13, 8), (23, 6), (7, 17), (17, 15), (12, 3), (7, 22), (14, 23), (0, 5), (12, 5), (13, 24), (27, 18), (17, 25), (22, 5), (25, 23), (18, 17), (18, 18), (6, 4), (6, 18), (20, 7), (5, 10), (18, 11), (23, 17), (10, 10), (15, 10), (21, 11), (6, 8), (23, 13), (1, 7), (3, 24), (24, 5), (18, 25), (9, 12), (10, 2), (19, 1), (7, 11), (2, 20), (22, 26), (11, 1), (19, 2), (16, 23), (11, 14), (16, 21), (17, 20), (21, 27), (11, 25), (11, 24), (15, 4), (25, 3), (1, 23), (19, 17), (6, 11), (24, 12), (24, 15), (8, 5), (8, 4), (8, 8), (6, 9), (25, 5), (17, 22), (24, 18), (19, 12), (7, 5), (3, 19), (21, 26), (0, 15), (9, 13), (23, 10), (2, 11), (17, 11), (0, 10), (7, 13), (8, 7), (19, 15), (1, 22), (16, 0), (3, 25), (27, 23), (11, 23), (0, 4), (1, 18), (20, 17), (18, 1), (13, 3), (10, 21), (12, 17), (26, 4), (6, 0), (20, 18), (14, 25), (12, 25), (23, 8), (22, 17), (3, 14), (8, 2), (11, 26), (26, 23), (3, 1), (17, 1), (0, 11), (13, 11), (3, 10), (19, 25), (9, 25), (27, 7), (17, 0), (0, 18), (5, 8), (18, 27), (11, 17), (7, 0), (25, 7), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604044", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (14, 8), (4, 20), (13, 4), (10, 18), (20, 25), (7, 9), (0, 18), (18, 24), (17, 16), (14, 7), (16, 25), (8, 1), (11, 6), (5, 26), (9, 6), (14, 10), (14, 17), (2, 16), (4, 2), (4, 24), (12, 15), (19, 15), (5, 12), (14, 2), (18, 26), (20, 4), (3, 6), (1, 18), (13, 23), (3, 10), (6, 5), (10, 15), (9, 11), (6, 20), (5, 18), (10, 26), (7, 5), (13, 25), (12, 5), (20, 10), (19, 0), (6, 13), (18, 21), (5, 17), (6, 0), (0, 2), (11, 10), (9, 25), (8, 25), (13, 13), (9, 2), (19, 8), (7, 6), (13, 18), (0, 24), (7, 12), (12, 23), (17, 2), (8, 3), (6, 9), (10, 19), (2, 13), (12, 13), (9, 4), (16, 24), (6, 6), (13, 20), (1, 6), (9, 12), (15, 13), (14, 18), (10, 17), (15, 0), (3, 25), (10, 10), (18, 2), (13, 26), (1, 5), (12, 22), (20, 9), (8, 8), (19, 5), (14, 16), (6, 11), (0, 12), (16, 12), (19, 12), (7, 8), (17, 23), (9, 17), (7, 23), (15, 2), (15, 15), (4, 16), (2, 5), (17, 10), (14, 0), (12, 10), (6, 24), (9, 24), (16, 19), (6, 14), (5, 23), (6, 10), (17, 21), (1, 19), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895562", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), 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), (13, 11), (3, 20), (19, 12), (19, 2), (5, 8), (9, 17), (14, 5), (14, 0), (9, 14), (13, 9), (11, 6), (19, 16), (15, 22), (17, 8), (2, 2), (18, 16), (5, 22), (17, 15), (17, 12), (7, 17), (8, 12), (3, 22), (3, 2), (3, 11), (0, 17), (18, 0), (19, 18), (13, 20), (1, 6), (1, 4), (10, 3), (17, 9), (15, 7), (9, 10), (1, 2), (9, 11), (7, 6), (4, 16), (13, 5), (1, 13), (11, 17), (8, 21), (10, 15), (16, 6), (10, 8), (15, 12), (9, 18), (19, 1), (15, 9), (12, 11), (3, 19), (11, 7), (11, 0), (3, 18), (16, 7), (14, 3), (12, 16), (15, 4), (5, 3), (5, 0), (12, 6), (12, 5), (20, 11), (16, 5), (1, 21), (11, 22), (1, 19), (12, 13), (2, 22), (17, 5), (14, 21), (5, 17), (18, 1), (10, 21), (8, 4), (6, 2), (1, 5), (7, 18), (12, 21), (5, 7), (8, 19), (11, 4), (13, 4), (1, 9), (17, 14), (8, 17), (7, 8), (6, 12), (8, 11), (9, 20), (9, 6), (4, 14), (9, 3), (13, 13), (9, 13), (1, 12), (20, 5), (11, 19), (18, 7), (19, 22), (16, 13), (2, 15), (1, 18), (10, 19), (20, 13), (3, 13), (6, 11), (0, 22), (1, 20), (8, 9), (11, 16), (2, 18), (0, 21), (20, 6), (9, 2), (8, 3), (18, 15), (7, 15), (12, 2), (0, 3), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474052", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 26), (17, 23), (24, 19), (3, 8), (18, 12), (23, 17), (2, 26), (24, 16), (19, 13), (8, 10), (0, 16), (20, 10), (9, 21), (15, 13), (23, 15), (28, 25), (1, 25), (16, 10), (6, 10), (21, 1), (22, 19), (11, 6), (7, 5), (12, 23), (10, 9), (20, 13), (0, 10), (25, 25), (3, 13), (15, 17), (21, 6), (11, 0), (8, 25), (26, 17), (13, 7), (18, 25), (16, 15), (21, 13), (28, 6), (28, 21), (10, 1), (9, 25), (27, 10), (15, 25), (4, 21), (22, 20), (25, 10), (10, 17), (1, 4), (27, 23), (5, 8), (27, 0), (4, 14), (25, 1), (11, 8), (9, 14), (24, 24), (14, 12), (14, 7), (23, 1), (24, 4), (14, 1), (9, 7), (27, 25), (0, 9), (26, 25), (14, 25), (14, 14), (14, 8), (2, 9), (2, 11), (16, 20), (28, 13), (15, 8), (1, 18), (26, 1), (6, 3), (21, 21), (17, 1), (24, 10), (23, 25), (8, 21), (7, 22), (20, 25), (0, 11), (7, 2), (5, 10), (17, 7), (6, 6), (18, 23), (23, 2), (19, 2), (9, 6), (19, 23), (15, 12), (19, 22), (7, 9), (14, 17), (13, 21), (12, 20), (5, 19), (18, 2), (11, 15), (12, 9), (28, 15), (21, 26), (6, 26), (1, 2), (23, 14), (13, 3), (12, 11), (8, 4), (22, 10), (12, 10), (9, 22), (24, 22), (18, 20), (5, 1), (25, 4), (2, 10), (14, 18), (5, 7), (10, 22), (6, 2), (2, 17), (27, 11), (2, 2), (22, 17), (12, 2), (0, 19), (9, 4), (23, 22), (3, 20), (7, 4), (10, 13), (0, 5), (28, 17), (7, 12), (6, 14), (13, 26), (0, 22), (5, 2), (14, 5), (12, 8), (6, 1), (14, 11), (8, 12), (1, 0), (3, 0), (21, 16), (11, 23), (20, 4), (20, 24), (2, 6), (13, 1), (14, 16), (22, 6), (6, 9), (13, 22), (20, 16), (25, 18), (10, 20), (7, 21), (12, 25), (16, 21), (21, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195966", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 23), (28, 14), (25, 7), (21, 12), (10, 13), (21, 5), (3, 14), (23, 9), (24, 18), (0, 7), (17, 19), (20, 16), (28, 7), (26, 9), (9, 8), (18, 8), (17, 11), (11, 19), (7, 18), (24, 20), (6, 4), (14, 17), (17, 21), (20, 14), (15, 5), (13, 11), (9, 14), (15, 16), (4, 8), (1, 7), (17, 10), (22, 21), (16, 4), (19, 9), (8, 12), (4, 9), (3, 8), (22, 4), (26, 0), (4, 16), (27, 16), (26, 10), (5, 2), (13, 14), (3, 17), (23, 6), (3, 22), (14, 11), (7, 0), (12, 19), (17, 5), (24, 5), (12, 13), (19, 5), (28, 10), (28, 4), (14, 12), (14, 20), (28, 19), (4, 20), (19, 1), (5, 12), (5, 20), (12, 9), (16, 10), (25, 21), (1, 14), (2, 6), (7, 3), (16, 17), (17, 0), (3, 4), (15, 13), (27, 4), (19, 22), (21, 10), (6, 17), (20, 19), (13, 10), (3, 11), (15, 1), (17, 8), (25, 17), (6, 10), (26, 4), (23, 2), (18, 23), (24, 4), (17, 3), (26, 1), (0, 1), (22, 23), (2, 21), (2, 10), (6, 23), (24, 1), (28, 12), (21, 3), (5, 0), (23, 15), (18, 0), (24, 23), (19, 8), (14, 6), (13, 5), (27, 7), (24, 17), (12, 4), (22, 10), (22, 18), (12, 21), (11, 5), (19, 6), (14, 1), (20, 7), (5, 11), (8, 9), (20, 10), (6, 13), (11, 3), (19, 18), (12, 0), (18, 20), (6, 14), (11, 17), (3, 3), (23, 21), (4, 13), (3, 19), (28, 17), (23, 1), (5, 19), (18, 17), (18, 11), (18, 2), (10, 8), (16, 11), (6, 11), (21, 13), (1, 17), (2, 4), (5, 7), (4, 15), (10, 16), (12, 8), (19, 10), (15, 11), (11, 23), (4, 11), (2, 12), (10, 15), (7, 1), (12, 7), (22, 16), (6, 18), (26, 3), (10, 19), (12, 12), (25, 1), (15, 21), (3, 1), (15, 7), (14, 2), (14, 19), (27, 6), (26, 20), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712380", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (20, 1), (4, 20), (4, 22), (3, 18), (21, 1), (19, 18), (1, 20), (1, 16), (15, 14), (12, 15), (21, 18), (5, 1), (15, 6), (14, 24), (16, 2), (5, 8), (16, 1), (12, 25), (18, 7), (9, 10), (18, 24), (5, 17), (17, 12), (19, 22), (16, 21), (8, 7), (5, 23), (8, 6), (15, 19), (18, 18), (4, 15), (4, 9), (7, 20), (18, 16), (14, 0), (11, 8), (14, 5), (1, 15), (19, 13), (8, 2), (21, 23), (5, 25), (4, 14), (18, 23), (13, 11), (18, 14), (2, 6), (7, 9), (19, 17), (15, 8), (2, 17), (6, 21), (13, 8), (17, 6), (15, 17), (1, 9), (2, 11), (10, 13), (17, 0), (7, 14), (11, 19), (20, 15), (19, 21), (12, 24), (8, 17), (15, 20), (14, 2), (21, 16), (4, 24), (3, 2), (14, 8), (1, 6), (20, 8), (14, 13), (13, 6), (15, 7), (4, 17), (4, 12), (20, 11), (5, 4), (11, 14), (10, 22), (14, 4), (18, 22), (12, 18), (6, 3), (5, 16), (14, 22), (15, 3), (1, 19), (7, 3), (21, 9), (21, 5), (17, 21), (21, 15), (2, 7), (6, 5), (10, 0), (16, 18), (1, 1), (11, 10), (16, 8), (0, 7), (4, 16), (8, 25), (7, 18), (3, 8), (21, 24), (18, 12), (3, 4), (11, 9), (21, 13), (0, 11), (15, 13), (6, 6), (13, 21), (7, 6), (13, 15), (18, 8), (11, 2), (5, 15), (21, 12), (12, 22), (20, 0), (6, 10), (20, 9), (0, 15), (14, 18), (4, 10), (9, 23), (19, 1), (20, 14), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949500", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 26), (9, 20), (16, 4), (17, 14), (1, 10), (11, 1), (20, 17), (6, 13), (19, 23), (1, 26), (20, 14), (16, 9), (13, 21), (3, 6), (7, 4), (7, 0), (23, 23), (25, 19), (13, 14), (13, 26), (23, 17), (4, 21), (9, 10), (16, 24), (9, 18), (10, 10), (12, 15), (0, 17), (25, 20), (2, 13), (18, 23), (23, 24), (11, 5), (16, 17), (11, 25), (13, 20), (23, 10), (16, 15), (21, 25), (9, 8), (10, 23), (23, 16), (7, 19), (9, 9), (21, 8), (15, 18), (1, 3), (18, 0), (7, 11), (7, 16), (21, 11), (10, 21), (4, 1), (3, 16), (21, 6), (10, 2), (12, 10), (11, 18), (13, 23), (12, 22), (22, 3), (11, 16), (18, 5), (10, 8), (9, 13), (22, 1), (9, 22), (0, 2), (12, 4), (19, 1), (22, 2), (5, 11), (1, 20), (10, 24), (23, 2), (21, 1), (12, 23), (16, 0), (13, 4), (4, 16), (18, 22), (22, 25), (15, 20), (20, 15), (4, 15), (3, 9), (25, 15), (1, 24), (20, 12), (12, 1), (13, 0), (5, 23), (6, 6), (20, 16), (17, 21), (15, 25), (16, 7), (11, 9), (2, 24), (5, 3), (11, 20), (8, 25), (15, 26), (1, 2), (24, 14), (25, 18), (7, 18), (20, 7), (23, 18), (14, 19), (16, 1), (5, 5), (14, 9), (13, 16), (20, 23), (24, 2), (6, 14), (9, 5), (6, 22), (0, 8), (0, 3), (6, 20), (4, 26), (14, 0), (14, 5), (18, 24), (18, 11), (10, 4), (13, 24), (10, 12), (11, 15), (9, 26), (10, 6), (23, 22), (19, 11), (21, 19), (5, 22), (25, 5), (13, 2), (0, 10), (16, 22), (22, 15), (4, 2), (5, 16), (24, 11), (8, 5), (13, 15), (14, 14), (24, 22), (17, 18), (11, 13), (19, 2), (23, 25), (16, 12), (19, 25), (0, 14), (7, 5), (25, 1), (3, 21), (5, 8), (8, 7), (10, 7), (5, 14), (24, 5), (8, 19), (18, 7), (6, 25), (4, 20), (21, 15), (17, 7), (22, 17), (7, 12), (2, 25), (6, 7), (5, 21), (14, 2), (3, 13), (6, 3), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "595041", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 8), (1, 7), (19, 19), (13, 16), (0, 13), (11, 20), (4, 0), (9, 20), (17, 3), (1, 11), (15, 19), (7, 1), (11, 5), (17, 13), (8, 2), (9, 5), (18, 21), (16, 6), (2, 6), (12, 12), (14, 5), (12, 15), (0, 5), (1, 13), (12, 9), (6, 5), (3, 10), (9, 11), (1, 16), (14, 14), (7, 12), (9, 10), (19, 7), (6, 17), (11, 21), (12, 7), (2, 0), (17, 7), (17, 20), (5, 16), (17, 14), (15, 8), (17, 9), (19, 3), (9, 2), (14, 9), (15, 5), (15, 2), (15, 17), (5, 3), (6, 18), (3, 3), (16, 14), (4, 4), (1, 12), (0, 7), (7, 4), (2, 3), (3, 8), (4, 18), (7, 18), (18, 5), (15, 18), (13, 14), (16, 21), (13, 17), (4, 2), (4, 10), (15, 0), (17, 17), (8, 1), (18, 10), (14, 12), (10, 1), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555320", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 21), (3, 0), (19, 4), (8, 13), (3, 10), (16, 17), (8, 6), (9, 1), (4, 12), (5, 0), (5, 14), (7, 20), (20, 2), (0, 11), (13, 11), (9, 12), (15, 12), (5, 19), (19, 7), (5, 1), (16, 20), (6, 0), (10, 11), (0, 20), (5, 4), (20, 15), (6, 13), (19, 6), (11, 14), (17, 17), (3, 17), (9, 16), (9, 7), (3, 7), (19, 14), (8, 14), (9, 18), (1, 10), (18, 7), (17, 4), (2, 20), (1, 6), (3, 9), (1, 18), (4, 14), (0, 13), (12, 21), (16, 16), (11, 12), (15, 4), (4, 11), (7, 7), (11, 15), (3, 4), (17, 13), (18, 8), (18, 9), (11, 10), (7, 12), (18, 13), (13, 1), (3, 14), (9, 17), (16, 4), (7, 2), (11, 7), (12, 13), (13, 8), (15, 5), (10, 9), (1, 13), (10, 4), (15, 16), (13, 10), (8, 11), (11, 0), (4, 15), (13, 20), (11, 5), (3, 2), (17, 9), (8, 5), (10, 15), (18, 14), (11, 21), (0, 6), (12, 14), (5, 11), (6, 3), (20, 16), (8, 12), (16, 19), (19, 21), (18, 10), (18, 5), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "881828", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), 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), (19, 16), (6, 5), (0, 8), (9, 12), (16, 8), (5, 22), (5, 19), (4, 16), (3, 17), (19, 2), (24, 3), (14, 1), (10, 18), (17, 20), (2, 0), (5, 4), (27, 0), (1, 8), (18, 13), (22, 11), (12, 28), (15, 17), (8, 5), (0, 19), (18, 18), (27, 8), (5, 17), (10, 0), (10, 15), (26, 18), (17, 21), (14, 6), (27, 4), (19, 12), (22, 6), (12, 3), (13, 8), (9, 18), (22, 26), (5, 11), (10, 2), (19, 28), (27, 14), (6, 12), (9, 9), (25, 12), (7, 6), (0, 1), (6, 16), (24, 27), (27, 6), (18, 3), (14, 5), (25, 5), (5, 24), (22, 7), (20, 10), (19, 27), (27, 28), (7, 18), (21, 6), (13, 26), (14, 18), (15, 18), (13, 3), (20, 12), (2, 22), (12, 26), (0, 15), (16, 20), (23, 18), (3, 7), (7, 14), (3, 16), (27, 27), (10, 7), (24, 7), (20, 4), (5, 8), (16, 23), (26, 12), (8, 26), (16, 21), (18, 20), (5, 1), (20, 8), (10, 22), (11, 25), (27, 11), (2, 7), (21, 16), (18, 11), (24, 13), (17, 18), (25, 7), (15, 27), (7, 25), (11, 11), (11, 17), (13, 11), (22, 8), (24, 11), (17, 6), (27, 23), (9, 5), (9, 4), (14, 9), (2, 15), (7, 4), (21, 20), (16, 18), (9, 28), (16, 19), (1, 9), (12, 14), (24, 9), (8, 25), (6, 11), (2, 13), (11, 23), (13, 14), (3, 10), (0, 5), (10, 23), (2, 5), (21, 27), (15, 12), (14, 25), (10, 17), (17, 17), (24, 18), (18, 9), (27, 3), (18, 0), (9, 20), (3, 4), (14, 12), (3, 18), (28, 10), (9, 14), (15, 23), (10, 4), (28, 23), (12, 10), (28, 8), (9, 10), (25, 23), (17, 26), (17, 16), (0, 12), (6, 4), (13, 20), (12, 9), (2, 23), (25, 22), (1, 12), (26, 15), (24, 25), (20, 6), (8, 24), (1, 18), (19, 13), (12, 8), (25, 8), (15, 15), (20, 1), (7, 24), (22, 27), (18, 6), (6, 17), (23, 25), (3, 14), (0, 28), (19, 17), (26, 26), (1, 6), (23, 10), (4, 7), (8, 8), (14, 8), (9, 25), (28, 2), (25, 9), (11, 27), (17, 2), (2, 6), (20, 24), (22, 2), (10, 16), (28, 25), (21, 9), (24, 26), (5, 12), (12, 22), (24, 24), (22, 10), (3, 25), (22, 17), (25, 3), (4, 8), (20, 23), (3, 3), (20, 13), (6, 28), (27, 12), (1, 7), (15, 25), (24, 21), (4, 25), (1, 17), (14, 22), (12, 7), (3, 6), (13, 25), (21, 0), (10, 13), (14, 16), (16, 0), (6, 26), (1, 4), (21, 14), (4, 13), (17, 28), (13, 23), (17, 7), (20, 26), (19, 0), (10, 24), (14, 7), (9, 3), (6, 18), (21, 24), (5, 14), (5, 15), (8, 22), (12, 4), (14, 4), (15, 0), (16, 27), (15, 21), (11, 28), (17, 1), (26, 19), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634752", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 20), (19, 0), (10, 15), (16, 4), (19, 4), (4, 15), (8, 21), (1, 3), (0, 9), (6, 12), (2, 2), (17, 7), (4, 4), (6, 7), (8, 19), (8, 2), (15, 20), (4, 6), (1, 21), (12, 2), (20, 25), (13, 9), (3, 13), (1, 24), (11, 16), (17, 4), (10, 0), (17, 20), (4, 14), (9, 1), (14, 11), (17, 21), (9, 11), (13, 21), (8, 4), (21, 12), (11, 4), (13, 14), (12, 22), (10, 25), (5, 2), (19, 22), (0, 18), (19, 1), (12, 12), (21, 21), (9, 25), (7, 4), (14, 5), (1, 6), (13, 6), (13, 25), (20, 20), (3, 23), (0, 10), (14, 25), (13, 11), (1, 7), (7, 21), (7, 14), (2, 15), (17, 6), (4, 12), (20, 18), (8, 14), (13, 10), (17, 13), (9, 15), (14, 15), (7, 25), (9, 18), (18, 9), (10, 13), (13, 3), (3, 21), (16, 6), (11, 17), (18, 4), (4, 13), (17, 23), (12, 21), (12, 3), (21, 20), (1, 20), (14, 16), (18, 23), (9, 14), (11, 12), (1, 5), (5, 20), (17, 0), (16, 17), (11, 2), (14, 20), (8, 13), (0, 8), (21, 23), (18, 13), (8, 9), (4, 18), (21, 19), (14, 0), (12, 17), (9, 9), (0, 14), (18, 6), (8, 15), (3, 5), (0, 17), (10, 23), (9, 3), (4, 2), (15, 4), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154642", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (13, 23), (24, 4), (17, 21), (3, 5), (22, 11), (17, 18), (13, 17), (13, 14), (3, 23), (15, 4), (6, 12), (5, 6), (23, 21), (2, 8), (2, 5), (23, 8), (24, 5), (1, 21), (12, 8), (0, 24), (20, 2), (17, 7), (18, 20), (4, 12), (14, 5), (18, 18), (15, 13), (6, 15), (4, 21), (18, 14), (4, 5), (20, 9), (15, 3), (23, 11), (14, 24), (1, 9), (23, 17), (8, 15), (11, 16), (9, 17), (9, 21), (20, 10), (16, 20), (5, 23), (15, 16), (8, 3), (12, 7), (3, 22), (21, 4), (12, 15), (19, 8), (4, 4), (3, 15), (4, 17), (10, 5), (11, 22), (4, 18), (4, 11), (16, 2), (16, 6), (11, 0), (3, 4), (1, 2), (14, 15), (23, 14), (7, 23), (22, 22), (11, 13), (2, 14), (1, 1), (18, 10), (8, 1), (17, 19), (17, 15), (10, 4), (22, 4), (16, 8), (24, 14), (7, 7), (3, 13), (9, 9), (14, 22), (16, 5), (15, 14), (24, 19), (16, 19), (13, 24), (24, 3), (20, 6), (5, 7), (9, 2), (2, 17), (10, 0), (19, 19), (2, 11), (17, 4), (0, 4), (17, 22), (14, 9), (23, 4), (5, 12), (5, 1), (3, 20), (3, 9), (20, 7), (17, 0), (2, 0), (10, 22), (13, 20), (14, 19), (2, 3), (21, 6), (21, 11), (17, 9), (21, 24), (9, 22), (22, 9), (6, 18), (13, 1), (3, 24), (23, 5), (11, 7), (8, 8), (16, 13), (23, 0), (19, 21), (24, 2), (14, 18), (3, 7), (13, 16), (7, 5), (7, 17), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701620", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), 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), (0, 6), (10, 13), (0, 8), (22, 0), (18, 8), (6, 18), (15, 18), (23, 16), (18, 21), (8, 2), (9, 16), (10, 8), (19, 7), (11, 13), (9, 21), (22, 16), (22, 5), (4, 12), (11, 6), (12, 12), (17, 7), (10, 0), (23, 11), (2, 21), (5, 7), (6, 12), (14, 16), (9, 2), (22, 2), (14, 14), (2, 10), (1, 21), (21, 12), (12, 17), (10, 15), (1, 0), (21, 14), (3, 12), (6, 15), (3, 5), (13, 4), (5, 18), (21, 6), (3, 11), (4, 15), (12, 11), (2, 16), (17, 5), (7, 2), (16, 16), (9, 13), (17, 12), (22, 14), (10, 10), (7, 15), (8, 19), (4, 6), (0, 21), (8, 12), (12, 0), (6, 3), (17, 2), (2, 7), (18, 20), (23, 10), (23, 15), (4, 5), (14, 12), (20, 3), (18, 18), (7, 8), (4, 13), (1, 16), (8, 5), (2, 13), (10, 20), (10, 14), (12, 10), (11, 20), (19, 17), (1, 12), (12, 14), (9, 0), (13, 21), (13, 12), (23, 2), (23, 8), (18, 5), (23, 18), (15, 6), (16, 11), (23, 19), (0, 16), (3, 2), (7, 6), (14, 20), (21, 19), (14, 4), (13, 19), (14, 8), (7, 12), (15, 8), (16, 20), (7, 9), (16, 19), (3, 19), (7, 11), (10, 2), (7, 3), (11, 14), (3, 15), (9, 9), (0, 19), (4, 0), (20, 6), (2, 6), (17, 21), (12, 1), (0, 20), (0, 3), (22, 13), (9, 18), (16, 7), (2, 12), (13, 14), (2, 9), (13, 13), (19, 19), (18, 1), (11, 8), (9, 17), (4, 2), (5, 9), (8, 7), (9, 6), (5, 10), (15, 1), (12, 7), (13, 10), (17, 1), (11, 18), (11, 7), (22, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376320", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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, 8), (14, 10), (11, 22), (14, 9), (3, 15), (4, 8), (6, 10), (6, 24), (21, 8), (21, 3), (8, 22), (6, 5), (4, 21), (23, 3), (9, 13), (3, 6), (18, 19), (17, 11), (12, 21), (2, 3), (20, 2), (14, 1), (6, 15), (15, 21), (3, 21), (22, 16), (12, 12), (0, 7), (12, 10), (12, 22), (15, 15), (2, 24), (16, 9), (22, 15), (10, 9), (20, 21), (17, 2), (19, 6), (22, 4), (5, 23), (7, 16), (16, 15), (20, 1), (11, 18), (19, 12), (13, 21), (22, 19), (20, 4), (9, 11), (21, 10), (1, 5), (15, 13), (0, 12), (8, 15), (5, 6), (22, 14), (10, 10), (3, 9), (20, 0), (2, 4), (4, 1), (23, 23), (6, 19), (6, 14), (10, 22), (17, 16), (10, 24), (5, 3), (7, 2), (20, 17), (12, 20), (4, 24), (10, 1), (4, 0), (5, 5), (13, 4), (9, 18), (11, 10), (0, 2), (3, 24), (8, 13), (21, 1), (4, 7), (2, 17), (7, 20), (10, 2), (2, 13), (23, 15), (19, 9), (3, 13), (16, 4), (13, 6), (18, 14), (4, 2), (23, 11), (13, 9), (9, 4), (22, 13), (17, 4), (15, 7), (11, 4), (7, 1), (19, 2), (10, 7), (2, 1), (13, 1), (8, 18), (18, 1), (4, 13), (15, 20), (5, 11), (7, 24), (20, 10), (8, 10), (16, 11), (16, 8), (23, 20), (12, 6), (11, 2), (4, 15), (4, 3), (16, 1), (15, 8), (10, 4), (16, 20), (0, 23), (19, 11), (15, 11), (9, 20), (1, 11), (4, 16), (1, 9), (3, 23), (12, 7), (13, 5), (10, 16), (9, 7), (16, 22), (2, 19), (1, 22), (17, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907323", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 20), (15, 14), (16, 9), (8, 9), (17, 4), (10, 0), (20, 15), (20, 7), (21, 14), (21, 8), (13, 17), (13, 18), (23, 3), (7, 10), (23, 13), (18, 1), (5, 14), (23, 16), (8, 17), (22, 12), (22, 14), (19, 0), (22, 6), (22, 16), (20, 3), (22, 15), (4, 12), (7, 17), (19, 1), (16, 15), (13, 13), (5, 8), (14, 5), (0, 11), (19, 8), (9, 19), (0, 18), (22, 11), (2, 0), (15, 13), (20, 11), (18, 14), (9, 13), (1, 18), (23, 5), (14, 10), (0, 12), (11, 10), (19, 17), (11, 18), (15, 8), (10, 1), (6, 2), (8, 8), (13, 19), (15, 0), (7, 8), (1, 2), (0, 10), (15, 18), (8, 7), (20, 17), (6, 14), (4, 17), (6, 16), (2, 7), (4, 9), (10, 13), (9, 12), (15, 19), (10, 20), (14, 4), (5, 10), (3, 17), (4, 10), (11, 5), (14, 8), (11, 16), (11, 13), (2, 11), (1, 9), (2, 8), (23, 18), (13, 20), (21, 19), (20, 18), (1, 11), (6, 9), (2, 6), (23, 15), (19, 18), (3, 3), (18, 12), (18, 17), (19, 10), (7, 0), (12, 7), (18, 8), (9, 5), (9, 10), (17, 12), (16, 4), (4, 4), (12, 2), (12, 4), (1, 5), (20, 5), (0, 9), (17, 2), (16, 10), (3, 4), (12, 8), (23, 8), (0, 16), (1, 3), (9, 4), (22, 20), (13, 6), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977958", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 27), (27, 23), (16, 9), (1, 14), (8, 9), (7, 13), (6, 13), (16, 4), (20, 20), (19, 5), (20, 8), (7, 26), (0, 26), (25, 19), (6, 22), (26, 7), (12, 23), (13, 7), (14, 23), (11, 25), (26, 25), (27, 2), (20, 28), (18, 17), (27, 16), (28, 26), (15, 26), (21, 24), (28, 17), (11, 24), (16, 1), (13, 25), (17, 10), (27, 11), (8, 16), (16, 18), (19, 7), (6, 25), (17, 20), (6, 11), (1, 5), (3, 5), (25, 1), (0, 15), (26, 13), (5, 22), (18, 12), (8, 11), (24, 3), (18, 28), (28, 24), (9, 1), (17, 19), (8, 13), (19, 21), (19, 4), (18, 0), (11, 6), (10, 8), (15, 16), (24, 27), (26, 18), (17, 2), (4, 25), (5, 9), (3, 12), (8, 25), (15, 0), (13, 1), (4, 16), (4, 3), (14, 15), (8, 27), (4, 4), (11, 9), (11, 23), (14, 10), (16, 7), (12, 1), (5, 11), (0, 22), (7, 11), (27, 25), (28, 3), (6, 12), (6, 19), (8, 18), (15, 5), (4, 5), (27, 27), (22, 10), (17, 16), (28, 7), (14, 27), (15, 3), (18, 6), (7, 21), (10, 28), (11, 16), (0, 23), (5, 21), (25, 12), (1, 16), (21, 4), (2, 27), (16, 23), (24, 17), (24, 21), (1, 8), (24, 5), (5, 0), (13, 6), (8, 23), (21, 21), (24, 15), (27, 6), (24, 11), (3, 7), (24, 19), (3, 13), (27, 8), (12, 24), (12, 21), (7, 27), (12, 18), (4, 18), (0, 7), (10, 23), (24, 28), (8, 2), (10, 11), (22, 25), (12, 17), (1, 28), (18, 3), (7, 23), (27, 22), (19, 3), (27, 0), (26, 26), (22, 3), (19, 17), (16, 8), (4, 7), (21, 28), (28, 12), (28, 21), (18, 14), (20, 4), (11, 20), (10, 6), (19, 13), (24, 16), (12, 8), (10, 1), (24, 23), (20, 7), (11, 8), (11, 19), (13, 18), (6, 21), (0, 18), (4, 1), (1, 20), (9, 19), (24, 18), (15, 18), (7, 14), (3, 0), (24, 24), (21, 13), (28, 23), (8, 8), (5, 25), (0, 14), (1, 9), (22, 21), (6, 20), (22, 2), (1, 19), (19, 15), (20, 2), (28, 22), (19, 26), (22, 4), (28, 6), (13, 16), (10, 15), (17, 1), (20, 24), (8, 28), (23, 3), (13, 12), (15, 11), (6, 24), (6, 10), (11, 27), (13, 14), (9, 8), (15, 24), (28, 4), (23, 6), (15, 23), (13, 23), (22, 6), (17, 22), (2, 20), (11, 28), (2, 17), (25, 17), (7, 2), (10, 20), (7, 10), (7, 17), (23, 15), (14, 7), (25, 16), (23, 16), (14, 18), (3, 27), (7, 28), (16, 6), (6, 5), (2, 25), (10, 16), (3, 3), (24, 14), (22, 17), (16, 24), (23, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919296", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 11), (21, 9), (12, 3), (9, 6), (11, 8), (9, 7), (20, 8), (21, 13), (11, 18), (23, 13), (0, 2), (20, 13), (9, 4), (18, 2), (13, 12), (9, 14), (7, 0), (21, 21), (20, 21), (12, 20), (10, 15), (4, 1), (2, 13), (19, 17), (17, 0), (14, 18), (5, 5), (21, 4), (8, 21), (14, 16), (20, 4), (23, 8), (15, 8), (15, 1), (16, 21), (12, 18), (22, 15), (10, 17), (10, 11), (14, 2), (7, 3), (3, 2), (13, 17), (4, 4), (14, 8), (3, 0), (1, 4), (21, 16), (0, 21), (20, 3), (20, 0), (6, 2), (1, 17), (1, 13), (16, 9), (2, 9), (7, 18), (18, 17), (23, 5), (24, 13), (21, 18), (9, 8), (6, 7), (19, 14), (12, 19), (10, 7), (20, 12), (20, 16), (20, 18), (23, 0), (23, 17), (16, 16), (11, 14), (7, 15), (5, 10), (7, 17), (21, 2), (22, 3), (24, 10), (18, 15), (16, 2), (12, 16), (5, 8), (8, 16), (19, 13), (9, 11), (6, 10), (21, 1), (11, 4), (8, 11), (14, 9), (5, 7), (6, 14), (9, 19), (6, 21), (7, 21), (13, 1), (16, 10), (20, 1), (18, 21), (13, 7), (20, 7), (2, 20), (5, 17), (13, 5), (2, 17), (23, 9), (7, 7), (4, 19), (12, 11), (18, 10), (15, 13), (9, 3), (20, 14), (6, 17), (23, 14), (16, 12), (2, 8), (10, 20), (13, 2), (18, 18), (14, 17), (2, 16), (14, 0), (6, 4), (21, 7), (5, 1), (17, 3), (18, 7), (22, 14), (0, 7), (18, 11), (11, 5), (16, 4), (7, 1), (12, 7), (22, 13), (6, 16), (1, 0), (19, 2), (16, 17), (15, 9), (6, 15), (9, 12), (5, 11), (21, 6), (2, 0), (11, 2), (10, 13), (4, 0), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359604", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (20, 12), (7, 3), (5, 10), (8, 17), (25, 10), (24, 22), (12, 9), (16, 13), (16, 16), (21, 8), (18, 14), (14, 7), (9, 18), (22, 7), (10, 4), (13, 9), (17, 1), (24, 7), (3, 0), (0, 2), (4, 11), (14, 13), (10, 21), (0, 14), (15, 2), (17, 15), (7, 4), (11, 5), (10, 20), (13, 0), (15, 14), (14, 10), (19, 7), (22, 19), (15, 11), (15, 8), (23, 0), (20, 11), (6, 18), (21, 22), (5, 21), (26, 7), (18, 19), (17, 19), (4, 15), (23, 21), (23, 11), (5, 15), (19, 9), (2, 8), (19, 10), (21, 13), (19, 18), (9, 7), (21, 4), (18, 0), (8, 6), (24, 13), (6, 13), (2, 19), (15, 10), (4, 21), (10, 5), (9, 5), (4, 2), (15, 7), (18, 9), (24, 6), (7, 12), (24, 5), (6, 4), (0, 4), (6, 5), (5, 7), (20, 0), (14, 0), (25, 2), (23, 4), (6, 16), (18, 11), (26, 12), (16, 10), (10, 17), (16, 17), (21, 20), (26, 20), (4, 4), (26, 14), (22, 20), (19, 16), (13, 12), (20, 5), (22, 22), (3, 22), (3, 20), (10, 22), (23, 14), (24, 18), (11, 6), (25, 1), (9, 2), (22, 0), (23, 17), (25, 7), (16, 22), (11, 17), (16, 12), (6, 9), (11, 9), (24, 3), (15, 13), (3, 12), (25, 22), (18, 12), (20, 3), (26, 19), (23, 19), (4, 10), (0, 8), (3, 4), (4, 17), (20, 21), (26, 18), (24, 11), (2, 9), (16, 11), (20, 4), (25, 9), (4, 5), (2, 13), (3, 17), (14, 8), (5, 5), (12, 1), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280722", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 15), (19, 0), (13, 2), (4, 14), (5, 6), (17, 2), (1, 9), (12, 13), (5, 14), (0, 9), (19, 13), (3, 18), (9, 13), (4, 5), (0, 18), (15, 9), (16, 6), (5, 18), (6, 19), (7, 18), (13, 19), (12, 15), (5, 15), (17, 8), (1, 8), (7, 11), (0, 19), (9, 7), (15, 14), (13, 11), (3, 9), (15, 17), (7, 12), (8, 13), (11, 8), (12, 3), (11, 13), (14, 8), (10, 11), (4, 18), (4, 19), (3, 11), (8, 5), (11, 3), (9, 12), (18, 0), (19, 1), (1, 3), (9, 18), (15, 16), (4, 11), (19, 14), (16, 11), (1, 7), (2, 7), (4, 13), (13, 10), (16, 4), (12, 5), (20, 15), (15, 8), (19, 7), (10, 8), (20, 8), (15, 6), (14, 9), (15, 0), (18, 9), (15, 12), (2, 1), (3, 5), (8, 19), (12, 7), (8, 10), (14, 2), (8, 6), (20, 6), (0, 6), (18, 1), (15, 5), (16, 0), (18, 3), (11, 11), (9, 19), (1, 6), (1, 14), (12, 2), (6, 4), (9, 2), (8, 1), (17, 9), (3, 14), (0, 10), (2, 14), (7, 8), (12, 4), (3, 10), (2, 3), (13, 17), (3, 3), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971214", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 25), (20, 24), (20, 15), (0, 10), (6, 22), (5, 17), (9, 3), (2, 2), (0, 20), (5, 11), (5, 9), (15, 24), (10, 21), (6, 7), (17, 11), (18, 4), (22, 6), (13, 22), (10, 13), (19, 23), (20, 16), (2, 23), (6, 3), (3, 16), (9, 25), (17, 6), (12, 15), (12, 1), (5, 14), (7, 0), (8, 15), (15, 9), (8, 19), (3, 23), (6, 6), (8, 5), (16, 13), (5, 13), (14, 20), (17, 14), (21, 11), (9, 13), (2, 25), (12, 11), (2, 19), (20, 22), (13, 12), (13, 16), (16, 15), (17, 3), (7, 10), (15, 13), (18, 1), (14, 15), (6, 24), (22, 18), (21, 2), (20, 12), (21, 24), (3, 9), (10, 8), (16, 24), (12, 9), (3, 24), (17, 22), (18, 21), (9, 20), (11, 21), (18, 19), (21, 14), (4, 10), (15, 16), (21, 9), (10, 14), (10, 1), (6, 25), (2, 5), (16, 4), (20, 13), (2, 3), (12, 7), (5, 8), (13, 2), (1, 21), (14, 21), (4, 5), (2, 8), (21, 17), (9, 10), (18, 13), (19, 9), (13, 3), (21, 19), (1, 15), (7, 14), (22, 23), (11, 2), (16, 16), (22, 7), (22, 5), (20, 23), (3, 18), (12, 20), (18, 16), (8, 24), (19, 16), (8, 1), (19, 21), (10, 16), (17, 9), (0, 19), (17, 1), (13, 9), (2, 6), (3, 8), (9, 12), (13, 18), (13, 13), (15, 3), (13, 23), (18, 24), (0, 16), (0, 13), (8, 12), (10, 12), (7, 6), (9, 5), (22, 14), (2, 0), (11, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670980", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 16), (8, 2), (5, 4), (21, 6), (11, 3), (18, 13), (11, 7), (5, 0), (18, 16), (0, 4), (19, 11), (8, 16), (13, 15), (17, 6), (10, 7), (12, 16), (2, 12), (19, 6), (19, 3), (17, 3), (2, 11), (12, 8), (19, 1), (0, 11), (0, 14), (9, 12), (1, 15), (8, 3), (5, 1), (2, 10), (22, 5), (4, 14), (10, 15), (4, 0), (0, 1), (3, 15), (10, 3), (7, 14), (8, 4), (11, 2), (3, 3), (11, 17), (15, 5), (10, 19), (10, 8), (17, 8), (20, 14), (14, 18), (13, 17), (14, 10), (15, 12), (18, 7), (21, 0), (4, 8), (6, 17), (9, 16), (2, 9), (13, 13), (10, 1), (4, 9), (14, 12), (3, 12), (14, 8), (1, 8), (0, 3), (12, 3), (21, 9), (8, 14), (15, 3), (18, 0), (6, 11), (4, 5), (17, 13), (9, 17), (5, 17), (11, 5), (20, 6), (15, 15), (9, 14), (16, 8), (14, 4), (17, 7), (4, 3), (19, 13), (6, 8), (18, 19), (15, 17), (12, 10), (2, 4), (9, 5), (21, 3), (8, 13), (14, 19), (12, 18), (15, 14), (8, 6), (11, 4), (5, 13), (4, 1), (1, 1), (2, 19), (3, 5), (12, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981849", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 7), (7, 5), (0, 5), (21, 10), (25, 11), (3, 6), (7, 22), (22, 16), (10, 16), (4, 12), (21, 2), (23, 10), (19, 4), (24, 3), (16, 15), (15, 6), (24, 7), (0, 11), (2, 19), (12, 26), (22, 24), (19, 2), (15, 4), (18, 14), (17, 8), (15, 7), (22, 3), (13, 11), (21, 6), (20, 1), (1, 19), (6, 27), (21, 12), (4, 2), (13, 20), (15, 18), (7, 17), (17, 22), (18, 27), (3, 14), (5, 19), (12, 24), (14, 1), (3, 5), (19, 1), (22, 10), (24, 20), (6, 19), (16, 10), (8, 6), (5, 5), (9, 3), (5, 8), (9, 28), (2, 21), (9, 2), (3, 9), (2, 12), (22, 7), (6, 0), (11, 27), (22, 25), (20, 15), (16, 24), (10, 23), (23, 18), (14, 10), (11, 26), (5, 0), (10, 21), (21, 26), (7, 18), (20, 11), (17, 12), (11, 16), (14, 21), (8, 3), (11, 19), (25, 17), (4, 15), (20, 2), (23, 3), (5, 28), (10, 8), (13, 23), (25, 4), (16, 18), (25, 13), (18, 9), (17, 24), (0, 17), (1, 21), (23, 27), (12, 9), (17, 17), (14, 18), (0, 22), (5, 16), (19, 20), (18, 1), (25, 16), (25, 24), (15, 10), (22, 1), (15, 14), (18, 26), (18, 6), (12, 10), (1, 1), (1, 4), (20, 17), (8, 2), (22, 28), (0, 2), (8, 22), (2, 26), (2, 9), (22, 9), (11, 2), (15, 15), (23, 19), (14, 26), (9, 24), (12, 6), (5, 22), (15, 28), (17, 16), (9, 14), (0, 7), (5, 27), (6, 13), (18, 28), (5, 14), (15, 24), (11, 18), (21, 22), (9, 0), (16, 28), (10, 24), (16, 23), (24, 18), (22, 21), (16, 27), (7, 28), (1, 24), (17, 2), (24, 17), (11, 13), (15, 22), (19, 0), (5, 13), (22, 18), (14, 20), (6, 5), (17, 4), (18, 24), (20, 16), (23, 7), (0, 23), (19, 28), (16, 0), (0, 16), (23, 24), (20, 6), (12, 16), (21, 23), (20, 4), (18, 17), (6, 25), (20, 14), (25, 0), (6, 22), (3, 27), (17, 25), (20, 8), (4, 26), (16, 16), (11, 25), (2, 1), (16, 2), (2, 13), (11, 12), (1, 12), (15, 21), (6, 17), (19, 7), (9, 5), (13, 24), (21, 16), (24, 8), (9, 21), (7, 11), (1, 17), (14, 25), (3, 22), (7, 14), (3, 17), (17, 21), (1, 22), (9, 15), (21, 13), (10, 11), (23, 1), (4, 7), (9, 12), (11, 22), (25, 2), (19, 5), (8, 1), (14, 16), (10, 19), (19, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362400", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 10), (20, 17), (17, 17), (21, 14), (20, 18), (12, 5), (7, 18), (21, 2), (6, 16), (23, 17), (17, 21), (3, 6), (9, 22), (22, 20), (1, 9), (14, 14), (24, 0), (11, 8), (24, 17), (20, 2), (23, 16), (6, 2), (17, 12), (15, 10), (15, 17), (17, 7), (22, 11), (17, 18), (16, 1), (23, 4), (24, 11), (16, 14), (22, 5), (24, 1), (3, 16), (21, 7), (13, 2), (17, 0), (8, 16), (7, 21), (18, 7), (2, 20), (9, 13), (18, 8), (15, 6), (19, 7), (5, 20), (18, 9), (13, 0), (12, 18), (8, 20), (21, 0), (4, 14), (14, 5), (3, 7), (4, 19), (25, 3), (6, 11), (23, 9), (1, 12), (10, 9), (20, 0), (24, 9), (5, 1), (15, 13), (24, 2), (11, 18), (16, 19), (20, 3), (13, 4), (11, 5), (24, 6), (4, 22), (17, 8), (4, 3), (5, 5), (20, 20), (9, 19), (16, 17), (5, 11), (2, 13), (4, 16), (15, 20), (20, 11), (19, 3), (23, 6), (4, 18), (25, 4), (3, 0), (6, 5), (18, 3), (14, 21), (16, 5), (13, 5), (22, 17), (5, 15), (18, 4), (10, 17), (20, 15), (12, 6), (18, 19), (4, 13), (3, 12), (9, 2), (5, 2), (5, 19), (5, 7), (0, 15), (3, 2), (6, 18), (1, 8), (19, 13), (12, 14), (22, 22), (12, 15), (25, 6), (24, 3), (12, 9), (16, 2), (10, 7), (13, 10), (20, 7), (20, 19), (16, 6), (17, 14), (11, 0), (13, 13), (7, 0), (12, 4), (0, 20), (16, 3), (4, 10), (23, 2), (17, 2), (16, 21), (2, 10), (10, 11), (16, 15), (20, 9), (16, 12), (12, 17), (1, 0), (9, 6), (20, 22), (19, 10), (21, 20), (7, 9), (15, 1), (25, 18), (1, 14), (16, 20), (10, 22), (11, 6), (15, 19), (19, 15), (12, 2), (24, 7), (10, 4), (4, 12), (8, 18), (11, 15), (7, 20), (19, 8), (0, 18), (21, 5), (25, 8), (14, 17), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236673", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), 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), (22, 20), (21, 4), (1, 13), (1, 7), (21, 14), (10, 14), (23, 7), (14, 19), (2, 2), (18, 9), (19, 16), (3, 2), (2, 19), (25, 0), (24, 20), (24, 17), (11, 4), (23, 8), (16, 5), (1, 19), (5, 14), (17, 0), (10, 17), (11, 10), (4, 18), (20, 13), (14, 1), (8, 4), (13, 20), (24, 10), (20, 0), (2, 18), (20, 21), (1, 1), (18, 17), (8, 9), (15, 7), (5, 0), (9, 1), (24, 15), (9, 3), (1, 20), (13, 6), (25, 13), (8, 17), (4, 7), (17, 20), (3, 9), (21, 5), (8, 2), (19, 12), (15, 16), (8, 10), (14, 6), (18, 18), (5, 20), (12, 6), (7, 7), (17, 12), (0, 18), (3, 3), (19, 11), (24, 14), (18, 16), (16, 2), (0, 9), (12, 21), (13, 10), (16, 16), (14, 11), (10, 5), (24, 16), (8, 7), (17, 16), (23, 2), (2, 17), (5, 18), (4, 5), (8, 18), (5, 3), (20, 12), (12, 19), (4, 19), (5, 19), (18, 12), (12, 0), (21, 21), (21, 18), (22, 16), (6, 21), (21, 9), (1, 2), (3, 12), (1, 12), (3, 16), (22, 19), (7, 17), (16, 0), (8, 13), (20, 19), (8, 20), (7, 13), (22, 18), (25, 11), (0, 7), (25, 16), (13, 2), (18, 20), (3, 11), (6, 19), (13, 15), (24, 13), (19, 1), (6, 20), (12, 3), (24, 2), (20, 16), (15, 10), (13, 18), (21, 19), (9, 17), (7, 21), (17, 17), (19, 9), (8, 15), (22, 9), (6, 3), (5, 13), (0, 10), (15, 0), (19, 8), (19, 20), (1, 0), (6, 6), (7, 14), (23, 1), (24, 3), (10, 10), (6, 18), (5, 7), (3, 19), (15, 5), (16, 20), (7, 2), (2, 14), (4, 12), (5, 11), (23, 12), (22, 13), (9, 16), (0, 16), (9, 21), (17, 7), (9, 12), (25, 17), (7, 19), (18, 4), (2, 13), (11, 7), (20, 10), (1, 5), (13, 0), (18, 1), (19, 3), (20, 2), (14, 0), (18, 8), (12, 18), (12, 7), (0, 4), (25, 5), (18, 19), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996480", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 22), (26, 19), (25, 21), (21, 3), (25, 7), (5, 17), (13, 13), (16, 10), (26, 22), (10, 11), (10, 1), (10, 4), (5, 10), (7, 22), (6, 12), (11, 11), (20, 12), (5, 21), (9, 19), (22, 19), (5, 5), (27, 0), (24, 22), (3, 14), (13, 0), (18, 19), (8, 13), (4, 1), (8, 16), (1, 2), (17, 12), (18, 7), (15, 15), (21, 8), (1, 19), (27, 4), (6, 1), (5, 22), (6, 7), (10, 2), (17, 9), (5, 4), (4, 6), (9, 3), (6, 8), (17, 1), (16, 23), (19, 18), (1, 21), (12, 13), (13, 10), (13, 16), (13, 4), (5, 1), (12, 22), (25, 14), (24, 20), (8, 1), (4, 7), (16, 4), (3, 7), (5, 7), (8, 22), (16, 1), (7, 7), (26, 16), (7, 9), (12, 16), (27, 13), (0, 23), (16, 18), (10, 16), (20, 2), (24, 5), (22, 6), (19, 2), (9, 22), (8, 4), (23, 23), (23, 0), (24, 0), (20, 13), (11, 5), (4, 0), (4, 19), (6, 3), (15, 11), (21, 17), (5, 19), (25, 23), (1, 22), (18, 16), (12, 9), (8, 5), (23, 22), (10, 3), (1, 17), (0, 2), (15, 5), (18, 21), (9, 20), (8, 15), (17, 4), (26, 21), (15, 3), (18, 20), (25, 9), (22, 16), (20, 4), (23, 10), (13, 6), (20, 9), (14, 23), (8, 17), (15, 4), (19, 19), (3, 16), (12, 23), (18, 8), (19, 21), (6, 2), (17, 18), (15, 6), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685908", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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, 13), (8, 12), (3, 10), (20, 2), (3, 11), (24, 5), (7, 16), (17, 18), (7, 20), (21, 2), (11, 15), (3, 2), (11, 5), (21, 18), (21, 8), (0, 5), (26, 1), (0, 18), (13, 4), (26, 10), (24, 12), (13, 8), (24, 13), (7, 13), (23, 7), (6, 8), (20, 18), (7, 3), (6, 13), (0, 14), (20, 16), (17, 19), (19, 0), (6, 10), (0, 12), (25, 18), (18, 0), (17, 3), (2, 12), (11, 4), (7, 8), (7, 4), (17, 4), (19, 13), (26, 11), (11, 14), (14, 8), (14, 10), (3, 16), (4, 10), (1, 8), (6, 11), (5, 9), (6, 14), (1, 7), (26, 16), (20, 1), (18, 13), (7, 1), (22, 1), (16, 6), (4, 19), (7, 18), (21, 20), (4, 4), (25, 19), (24, 14), (15, 17), (5, 18), (20, 20), (12, 14), (18, 15), (10, 3), (26, 14), (15, 1), (21, 1), (25, 12), (25, 10), (12, 1), (20, 0), (24, 4), (2, 1), (3, 6), (10, 14), (2, 7), (14, 14), (25, 11), (24, 11), (9, 13), (11, 16), (24, 10), (13, 18), (7, 10), (16, 11), (8, 17), (11, 9), (13, 15), (13, 19), (21, 13), (24, 15), (11, 19), (12, 2), (10, 2), (13, 3), (13, 5), (5, 5), (9, 15), (16, 9), (22, 16), (0, 17), (10, 6), (5, 0), (14, 15), (24, 6), (13, 17), (10, 12), (4, 7), (21, 14), (2, 0), (3, 19), (23, 15), (11, 7), (24, 8), (14, 18), (1, 16), (25, 16), (19, 4), (3, 18), (1, 10), (4, 1), (18, 16), (6, 18), (14, 16), (3, 0), (9, 17), (10, 11), (14, 12), (1, 12), (26, 6), (8, 9), (11, 18), (1, 18), (16, 7), (7, 15), (14, 2), (8, 18), (18, 17), (10, 5), (8, 0), (5, 11), (22, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525396", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (5, 22), (12, 6), (19, 15), (13, 9), (7, 16), (13, 5), (22, 10), (19, 18), (6, 22), (0, 24), (20, 19), (9, 8), (5, 1), (6, 16), (14, 24), (15, 4), (16, 1), (14, 8), (3, 3), (14, 15), (3, 21), (19, 9), (23, 23), (0, 21), (21, 20), (18, 10), (18, 1), (11, 7), (3, 24), (9, 16), (12, 19), (6, 17), (7, 22), (20, 16), (11, 10), (0, 16), (10, 13), (19, 10), (3, 22), (9, 7), (12, 22), (8, 24), (12, 9), (17, 4), (13, 16), (10, 18), (15, 0), (0, 5), (0, 12), (23, 5), (2, 25), (22, 18), (21, 18), (18, 9), (12, 17), (5, 10), (3, 25), (10, 23), (9, 11), (21, 15), (23, 8), (2, 0), (12, 1), (3, 23), (10, 2), (5, 20), (13, 13), (20, 4), (13, 15), (4, 19), (0, 19), (10, 7), (21, 19), (8, 12), (22, 15), (15, 6), (2, 10), (9, 0), (19, 17), (10, 24), (23, 9), (3, 0), (8, 25), (3, 19), (1, 1), (21, 5), (1, 6), (22, 24), (11, 6), (2, 18), (14, 5), (6, 8), (1, 21), (9, 17), (4, 3), (12, 4), (7, 4), (23, 20), (23, 2), (11, 23), (4, 11), (2, 15), (19, 20), (7, 21), (7, 2), (2, 17), (19, 2), (22, 2), (0, 8), (12, 20), (8, 6), (20, 12), (16, 14), (8, 14), (17, 21), (16, 25), (19, 3), (2, 7), (15, 10), (4, 20), (15, 16), (16, 12), (2, 9), (9, 5), (20, 9), (7, 9), (7, 18), (15, 5), (8, 19), (1, 4), (23, 19), (12, 14), (15, 14), (15, 18), (19, 14), (10, 11), (17, 23), (23, 7), (4, 0), (4, 14), (1, 12), (8, 13), (7, 0), (5, 7), (19, 23), (19, 22), (9, 6), (11, 16), (14, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550566", "dataset": "MATH"}
{"messages": [{"content": "In a 26x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 19), 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, 11), (17, 13), (13, 6), (15, 10), (5, 18), (6, 10), (14, 13), (19, 14), (5, 9), (4, 19), (7, 15), (15, 12), (24, 1), (20, 6), (3, 13), (2, 3), (1, 3), (9, 5), (10, 18), (3, 4), (20, 8), (20, 2), (1, 5), (6, 11), (23, 12), (3, 2), (6, 1), (17, 10), (4, 0), (8, 17), (20, 18), (9, 10), (18, 3), (8, 18), (22, 14), (6, 19), (3, 6), (15, 9), (7, 12), (21, 2), (12, 1), (3, 5), (19, 4), (23, 8), (9, 6), (5, 3), (11, 13), (21, 15), (1, 7), (17, 2), (19, 17), (2, 2), (9, 7), (24, 11), (0, 1), (25, 15), (3, 8), (5, 17), (10, 7), (25, 17), (19, 19), (12, 10), (12, 11), (16, 3), (8, 10), (10, 2), (3, 17), (9, 16), (1, 19), (24, 3), (15, 4), (14, 5), (20, 0), (11, 12), (12, 7), (2, 11), (9, 14), (16, 19), (13, 0), (4, 2), (22, 19), (15, 13), (25, 6), (10, 5), (14, 18), (25, 2), (16, 6), (11, 11), (25, 8), (13, 8), (14, 8), (0, 9), (24, 6), (12, 12), (17, 19), (24, 14), (22, 0), (1, 13), (2, 9), (7, 9), (23, 3), (17, 5), (22, 7), (17, 11), (9, 9), (16, 1), (15, 5), (11, 7), (23, 6), (1, 10), (23, 7), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483327", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 14), (24, 17), (3, 26), (15, 22), (21, 0), (5, 2), (10, 4), (12, 10), (4, 7), (9, 18), (23, 16), (0, 12), (4, 15), (6, 6), (1, 10), (1, 22), (4, 8), (19, 13), (22, 24), (11, 19), (24, 20), (12, 13), (9, 10), (0, 21), (4, 12), (8, 20), (19, 1), (3, 1), (24, 16), (0, 6), (18, 4), (0, 2), (9, 21), (22, 5), (11, 14), (4, 18), (16, 9), (18, 7), (7, 17), (13, 14), (18, 27), (16, 14), (3, 8), (22, 22), (11, 21), (10, 6), (20, 2), (14, 15), (23, 3), (9, 27), (1, 18), (24, 19), (9, 25), (8, 28), (2, 20), (5, 26), (13, 2), (7, 3), (5, 11), (0, 14), (9, 0), (23, 6), (2, 14), (7, 10), (4, 19), (15, 1), (24, 15), (20, 18), (18, 20), (8, 24), (16, 27), (5, 14), (23, 23), (10, 28), (3, 23), (9, 8), (19, 16), (2, 23), (23, 25), (23, 13), (17, 8), (5, 9), (4, 9), (21, 6), (11, 4), (18, 2), (19, 9), (11, 24), (21, 3), (2, 15), (7, 18), (10, 26), (14, 20), (21, 23), (22, 25), (12, 20), (11, 27), (18, 10), (15, 28), (8, 8), (19, 8), (16, 13), (7, 21), (1, 5), (16, 19), (8, 9), (12, 9), (6, 17), (12, 18), (10, 22), (14, 21), (16, 21), (13, 7), (11, 25), (20, 8), (13, 25), (10, 13), (8, 27), (16, 20), (14, 10), (11, 8), (17, 14), (0, 15), (23, 8), (2, 24), (1, 13), (21, 14), (21, 25), (21, 19), (1, 28), (9, 17), (16, 17), (24, 27), (14, 27), (12, 4), (14, 1), (16, 6), (20, 0), (17, 7), (15, 9), (1, 17), (13, 8), (22, 19), (17, 16), (0, 22), (15, 26), (9, 28), (1, 1), (22, 0), (14, 9), (10, 16), (19, 19), (2, 17), (3, 7), (14, 28), (23, 17), (1, 25), (1, 4), (6, 28), (5, 17), (20, 13), (19, 26), (8, 18), (8, 15), (3, 24), (4, 3), (13, 22), (14, 23), (17, 13), (11, 22), (17, 9), (1, 26), (7, 8), (19, 0), (22, 11), (13, 11), (21, 10), (9, 11), (21, 26), (8, 12), (3, 6), (3, 12), (1, 11), (7, 19), (21, 15), (16, 16), (9, 16), (11, 12), (0, 3), (16, 1), (11, 17), (12, 1), (18, 15), (23, 19), (4, 25), (16, 10), (5, 20), (3, 0), (14, 24), (5, 28), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390852", "dataset": "MATH"}
{"messages": [{"content": "In a 27x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 24), 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), (15, 18), (7, 0), (2, 11), (22, 5), (24, 14), (0, 23), (0, 3), (12, 16), (17, 9), (25, 4), (16, 13), (8, 21), (5, 0), (13, 7), (23, 13), (19, 22), (17, 4), (1, 12), (10, 24), (21, 0), (20, 17), (24, 9), (6, 24), (4, 2), (1, 18), (24, 18), (10, 8), (19, 23), (18, 16), (6, 7), (6, 8), (0, 18), (22, 6), (9, 3), (4, 18), (5, 9), (2, 16), (17, 24), (0, 22), (7, 4), (10, 15), (23, 16), (25, 17), (7, 9), (26, 7), (3, 5), (0, 13), (22, 21), (6, 23), (13, 23), (25, 14), (20, 14), (0, 2), (25, 11), (22, 3), (23, 3), (8, 13), (21, 12), (7, 5), (15, 8), (24, 7), (25, 15), (9, 17), (7, 2), (9, 1), (6, 14), (26, 16), (10, 9), (4, 13), (10, 2), (0, 8), (26, 5), (3, 20), (21, 23), (17, 6), (10, 20), (20, 8), (17, 7), (16, 5), (11, 1), (0, 6), (8, 15), (13, 17), (17, 22), (4, 8), (1, 7), (1, 9), (25, 19), (10, 12), (24, 20), (26, 0), (3, 8), (14, 23), (11, 24), (17, 2), (11, 10), (17, 21), (17, 1), (15, 4), (2, 18), (11, 8), (6, 16), (4, 5), (10, 7), (7, 18), (16, 7), (24, 16), (5, 11), (13, 3), (18, 22), (24, 22), (14, 1), (15, 21), (11, 18), (24, 21), (5, 13), (15, 7), (14, 17), (1, 3), (0, 5), (18, 7), (23, 18), (4, 16), (12, 6), (8, 18), (13, 20), (11, 7), (4, 4), (6, 6), (24, 10), (6, 19), (18, 23), (11, 16), (11, 14), (4, 21), (2, 24), (20, 21), (20, 7), (5, 8), (22, 20), (11, 12), (0, 14), (22, 16), (7, 21), (2, 23), (26, 1), (16, 21), (17, 3), (9, 0), (24, 6), (21, 5), (19, 17), (8, 23), (3, 18), (12, 11), (5, 21), (2, 7), (8, 8), (0, 12), (23, 12), (18, 17), (20, 20), (22, 17), (8, 0), (6, 9), (17, 19), (21, 24), (19, 14), (13, 9), (12, 21), (7, 6), (9, 18), (24, 8), (22, 7), (10, 4), (17, 17), (6, 5), (22, 1), (14, 11), (17, 23), (16, 18), (16, 22), (9, 14), (12, 1), (19, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832320", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 19), (1, 15), (5, 12), (13, 0), (3, 0), (22, 11), (8, 6), (10, 7), (12, 20), (21, 4), (4, 20), (4, 17), (5, 6), (16, 19), (4, 6), (8, 3), (13, 11), (10, 10), (0, 13), (10, 18), (19, 0), (6, 18), (4, 19), (6, 20), (17, 1), (3, 20), (15, 4), (3, 18), (23, 11), (16, 4), (15, 9), (24, 10), (24, 3), (10, 14), (9, 7), (13, 9), (11, 19), (2, 12), (10, 13), (23, 15), (17, 12), (16, 8), (14, 10), (11, 8), (5, 10), (1, 4), (5, 11), (8, 1), (18, 5), (23, 6), (4, 13), (23, 1), (9, 12), (10, 6), (14, 16), (11, 6), (9, 19), (15, 10), (6, 10), (14, 20), (3, 16), (2, 14), (11, 11), (9, 14), (2, 6), (8, 14), (3, 1), (16, 9), (2, 17), (8, 2), (21, 20), (13, 17), (21, 15), (16, 7), (15, 20), (10, 15), (3, 19), (24, 18), (19, 1), (23, 3), (17, 13), (18, 6), (24, 1), (6, 15), (19, 16), (9, 5), (20, 5), (8, 9), (1, 11), (24, 12), (8, 7), (19, 3), (8, 11), (1, 10), (24, 6), (9, 0), (20, 12), (6, 11), (2, 5), (7, 10), (15, 15), (5, 8), (2, 4), (23, 18), (6, 7), (6, 13), (0, 16), (1, 13), (12, 9), (11, 10), (21, 0), (18, 11), (18, 1), (5, 4), (1, 16), (23, 14), (6, 2), (8, 4), (21, 19), (10, 16), (22, 1), (2, 11), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759882", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 18), (7, 6), (15, 5), (8, 21), (1, 7), (19, 7), (12, 15), (0, 12), (18, 23), (10, 3), (11, 12), (7, 12), (7, 18), (16, 17), (5, 10), (11, 13), (11, 16), (13, 20), (9, 15), (9, 13), (3, 17), (6, 12), (15, 9), (10, 2), (3, 20), (2, 23), (8, 2), (8, 7), (13, 18), (19, 0), (5, 7), (10, 22), (13, 8), (5, 21), (5, 8), (5, 1), (7, 11), (17, 18), (6, 21), (15, 4), (9, 4), (7, 23), (6, 19), (4, 23), (2, 11), (1, 0), (6, 22), (12, 6), (19, 6), (6, 9), (19, 2), (10, 17), (4, 17), (2, 10), (11, 20), (10, 14), (20, 11), (13, 15), (13, 13), (14, 8), (9, 3), (10, 6), (13, 5), (20, 21), (12, 2), (5, 5), (12, 22), (0, 5), (7, 7), (3, 23), (5, 9), (14, 3), (20, 16), (21, 10), (4, 2), (2, 8), (9, 17), (10, 15), (0, 13), (11, 0), (15, 13), (8, 14), (15, 3), (9, 2), (19, 1), (3, 18), (11, 10), (3, 21), (5, 0), (14, 5), (11, 2), (9, 20), (12, 14), (21, 7), (9, 22), (21, 0), (15, 20), (14, 13), (4, 9), (4, 7), (13, 0), (21, 16), (16, 8), (18, 5), (17, 1), (19, 9), (9, 10), (20, 19), (19, 10), (8, 6), (20, 3), (19, 4), (2, 18), (2, 4), (17, 4), (14, 22), (18, 21), (17, 12), (9, 11), (8, 9), (8, 8), (2, 22), (19, 12), (1, 15), (0, 21), (20, 18), (2, 9), (21, 2), (2, 19), (7, 0), (7, 1), (1, 2), (15, 15), (18, 11), (14, 21), (3, 14), (19, 16), (11, 5), (4, 11), (12, 8), (13, 11), (17, 17), (13, 12), (21, 20), (5, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888480", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), 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), (21, 10), (1, 11), (0, 1), (13, 9), (3, 11), (15, 9), (5, 6), (22, 1), (19, 17), (17, 4), (18, 5), (6, 13), (10, 9), (14, 1), (15, 5), (3, 13), (11, 16), (9, 3), (8, 3), (20, 4), (15, 19), (20, 5), (18, 16), (0, 16), (16, 19), (14, 18), (16, 7), (10, 7), (6, 11), (10, 20), (10, 2), (15, 20), (9, 7), (8, 6), (1, 3), (20, 19), (7, 17), (2, 13), (23, 5), (3, 15), (18, 21), (10, 0), (17, 14), (8, 11), (5, 10), (4, 10), (17, 12), (12, 3), (20, 1), (20, 15), (8, 2), (1, 10), (4, 17), (22, 3), (0, 12), (15, 15), (11, 2), (18, 15), (4, 7), (10, 3), (10, 4), (5, 1), (3, 9), (6, 3), (6, 5), (10, 16), (22, 18), (20, 9), (0, 10), (21, 8), (17, 13), (13, 2), (10, 5), (5, 16), (7, 13), (13, 7), (13, 5), (21, 12), (11, 17), (6, 12), (17, 11), (22, 17), (7, 20), (20, 14), (1, 18), (19, 16), (9, 9), (12, 6), (12, 14), (13, 20), (19, 7), (16, 5), (23, 4), (17, 15), (19, 11), (0, 14), (17, 2), (16, 6), (13, 11), (3, 7), (4, 12), (11, 8), (4, 0), (22, 9), (9, 17), (2, 12), (6, 10), (3, 10), (17, 3), (14, 4), (17, 1), (13, 12), (13, 6), (8, 10), (20, 10), (15, 14), (16, 12), (3, 17), (16, 8), (22, 0), (6, 19), (3, 6), (13, 13), (23, 11), (12, 5), (23, 10), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "418176", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), 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), (23, 20), (24, 23), (25, 15), (20, 2), (8, 2), (10, 7), (0, 8), (26, 15), (27, 23), (4, 13), (26, 0), (28, 1), (14, 6), (0, 13), (3, 1), (20, 17), (23, 14), (22, 22), (16, 0), (18, 0), (8, 17), (17, 20), (10, 18), (1, 23), (11, 10), (19, 11), (8, 0), (23, 2), (13, 23), (7, 1), (22, 16), (5, 5), (17, 15), (6, 22), (22, 19), (25, 16), (18, 8), (8, 19), (15, 18), (16, 2), (7, 5), (3, 13), (1, 12), (25, 9), (14, 4), (5, 18), (8, 3), (13, 18), (4, 2), (12, 21), (25, 1), (4, 18), (0, 7), (12, 15), (27, 18), (3, 20), (7, 18), (21, 11), (19, 19), (10, 11), (14, 3), (13, 5), (27, 1), (3, 6), (1, 2), (13, 0), (17, 23), (15, 7), (8, 14), (18, 20), (8, 22), (6, 20), (2, 10), (19, 0), (17, 14), (0, 23), (11, 2), (23, 0), (16, 10), (16, 13), (25, 11), (15, 16), (6, 10), (25, 5), (18, 7), (9, 7), (6, 16), (25, 21), (21, 7), (8, 9), (16, 16), (2, 8), (5, 15), (27, 19), (26, 21), (4, 19), (15, 8), (12, 7), (6, 2), (5, 17), (28, 21), (16, 5), (2, 16), (18, 5), (24, 5), (12, 23), (24, 1), (11, 15), (15, 14), (8, 21), (26, 16), (20, 11), (7, 22), (14, 17), (5, 0), (9, 23), (11, 22), (17, 0), (21, 20), (18, 3), (7, 7), (21, 3), (13, 3), (1, 18), (25, 10), (8, 4), (8, 8), (10, 12), (14, 10), (19, 14), (3, 3), (4, 14), (15, 10), (20, 22), (2, 4), (1, 20), (20, 6), (11, 20), (6, 0), (26, 20), (22, 6), (7, 0), (13, 21), (26, 12), (22, 9), (14, 23), (6, 17), (0, 4), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86286", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 14), (9, 12), (0, 5), (2, 23), (12, 15), (14, 23), (24, 24), (23, 21), (13, 26), (21, 16), (19, 12), (4, 6), (13, 3), (8, 14), (7, 16), (18, 24), (21, 1), (21, 5), (9, 8), (18, 21), (23, 7), (26, 3), (21, 18), (20, 12), (2, 24), (9, 3), (0, 17), (22, 25), (19, 3), (27, 25), (22, 2), (20, 19), (3, 18), (11, 22), (6, 2), (15, 8), (28, 16), (9, 20), (12, 19), (13, 17), (8, 26), (11, 5), (9, 21), (0, 26), (24, 23), (8, 2), (26, 1), (11, 17), (25, 13), (8, 12), (11, 9), (15, 0), (28, 13), (5, 10), (24, 3), (26, 20), (1, 16), (19, 13), (15, 10), (25, 19), (0, 10), (14, 13), (11, 23), (13, 8), (23, 17), (10, 14), (3, 23), (6, 8), (7, 24), (3, 25), (23, 16), (6, 24), (26, 24), (9, 16), (19, 17), (27, 13), (0, 11), (3, 16), (19, 0), (15, 21), (13, 21), (23, 15), (16, 6), (17, 5), (3, 11), (12, 11), (18, 4), (24, 8), (28, 4), (0, 23), (28, 6), (6, 9), (3, 10), (13, 22), (17, 2), (6, 15), (13, 12), (26, 15), (24, 1), (11, 0), (24, 12), (14, 19), (26, 13), (25, 5), (26, 18), (0, 12), (3, 4), (20, 7), (2, 25), (12, 17), (15, 17), (27, 0), (16, 26), (18, 1), (6, 5), (6, 20), (3, 17), (4, 10), (23, 19), (20, 3), (4, 3), (24, 20), (25, 0), (20, 22), (12, 25), (14, 24), (4, 18), (20, 5), (14, 26), (9, 19), (15, 22), (28, 9), (21, 24), (17, 12), (13, 14), (25, 15), (11, 3), (21, 26), (10, 22), (14, 17), (20, 15), (21, 12), (14, 16), (12, 16), (10, 8), (10, 24), (17, 7), (3, 6), (27, 21), (28, 12), (26, 21), (5, 15), (22, 26), (0, 18), (6, 6), (6, 22), (25, 3), (18, 8), (22, 10), (9, 14), (23, 10), (28, 0), (27, 15), (27, 5), (25, 21), (28, 3), (7, 25), (10, 5), (19, 6), (26, 12), (6, 4), (0, 15), (12, 4), (18, 7), (27, 11), (4, 15), (21, 0), (12, 0), (0, 24), (13, 15), (15, 6), (24, 11), (25, 7), (24, 18), (11, 16), (17, 8), (23, 4), (4, 23), (22, 3), (20, 21), (6, 16), (21, 2), (14, 2), (25, 6), (12, 7), (27, 16), (17, 19), (15, 5), (22, 21), (14, 6), (6, 3), (9, 11), (16, 3), (4, 26), (26, 9), (18, 13), (5, 11), (7, 15), (25, 9), (15, 3), (23, 1), (16, 18), (2, 20), (19, 25), (18, 11), (1, 23), (21, 11), (15, 12), (11, 13), (22, 12), (25, 18), (12, 24), (20, 24), (6, 0), (7, 1), (23, 18), (11, 26), (8, 24), (5, 13), (27, 1), (28, 11), (6, 1), (10, 1), (14, 18), (18, 9), (10, 12), (1, 14), (7, 2), (21, 17), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149739", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 17), (4, 6), (24, 1), (14, 15), (12, 0), (14, 3), (22, 10), (7, 9), (16, 11), (18, 15), (19, 20), (12, 19), (11, 19), (15, 10), (12, 3), (9, 9), (14, 16), (3, 15), (5, 19), (19, 7), (12, 1), (8, 13), (9, 6), (21, 0), (11, 18), (3, 0), (5, 13), (18, 12), (22, 5), (22, 13), (15, 0), (2, 7), (15, 21), (20, 21), (16, 2), (5, 1), (3, 2), (4, 11), (7, 2), (9, 15), (0, 20), (23, 1), (25, 2), (1, 6), (11, 0), (10, 6), (7, 5), (3, 11), (15, 9), (18, 21), (15, 6), (16, 10), (5, 21), (0, 11), (15, 12), (23, 9), (5, 2), (23, 21), (5, 8), (4, 10), (1, 12), (21, 12), (2, 19), (8, 10), (6, 1), (21, 5), (22, 0), (12, 11), (4, 7), (25, 10), (22, 16), (5, 22), (21, 22), (9, 2), (12, 9), (8, 8), (4, 5), (11, 5), (22, 15), (18, 16), (25, 9), (23, 20), (12, 13), (25, 3), (11, 9), (1, 22), (3, 7), (14, 5), (3, 9), (25, 17), (20, 10), (24, 18), (3, 8), (12, 2), (19, 21), (16, 12), (1, 18), (21, 13), (5, 20), (18, 2), (2, 16), (22, 9), (17, 14), (6, 4), (7, 4), (25, 19), (20, 14), (2, 0), (1, 19), (6, 0), (13, 2), (5, 11), (12, 15), (24, 21), (4, 22), (23, 4), (13, 5), (24, 7), (3, 17), (11, 15), (23, 18), (13, 14), (3, 3), (16, 7), (14, 9), (0, 4), (25, 7), (1, 13), (9, 11), (13, 19), (0, 15), (10, 11), (3, 4), (4, 20), (25, 4), (11, 16), (24, 15), (13, 7), (22, 7), (23, 14), (8, 19), (3, 5), (25, 16), (15, 3), (22, 12), (13, 15), (4, 18), (21, 1), (11, 3), (13, 10), (13, 3), (2, 11), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721968", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 18), (11, 12), (13, 11), (26, 13), (17, 13), (18, 7), (5, 5), (19, 17), (15, 7), (2, 16), (24, 17), (25, 17), (6, 11), (16, 1), (9, 22), (25, 16), (27, 3), (25, 19), (22, 20), (25, 13), (3, 17), (0, 3), (14, 22), (19, 15), (9, 8), (10, 11), (21, 17), (11, 21), (17, 2), (7, 21), (1, 2), (19, 12), (4, 3), (26, 21), (12, 7), (11, 3), (5, 9), (0, 18), (8, 11), (0, 15), (10, 10), (7, 16), (19, 0), (14, 4), (5, 20), (21, 18), (13, 18), (6, 23), (15, 22), (10, 18), (6, 5), (4, 15), (2, 7), (26, 6), (13, 6), (20, 14), (3, 18), (3, 2), (10, 23), (1, 1), (0, 11), (0, 23), (21, 14), (17, 5), (11, 14), (24, 14), (24, 15), (28, 2), (25, 11), (20, 4), (16, 8), (26, 0), (15, 17), (2, 4), (3, 6), (5, 13), (19, 6), (13, 4), (9, 3), (10, 19), (6, 13), (28, 6), (25, 20), (18, 9), (23, 15), (16, 5), (7, 2), (2, 11), (11, 23), (7, 23), (17, 9), (6, 20), (20, 2), (11, 0), (9, 1), (27, 11), (27, 1), (9, 16), (9, 9), (16, 21), (24, 18), (15, 19), (7, 10), (11, 9), (3, 19), (8, 9), (28, 20), (8, 19), (1, 23), (18, 11), (23, 22), (23, 21), (25, 18), (2, 3), (21, 5), (5, 19), (6, 22), (27, 18), (25, 10), (1, 11), (11, 1), (19, 20), (18, 23), (28, 19), (17, 7), (23, 8), (25, 4), (1, 3), (6, 19), (20, 12), (1, 17), (24, 0), (11, 15), (4, 7), (28, 13), (11, 5), (3, 20), (1, 15), (18, 8), (20, 10), (19, 22), (0, 20), (7, 12), (15, 16), (8, 2), (1, 4), (6, 21), (3, 10), (20, 20), (5, 21), (7, 9), (22, 11), (19, 5), (18, 21), (4, 8), (17, 15), (18, 17), (26, 23), (13, 0), (19, 4), (4, 17), (28, 14), (10, 4), (22, 7), (16, 20), (1, 22), (3, 9), (15, 20), (13, 10), (25, 12), (2, 17), (17, 6), (24, 23), (14, 2), (0, 2), (26, 5), (9, 18), (4, 12), (2, 8), (18, 18), (1, 14), (8, 7), (2, 22), (10, 3), (10, 1), (28, 7), (12, 13), (18, 10), (5, 6), (20, 7), (15, 3), (9, 2), (24, 22), (19, 19), (18, 19), (12, 5), (10, 2), (5, 18), (1, 18), (7, 15), (26, 16), (25, 7), (22, 6), (6, 17), (23, 5), (6, 9), (9, 4), (14, 1), (8, 23), (27, 8), (21, 2), (26, 2), (19, 14), (16, 14), (26, 11), (15, 8), (11, 16), (0, 22), (27, 15), (20, 19), (16, 7), (11, 11), (7, 0), (16, 16), (0, 1), (17, 0), (9, 5), (14, 19), (6, 1), (22, 2), (23, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276080", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 27), (25, 0), (24, 1), (24, 4), (1, 14), (18, 1), (18, 25), (26, 26), (6, 10), (9, 2), (18, 19), (12, 15), (20, 25), (3, 19), (6, 16), (21, 13), (13, 11), (20, 20), (26, 22), (7, 24), (11, 13), (21, 10), (17, 22), (24, 24), (0, 12), (7, 7), (9, 10), (13, 21), (9, 4), (3, 7), (20, 22), (21, 4), (18, 10), (9, 13), (4, 17), (18, 27), (2, 16), (13, 1), (23, 4), (10, 27), (11, 14), (24, 2), (25, 1), (7, 17), (25, 6), (8, 10), (0, 8), (16, 24), (8, 21), (4, 10), (17, 6), (5, 5), (22, 18), (19, 15), (10, 17), (8, 16), (13, 25), (13, 24), (17, 16), (8, 15), (13, 6), (7, 11), (16, 1), (13, 10), (2, 9), (1, 2), (6, 24), (23, 16), (11, 2), (15, 20), (14, 24), (3, 9), (1, 0), (15, 12), (19, 21), (22, 20), (0, 20), (17, 24), (24, 16), (13, 13), (23, 21), (11, 18), (6, 1), (14, 18), (21, 0), (3, 8), (20, 4), (16, 26), (26, 1), (21, 27), (8, 18), (9, 9), (2, 25), (20, 15), (18, 8), (7, 5), (16, 15), (21, 20), (19, 8), (9, 24), (0, 9), (3, 16), (22, 19), (18, 20), (25, 26), (7, 4), (10, 0), (3, 27), (7, 19), (4, 15), (11, 5), (25, 11), (19, 23), (22, 5), (16, 20), (17, 3), (15, 16), (10, 22), (6, 2), (25, 2), (12, 26), (21, 11), (9, 11), (18, 16), (5, 2), (5, 18), (17, 17), (5, 4), (11, 0), (24, 23), (0, 19), (7, 25), (4, 12), (7, 14), (2, 6), (20, 6), (17, 7), (21, 21), (16, 21), (25, 12), (1, 19), (0, 25), (15, 26), (4, 6), (2, 12), (11, 9), (1, 10), (9, 3), (5, 15), (25, 17), (3, 6), (14, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901236", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (10, 12), (11, 5), (14, 3), (13, 11), (12, 16), (11, 2), (3, 18), (5, 11), (14, 5), (14, 25), (20, 17), (2, 5), (0, 16), (20, 7), (8, 11), (4, 2), (18, 3), (17, 23), (0, 7), (0, 9), (0, 11), (11, 13), (14, 7), (18, 12), (15, 21), (6, 5), (16, 13), (14, 14), (4, 15), (4, 24), (11, 16), (9, 12), (1, 22), (0, 5), (2, 23), (16, 8), (17, 18), (14, 6), (7, 22), (16, 11), (11, 23), (19, 18), (17, 6), (10, 23), (10, 11), (18, 24), (1, 1), (12, 17), (12, 25), (11, 0), (8, 18), (2, 16), (14, 16), (20, 10), (0, 19), (8, 5), (4, 4), (0, 10), (19, 3), (5, 13), (9, 8), (20, 24), (16, 22), (20, 16), (18, 5), (4, 0), (0, 25), (10, 0), (6, 14), (4, 11), (17, 2), (14, 8), (19, 7), (4, 5), (14, 11), (8, 8), (15, 8), (3, 12), (20, 20), (19, 13), (4, 7), (0, 23), (8, 24), (1, 6), (11, 9), (2, 12), (5, 18), (10, 18), (3, 16), (9, 24), (15, 17), (18, 19), (4, 6), (10, 2), (3, 15), (15, 3), (10, 5), (12, 2), (10, 7), (5, 14), (10, 22), (16, 4), (5, 12), (3, 7), (17, 5), (5, 3), (3, 14), (15, 15), (0, 14), (14, 20), (19, 22), (19, 15), (2, 7), (14, 2), (9, 7), (16, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932186", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 11), (4, 1), (4, 0), (20, 2), (11, 1), (1, 7), (10, 13), (2, 13), (25, 17), (11, 9), (3, 11), (16, 1), (19, 3), (23, 9), (25, 9), (13, 10), (10, 9), (19, 9), (24, 0), (14, 13), (21, 18), (12, 7), (23, 1), (21, 5), (14, 11), (16, 6), (5, 19), (21, 9), (12, 11), (12, 17), (4, 17), (26, 9), (1, 14), (23, 15), (2, 8), (24, 8), (6, 4), (3, 9), (10, 17), (14, 16), (9, 0), (22, 9), (18, 11), (5, 10), (6, 5), (14, 3), (17, 5), (12, 6), (13, 18), (1, 3), (12, 1), (24, 9), (25, 16), (7, 0), (24, 13), (22, 14), (27, 15), (16, 17), (17, 14), (7, 1), (20, 3), (20, 16), (19, 6), (5, 11), (13, 4), (15, 14), (1, 19), (3, 0), (26, 1), (11, 5), (16, 3), (15, 8), (7, 13), (8, 11), (22, 3), (23, 3), (10, 3), (26, 0), (21, 19), (19, 1), (22, 10), (17, 16), (8, 3), (7, 8), (13, 7), (5, 12), (25, 13), (20, 0), (24, 1), (23, 19), (20, 9), (8, 13), (2, 19), (27, 13), (8, 0), (23, 16), (23, 2), (11, 4), (13, 13), (2, 6), (9, 8), (24, 2), (0, 15), (16, 15), (6, 6), (4, 18), (25, 6), (2, 17), (15, 12), (14, 15), (20, 15), (14, 5), (27, 8), (4, 11), (2, 12), (4, 5), (3, 15), (17, 7), (0, 12), (6, 2), (14, 2), (17, 18), (20, 11), (8, 7), (2, 4), (18, 5), (20, 14), (12, 4), (5, 0), (16, 19), (19, 14), (1, 2), (4, 10), (15, 13), (20, 7), (9, 17), (3, 12), (21, 13), (27, 12), (6, 18), (8, 16), (15, 17), (27, 10), (25, 12), (9, 18), (15, 1), (24, 19), (21, 2), (19, 12), (16, 18), (5, 8), (14, 1), (2, 0), (6, 0), (1, 4), (15, 11), (13, 5), (24, 14), (19, 8), (9, 13), (27, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730296", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 11), (7, 11), (11, 15), (26, 4), (23, 9), (8, 21), (6, 17), (5, 4), (20, 18), (6, 5), (0, 20), (24, 10), (21, 3), (10, 2), (21, 16), (14, 5), (23, 1), (18, 14), (11, 12), (13, 15), (24, 13), (22, 18), (16, 13), (18, 5), (0, 21), (12, 4), (20, 20), (26, 5), (1, 6), (22, 0), (22, 2), (7, 12), (8, 1), (1, 16), (4, 8), (22, 6), (1, 8), (0, 15), (10, 0), (4, 7), (7, 14), (19, 13), (19, 8), (22, 7), (5, 5), (4, 3), (18, 4), (3, 12), (23, 3), (16, 8), (15, 10), (17, 3), (3, 19), (15, 18), (19, 21), (10, 8), (24, 12), (25, 18), (7, 8), (10, 3), (10, 14), (4, 0), (1, 7), (27, 20), (19, 10), (9, 19), (24, 14), (3, 10), (7, 18), (10, 18), (23, 12), (10, 6), (17, 6), (16, 5), (22, 17), (7, 15), (15, 17), (3, 18), (1, 1), (22, 3), (25, 5), (2, 1), (23, 0), (14, 11), (13, 6), (4, 4), (20, 19), (10, 12), (8, 8), (16, 2), (12, 10), (6, 8), (17, 5), (24, 0), (14, 9), (2, 21), (26, 7), (18, 18), (11, 1), (25, 6), (14, 15), (13, 18), (2, 17), (17, 18), (17, 8), (17, 12), (24, 17), (7, 1), (24, 11), (24, 5), (0, 11), (14, 6), (22, 5), (19, 3), (6, 13), (4, 6), (25, 0), (20, 12), (21, 1), (14, 3), (7, 0), (10, 21), (7, 21), (9, 12), (13, 11), (12, 13), (15, 0), (17, 7), (11, 0), (26, 11), (7, 10), (13, 17), (20, 14), (13, 2), (27, 17), (24, 9), (15, 15), (11, 10), (8, 13), (5, 9), (17, 9), (24, 16), (22, 10), (21, 8), (21, 20), (17, 21), (25, 8), (1, 5), (10, 19), (1, 11), (17, 1), (13, 13), (8, 0), (26, 14), (16, 21), (10, 15), (27, 9), (8, 20), (5, 20), (5, 16), (19, 1), (21, 12), (2, 7), (6, 21), (14, 7), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946125", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 26), (2, 22), (17, 16), (13, 26), (6, 25), (10, 26), (17, 11), (3, 13), (7, 18), (15, 20), (15, 8), (5, 9), (6, 12), (14, 17), (1, 14), (18, 19), (10, 9), (18, 4), (11, 16), (19, 24), (17, 0), (0, 13), (2, 15), (5, 17), (12, 22), (18, 12), (15, 15), (1, 0), (1, 11), (9, 23), (1, 5), (18, 9), (13, 16), (4, 17), (11, 12), (1, 9), (6, 1), (12, 0), (9, 9), (8, 3), (16, 1), (2, 9), (9, 12), (9, 22), (14, 13), (6, 2), (18, 1), (15, 25), (2, 0), (14, 25), (16, 13), (14, 1), (19, 2), (4, 9), (3, 0), (1, 15), (7, 20), (7, 5), (7, 8), (0, 3), (16, 2), (9, 3), (8, 10), (2, 16), (4, 22), (0, 16), (16, 6), (8, 18), (8, 16), (5, 7), (17, 8), (16, 25), (6, 9), (19, 20), (5, 8), (6, 24), (8, 22), (8, 15), (2, 20), (0, 23), (13, 2), (5, 10), (18, 14), (4, 12), (15, 1), (12, 8), (1, 19), (15, 6), (1, 13), (3, 21), (18, 13), (7, 14), (3, 11), (1, 7), (8, 21), (14, 6), (9, 15), (19, 7), (2, 19), (0, 22), (13, 14), (3, 12), (14, 5), (6, 17), (9, 16), (19, 11), (2, 12), (10, 22), (9, 19), (11, 1), (13, 17), (4, 20), (18, 18), (8, 25), (14, 23), (17, 21), (14, 16), (1, 6), (16, 18), (12, 7), (15, 18), (16, 24), (4, 11), (17, 14), (3, 9), (6, 11), (9, 25), (19, 23), (14, 3), (7, 6), (2, 5), (17, 15), (10, 20), (7, 23), (10, 1), (18, 0), (16, 20), (1, 23), (16, 19), (11, 11), (18, 16), (13, 11), (7, 11), (4, 2), (1, 10), (6, 23), (18, 2), (13, 1), (11, 5), (1, 22), (9, 20), (18, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500664", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 9), (1, 17), (26, 24), (7, 19), (17, 9), (26, 13), (28, 15), (5, 15), (19, 13), (12, 5), (12, 17), (11, 8), (27, 0), (5, 22), (22, 8), (27, 16), (12, 19), (7, 22), (7, 7), (4, 26), (25, 2), (16, 0), (5, 25), (0, 5), (9, 17), (11, 4), (28, 8), (15, 9), (17, 18), (14, 25), (26, 8), (7, 25), (14, 24), (5, 11), (17, 23), (11, 6), (13, 21), (8, 26), (13, 9), (16, 17), (18, 9), (26, 17), (11, 23), (27, 23), (2, 6), (6, 4), (12, 24), (10, 23), (12, 8), (1, 26), (6, 25), (0, 12), (5, 2), (4, 24), (14, 15), (17, 11), (0, 14), (8, 21), (15, 2), (14, 10), (4, 4), (26, 5), (18, 21), (26, 21), (11, 12), (9, 10), (22, 12), (6, 20), (18, 24), (10, 20), (16, 19), (19, 20), (26, 6), (11, 16), (25, 15), (5, 4), (17, 4), (20, 21), (13, 2), (22, 26), (17, 21), (26, 0), (4, 17), (19, 0), (13, 17), (5, 8), (20, 1), (22, 25), (23, 23), (18, 17), (25, 3), (2, 13), (10, 7), (17, 7), (6, 9), (19, 25), (14, 13), (13, 14), (9, 12), (8, 22), (5, 24), (9, 1), (27, 10), (25, 7), (10, 5), (13, 24), (19, 9), (2, 10), (10, 2), (21, 24), (7, 15), (20, 19), (9, 19), (3, 24), (13, 8), (1, 22), (23, 10), (23, 6), (1, 8), (26, 20), (12, 10), (14, 16), (6, 18), (15, 25), (10, 14), (27, 13), (24, 7), (12, 18), (4, 22), (21, 27), (27, 4), (21, 3), (18, 1), (25, 23), (25, 21), (2, 11), (14, 4), (4, 14), (5, 7), (12, 6), (8, 25), (7, 18), (23, 0), (6, 11), (17, 19), (0, 10), (2, 26), (13, 13), (3, 22), (24, 12), (7, 14), (11, 19), (23, 24), (22, 7), (3, 4), (18, 15), (9, 22), (13, 16), (12, 25), (11, 5), (12, 14), (13, 7), (2, 20), (23, 11), (15, 21), (6, 26), (13, 23), (1, 16), (27, 15), (5, 5), (28, 1), (22, 18), (21, 20), (2, 9), (16, 8), (9, 8), (9, 3), (3, 5), (12, 23), (12, 3), (27, 19), (27, 6), (16, 5), (2, 21), (6, 1), (9, 4), (22, 17), (8, 12), (15, 27), (24, 16), (10, 21), (20, 4), (11, 13), (27, 11), (22, 27), (15, 11), (1, 2), (17, 27), (25, 9), (0, 20), (26, 16), (0, 19), (24, 23), (5, 26), (26, 12), (21, 19), (7, 23), (2, 16), (0, 27), (12, 7), (25, 24), (15, 20), (23, 2), (7, 13), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141300", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), 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), (9, 10), (17, 0), (4, 2), (1, 9), (11, 4), (3, 1), (9, 9), (13, 4), (9, 3), (13, 10), (10, 14), (9, 5), (7, 18), (5, 16), (2, 3), (19, 20), (9, 1), (3, 18), (13, 15), (19, 19), (15, 14), (12, 19), (16, 3), (15, 10), (20, 11), (14, 0), (2, 14), (7, 8), (1, 7), (19, 8), (6, 6), (9, 18), (9, 16), (10, 13), (0, 4), (5, 9), (19, 4), (18, 3), (14, 19), (2, 7), (5, 20), (10, 8), (14, 9), (5, 12), (20, 14), (11, 14), (7, 4), (8, 17), (18, 20), (1, 18), (16, 15), (7, 5), (6, 12), (20, 8), (6, 18), (7, 20), (8, 12), (17, 12), (13, 3), (8, 7), (10, 5), (8, 13), (20, 13), (19, 2), (18, 2), (15, 18), (1, 10), (6, 8), (19, 13), (5, 5), (4, 9), (18, 6), (8, 20), (14, 18), (0, 16), (18, 8), (18, 9), (2, 15), (6, 2), (19, 7), (18, 10), (2, 10), (8, 10), (2, 11), (6, 5), (3, 5), (0, 17), (11, 15), (3, 12), (6, 4), (8, 15), (14, 2), (10, 9), (10, 4), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734760", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (17, 14), (6, 14), (7, 19), (18, 4), (21, 5), (22, 11), (18, 3), (24, 2), (4, 14), (17, 0), (2, 19), (14, 19), (24, 5), (5, 4), (6, 17), (15, 6), (18, 2), (15, 0), (24, 8), (27, 16), (6, 15), (27, 18), (10, 10), (3, 5), (21, 14), (22, 2), (23, 7), (7, 10), (2, 7), (27, 8), (13, 12), (7, 3), (18, 6), (18, 15), (2, 1), (14, 11), (25, 1), (9, 15), (6, 3), (4, 4), (9, 14), (10, 5), (20, 7), (2, 15), (13, 10), (27, 7), (22, 14), (21, 2), (13, 3), (2, 16), (24, 4), (3, 3), (11, 6), (0, 6), (8, 10), (9, 6), (20, 10), (1, 13), (1, 14), (2, 18), (25, 12), (24, 1), (0, 3), (26, 4), (22, 13), (24, 15), (11, 7), (8, 8), (2, 12), (5, 0), (19, 5), (0, 14), (19, 2), (0, 1), (3, 11), (5, 17), (9, 10), (1, 8), (3, 2), (16, 12), (18, 10), (24, 9), (24, 10), (9, 2), (14, 3), (2, 11), (6, 4), (25, 19), (26, 7), (25, 7), (8, 14), (14, 14), (8, 0), (9, 17), (7, 8), (12, 7), (5, 13), (13, 0), (20, 16), (10, 4), (5, 14), (22, 18), (11, 13), (25, 16), (6, 9), (3, 4), (21, 17), (23, 12), (12, 3), (16, 2), (13, 9), (22, 6), (20, 3), (17, 16), (11, 10), (18, 12), (18, 8), (23, 3), (5, 6), (26, 13), (15, 7), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915984", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 22), (12, 19), (15, 4), (15, 22), (6, 0), (6, 11), (13, 9), (19, 12), (12, 8), (13, 15), (14, 10), (15, 21), (7, 13), (7, 5), (14, 6), (0, 8), (6, 22), (7, 3), (5, 0), (15, 20), (0, 9), (15, 0), (5, 15), (19, 17), (0, 13), (1, 6), (1, 15), (8, 14), (5, 13), (6, 21), (4, 3), (4, 14), (3, 7), (19, 8), (18, 6), (4, 12), (12, 15), (11, 1), (17, 10), (18, 10), (15, 3), (7, 22), (1, 13), (2, 7), (19, 7), (10, 14), (13, 19), (13, 7), (12, 17), (12, 14), (5, 21), (8, 7), (9, 22), (3, 2), (16, 5), (5, 1), (7, 10), (5, 2), (5, 16), (19, 2), (14, 22), (11, 21), (14, 13), (13, 18), (15, 14), (11, 17), (17, 7), (12, 5), (16, 9), (4, 20), (11, 9), (16, 11), (9, 16), (18, 13), (10, 22), (12, 21), (2, 20), (14, 21), (7, 6), (3, 9), (1, 7), (8, 19), (9, 7), (19, 0), (8, 10), (2, 16), (11, 6), (16, 19), (17, 16), (5, 22), (16, 13), (13, 10), (10, 3), (14, 2), (4, 4), (4, 10), (9, 13), (4, 9), (10, 10), (9, 20), (0, 3), (19, 5), (8, 20), (11, 10), (13, 16), (4, 11), (16, 6), (11, 12), (10, 2), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162720", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (18, 15), (18, 20), (13, 17), (13, 18), (4, 12), (13, 12), (19, 6), (12, 0), (9, 1), (2, 2), (19, 7), (8, 6), (8, 12), (2, 4), (6, 1), (1, 11), (5, 2), (4, 19), (4, 17), (18, 11), (1, 13), (6, 7), (10, 12), (14, 18), (3, 9), (3, 19), (13, 4), (6, 12), (9, 19), (6, 5), (15, 9), (4, 7), (7, 5), (10, 16), (12, 20), (1, 15), (8, 19), (19, 3), (1, 10), (12, 11), (15, 2), (19, 17), (16, 12), (17, 16), (15, 17), (13, 19), (13, 1), (18, 3), (17, 6), (11, 18), (18, 8), (18, 4), (4, 5), (8, 2), (8, 17), (8, 16), (7, 14), (11, 0), (19, 10), (10, 15), (19, 18), (5, 8), (4, 6), (6, 18), (10, 1), (13, 8), (5, 14), (11, 8), (4, 20), (12, 6), (3, 15), (19, 16), (12, 1), (9, 4), (1, 7), (13, 6), (0, 7), (10, 2), (10, 20), (7, 20), (7, 2), (12, 5), (12, 16), (3, 5), (11, 5), (16, 2), (5, 17), (11, 3), (8, 8), (14, 1), (10, 9), (0, 6), (5, 15), (17, 5), (11, 11), (12, 12), (13, 5), (19, 8), (6, 3), (4, 10), (15, 8), (5, 0), (0, 17), (17, 4), (8, 18), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "879912", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 21), (20, 2), (1, 17), (14, 3), (4, 4), (0, 21), (13, 16), (19, 19), (2, 2), (16, 0), (17, 13), (6, 7), (4, 0), (7, 15), (10, 18), (2, 15), (6, 15), (17, 8), (4, 2), (1, 11), (18, 17), (0, 9), (19, 2), (10, 21), (3, 5), (6, 18), (3, 6), (0, 2), (16, 17), (10, 1), (6, 3), (16, 19), (3, 12), (7, 13), (13, 9), (0, 7), (1, 10), (6, 17), (1, 4), (21, 18), (12, 8), (10, 9), (1, 12), (21, 8), (4, 19), (18, 20), (12, 15), (15, 15), (13, 19), (6, 10), (12, 1), (19, 5), (1, 6), (4, 18), (1, 7), (20, 6), (20, 0), (21, 4), (21, 11), (18, 12), (5, 11), (10, 14), (11, 5), (10, 19), (5, 14), (7, 20), (7, 12), (3, 15), (14, 5), (21, 6), (2, 18), (16, 14), (12, 4), (18, 5), (9, 6), (21, 20), (9, 20), (16, 1), (21, 16), (0, 20), (12, 6), (3, 13), (1, 0), (16, 12), (3, 17), (13, 11), (17, 11), (2, 13), (2, 10), (8, 21), (18, 13), (12, 20), (14, 12), (17, 20), (11, 18), (16, 2), (16, 20), (3, 2), (18, 19), (0, 15), (5, 10), (1, 14), (9, 21), (7, 21), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866933", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 18), (5, 25), (27, 23), (8, 22), (13, 6), (14, 17), (21, 9), (25, 5), (19, 21), (15, 28), (28, 25), (18, 2), (7, 5), (6, 20), (1, 17), (28, 13), (15, 15), (28, 26), (24, 3), (1, 5), (13, 16), (3, 6), (26, 16), (23, 15), (12, 22), (4, 8), (8, 17), (6, 28), (17, 17), (20, 7), (6, 1), (7, 28), (2, 16), (14, 13), (21, 20), (21, 10), (15, 17), (4, 16), (22, 21), (28, 11), (28, 20), (16, 6), (0, 2), (3, 7), (5, 9), (23, 14), (0, 8), (22, 3), (8, 1), (7, 17), (7, 7), (20, 14), (28, 3), (21, 22), (5, 26), (19, 13), (6, 12), (26, 8), (1, 26), (9, 6), (0, 20), (12, 16), (16, 12), (17, 15), (24, 15), (27, 16), (1, 1), (2, 13), (6, 25), (28, 6), (3, 13), (2, 10), (23, 26), (10, 13), (13, 17), (26, 4), (18, 15), (3, 8), (25, 20), (23, 5), (14, 24), (16, 27), (23, 11), (25, 15), (19, 17), (27, 17), (12, 15), (24, 10), (19, 12), (17, 21), (13, 25), (13, 10), (11, 13), (4, 3), (13, 1), (20, 25), (22, 24), (15, 26), (15, 4), (0, 26), (8, 16), (16, 19), (11, 1), (7, 8), (13, 11), (24, 17), (14, 10), (26, 23), (15, 5), (9, 21), (15, 11), (15, 13), (19, 3), (18, 19), (28, 5), (3, 28), (6, 6), (27, 6), (28, 15), (16, 23), (28, 4), (10, 28), (26, 18), (24, 16), (28, 19), (16, 3), (13, 8), (7, 27), (18, 18), (6, 22), (23, 20), (13, 28), (0, 6), (28, 9), (1, 28), (8, 23), (22, 7), (2, 1), (12, 7), (6, 27), (11, 24), (18, 13), (12, 3), (3, 9), (5, 2), (13, 9), (23, 3), (21, 2), (9, 1), (12, 11), (1, 19), (0, 13), (13, 26), (5, 6), (8, 6), (8, 11), (2, 8), (5, 21), (18, 25), (5, 12), (18, 26), (25, 11), (20, 1), (6, 8), (1, 8), (3, 17), (20, 4), (10, 15), (5, 4), (14, 14), (13, 15), (25, 22), (18, 9), (19, 23), (12, 26), (10, 2), (1, 22), (19, 11), (17, 12), (12, 8), (0, 23), (23, 6), (7, 10), (8, 2), (20, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258880", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 20), (1, 17), (18, 6), (10, 25), (10, 24), (11, 25), (12, 24), (8, 20), (4, 11), (18, 14), (13, 26), (1, 22), (7, 23), (2, 5), (4, 14), (18, 8), (15, 22), (15, 20), (14, 17), (9, 21), (2, 11), (12, 20), (8, 22), (5, 6), (19, 26), (14, 26), (5, 18), (8, 8), (17, 5), (4, 23), (5, 0), (1, 15), (17, 20), (3, 11), (13, 14), (14, 10), (3, 22), (16, 2), (15, 6), (5, 24), (15, 24), (0, 16), (4, 12), (2, 18), (3, 10), (20, 12), (15, 12), (17, 8), (11, 24), (0, 11), (15, 1), (16, 16), (6, 16), (2, 9), (10, 20), (1, 0), (9, 8), (3, 7), (10, 19), (7, 20), (14, 13), (6, 26), (13, 7), (3, 12), (13, 5), (17, 7), (9, 20), (13, 13), (16, 1), (11, 9), (13, 24), (7, 4), (3, 25), (7, 24), (16, 22), (18, 3), (5, 14), (8, 23), (6, 0), (2, 27), (13, 9), (6, 15), (0, 21), (16, 21), (5, 9), (5, 1), (10, 5), (18, 21), (2, 15), (6, 22), (7, 1), (8, 18), (3, 0), (10, 14), (8, 14), (10, 0), (14, 12), (10, 22), (2, 17), (11, 17), (17, 25), (10, 1), (20, 19), (0, 19), (7, 21), (1, 16), (18, 15), (19, 24), (16, 15), (9, 4), (20, 7), (6, 4), (6, 2), (12, 5), (14, 19), (0, 17), (18, 0), (15, 25), (2, 16), (16, 20), (3, 3), (12, 8), (10, 6), (18, 13), (10, 15), (16, 14), (17, 0), (0, 9), (6, 13), (9, 10), (16, 0), (1, 10), (15, 18), (2, 22), (15, 10), (19, 10), (5, 13), (0, 26), (14, 25), (4, 18), (6, 25), (7, 11), (11, 26), (3, 17), (17, 23), (20, 18), (13, 8), (3, 9), (12, 1), (8, 1), (20, 13), (1, 5), (12, 22), (19, 23), (19, 19), (4, 27), (5, 2), (20, 0), (8, 24), (5, 4), (9, 27), (19, 22), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896280", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 16), (5, 13), (4, 17), (13, 17), (2, 12), (12, 20), (11, 16), (17, 15), (7, 16), (16, 17), (4, 23), (22, 1), (7, 18), (4, 11), (6, 6), (15, 19), (19, 3), (21, 1), (3, 7), (2, 16), (21, 18), (7, 4), (12, 12), (6, 3), (4, 18), (4, 19), (6, 22), (14, 17), (13, 1), (12, 17), (23, 4), (23, 1), (3, 2), (1, 8), (8, 3), (21, 0), (21, 23), (4, 8), (4, 14), (9, 2), (10, 10), (16, 21), (18, 7), (10, 5), (14, 5), (9, 7), (13, 8), (23, 16), (13, 3), (1, 3), (18, 22), (4, 13), (17, 4), (19, 11), (23, 3), (10, 21), (10, 13), (3, 18), (13, 10), (20, 5), (6, 15), (2, 17), (15, 6), (5, 6), (9, 13), (14, 14), (15, 17), (1, 10), (18, 3), (18, 9), (17, 0), (7, 23), (15, 7), (0, 13), (14, 0), (22, 22), (7, 7), (1, 5), (8, 15), (14, 1), (5, 2), (2, 6), (22, 5), (9, 20), (10, 16), (9, 6), (19, 10), (13, 16), (19, 22), (6, 20), (14, 20), (9, 19), (0, 15), (22, 11), (1, 2), (1, 9), (20, 19), (6, 8), (9, 21), (3, 14), (10, 17), (17, 8), (19, 20), (17, 17), (20, 1), (16, 8), (14, 3), (3, 1), (10, 0), (5, 21), (6, 14), (12, 8), (1, 13), (17, 12), (17, 11), (14, 8), (0, 17), (1, 20), (0, 6), (6, 19), (13, 2), (16, 3), (9, 12), (16, 13), (13, 23), (12, 0), (9, 22), (23, 17), (7, 6), (21, 12), (3, 16), (0, 10), (23, 6), (15, 1), (1, 15), (7, 19), (22, 2), (2, 5), (3, 12), (0, 4), (3, 5), (22, 6), (2, 15), (10, 19), (23, 7), (6, 21), (22, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4662", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 19), (17, 13), (26, 7), (19, 20), (17, 14), (24, 2), (12, 1), (10, 4), (20, 0), (7, 10), (20, 15), (19, 16), (12, 7), (24, 17), (6, 11), (23, 6), (19, 10), (16, 13), (4, 15), (20, 18), (14, 10), (25, 8), (2, 12), (6, 13), (23, 15), (7, 15), (27, 14), (9, 0), (22, 2), (9, 18), (2, 7), (26, 0), (8, 4), (5, 1), (24, 7), (13, 19), (22, 8), (15, 1), (0, 8), (14, 17), (21, 2), (1, 3), (8, 21), (5, 3), (25, 6), (26, 6), (24, 8), (10, 11), (25, 13), (15, 7), (4, 6), (27, 12), (6, 8), (1, 19), (19, 19), (2, 21), (20, 10), (3, 13), (4, 9), (13, 14), (21, 12), (3, 2), (25, 17), (21, 8), (3, 5), (15, 21), (24, 20), (10, 15), (6, 14), (18, 0), (6, 20), (25, 19), (10, 14), (1, 9), (21, 5), (7, 20), (21, 19), (12, 4), (23, 13), (13, 15), (23, 4), (8, 13), (14, 9), (4, 18), (16, 9), (8, 2), (9, 17), (24, 1), (17, 6), (26, 8), (6, 19), (1, 15), (10, 5), (11, 14), (2, 6), (16, 5), (2, 18), (18, 13), (13, 12), (28, 5), (21, 7), (1, 4), (21, 9), (7, 4), (9, 5), (26, 1), (2, 0), (11, 15), (15, 11), (28, 7), (1, 17), (22, 6), (25, 21), (1, 2), (24, 13), (8, 5), (17, 18), (26, 3), (20, 11), (8, 9), (20, 14), (27, 18), (9, 16), (23, 17), (23, 18), (4, 7), (20, 5), (27, 9), (22, 0), (28, 20), (23, 14), (28, 9), (6, 12), (1, 20), (18, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840000", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (3, 19), (25, 16), (18, 1), (7, 4), (7, 10), (19, 3), (11, 2), (24, 18), (12, 3), (11, 18), (24, 4), (23, 12), (13, 6), (11, 15), (20, 9), (26, 3), (18, 6), (3, 20), (12, 13), (5, 13), (21, 19), (7, 3), (25, 4), (8, 18), (25, 9), (15, 6), (24, 10), (8, 8), (19, 9), (16, 17), (18, 20), (14, 0), (9, 5), (22, 3), (23, 18), (23, 20), (16, 20), (13, 12), (13, 3), (10, 15), (1, 19), (10, 0), (6, 18), (5, 11), (11, 3), (14, 13), (26, 8), (12, 17), (9, 8), (15, 3), (14, 3), (2, 10), (24, 12), (10, 20), (4, 2), (0, 3), (8, 14), (5, 15), (25, 13), (21, 6), (8, 20), (22, 6), (18, 19), (25, 5), (24, 20), (10, 9), (26, 16), (2, 14), (22, 1), (10, 14), (25, 7), (14, 16), (12, 9), (1, 15), (4, 16), (0, 9), (20, 1), (0, 2), (1, 2), (13, 7), (8, 15), (22, 0), (8, 7), (13, 9), (1, 4), (7, 2), (12, 19), (24, 14), (4, 1), (24, 16), (17, 19), (3, 11), (12, 10), (18, 11), (4, 6), (20, 2), (16, 6), (17, 2), (16, 8), (11, 6), (14, 17), (12, 12), (0, 4), (1, 12), (4, 4), (15, 4), (18, 0), (10, 19), (19, 17), (17, 13), (0, 13), (21, 7), (6, 16), (20, 14), (12, 15), (23, 13), (21, 18), (17, 8), (20, 3), (24, 19), (16, 4), (2, 7), (2, 20), (23, 3), (7, 7), (2, 17), (1, 3), (14, 9), (25, 0), (13, 5), (23, 19), (10, 3), (25, 15), (3, 4), (10, 13), (13, 13), (12, 2), (13, 16), (19, 12), (0, 6), (6, 9), (14, 18), (20, 12), (9, 3), (17, 16), (17, 11), (23, 2), (20, 0), (26, 9), (4, 5), (15, 15), (12, 1), (22, 20), (22, 17), (17, 15), (3, 16), (1, 9), (24, 11), (22, 7), (21, 16), (4, 17), (19, 6), (19, 18), (14, 4), (9, 9), (4, 18), (4, 15), (10, 10), (19, 5), (15, 18), (5, 9), (20, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "666272", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 8), (0, 7), (4, 0), (21, 6), (0, 2), (4, 20), (3, 27), (8, 0), (10, 2), (15, 15), (2, 12), (10, 6), (12, 15), (9, 27), (9, 13), (14, 25), (5, 5), (4, 8), (12, 22), (11, 22), (13, 9), (7, 21), (23, 26), (3, 15), (13, 12), (20, 18), (17, 6), (11, 16), (9, 12), (0, 24), (9, 19), (5, 26), (17, 20), (16, 27), (15, 26), (20, 26), (22, 23), (7, 15), (10, 16), (15, 22), (7, 23), (13, 27), (1, 19), (6, 12), (13, 22), (8, 24), (3, 8), (13, 13), (20, 15), (10, 27), (15, 11), (15, 14), (13, 7), (20, 9), (21, 18), (18, 18), (15, 12), (10, 21), (4, 16), (16, 2), (7, 11), (21, 4), (18, 7), (6, 9), (23, 27), (11, 3), (3, 2), (10, 10), (11, 21), (16, 11), (3, 9), (20, 23), (12, 16), (8, 15), (8, 27), (8, 10), (1, 27), (11, 27), (19, 9), (11, 17), (16, 21), (0, 8), (0, 12), (16, 7), (4, 3), (14, 17), (8, 20), (8, 25), (11, 19), (12, 4), (19, 4), (7, 3), (2, 27), (4, 12), (1, 2), (1, 3), (21, 15), (17, 5), (8, 7), (2, 21), (7, 24), (15, 24), (15, 3), (0, 5), (12, 23), (9, 1), (0, 21), (23, 13), (20, 21), (14, 23), (23, 12), (17, 2), (7, 16), (23, 21), (19, 7), (5, 18), (16, 20), (8, 3), (23, 17), (14, 14), (9, 18), (8, 13), (3, 18), (18, 5), (22, 19), (22, 14), (18, 22), (11, 18), (22, 0), (5, 22), (17, 21), (17, 11), (9, 22), (10, 28), (5, 25), (10, 0), (5, 9), (14, 4), (23, 20), (7, 18), (19, 17), (16, 15), (2, 22), (10, 25), (5, 12), (7, 4), (9, 15), (1, 5), (6, 18), (9, 24), (9, 28), (4, 26), (2, 8), (16, 22), (4, 5), (5, 8), (17, 16), (5, 27), (8, 5), (1, 9), (18, 4), (18, 16), (12, 27), (21, 25), (11, 14), (6, 10), (14, 21), (12, 9), (4, 25), (18, 13), (18, 17), (18, 24), (6, 2), (18, 14), (5, 21), (17, 18), (6, 14), (12, 19), (1, 14), (18, 15), (10, 18), (16, 4), (2, 18), (22, 25), (5, 28), (5, 23), (9, 4), (3, 20), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749952", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 20), (11, 9), (9, 22), (6, 22), (3, 8), (10, 13), (22, 11), (1, 3), (8, 19), (16, 23), (18, 0), (20, 18), (22, 19), (0, 16), (11, 8), (15, 22), (22, 17), (15, 17), (3, 7), (0, 23), (10, 11), (19, 0), (13, 22), (14, 16), (17, 7), (2, 12), (10, 12), (3, 23), (3, 14), (8, 7), (2, 18), (12, 17), (14, 21), (9, 4), (8, 5), (8, 12), (18, 19), (6, 8), (17, 0), (19, 5), (14, 9), (4, 19), (15, 16), (22, 20), (6, 21), (0, 18), (16, 10), (9, 15), (21, 20), (5, 8), (11, 16), (14, 2), (7, 19), (7, 12), (9, 17), (6, 23), (14, 8), (10, 5), (7, 6), (20, 8), (18, 22), (21, 4), (4, 15), (5, 12), (5, 9), (1, 23), (22, 6), (18, 8), (12, 6), (20, 13), (0, 22), (17, 16), (10, 8), (3, 21), (13, 14), (9, 13), (3, 5), (17, 6), (4, 10), (15, 14), (11, 11), (18, 2), (20, 0), (7, 11), (18, 21), (13, 2), (9, 0), (9, 2), (3, 0), (1, 13), (9, 10), (0, 6), (13, 23), (2, 2), (21, 14), (21, 9), (7, 17), (18, 11), (11, 23), (4, 9), (3, 16), (10, 14), (19, 11), (12, 15), (20, 9), (18, 7), (16, 5), (22, 15), (4, 23), (4, 2), (14, 10), (6, 13), (17, 20), (20, 20), (13, 18), (18, 5), (3, 19), (10, 3), (10, 15), (14, 12), (14, 3), (5, 10), (14, 23), (19, 23), (1, 16), (0, 17), (14, 14), (5, 1), (9, 23), (22, 7), (7, 16), (1, 19), (21, 19), (3, 18), (17, 1), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305100", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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, 14), (5, 21), (0, 3), (7, 13), (9, 11), (3, 12), (3, 20), (12, 23), (15, 17), (17, 14), (11, 5), (1, 17), (18, 20), (2, 24), (4, 9), (9, 14), (21, 7), (8, 24), (22, 22), (20, 13), (3, 8), (7, 8), (1, 5), (8, 1), (17, 16), (11, 18), (6, 9), (8, 2), (17, 21), (18, 17), (20, 7), (22, 2), (20, 9), (18, 19), (9, 3), (21, 8), (11, 11), (19, 15), (14, 17), (10, 4), (23, 14), (15, 18), (20, 4), (13, 15), (21, 11), (7, 16), (19, 6), (13, 18), (10, 21), (14, 18), (1, 0), (6, 23), (15, 4), (22, 1), (16, 20), (16, 9), (16, 2), (1, 23), (4, 2), (13, 21), (14, 13), (7, 3), (3, 7), (12, 21), (18, 9), (6, 17), (16, 10), (21, 21), (15, 0), (19, 20), (1, 21), (22, 0), (14, 19), (19, 12), (1, 11), (22, 9), (0, 24), (4, 20), (19, 3), (21, 17), (21, 19), (16, 13), (15, 20), (22, 6), (15, 11), (14, 0), (19, 8), (5, 17), (9, 17), (19, 24), (14, 16), (12, 7), (17, 19), (22, 19), (23, 18), (8, 9), (1, 3), (0, 9), (1, 16), (10, 13), (20, 10), (23, 6), (8, 3), (17, 18), (14, 4), (13, 23), (17, 9), (9, 8), (23, 3), (22, 3), (13, 7), (13, 8), (7, 1), (10, 18), (1, 20), (11, 13), (18, 0), (19, 17), (5, 5), (12, 15), (15, 2), (22, 11), (0, 19), (17, 20), (16, 24), (8, 13), (10, 5), (17, 3), (8, 16), (23, 20), (22, 14), (0, 4), (4, 1), (14, 11), (8, 4), (3, 2), (23, 17), (15, 14), (8, 10), (21, 13), (5, 7), (15, 3), (8, 19), (4, 8), (0, 20), (6, 16), (11, 1), (15, 23), (8, 18), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912813", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 23), (3, 10), (2, 21), (9, 15), (12, 2), (11, 11), (14, 5), (3, 19), (2, 10), (5, 6), (8, 11), (3, 20), (2, 26), (17, 19), (10, 17), (11, 10), (6, 13), (16, 16), (14, 25), (5, 21), (7, 8), (15, 14), (19, 12), (7, 7), (17, 22), (2, 2), (10, 6), (12, 10), (12, 23), (2, 23), (12, 14), (10, 10), (16, 8), (6, 0), (1, 21), (13, 4), (13, 2), (13, 1), (17, 25), (6, 8), (15, 13), (2, 19), (18, 21), (14, 18), (8, 9), (8, 22), (0, 15), (19, 1), (13, 23), (19, 2), (20, 1), (16, 10), (4, 18), (2, 17), (16, 20), (14, 10), (17, 17), (20, 4), (5, 3), (7, 12), (4, 11), (7, 13), (17, 9), (7, 19), (3, 9), (13, 24), (20, 24), (11, 17), (11, 0), (0, 5), (20, 13), (12, 15), (14, 17), (3, 0), (14, 23), (15, 9), (11, 20), (4, 9), (19, 4), (19, 14), (14, 24), (1, 10), (19, 7), (9, 8), (12, 22), (13, 9), (15, 4), (4, 14), (15, 15), (16, 5), (16, 11), (6, 11), (2, 24), (4, 6), (13, 19), (15, 20), (6, 12), (14, 20), (20, 10), (5, 12), (14, 2), (0, 11), (4, 21), (8, 25), (11, 21), (2, 16), (11, 5), (12, 5), (17, 20), (5, 17), (17, 14), (3, 5), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "916296", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), 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), (21, 14), (11, 13), (10, 4), (6, 13), (26, 16), (6, 11), (13, 18), (8, 15), (6, 15), (4, 16), (16, 9), (23, 20), (15, 7), (1, 17), (14, 15), (18, 21), (27, 12), (16, 4), (6, 0), (14, 4), (7, 12), (26, 8), (14, 19), (6, 9), (11, 14), (13, 5), (6, 2), (1, 6), (4, 15), (15, 1), (20, 2), (21, 2), (22, 15), (19, 2), (24, 22), (22, 1), (11, 22), (22, 3), (17, 14), (24, 9), (5, 19), (3, 9), (27, 0), (10, 2), (20, 1), (26, 4), (0, 1), (19, 0), (20, 3), (19, 5), (24, 12), (25, 17), (5, 20), (23, 1), (3, 19), (8, 9), (19, 19), (8, 12), (9, 14), (16, 22), (6, 8), (10, 12), (27, 10), (13, 11), (21, 12), (7, 4), (4, 20), (13, 3), (21, 6), (2, 8), (20, 11), (25, 21), (27, 19), (1, 8), (6, 4), (22, 8), (2, 3), (5, 2), (22, 6), (20, 21), (6, 17), (10, 3), (15, 21), (6, 5), (21, 22), (6, 6), (18, 15), (20, 12), (2, 18), (18, 20), (9, 18), (25, 8), (10, 15), (12, 22), (19, 22), (11, 11), (0, 13), (3, 5), (11, 4), (14, 7), (18, 4), (6, 22), (24, 20), (8, 22), (10, 5), (17, 16), (0, 22), (26, 17), (2, 4), (22, 21), (17, 8), (26, 10), (7, 10), (16, 11), (19, 14), (24, 1), (7, 14), (7, 6), (12, 6), (14, 12), (4, 4), (15, 5), (27, 6), (12, 11), (25, 19), (12, 16), (8, 16), (23, 18), (17, 12), (22, 0), (0, 9), (27, 2), (9, 19), (19, 10), (15, 13), (18, 0), (3, 2), (16, 12), (14, 16), (0, 8), (24, 11), (13, 19), (1, 4), (15, 3), (0, 5), (2, 6), (21, 3), (2, 16), (1, 15), (3, 20), (16, 16), (0, 14), (12, 4), (20, 17), (11, 15), (8, 5), (5, 6), (19, 21), (5, 7), (26, 13), (5, 15), (24, 3), (1, 14), (3, 11), (17, 4), (12, 14), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51120", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), 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), (11, 12), (9, 3), (5, 24), (0, 4), (8, 8), (13, 20), (7, 18), (14, 20), (11, 21), (19, 5), (5, 18), (3, 3), (20, 5), (2, 18), (1, 2), (4, 16), (16, 14), (12, 7), (9, 10), (19, 8), (5, 17), (16, 2), (13, 13), (4, 3), (0, 22), (4, 17), (6, 19), (2, 13), (2, 17), (8, 1), (5, 3), (10, 12), (1, 4), (1, 11), (13, 2), (20, 20), (8, 23), (10, 13), (20, 12), (12, 24), (1, 5), (17, 17), (15, 18), (7, 5), (15, 13), (10, 4), (2, 15), (8, 7), (11, 3), (12, 3), (19, 3), (18, 15), (19, 0), (4, 9), (13, 23), (4, 13), (5, 0), (18, 24), (0, 21), (20, 4), (1, 13), (0, 16), (8, 18), (5, 5), (7, 11), (11, 8), (12, 10), (13, 22), (4, 11), (7, 22), (10, 8), (16, 19), (4, 2), (14, 15), (3, 23), (16, 21), (7, 6), (11, 0), (3, 16), (12, 8), (20, 16), (12, 12), (7, 17), (16, 23), (19, 23), (15, 0), (10, 17), (8, 2), (14, 11), (7, 9), (3, 24), (1, 19), (19, 2), (20, 7), (10, 19), (11, 16), (20, 0), (15, 15), (20, 15), (12, 15), (3, 1), (19, 19), (15, 8), (17, 11), (7, 16), (20, 9), (15, 12), (16, 6), (8, 4), (9, 22), (13, 6), (10, 16), (4, 23), (18, 3), (19, 17), (14, 3), (4, 6), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993024", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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, 10), (17, 13), (10, 6), (20, 10), (19, 3), (15, 8), (25, 9), (17, 3), (14, 10), (10, 0), (11, 13), (19, 2), (9, 8), (12, 3), (17, 1), (20, 9), (7, 17), (16, 16), (9, 1), (17, 19), (26, 8), (23, 14), (0, 2), (18, 7), (3, 10), (4, 6), (17, 0), (0, 16), (24, 0), (16, 5), (21, 9), (16, 12), (2, 10), (21, 6), (5, 4), (18, 15), (22, 1), (22, 8), (22, 5), (8, 19), (19, 1), (15, 0), (5, 13), (4, 2), (18, 8), (5, 19), (22, 11), (12, 5), (9, 6), (14, 3), (16, 10), (5, 15), (0, 11), (24, 4), (12, 4), (19, 10), (21, 14), (6, 12), (25, 5), (9, 2), (9, 9), (2, 13), (26, 1), (8, 18), (9, 12), (25, 12), (12, 16), (24, 6), (13, 6), (14, 18), (18, 11), (12, 13), (5, 14), (17, 18), (0, 12), (1, 6), (13, 8), (22, 16), (25, 16), (23, 15), (14, 6), (20, 19), (6, 13), (1, 10), (26, 17), (24, 1), (25, 13), (12, 18), (15, 4), (11, 12), (13, 13), (16, 17), (3, 15), (13, 10), (1, 19), (4, 14), (3, 14), (17, 7), (2, 2), (16, 2), (10, 8), (16, 7), (6, 9), (0, 8), (19, 19), (18, 14), (14, 14), (15, 1), (24, 13), (19, 14), (10, 11), (10, 3), (24, 5), (8, 6), (8, 0), (25, 18), (20, 16), (7, 12), (9, 13), (13, 9), (21, 19), (11, 9), (1, 4), (24, 17), (25, 0), (17, 6), (21, 15), (26, 6), (6, 18), (11, 16), (10, 13), (26, 5), (22, 6), (1, 15), (5, 6), (17, 14), (0, 18), (6, 14), (3, 5), (4, 4), (4, 19), (8, 2), (17, 8), (1, 16), (10, 16), (18, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "473637", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 15), (16, 16), (8, 24), (21, 17), (22, 9), (8, 4), (24, 10), (14, 22), (21, 5), (10, 24), (11, 15), (8, 5), (12, 27), (10, 6), (18, 21), (16, 11), (4, 5), (14, 1), (1, 6), (7, 8), (13, 12), (15, 10), (23, 15), (24, 3), (14, 9), (22, 17), (9, 28), (24, 2), (16, 13), (14, 12), (4, 28), (22, 0), (20, 11), (7, 14), (2, 22), (7, 9), (22, 28), (7, 24), (21, 18), (4, 11), (15, 0), (14, 23), (10, 15), (20, 14), (5, 13), (0, 22), (21, 11), (19, 17), (4, 18), (20, 1), (11, 2), (1, 7), (16, 7), (15, 3), (19, 28), (12, 4), (12, 0), (20, 25), (22, 16), (3, 7), (0, 5), (17, 4), (14, 24), (21, 10), (10, 5), (1, 2), (4, 21), (13, 20), (12, 3), (10, 16), (4, 22), (23, 10), (1, 26), (3, 0), (11, 6), (10, 26), (12, 26), (19, 3), (17, 11), (22, 25), (4, 15), (16, 5), (1, 1), (15, 6), (22, 3), (24, 12), (3, 14), (15, 22), (5, 7), (24, 23), (20, 17), (7, 5), (3, 9), (15, 11), (1, 22), (9, 9), (23, 12), (3, 28), (13, 21), (1, 23), (6, 12), (7, 6), (2, 2), (5, 1), (19, 4), (23, 24), (13, 19), (23, 19), (6, 10), (9, 27), (12, 22), (14, 20), (17, 3), (5, 20), (11, 9), (24, 7), (13, 11), (9, 0), (16, 10), (12, 15), (6, 6), (23, 13), (2, 26), (19, 6), (7, 19), (4, 19), (13, 3), (18, 22), (6, 4), (4, 7), (11, 11), (22, 13), (11, 10), (20, 15), (11, 14), (20, 22), (0, 16), (17, 6), (9, 12), (23, 6), (22, 20), (3, 5), (10, 22), (17, 28), (18, 11), (12, 12), (0, 27), (2, 4), (21, 3), (19, 11), (6, 8), (8, 13), (14, 11), (10, 14), (19, 5), (14, 19), (3, 15), (4, 10), (10, 27), (19, 1), (1, 28), (19, 2), (5, 23), (20, 12), (15, 17), (18, 18), (5, 21), (18, 5), (2, 12), (23, 27), (21, 12), (6, 1), (7, 26), (17, 0), (9, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997032", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 4), (15, 13), (1, 19), (22, 20), (6, 1), (21, 9), (5, 6), (17, 0), (25, 4), (4, 18), (23, 9), (6, 8), (8, 19), (8, 13), (26, 17), (6, 5), (4, 11), (14, 13), (18, 14), (14, 6), (19, 17), (12, 20), (21, 13), (5, 12), (3, 14), (9, 16), (20, 4), (22, 15), (16, 4), (8, 15), (20, 3), (9, 18), (1, 17), (4, 3), (3, 5), (23, 5), (16, 3), (8, 7), (8, 18), (0, 10), (12, 19), (21, 7), (12, 8), (16, 8), (10, 20), (14, 3), (14, 4), (24, 5), (5, 14), (24, 20), (9, 10), (17, 12), (17, 13), (13, 0), (22, 14), (0, 18), (23, 4), (25, 12), (15, 16), (9, 13), (2, 5), (3, 16), (7, 4), (20, 20), (10, 1), (7, 12), (4, 8), (12, 4), (14, 11), (4, 9), (7, 9), (0, 1), (18, 1), (16, 2), (14, 7), (17, 10), (8, 6), (18, 19), (11, 7), (6, 13), (10, 16), (3, 15), (3, 7), (7, 2), (5, 17), (11, 6), (15, 20), (19, 12), (16, 5), (8, 12), (6, 0), (21, 12), (10, 5), (14, 14), (0, 14), (25, 2), (26, 10), (9, 19), (20, 8), (11, 13), (23, 7), (22, 0), (2, 4), (16, 12), (12, 2), (8, 3), (13, 4), (5, 0), (26, 11), (20, 17), (2, 15), (9, 8), (0, 4), (20, 9), (24, 0), (1, 11), (7, 5), (26, 2), (11, 10), (18, 7), (26, 16), (18, 2), (15, 19), (22, 6), (11, 1), (26, 9), (17, 20), (2, 2), (1, 10), (5, 9), (22, 16), (15, 6), (1, 16), (25, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623692", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 25), (12, 4), (8, 13), (6, 19), (3, 26), (9, 5), (21, 18), (13, 12), (16, 19), (11, 12), (1, 7), (3, 27), (8, 8), (15, 6), (8, 19), (14, 1), (7, 12), (17, 19), (6, 3), (4, 25), (20, 22), (0, 18), (17, 15), (3, 4), (17, 14), (7, 5), (19, 8), (7, 4), (2, 2), (20, 20), (5, 14), (20, 24), (1, 19), (13, 17), (9, 23), (5, 23), (11, 0), (5, 9), (10, 10), (13, 2), (11, 23), (18, 14), (15, 9), (21, 3), (1, 5), (13, 15), (2, 15), (5, 22), (4, 23), (5, 11), (8, 15), (16, 9), (2, 21), (6, 16), (17, 23), (11, 8), (1, 6), (9, 24), (8, 27), (7, 15), (14, 15), (10, 1), (11, 16), (2, 27), (13, 3), (12, 22), (2, 13), (2, 6), (21, 5), (15, 13), (13, 1), (17, 22), (21, 11), (8, 7), (15, 17), (5, 24), (9, 4), (17, 2), (21, 4), (15, 10), (3, 20), (7, 2), (2, 1), (21, 21), (17, 24), (2, 10), (14, 4), (16, 1), (16, 21), (6, 24), (6, 5), (2, 3), (1, 25), (11, 6), (8, 10), (15, 22), (17, 0), (5, 7), (20, 11), (7, 14), (12, 21), (10, 14), (11, 13), (7, 18), (8, 17), (18, 2), (13, 27), (6, 12), (15, 3), (14, 13), (0, 22), (0, 3), (12, 15), (6, 1), (0, 8), (20, 8), (17, 12), (0, 26), (11, 10), (2, 20), (1, 1), (2, 17), (9, 0), (5, 20), (3, 19), (14, 14), (16, 17), (6, 11), (14, 18), (9, 10), (2, 19), (8, 5), (16, 15), (7, 25), (19, 18), (6, 20), (19, 6), (13, 8), (3, 8), (10, 26), (18, 19), (9, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10535", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 9), (6, 11), (12, 3), (5, 0), (3, 10), (17, 0), (21, 0), (19, 15), (9, 16), (8, 12), (18, 22), (20, 4), (21, 20), (6, 25), (14, 14), (14, 9), (16, 8), (1, 20), (0, 3), (21, 2), (9, 15), (16, 25), (20, 13), (13, 2), (4, 9), (14, 3), (12, 19), (19, 3), (2, 26), (19, 7), (21, 4), (16, 20), (21, 17), (17, 22), (17, 24), (14, 24), (18, 11), (13, 7), (13, 5), (1, 9), (12, 7), (22, 7), (12, 25), (22, 12), (3, 14), (9, 17), (13, 13), (4, 26), (4, 22), (15, 9), (16, 5), (0, 13), (20, 24), (3, 26), (4, 7), (1, 18), (5, 25), (6, 23), (8, 23), (22, 17), (18, 12), (2, 4), (8, 16), (12, 20), (17, 20), (18, 18), (12, 17), (22, 22), (20, 6), (1, 7), (17, 2), (16, 15), (7, 20), (7, 14), (17, 15), (15, 12), (1, 3), (22, 16), (0, 10), (0, 18), (7, 11), (14, 12), (8, 21), (16, 17), (14, 8), (21, 14), (5, 13), (12, 0), (9, 4), (19, 5), (3, 6), (11, 23), (4, 10), (18, 7), (21, 5), (17, 16), (2, 3), (18, 24), (20, 18), (11, 25), (3, 24), (18, 25), (16, 19), (7, 4), (5, 24), (15, 1), (18, 17), (21, 13), (5, 5), (22, 13), (13, 12), (20, 7), (15, 10), (2, 25), (10, 3), (12, 11), (0, 24), (14, 0), (21, 6), (22, 10), (5, 20), (12, 12), (14, 6), (19, 25), (15, 17), (9, 14), (19, 24), (9, 0), (14, 20), (9, 8), (6, 18), (4, 6), (5, 16), (18, 13), (15, 26), (21, 8), (13, 23), (18, 8), (5, 23), (7, 16), (8, 1), (17, 14), (3, 8), (3, 20), (14, 25), (4, 4), (17, 9), (17, 21), (21, 18), (14, 23), (17, 1), (0, 20), (8, 20), (9, 5), (15, 2), (15, 13), (16, 22), (12, 5), (4, 24), (4, 25), (11, 18), (5, 2), (1, 11), (0, 2), (8, 17), (5, 6), (4, 14), (4, 17), (7, 7), (15, 0), (13, 10), (11, 4), (15, 6), (11, 11), (19, 12), (16, 12), (16, 24), (20, 22), (14, 17), (11, 6), (1, 16), (4, 13), (16, 7), (0, 11), (6, 4), (13, 0), (9, 25), (0, 25), (22, 11), (0, 9), (19, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "452736", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), 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), (21, 4), (6, 19), (8, 19), (0, 15), (14, 15), (8, 17), (20, 19), (2, 3), (12, 1), (25, 6), (22, 15), (24, 8), (1, 6), (17, 5), (28, 12), (24, 0), (21, 0), (11, 14), (9, 6), (28, 13), (7, 5), (7, 6), (22, 6), (1, 18), (28, 2), (18, 13), (9, 14), (26, 7), (25, 0), (3, 9), (17, 7), (21, 1), (2, 12), (12, 11), (14, 10), (15, 15), (12, 6), (23, 2), (28, 7), (9, 2), (14, 12), (15, 18), (1, 15), (5, 10), (15, 17), (6, 12), (2, 8), (25, 3), (12, 14), (3, 14), (25, 14), (10, 18), (13, 18), (28, 6), (15, 12), (14, 8), (16, 16), (16, 6), (12, 18), (17, 2), (24, 16), (27, 12), (17, 10), (18, 5), (13, 7), (18, 17), (11, 13), (26, 10), (24, 1), (0, 19), (9, 3), (9, 0), (27, 14), (15, 14), (23, 17), (10, 14), (19, 0), (10, 13), (3, 19), (1, 7), (10, 3), (23, 9), (5, 7), (8, 18), (6, 14), (17, 12), (28, 9), (22, 11), (6, 5), (7, 11), (20, 14), (7, 9), (2, 5), (6, 9), (3, 13), (27, 6), (21, 13), (20, 13), (10, 12), (19, 6), (10, 0), (20, 16), (20, 17), (11, 19), (4, 3), (26, 15), (26, 1), (15, 3), (11, 11), (16, 0), (12, 19), (16, 18), (19, 10), (22, 17), (22, 1), (17, 16), (18, 19), (23, 0), (20, 9), (4, 11), (28, 8), (14, 19), (5, 14), (18, 14), (8, 16), (10, 2), (23, 6), (7, 0), (16, 3), (11, 6), (15, 1), (25, 12), (19, 15), (25, 10), (22, 12), (15, 9), (18, 8), (13, 8), (15, 16), (16, 5), (4, 4), (24, 7), (0, 1), (2, 16), (9, 18), (9, 7), (26, 11), (21, 7), (22, 5), (8, 9), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551616", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), 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), (16, 26), (21, 20), (16, 19), (8, 14), (15, 16), (4, 2), (14, 2), (2, 18), (5, 16), (2, 21), (5, 13), (16, 25), (3, 8), (16, 16), (24, 0), (11, 5), (10, 26), (0, 2), (0, 26), (11, 15), (21, 18), (9, 1), (16, 3), (6, 17), (17, 17), (15, 26), (7, 24), (15, 7), (7, 23), (4, 24), (8, 22), (24, 20), (7, 16), (10, 10), (19, 21), (19, 0), (8, 20), (13, 4), (14, 10), (24, 17), (7, 10), (13, 21), (6, 5), (22, 20), (6, 1), (0, 5), (16, 2), (10, 0), (3, 2), (2, 22), (13, 18), (15, 25), (9, 0), (3, 18), (10, 13), (24, 2), (6, 20), (20, 13), (16, 15), (5, 20), (14, 21), (18, 20), (18, 15), (14, 20), (13, 2), (17, 9), (6, 13), (20, 2), (16, 22), (17, 8), (18, 25), (6, 25), (5, 1), (18, 3), (1, 23), (11, 13), (17, 0), (20, 6), (3, 6), (17, 2), (23, 11), (12, 12), (5, 25), (10, 9), (17, 16), (12, 2), (1, 26), (7, 14), (22, 12), (9, 2), (11, 3), (19, 9), (4, 17), (6, 21), (0, 18), (14, 1), (12, 22), (6, 24), (4, 5), (0, 22), (15, 6), (1, 7), (3, 7), (22, 14), (13, 12), (0, 7), (6, 6), (24, 6), (19, 20), (20, 0), (1, 19), (3, 11), (21, 17), (8, 5), (6, 22), (21, 11), (2, 10), (22, 7), (9, 17), (5, 19), (19, 8), (17, 15), (14, 12), (6, 3), (17, 25), (18, 23), (2, 11), (4, 6), (16, 5), (3, 21), (4, 20), (10, 11), (14, 26), (11, 4), (24, 4), (4, 4), (11, 0), (17, 22), (3, 1), (15, 15), (20, 24), (7, 12), (4, 11), (14, 14), (22, 9), (10, 6), (24, 23), (10, 7), (10, 5), (16, 0), (8, 0), (13, 9), (24, 8), (16, 11), (3, 24), (13, 15), (13, 0), (1, 16), (0, 20), (12, 11), (0, 25), (4, 1), (24, 19), (14, 6), (7, 26), (2, 12), (20, 5), (17, 19), (5, 9), (0, 6), (18, 0), (20, 14), (5, 26), (15, 17), (20, 15), (10, 25), (3, 17), (6, 19), (24, 18), (15, 8), (14, 25), (21, 12), (12, 24), (16, 10), (1, 0), (12, 7), (24, 7), (21, 0), (22, 3), (15, 23), (20, 9), (19, 18), (23, 14), (8, 11), (21, 4), (7, 25), (8, 9), (11, 2), (22, 6), (6, 26), (18, 24), (5, 21), (19, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "909252", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (7, 15), (13, 14), (0, 4), (0, 6), (14, 12), (7, 4), (2, 10), (21, 9), (19, 2), (17, 6), (1, 9), (5, 3), (20, 19), (8, 16), (12, 17), (11, 6), (7, 14), (23, 3), (19, 19), (0, 11), (10, 18), (23, 1), (15, 8), (19, 4), (22, 3), (20, 6), (0, 8), (15, 3), (16, 6), (14, 4), (9, 18), (7, 19), (21, 8), (2, 16), (7, 16), (8, 7), (7, 5), (20, 2), (22, 17), (15, 7), (16, 2), (19, 13), (0, 18), (14, 18), (22, 11), (5, 5), (3, 14), (7, 0), (12, 1), (1, 18), (22, 10), (18, 7), (3, 6), (10, 8), (18, 8), (23, 2), (21, 7), (13, 11), (19, 1), (13, 18), (15, 11), (1, 14), (0, 12), (14, 1), (11, 19), (19, 6), (13, 2), (4, 12), (9, 5), (14, 15), (8, 18), (9, 7), (6, 4), (3, 12), (17, 7), (5, 2), (16, 0), (11, 3), (23, 13), (16, 15), (17, 2), (7, 2), (17, 11), (3, 10), (23, 18), (13, 5), (20, 14), (4, 0), (1, 13), (7, 10), (5, 16), (17, 18), (16, 19), (5, 0), (13, 8), (22, 14), (23, 16), (20, 11), (18, 11), (22, 5), (10, 16), (6, 9), (13, 15), (6, 8), (17, 12), (21, 12), (11, 7), (2, 8), (11, 5), (7, 6), (18, 9), (18, 4), (5, 18), (19, 14), (15, 6), (21, 16), (9, 14), (19, 5), (3, 13), (12, 16), (0, 2), (1, 3), (19, 17), (5, 17), (0, 5), (15, 16), (10, 11), (1, 4), (11, 13), (14, 19), (2, 6), (16, 7), (1, 17), (15, 15), (22, 16), (7, 13), (2, 0), (2, 18), (22, 4), (12, 15), (5, 12), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "735184", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (12, 17), (7, 18), (22, 10), (9, 4), (26, 11), (19, 3), (21, 2), (23, 12), (15, 12), (21, 8), (25, 8), (15, 19), (18, 8), (15, 2), (13, 19), (7, 11), (22, 0), (17, 0), (11, 18), (9, 14), (23, 14), (15, 9), (5, 3), (14, 19), (7, 14), (1, 10), (17, 14), (11, 9), (22, 4), (25, 15), (2, 16), (22, 11), (19, 14), (18, 11), (20, 7), (0, 9), (19, 8), (1, 8), (13, 11), (13, 8), (11, 19), (10, 17), (11, 6), (8, 4), (15, 14), (14, 0), (2, 17), (18, 5), (11, 12), (16, 16), (12, 18), (6, 18), (8, 15), (16, 1), (23, 1), (15, 13), (11, 3), (19, 11), (20, 12), (17, 6), (19, 5), (24, 10), (17, 4), (1, 7), (8, 14), (1, 13), (5, 5), (10, 0), (14, 11), (0, 4), (25, 5), (23, 5), (12, 0), (8, 3), (10, 2), (2, 18), (3, 10), (23, 10), (7, 5), (3, 15), (25, 6), (7, 15), (18, 18), (11, 8), (8, 2), (7, 6), (17, 13), (0, 14), (22, 18), (4, 7), (18, 2), (0, 10), (7, 17), (14, 13), (18, 4), (16, 17), (2, 9), (26, 0), (14, 16), (4, 15), (19, 6), (21, 5), (5, 18), (4, 4), (16, 9), (0, 18), (20, 4), (8, 12), (21, 3), (8, 9), (5, 19), (6, 13), (5, 13), (21, 6), (18, 6), (6, 19), (10, 13), (4, 3), (19, 0), (2, 14), (14, 18), (4, 14), (15, 5), (5, 16), (23, 2), (8, 6), (15, 7), (13, 18), (9, 1), (11, 0), (9, 19), (4, 12), (9, 12), (5, 1), (17, 5), (4, 18), (1, 5), (17, 12), (20, 15), (5, 17), (2, 4), (24, 18), (5, 4), (20, 8), (24, 4), (2, 12), (7, 12), (25, 7), (24, 3), (20, 18), (12, 16), (13, 0), (10, 6), (20, 2), (13, 5), (3, 12), (24, 12), (7, 13), (5, 8), (14, 1), (3, 13), (9, 8), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "727968", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), 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, 14), (8, 18), (18, 9), (6, 8), (20, 10), (17, 3), (5, 12), (16, 5), (9, 6), (4, 11), (24, 5), (23, 19), (9, 1), (3, 1), (1, 12), (20, 9), (23, 14), (14, 3), (24, 2), (23, 10), (2, 8), (9, 8), (19, 0), (19, 8), (8, 5), (6, 2), (8, 10), (14, 15), (12, 4), (8, 13), (21, 7), (20, 5), (12, 6), (15, 11), (19, 2), (18, 17), (15, 17), (14, 8), (6, 6), (16, 6), (17, 19), (3, 18), (7, 16), (5, 16), (10, 8), (3, 6), (9, 19), (11, 18), (22, 13), (2, 12), (17, 0), (22, 19), (20, 6), (8, 7), (1, 8), (18, 2), (5, 15), (10, 0), (16, 7), (3, 12), (5, 18), (15, 5), (21, 14), (20, 15), (9, 3), (5, 1), (7, 15), (7, 4), (24, 15), (20, 7), (13, 1), (6, 13), (19, 17), (14, 10), (0, 7), (1, 15), (6, 4), (17, 6), (19, 13), (2, 3), (10, 6), (24, 13), (12, 19), (15, 7), (11, 0), (18, 11), (16, 0), (11, 8), (4, 7), (0, 16), (18, 0), (19, 14), (16, 14), (7, 10), (24, 12), (9, 15), (18, 4), (12, 9), (17, 13), (13, 15), (12, 13), (23, 13), (7, 2), (10, 3), (18, 14), (22, 3), (5, 3), (7, 14), (24, 0), (16, 10), (23, 3), (20, 18), (2, 2), (5, 5), (18, 8), (10, 13), (21, 9), (21, 6), (11, 9), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "692412", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 22), (11, 21), (10, 18), (2, 12), (6, 20), (8, 0), (18, 13), (19, 23), (10, 6), (12, 10), (17, 0), (13, 24), (15, 10), (3, 26), (14, 2), (9, 17), (0, 7), (0, 11), (5, 21), (12, 12), (18, 8), (16, 21), (7, 25), (14, 12), (18, 12), (8, 13), (6, 7), (20, 13), (4, 19), (15, 8), (19, 4), (10, 19), (1, 15), (17, 2), (2, 26), (2, 18), (6, 8), (3, 2), (7, 21), (16, 19), (17, 7), (2, 22), (14, 9), (7, 0), (9, 11), (15, 4), (11, 12), (13, 21), (16, 25), (9, 7), (21, 10), (4, 0), (0, 15), (13, 11), (2, 9), (16, 8), (15, 20), (13, 4), (7, 12), (17, 13), (18, 15), (17, 21), (20, 15), (10, 9), (2, 15), (14, 19), (14, 16), (20, 23), (18, 16), (6, 14), (12, 3), (13, 8), (13, 6), (4, 14), (21, 23), (16, 2), (6, 10), (21, 5), (0, 3), (15, 15), (13, 0), (15, 26), (10, 17), (11, 25), (8, 22), (18, 11), (10, 7), (17, 19), (14, 18), (9, 8), (21, 18), (16, 10), (21, 22), (19, 24), (5, 15), (6, 23), (17, 4), (1, 5), (15, 17), (18, 10), (11, 0), (10, 14), (19, 16), (5, 3), (16, 24), (13, 1), (6, 11), (15, 19), (0, 8), (16, 15), (13, 2), (17, 11), (7, 9), (10, 22), (9, 23), (8, 18), (8, 1), (0, 2), (14, 7), (19, 0), (11, 17), (5, 22), (8, 16), (12, 25), (18, 17), (19, 11), (14, 20), (8, 2), (6, 17), (6, 0), (5, 11), (5, 4), (6, 12), (7, 7), (3, 8), (21, 14), (1, 21), (19, 20), (18, 3), (4, 17), (15, 25), (16, 7), (2, 20), (5, 9), (0, 16), (7, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875760", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 14), (15, 18), (16, 27), (2, 21), (21, 10), (19, 5), (7, 19), (5, 25), (14, 26), (2, 15), (2, 17), (1, 9), (16, 2), (2, 7), (15, 21), (3, 21), (18, 11), (15, 27), (11, 19), (15, 7), (7, 20), (17, 24), (3, 0), (9, 16), (17, 27), (22, 2), (14, 13), (21, 21), (9, 13), (8, 23), (22, 20), (13, 15), (2, 26), (22, 10), (10, 27), (19, 0), (13, 25), (8, 8), (22, 9), (21, 4), (22, 14), (9, 26), (5, 1), (16, 13), (7, 27), (11, 25), (21, 1), (9, 7), (14, 8), (18, 12), (2, 6), (9, 24), (17, 16), (3, 20), (16, 7), (13, 14), (13, 1), (7, 12), (4, 24), (12, 17), (16, 4), (6, 17), (2, 5), (12, 8), (1, 14), (21, 19), (13, 2), (12, 21), (0, 1), (20, 1), (17, 2), (8, 6), (0, 22), (7, 18), (13, 13), (10, 18), (14, 5), (20, 14), (20, 0), (0, 15), (10, 23), (10, 12), (8, 20), (2, 22), (22, 17), (15, 12), (14, 4), (6, 4), (22, 15), (0, 25), (5, 27), (5, 5), (9, 3), (16, 5), (5, 16), (11, 3), (20, 2), (6, 13), (8, 21), (4, 25), (14, 2), (15, 24), (1, 27), (7, 3), (3, 3), (17, 9), (17, 6), (16, 10), (11, 20), (16, 0), (11, 17), (0, 27), (9, 23), (4, 12), (7, 10), (0, 9), (3, 10), (6, 20), (11, 12), (19, 26), (2, 16), (15, 5), (12, 4), (4, 8), (15, 10), (21, 7), (21, 2), (11, 11), (6, 0), (6, 19), (15, 19), (1, 1), (18, 2), (20, 27), (8, 13), (8, 0), (7, 2), (10, 25), (17, 4), (11, 5), (21, 24), (22, 13), (19, 13), (17, 13), (2, 27), (15, 0), (5, 24), (16, 14), (6, 24), (1, 16), (19, 27), (4, 14), (15, 20), (3, 17), (7, 5), (2, 19), (0, 24), (18, 3), (19, 18), (12, 0), (13, 19), (3, 15), (14, 0), (1, 26), (21, 18), (19, 1), (22, 24), (3, 7), (17, 1), (15, 17), (14, 20), (5, 0), (12, 19), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "646500", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (23, 18), (25, 10), (20, 0), (25, 21), (11, 2), (13, 3), (10, 21), (14, 16), (2, 9), (26, 19), (22, 20), (5, 14), (8, 7), (9, 10), (15, 3), (3, 3), (12, 5), (15, 12), (12, 11), (14, 12), (13, 18), (9, 8), (21, 14), (13, 21), (24, 14), (7, 5), (21, 2), (9, 5), (11, 6), (22, 7), (12, 12), (18, 9), (19, 14), (19, 12), (7, 15), (19, 2), (3, 10), (4, 10), (17, 3), (4, 3), (20, 12), (1, 17), (24, 6), (27, 7), (16, 4), (4, 2), (9, 14), (6, 6), (11, 13), (15, 14), (17, 20), (18, 18), (19, 17), (17, 2), (3, 15), (8, 8), (24, 5), (7, 9), (23, 13), (10, 11), (4, 1), (18, 10), (26, 17), (1, 19), (24, 9), (13, 13), (24, 12), (26, 21), (10, 2), (7, 1), (26, 0), (21, 4), (1, 13), (0, 18), (14, 8), (16, 10), (23, 19), (7, 4), (15, 13), (1, 16), (14, 21), (6, 21), (21, 12), (9, 18), (21, 16), (21, 3), (15, 7), (21, 6), (0, 4), (19, 19), (9, 7), (5, 18), (26, 20), (18, 7), (27, 3), (10, 12), (20, 9), (18, 8), (20, 11), (13, 20), (6, 3), (6, 20), (10, 18), (20, 19), (5, 7), (19, 4), (2, 17), (25, 15), (8, 12), (26, 5), (3, 13), (14, 15), (6, 2), (14, 1), (27, 5), (9, 17), (24, 15), (25, 1), (24, 13), (2, 4), (18, 19), (0, 17), (16, 5), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943620", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (3, 18), (12, 7), (2, 17), (15, 6), (1, 7), (18, 20), (6, 2), (11, 3), (1, 14), (12, 1), (2, 12), (15, 2), (8, 17), (7, 4), (16, 1), (1, 20), (13, 17), (2, 0), (7, 9), (18, 5), (12, 0), (17, 3), (2, 11), (4, 11), (5, 16), (6, 5), (12, 20), (1, 18), (3, 3), (15, 16), (7, 10), (4, 4), (4, 20), (0, 13), (11, 7), (5, 19), (4, 0), (10, 18), (15, 11), (7, 2), (13, 5), (11, 9), (19, 1), (11, 2), (11, 6), (12, 11), (0, 20), (16, 18), (12, 2), (12, 10), (7, 0), (19, 4), (7, 1), (9, 14), (7, 14), (11, 16), (19, 20), (13, 6), (10, 14), (9, 21), (2, 1), (4, 21), (2, 19), (2, 10), (8, 21), (8, 11), (1, 9), (14, 11), (9, 10), (16, 17), (17, 10), (2, 8), (17, 18), (12, 6), (16, 14), (18, 10), (16, 7), (16, 6), (0, 2), (5, 6), (9, 7), (8, 16), (1, 10), (9, 18), (19, 5), (13, 11), (5, 10), (18, 16), (10, 6), (0, 8), (1, 15), (16, 11), (6, 19), (2, 7), (8, 3), (15, 8), (12, 21), (4, 13), (6, 3), (6, 13), (11, 15), (2, 21), (7, 5), (15, 12), (9, 4), (18, 14), (19, 17), (14, 21), (16, 0), (10, 3), (13, 9), (16, 12), (6, 8), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477288", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 16), (23, 21), (24, 13), (19, 20), (22, 7), (12, 19), (8, 20), (1, 4), (3, 22), (7, 5), (15, 24), (24, 21), (21, 20), (3, 0), (19, 28), (24, 19), (9, 20), (21, 25), (1, 9), (5, 21), (24, 5), (13, 11), (10, 26), (0, 2), (1, 1), (15, 0), (7, 1), (3, 1), (7, 6), (17, 22), (18, 25), (6, 0), (15, 15), (24, 12), (4, 21), (8, 2), (8, 17), (8, 21), (8, 8), (25, 2), (16, 20), (21, 13), (2, 15), (25, 6), (11, 24), (8, 25), (14, 7), (12, 16), (12, 15), (17, 4), (14, 12), (9, 13), (21, 16), (6, 14), (0, 9), (3, 23), (10, 21), (14, 25), (8, 7), (13, 28), (1, 7), (16, 21), (2, 25), (20, 13), (4, 17), (10, 5), (13, 20), (6, 7), (16, 11), (13, 17), (21, 3), (11, 2), (4, 1), (16, 23), (20, 26), (13, 5), (9, 25), (13, 15), (6, 27), (24, 0), (0, 15), (18, 4), (0, 23), (19, 12), (1, 27), (5, 24), (8, 14), (10, 19), (15, 26), (20, 16), (10, 28), (12, 18), (9, 18), (17, 15), (10, 12), (2, 14), (12, 26), (1, 26), (16, 2), (0, 24), (2, 16), (12, 14), (5, 25), (23, 28), (17, 20), (4, 8), (22, 2), (20, 1), (3, 20), (2, 8), (18, 19), (10, 10), (18, 20), (5, 12), (5, 18), (5, 13), (25, 4), (7, 19), (19, 3), (4, 2), (25, 5), (21, 15), (24, 15), (22, 26), (22, 25), (22, 12), (11, 26), (2, 17), (1, 16), (20, 15), (24, 20), (6, 6), (7, 2), (13, 22), (17, 7), (18, 2), (6, 22), (20, 9), (8, 18), (21, 14), (24, 24), (5, 22), (5, 17), (17, 16), (8, 24), (22, 24), (7, 25), (13, 14), (7, 22), (5, 15), (23, 14), (16, 3), (15, 16), (3, 5), (5, 0), (3, 10), (13, 27), (13, 4), (24, 10), (1, 14), (12, 24), (7, 16), (11, 28), (7, 14), (6, 24), (7, 13), (16, 27), (24, 16), (22, 17), (7, 4), (11, 20), (18, 18), (18, 12), (8, 0), (3, 9), (10, 11), (13, 8), (12, 20), (4, 27), (8, 6), (15, 13), (5, 20), (6, 25), (23, 11), (7, 17), (24, 4), (0, 28), (15, 4), (7, 12), (13, 24), (1, 2), (3, 19), (5, 8), (15, 11), (11, 3), (8, 26), (12, 22), (25, 26), (19, 11), (12, 21), (0, 4), (12, 1), (20, 21), (18, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863784", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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, 12), (21, 20), (4, 11), (1, 7), (5, 19), (20, 19), (3, 10), (18, 2), (12, 19), (19, 14), (8, 8), (2, 17), (6, 4), (8, 12), (1, 0), (12, 10), (19, 3), (9, 8), (20, 18), (7, 0), (9, 1), (20, 20), (17, 15), (8, 6), (5, 0), (22, 13), (11, 3), (20, 15), (6, 14), (2, 0), (2, 10), (10, 10), (17, 8), (19, 13), (2, 12), (19, 11), (9, 5), (12, 18), (17, 18), (15, 7), (5, 1), (3, 13), (14, 16), (10, 1), (0, 17), (16, 13), (19, 2), (4, 14), (4, 13), (2, 6), (7, 12), (20, 10), (5, 6), (7, 8), (8, 3), (10, 3), (15, 1), (6, 19), (16, 17), (0, 19), (9, 3), (1, 2), (11, 13), (22, 6), (7, 7), (11, 11), (1, 4), (6, 1), (15, 16), (18, 19), (6, 8), (6, 18), (22, 14), (0, 9), (8, 18), (14, 3), (14, 10), (5, 10), (14, 0), (0, 13), (7, 5), (17, 20), (12, 9), (14, 9), (11, 2), (5, 12), (12, 1), (7, 11), (16, 15), (13, 8), (19, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930512", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 19), (18, 0), (16, 20), (3, 10), (14, 14), (3, 15), (11, 25), (2, 8), (4, 25), (3, 12), (6, 19), (15, 8), (4, 20), (19, 9), (18, 2), (5, 7), (8, 17), (17, 8), (8, 2), (12, 17), (13, 18), (16, 24), (18, 20), (11, 23), (13, 14), (13, 2), (11, 10), (3, 21), (1, 20), (11, 26), (7, 13), (0, 13), (11, 19), (12, 5), (12, 15), (2, 4), (16, 16), (11, 14), (10, 23), (17, 0), (14, 12), (10, 13), (10, 24), (13, 19), (10, 8), (3, 0), (6, 11), (10, 20), (12, 21), (12, 3), (2, 2), (14, 18), (16, 15), (19, 15), (8, 1), (1, 21), (3, 13), (7, 20), (15, 9), (15, 12), (14, 1), (18, 18), (4, 14), (11, 2), (15, 3), (4, 26), (15, 17), (0, 12), (8, 13), (9, 6), (2, 23), (17, 6), (19, 4), (11, 18), (17, 15), (19, 7), (13, 9), (9, 0), (8, 14), (18, 10), (17, 7), (4, 23), (4, 24), (13, 8), (3, 14), (15, 1), (6, 3), (7, 9), (17, 24), (8, 20), (1, 12), (19, 17), (19, 20), (16, 18), (9, 11), (5, 0), (4, 3), (15, 19), (7, 17), (11, 21), (7, 24), (17, 25), (2, 20), (4, 11), (7, 21), (0, 1), (6, 6), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915432", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 14), (14, 0), (14, 6), (16, 22), (5, 8), (27, 6), (1, 14), (13, 1), (20, 3), (0, 3), (11, 4), (26, 22), (4, 4), (8, 8), (6, 4), (20, 19), (1, 0), (24, 20), (11, 6), (0, 20), (3, 8), (7, 13), (2, 20), (12, 3), (23, 19), (7, 11), (18, 21), (27, 9), (2, 10), (15, 12), (11, 15), (14, 3), (3, 22), (15, 23), (16, 13), (8, 13), (8, 1), (13, 19), (3, 20), (8, 14), (23, 15), (18, 14), (21, 12), (24, 5), (13, 11), (9, 8), (2, 23), (28, 15), (13, 8), (24, 13), (25, 0), (15, 14), (16, 23), (22, 6), (20, 8), (13, 4), (20, 1), (16, 10), (5, 21), (9, 21), (22, 22), (24, 0), (5, 18), (1, 13), (26, 5), (1, 5), (3, 15), (18, 11), (1, 7), (19, 14), (26, 1), (7, 18), (27, 12), (23, 17), (2, 3), (3, 5), (17, 23), (24, 10), (2, 21), (5, 5), (26, 9), (7, 4), (9, 1), (25, 10), (6, 7), (12, 11), (0, 12), (16, 21), (8, 4), (3, 10), (13, 23), (18, 12), (16, 6), (16, 15), (0, 6), (22, 13), (10, 17), (3, 21), (15, 22), (20, 16), (7, 14), (12, 16), (7, 15), (26, 4), (3, 12), (23, 12), (26, 0), (11, 1), (12, 6), (26, 3), (5, 19), (4, 22), (17, 17), (1, 20), (5, 0), (21, 22), (12, 5), (21, 2), (16, 11), (25, 7), (4, 5), (27, 3), (26, 10), (22, 1), (9, 5), (9, 0), (18, 16), (3, 0), (6, 20), (19, 21), (3, 18), (9, 13), (15, 6), (9, 3), (27, 1), (15, 7), (22, 21), (18, 4), (9, 12), (12, 7), (12, 15), (5, 2), (8, 6), (9, 22), (28, 13), (14, 1), (7, 0), (19, 20), (18, 1), (14, 8), (7, 8), (28, 4), (5, 6), (24, 16), (25, 3), (8, 23), (17, 0), (11, 21), (12, 8), (20, 15), (3, 6), (20, 0), (12, 21), (28, 7), (25, 18), (7, 6), (17, 15), (2, 15), (25, 15), (23, 3), (9, 2), (1, 15), (14, 21), (28, 18), (17, 9), (12, 9), (6, 19), (9, 14), (23, 20), (17, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641976", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 23), (5, 8), (1, 16), (1, 2), (0, 4), (16, 15), (21, 2), (9, 25), (15, 12), (6, 25), (10, 9), (8, 5), (23, 9), (22, 11), (12, 15), (23, 21), (10, 14), (22, 25), (15, 4), (3, 5), (19, 13), (17, 21), (24, 16), (11, 16), (2, 27), (16, 17), (11, 8), (20, 13), (12, 14), (5, 14), (25, 25), (24, 5), (12, 21), (5, 12), (18, 19), (10, 3), (16, 3), (4, 21), (22, 23), (17, 1), (6, 7), (6, 17), (6, 27), (6, 1), (25, 19), (10, 20), (13, 21), (21, 18), (26, 10), (8, 16), (0, 20), (9, 22), (16, 4), (20, 8), (25, 26), (26, 24), (13, 14), (4, 11), (9, 3), (4, 3), (20, 14), (9, 24), (3, 17), (22, 18), (3, 24), (11, 25), (6, 11), (15, 0), (24, 0), (13, 16), (13, 11), (14, 4), (14, 7), (19, 12), (24, 22), (17, 19), (5, 5), (15, 17), (4, 6), (19, 5), (5, 18), (23, 16), (1, 24), (0, 9), (20, 5), (0, 14), (15, 6), (20, 9), (6, 8), (12, 10), (2, 19), (20, 15), (21, 24), (11, 4), (9, 27), (19, 8), (17, 24), (19, 20), (15, 14), (18, 2), (4, 14), (0, 6), (3, 18), (20, 3), (2, 4), (8, 24), (16, 16), (18, 11), (20, 22), (18, 3), (24, 15), (9, 26), (5, 1), (8, 14), (19, 4), (3, 4), (3, 16), (1, 7), (25, 18), (14, 15), (17, 10), (11, 22), (25, 13), (12, 11), (12, 9), (13, 13), (13, 3), (23, 2), (16, 12), (15, 24), (2, 12), (19, 6), (4, 0), (16, 14), (24, 17), (14, 12), (4, 19), (26, 18), (18, 14), (22, 7), (0, 22), (7, 6), (11, 0), (15, 2), (6, 12), (19, 26), (13, 2), (14, 14), (7, 24), (19, 18), (2, 18), (5, 26), (10, 27), (7, 9), (17, 2), (26, 4), (8, 25), (16, 0), (24, 21), (26, 0), (9, 15), (21, 13), (17, 23), (23, 13), (9, 19), (6, 9), (25, 14), (22, 21), (20, 2), (5, 17), (20, 17), (11, 23), (19, 1), (17, 15), (19, 2), (6, 15), (5, 2), (24, 25), (0, 12), (5, 21), (0, 23), (9, 21), (25, 8), (12, 18), (20, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524392", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 4), (3, 9), (13, 5), (5, 7), (13, 19), (10, 11), (25, 14), (4, 28), (1, 2), (3, 1), (16, 9), (17, 8), (22, 11), (0, 8), (2, 11), (1, 21), (9, 13), (27, 27), (2, 19), (22, 10), (12, 0), (9, 4), (13, 21), (25, 1), (27, 4), (4, 17), (11, 18), (18, 23), (2, 25), (17, 16), (18, 14), (5, 20), (4, 10), (1, 15), (16, 26), (15, 3), (6, 4), (7, 25), (4, 25), (13, 27), (24, 5), (18, 7), (14, 1), (13, 4), (11, 10), (16, 5), (7, 14), (23, 21), (13, 20), (13, 14), (10, 4), (11, 26), (20, 11), (18, 0), (22, 25), (20, 22), (21, 27), (2, 17), (9, 15), (11, 27), (7, 4), (5, 13), (3, 19), (3, 7), (21, 24), (4, 23), (13, 18), (13, 8), (23, 7), (13, 28), (5, 10), (5, 14), (24, 1), (14, 8), (10, 26), (24, 16), (17, 12), (10, 19), (3, 6), (8, 10), (20, 6), (10, 2), (17, 11), (7, 24), (15, 19), (14, 17), (27, 9), (20, 15), (6, 11), (12, 11), (25, 5), (4, 6), (10, 16), (16, 8), (16, 25), (18, 17), (22, 17), (18, 20), (19, 8), (8, 9), (7, 10), (5, 3), (14, 13), (7, 8), (25, 6), (5, 26), (6, 26), (11, 21), (15, 2), (15, 17), (7, 15), (16, 17), (8, 21), (25, 9), (19, 5), (3, 27), (5, 0), (26, 4), (1, 4), (7, 22), (16, 2), (4, 22), (6, 3), (12, 23), (27, 0), (7, 20), (4, 19), (14, 23), (13, 13), (23, 5), (13, 22), (22, 12), (9, 5), (8, 18), (25, 11), (25, 26), (21, 4), (18, 3), (14, 10), (19, 15), (25, 28), (17, 13), (11, 5), (22, 7), (0, 3), (12, 24), (8, 11), (4, 15), (19, 18), (7, 3), (13, 2), (18, 18), (27, 1), (2, 21), (6, 18), (21, 0), (4, 14), (23, 11), (24, 6), (15, 27), (10, 5), (8, 16), (26, 9), (24, 10), (24, 18), (6, 13), (13, 11), (20, 16), (19, 1), (12, 15), (16, 0), (25, 0), (7, 19), (2, 20), (9, 25), (24, 4), (5, 18), (21, 7), (13, 7), (8, 22), (23, 3), (7, 23), (19, 2), (13, 17), (26, 20), (2, 0), (27, 19), (21, 15), (18, 19), (10, 23), (6, 23), (23, 28), (21, 3), (15, 11), (1, 7), (3, 10), (20, 24), (18, 9), (8, 23), (0, 9), (15, 20), (9, 20), (23, 25), (12, 4), (8, 2), (13, 9), (14, 21), (16, 14), (10, 9), (22, 0), (9, 17), (1, 12), (3, 15), (26, 2), (27, 11), (17, 27), (12, 5), (17, 6), (13, 15), (9, 12), (25, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "889856", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 15), (22, 14), (5, 11), (4, 5), (21, 3), (6, 0), (7, 18), (9, 0), (1, 22), (5, 9), (17, 22), (23, 19), (21, 14), (0, 11), (17, 6), (3, 8), (6, 4), (3, 17), (2, 16), (20, 22), (13, 5), (1, 9), (19, 10), (5, 23), (2, 19), (1, 6), (5, 21), (4, 11), (19, 19), (9, 5), (9, 3), (16, 8), (15, 0), (3, 12), (13, 21), (6, 10), (8, 23), (16, 3), (9, 15), (11, 10), (22, 12), (19, 3), (14, 22), (7, 19), (12, 18), (1, 14), (6, 11), (17, 17), (6, 17), (7, 13), (18, 14), (22, 15), (11, 5), (0, 8), (22, 11), (4, 10), (8, 15), (22, 18), (17, 23), (16, 23), (7, 17), (10, 6), (13, 2), (3, 19), (14, 21), (4, 21), (12, 11), (18, 21), (12, 7), (12, 3), (11, 19), (0, 4), (8, 8), (4, 2), (18, 0), (1, 2), (11, 7), (17, 15), (12, 4), (8, 10), (16, 16), (23, 2), (13, 13), (12, 16), (6, 5), (8, 19), (0, 5), (19, 6), (0, 20), (19, 7), (18, 23), (8, 2), (21, 12), (1, 8), (10, 21), (12, 6), (7, 22), (2, 11), (0, 2), (21, 10), (16, 20), (23, 3), (12, 8), (22, 10), (9, 10), (6, 21), (3, 4), (16, 22), (4, 18), (14, 7), (3, 5), (20, 11), (0, 9), (16, 15), (2, 21), (22, 5), (10, 4), (9, 12), (16, 19), (14, 11), (10, 15), (13, 10), (3, 23), (14, 20), (5, 4), (15, 21), (18, 4), (4, 4), (10, 9), (8, 6), (0, 16), (7, 12), (1, 23), (16, 14), (4, 6), (21, 23), (13, 16), (21, 6), (4, 19), (18, 19), (19, 8), (7, 4), (15, 8), (10, 10), (6, 7), (7, 3), (13, 14), (21, 1), (18, 18), (2, 23), (4, 8), (20, 5), (23, 12), (6, 3), (3, 22), (22, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553650", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 20), (2, 15), (20, 27), (19, 25), (19, 27), (18, 23), (11, 22), (6, 19), (15, 27), (1, 3), (2, 21), (10, 19), (12, 10), (20, 16), (13, 25), (3, 22), (12, 19), (22, 8), (12, 25), (4, 15), (9, 10), (22, 12), (6, 21), (3, 23), (16, 21), (1, 26), (24, 21), (6, 3), (6, 9), (24, 4), (16, 5), (23, 7), (14, 24), (6, 13), (3, 17), (11, 15), (13, 11), (9, 22), (10, 7), (6, 7), (5, 6), (14, 25), (22, 11), (5, 0), (19, 10), (6, 24), (17, 4), (1, 7), (23, 6), (20, 4), (12, 20), (9, 24), (16, 19), (9, 18), (8, 11), (5, 12), (5, 17), (20, 26), (10, 6), (25, 24), (11, 8), (14, 4), (17, 25), (20, 8), (8, 10), (22, 15), (8, 6), (22, 20), (2, 24), (22, 26), (7, 25), (12, 26), (9, 2), (17, 7), (15, 11), (5, 14), (17, 14), (7, 6), (4, 6), (22, 4), (1, 25), (3, 2), (25, 5), (12, 8), (1, 13), (12, 3), (9, 5), (10, 25), (4, 23), (25, 18), (20, 9), (22, 0), (11, 5), (20, 11), (25, 20), (8, 20), (9, 4), (25, 17), (19, 11), (15, 18), (11, 24), (20, 10), (18, 18), (2, 17), (21, 21), (19, 22), (24, 13), (24, 3), (13, 15), (24, 18), (2, 27), (21, 17), (22, 16), (22, 2), (22, 19), (1, 15), (25, 21), (7, 14), (0, 10), (8, 3), (16, 22), (13, 9), (19, 18), (2, 19), (25, 11), (23, 24), (0, 12), (15, 9), (9, 15), (11, 14), (19, 20), (4, 22), (9, 11), (1, 4), (8, 0), (17, 24), (12, 18), (0, 23), (5, 20), (20, 17), (1, 5), (8, 23), (3, 6), (8, 21), (9, 13), (3, 18), (22, 18), (12, 6), (17, 5), (13, 14), (25, 19), (19, 9), (9, 0), (7, 5), (14, 5), (10, 5), (13, 13), (3, 0), (16, 8), (6, 26), (14, 8), (22, 23), (20, 1), (12, 1), (6, 12), (19, 7), (12, 23), (5, 8), (20, 13), (17, 22), (12, 2), (2, 0), (10, 4), (15, 17), (6, 8), (3, 15), (24, 26), (25, 14), (2, 2), (21, 18), (23, 15), (22, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694800", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 12), (21, 19), (0, 20), (2, 10), (7, 15), (0, 8), (14, 11), (4, 3), (20, 10), (17, 12), (19, 20), (13, 23), (17, 14), (21, 16), (14, 24), (0, 22), (21, 0), (19, 18), (7, 7), (11, 1), (18, 7), (3, 6), (9, 13), (8, 18), (3, 14), (12, 13), (13, 16), (2, 15), (16, 20), (11, 11), (1, 15), (17, 19), (9, 2), (0, 1), (14, 6), (0, 23), (10, 1), (5, 21), (0, 17), (8, 23), (4, 17), (10, 15), (21, 7), (17, 7), (2, 24), (4, 4), (11, 4), (7, 12), (17, 21), (1, 5), (21, 12), (8, 22), (1, 9), (0, 3), (21, 18), (5, 17), (5, 14), (6, 2), (7, 20), (19, 8), (20, 0), (13, 8), (0, 14), (20, 4), (16, 22), (15, 3), (12, 3), (14, 10), (15, 17), (16, 23), (17, 9), (1, 16), (18, 13), (8, 9), (1, 11), (3, 1), (10, 10), (0, 24), (9, 3), (18, 11), (16, 1), (16, 6), (7, 14), (13, 4), (18, 9), (18, 12), (1, 23), (6, 3), (3, 20), (14, 13), (9, 22), (21, 22), (19, 1), (8, 15), (2, 17), (17, 18), (4, 21), (3, 12), (6, 16), (18, 23), (6, 1), (1, 20), (9, 0), (11, 24), (16, 0), (3, 3), (14, 23), (15, 14), (19, 17), (9, 19), (15, 2), (2, 13), (14, 0), (18, 2), (5, 11), (7, 9), (0, 16), (2, 7), (20, 24), (19, 19), (13, 24), (19, 16), (17, 5), (10, 3), (19, 13), (13, 22), (2, 6), (6, 18), (17, 6), (11, 19), (12, 9), (5, 0), (18, 14), (4, 20), (0, 21), (20, 3), (0, 7), (13, 5), (20, 16), (16, 24), (11, 14), (16, 16), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "893850", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (5, 7), (4, 4), (6, 16), (22, 1), (9, 5), (12, 3), (7, 4), (1, 13), (3, 14), (21, 19), (20, 7), (22, 18), (8, 15), (13, 18), (2, 10), (26, 1), (0, 14), (17, 19), (24, 20), (23, 18), (11, 21), (6, 15), (19, 4), (20, 20), (20, 9), (27, 20), (22, 19), (2, 11), (13, 7), (20, 5), (27, 2), (5, 16), (20, 15), (0, 11), (6, 21), (3, 18), (15, 15), (3, 4), (2, 14), (24, 0), (5, 5), (24, 21), (16, 14), (4, 5), (6, 0), (3, 9), (11, 6), (22, 2), (9, 19), (23, 5), (15, 8), (10, 15), (22, 12), (12, 0), (5, 2), (12, 4), (25, 1), (21, 18), (16, 6), (27, 1), (11, 7), (24, 6), (16, 16), (27, 14), (5, 6), (21, 1), (2, 4), (8, 3), (21, 21), (12, 1), (16, 9), (22, 7), (13, 13), (22, 5), (16, 10), (25, 9), (10, 12), (24, 15), (8, 9), (15, 16), (0, 17), (25, 7), (11, 9), (19, 9), (21, 7), (13, 10), (20, 14), (17, 0), (9, 11), (18, 3), (1, 8), (0, 18), (27, 18), (7, 7), (19, 10), (6, 18), (5, 15), (4, 8), (16, 0), (23, 3), (10, 17), (8, 1), (17, 15), (5, 17), (11, 4), (4, 2), (14, 5), (26, 11), (3, 21), (9, 21), (18, 2), (26, 14), (11, 16), (8, 11), (17, 1), (20, 4), (16, 1), (13, 21), (18, 14), (2, 6), (24, 10), (2, 7), (10, 13), (7, 11), (11, 11), (0, 19), (18, 13), (24, 13), (23, 15), (13, 9), (2, 18), (26, 13), (16, 18), (5, 20), (10, 0), (26, 20), (10, 20), (16, 7), (19, 19), (10, 16), (4, 21), (5, 13), (2, 2), (7, 16), (18, 8), (24, 18), (21, 17), (20, 3), (6, 7), (6, 13), (4, 9), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964714", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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, 11), (20, 2), (26, 23), (3, 20), (9, 18), (19, 6), (9, 24), (8, 17), (6, 14), (17, 2), (22, 2), (18, 10), (26, 12), (10, 20), (24, 7), (0, 21), (27, 26), (25, 26), (14, 6), (17, 14), (12, 22), (17, 15), (22, 18), (7, 21), (3, 14), (24, 0), (27, 12), (15, 25), (20, 17), (5, 10), (4, 7), (23, 22), (10, 6), (25, 10), (26, 20), (19, 17), (24, 22), (10, 0), (19, 13), (16, 25), (25, 24), (14, 0), (24, 25), (6, 18), (4, 11), (18, 15), (3, 18), (9, 8), (14, 4), (10, 9), (25, 12), (20, 1), (21, 24), (0, 12), (23, 21), (6, 24), (26, 10), (13, 17), (8, 4), (22, 9), (27, 2), (20, 20), (14, 25), (12, 0), (11, 19), (6, 15), (17, 18), (17, 11), (28, 21), (24, 3), (16, 7), (15, 2), (24, 15), (7, 12), (26, 18), (2, 20), (3, 21), (21, 26), (24, 20), (23, 15), (15, 22), (4, 13), (3, 22), (10, 4), (5, 2), (8, 23), (3, 17), (12, 10), (28, 7), (21, 17), (15, 26), (28, 6), (13, 4), (18, 9), (9, 7), (26, 5), (21, 9), (12, 25), (12, 5), (8, 2), (15, 9), (1, 9), (24, 9), (25, 7), (1, 3), (16, 0), (8, 20), (10, 24), (8, 14), (17, 22), (25, 22), (17, 21), (21, 19), (18, 20), (10, 11), (7, 6), (26, 1), (24, 10), (0, 22), (26, 21), (10, 19), (18, 16), (27, 11), (24, 21), (20, 10), (16, 13), (0, 5), (28, 9), (13, 15), (16, 16), (19, 10), (16, 3), (26, 13), (22, 25), (15, 8), (3, 6), (22, 1), (7, 23), (4, 4), (3, 24), (14, 12), (1, 14), (7, 7), (1, 6), (7, 5), (11, 5), (2, 22), (23, 6), (22, 17), (24, 26), (27, 14), (18, 2), (16, 17), (22, 23), (27, 10), (8, 22), (4, 14), (12, 12), (11, 22), (13, 20), (0, 17), (9, 14), (5, 11), (17, 12), (17, 16), (21, 18), (1, 15), (6, 17), (2, 2), (0, 7), (7, 17), (4, 24), (7, 22), (26, 14), (4, 9), (16, 1), (12, 21), (26, 17), (16, 23), (1, 10), (18, 18), (3, 23), (11, 26), (25, 5), (3, 12), (14, 19), (1, 13), (24, 6), (2, 5), (16, 18), (25, 8), (10, 3), (18, 17), (2, 17), (25, 20), (9, 13), (6, 26), (15, 20), (10, 7), (15, 1), (9, 25), (7, 2), (11, 12), (19, 20), (27, 23), (19, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836640", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), 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), (15, 23), (11, 21), (5, 17), (18, 16), (8, 20), (8, 7), (23, 14), (4, 15), (2, 5), (13, 13), (19, 1), (15, 14), (21, 20), (23, 22), (7, 14), (16, 0), (8, 22), (9, 5), (4, 7), (19, 6), (1, 17), (6, 8), (4, 10), (7, 10), (17, 11), (17, 22), (15, 22), (9, 6), (11, 22), (0, 2), (9, 18), (0, 14), (12, 8), (13, 9), (18, 22), (12, 19), (19, 19), (22, 17), (9, 14), (16, 23), (21, 21), (18, 21), (17, 23), (12, 21), (5, 15), (0, 7), (0, 22), (16, 21), (20, 18), (15, 5), (6, 21), (19, 8), (15, 16), (3, 19), (13, 3), (14, 8), (20, 10), (0, 21), (21, 7), (20, 15), (4, 11), (21, 5), (2, 15), (12, 14), (12, 6), (8, 16), (13, 17), (21, 23), (15, 7), (13, 0), (5, 4), (9, 12), (17, 16), (23, 9), (2, 3), (7, 15), (5, 13), (4, 2), (19, 13), (11, 19), (18, 0), (3, 15), (11, 7), (10, 17), (14, 13), (3, 23), (7, 20), (21, 13), (2, 0), (20, 23), (6, 11), (3, 20), (23, 18), (15, 21), (9, 9), (22, 11), (11, 16), (20, 19), (7, 8), (4, 22), (2, 13), (1, 21), (18, 15), (2, 19), (19, 16), (4, 14), (3, 8), (23, 5), (18, 7), (5, 9), (20, 11), (3, 18), (8, 6), (13, 14), (4, 23), (15, 2), (9, 2), (3, 21), (21, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "468460", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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, 5), (17, 6), (3, 12), (8, 15), (11, 5), (13, 15), (18, 4), (17, 14), (16, 6), (7, 10), (21, 14), (17, 1), (1, 2), (4, 17), (12, 13), (11, 16), (20, 9), (2, 8), (3, 17), (3, 15), (9, 13), (8, 0), (18, 7), (4, 4), (0, 6), (16, 19), (2, 20), (15, 10), (16, 14), (21, 4), (15, 18), (0, 12), (3, 7), (7, 2), (20, 6), (5, 4), (9, 2), (10, 17), (15, 15), (10, 5), (17, 15), (20, 19), (19, 4), (0, 17), (18, 17), (5, 5), (4, 16), (12, 10), (12, 15), (19, 2), (14, 1), (6, 17), (7, 6), (16, 12), (4, 20), (14, 6), (5, 17), (1, 11), (1, 9), (10, 12), (4, 14), (21, 3), (2, 13), (19, 15), (6, 11), (1, 0), (8, 5), (18, 3), (6, 5), (6, 2), (15, 8), (9, 3), (4, 8), (3, 11), (20, 0), (4, 0), (2, 2), (19, 10), (3, 13), (20, 15), (8, 13), (2, 7), (7, 11), (19, 0), (21, 12), (13, 8), (17, 20), (4, 9), (10, 2), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643174", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 12), (9, 1), (7, 13), (15, 0), (3, 17), (1, 9), (11, 4), (16, 14), (24, 7), (9, 9), (12, 19), (0, 3), (2, 8), (11, 9), (6, 19), (9, 14), (5, 8), (11, 15), (8, 9), (10, 19), (13, 17), (21, 17), (18, 3), (16, 0), (15, 2), (16, 2), (12, 8), (16, 3), (7, 14), (11, 2), (2, 1), (20, 1), (22, 14), (3, 15), (6, 8), (23, 5), (11, 6), (13, 11), (2, 6), (12, 0), (7, 3), (17, 16), (12, 7), (21, 18), (0, 6), (0, 4), (1, 14), (18, 20), (22, 9), (18, 1), (9, 3), (10, 8), (14, 8), (19, 17), (2, 12), (14, 9), (22, 7), (18, 4), (10, 20), (1, 6), (17, 13), (15, 16), (16, 8), (12, 1), (10, 3), (10, 13), (2, 3), (6, 7), (20, 16), (24, 9), (24, 5), (8, 18), (14, 20), (18, 5), (14, 19), (3, 9), (7, 16), (16, 17), (20, 5), (19, 14), (9, 17), (6, 10), (0, 16), (4, 14), (23, 17), (19, 15), (24, 0), (1, 17), (23, 8), (2, 9), (13, 9), (20, 20), (21, 1), (23, 7), (9, 7), (6, 12), (15, 5), (18, 2), (0, 2), (10, 14), (3, 14), (15, 6), (24, 16), (17, 2), (15, 20), (22, 11), (8, 10), (22, 8), (4, 20), (16, 16), (19, 19), (12, 4), (0, 20), (4, 18), (15, 18), (17, 8), (12, 18), (1, 2), (4, 2), (1, 7), (21, 19), (9, 4), (16, 19), (24, 13), (19, 16), (1, 13), (13, 20), (4, 13), (3, 5), (11, 16), (1, 18), (19, 7), (22, 10), (14, 13), (24, 6), (10, 12), (18, 19), (17, 1), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956340", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), 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), (6, 8), (10, 0), (4, 13), (3, 7), (12, 12), (10, 27), (19, 4), (6, 26), (8, 22), (3, 28), (0, 16), (24, 1), (2, 28), (25, 13), (19, 15), (6, 17), (23, 27), (20, 0), (2, 23), (21, 23), (18, 13), (12, 2), (20, 26), (18, 1), (12, 9), (13, 0), (10, 3), (20, 12), (22, 23), (11, 4), (11, 12), (26, 21), (15, 19), (9, 15), (24, 5), (19, 19), (20, 1), (15, 21), (25, 18), (4, 27), (21, 14), (7, 11), (11, 22), (10, 16), (19, 17), (26, 16), (23, 10), (19, 7), (4, 21), (9, 19), (15, 22), (3, 11), (0, 1), (22, 6), (10, 7), (12, 15), (13, 12), (2, 14), (26, 20), (20, 25), (12, 14), (1, 4), (3, 10), (20, 20), (10, 4), (14, 13), (6, 27), (19, 8), (16, 11), (8, 19), (6, 24), (17, 10), (0, 6), (26, 14), (2, 2), (12, 8), (4, 8), (8, 7), (14, 4), (5, 24), (8, 5), (18, 19), (23, 0), (25, 8), (25, 0), (9, 26), (6, 13), (13, 19), (4, 23), (14, 22), (14, 23), (24, 17), (8, 16), (24, 27), (14, 2), (17, 21), (21, 0), (20, 19), (26, 15), (14, 8), (10, 9), (0, 22), (10, 25), (26, 23), (4, 9), (24, 14), (16, 24), (15, 5), (14, 7), (13, 26), (10, 28), (19, 3), (12, 21), (21, 4), (17, 0), (4, 25), (11, 8), (17, 24), (13, 10), (23, 26), (25, 26), (0, 10), (7, 16), (13, 16), (1, 22), (22, 15), (15, 3), (14, 19), (18, 7), (16, 10), (10, 1), (7, 14), (24, 10), (10, 23), (9, 5), (24, 24), (24, 13), (22, 14), (2, 21), (19, 28), (3, 13), (0, 9), (11, 25), (12, 27), (17, 22), (9, 10), (7, 12), (2, 4), (11, 6), (8, 28), (18, 15), (13, 21), (4, 6), (26, 25), (7, 5), (2, 15), (25, 20), (17, 13), (1, 3), (24, 21), (10, 10), (19, 5), (18, 26), (15, 26), (3, 12), (22, 10), (13, 15), (9, 0), (7, 21), (1, 19), (5, 2), (13, 28), (22, 21), (15, 11), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685683", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 17), (6, 1), (0, 7), (2, 8), (22, 15), (4, 6), (9, 5), (17, 9), (16, 5), (6, 0), (17, 1), (9, 15), (20, 15), (13, 18), (3, 8), (5, 16), (0, 5), (4, 4), (10, 11), (16, 12), (21, 12), (17, 7), (15, 16), (16, 13), (19, 13), (20, 16), (0, 6), (22, 4), (1, 5), (9, 4), (24, 9), (13, 17), (7, 7), (21, 5), (22, 8), (8, 12), (9, 14), (19, 8), (20, 4), (18, 17), (7, 13), (21, 15), (9, 0), (7, 9), (4, 5), (4, 8), (2, 17), (0, 9), (12, 3), (9, 1), (15, 12), (14, 15), (3, 18), (9, 8), (11, 9), (23, 8), (2, 15), (11, 2), (8, 14), (20, 18), (7, 16), (9, 6), (16, 3), (7, 8), (20, 12), (5, 12), (16, 10), (8, 17), (2, 6), (20, 17), (10, 17), (1, 8), (5, 6), (13, 4), (18, 6), (0, 11), (13, 11), (14, 9), (2, 10), (12, 12), (7, 3), (24, 7), (5, 9), (6, 10), (8, 1), (0, 18), (18, 14), (20, 9), (6, 6), (20, 1), (23, 18), (15, 8), (10, 6), (22, 13), (4, 13), (19, 15), (19, 19), (15, 9), (0, 17), (6, 13), (18, 5), (10, 12), (14, 18), (18, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398580", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (11, 6), (3, 9), (20, 24), (18, 27), (8, 25), (1, 18), (13, 0), (15, 7), (21, 19), (15, 10), (22, 8), (12, 7), (21, 1), (12, 1), (8, 14), (6, 20), (16, 0), (1, 16), (22, 0), (0, 17), (5, 17), (20, 15), (3, 26), (23, 23), (2, 18), (15, 21), (2, 12), (12, 4), (6, 14), (17, 14), (10, 25), (5, 11), (14, 5), (11, 26), (16, 16), (6, 26), (3, 7), (3, 13), (8, 24), (12, 3), (12, 19), (10, 5), (9, 4), (4, 17), (23, 25), (3, 19), (6, 0), (20, 16), (12, 8), (10, 26), (17, 13), (15, 2), (22, 21), (16, 25), (21, 9), (6, 21), (16, 6), (3, 4), (17, 15), (20, 5), (3, 24), (11, 23), (9, 0), (12, 16), (19, 1), (23, 13), (20, 20), (13, 19), (16, 21), (11, 5), (4, 6), (2, 7), (22, 9), (9, 27), (19, 6), (5, 14), (23, 12), (11, 7), (21, 0), (23, 3), (21, 8), (10, 21), (10, 20), (4, 25), (23, 4), (16, 19), (12, 6), (1, 27), (1, 23), (21, 6), (7, 12), (8, 6), (3, 12), (22, 4), (14, 2), (6, 5), (4, 14), (3, 16), (22, 7), (0, 10), (10, 18), (0, 14), (22, 22), (11, 0), (4, 27), (0, 23), (1, 10), (0, 13), (20, 3), (7, 11), (10, 27), (17, 9), (10, 16), (8, 9), (15, 4), (20, 19), (5, 24), (8, 27), (16, 23), (12, 25), (14, 12), (11, 9), (3, 2), (12, 12), (3, 18), (14, 19), (22, 5), (16, 22), (20, 1), (0, 18), (0, 27), (16, 8), (2, 15), (10, 17), (4, 9), (10, 14), (7, 27), (1, 15), (21, 17), (13, 8), (2, 23), (22, 6), (15, 23), (8, 18), (22, 24), (13, 9), (14, 7), (17, 11), (12, 11), (7, 5), (5, 0), (18, 15), (16, 11), (7, 8), (2, 1), (1, 8), (20, 7), (7, 3), (2, 10), (16, 3), (16, 7), (3, 3), (19, 27), (10, 12), (2, 8), (17, 3), (8, 23), (19, 26), (8, 11), (1, 22), (5, 18), (15, 19), (4, 20), (15, 27), (0, 4), (15, 12), (21, 4), (3, 25), (19, 10), (13, 11), (6, 9), (10, 23), (17, 17), (22, 27), (14, 11), (4, 3), (1, 5), (4, 13), (7, 19), (6, 3), (5, 22), (17, 20), (1, 12), (17, 24), (10, 11), (13, 21), (14, 26), (10, 3), (13, 3), (11, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475310", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 20), (0, 3), (17, 5), (17, 17), (5, 25), (16, 6), (4, 17), (6, 3), (18, 7), (19, 11), (7, 7), (7, 17), (10, 0), (6, 8), (4, 3), (18, 20), (19, 16), (16, 22), (10, 17), (19, 3), (5, 2), (9, 3), (0, 17), (19, 19), (14, 14), (19, 21), (13, 8), (9, 8), (1, 4), (0, 15), (7, 6), (2, 22), (16, 16), (17, 4), (9, 17), (3, 10), (0, 21), (17, 9), (12, 6), (4, 20), (5, 23), (14, 25), (5, 13), (14, 8), (10, 7), (16, 10), (18, 17), (16, 17), (3, 2), (13, 2), (12, 23), (9, 16), (1, 21), (16, 2), (1, 13), (7, 22), (6, 15), (16, 4), (3, 18), (4, 14), (7, 19), (18, 24), (17, 3), (12, 14), (3, 16), (15, 5), (8, 19), (4, 18), (2, 14), (18, 22), (18, 11), (18, 14), (8, 15), (12, 13), (15, 8), (8, 1), (0, 25), (8, 2), (15, 23), (4, 12), (1, 10), (5, 17), (18, 18), (3, 4), (16, 24), (8, 17), (13, 24), (12, 20), (6, 2), (10, 4), (14, 9), (1, 0), (11, 10), (4, 2), (8, 16), (9, 11), (7, 1), (14, 1), (15, 3), (4, 6), (9, 21), (6, 12), (12, 7), (15, 14), (17, 0), (7, 15), (5, 3), (8, 18), (11, 5), (9, 15), (1, 19), (19, 15), (8, 23), (11, 22), (1, 2), (8, 8), (2, 24), (18, 9), (18, 12), (19, 9), (13, 7), (13, 13), (17, 19), (7, 13), (3, 17), (0, 10), (11, 14), (14, 11), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902629", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 23), (27, 17), (5, 1), (16, 12), (27, 19), (22, 1), (25, 2), (9, 6), (17, 14), (24, 9), (7, 24), (12, 24), (22, 2), (7, 2), (23, 14), (7, 16), (22, 16), (8, 2), (15, 4), (14, 14), (23, 16), (16, 20), (21, 4), (16, 11), (18, 23), (18, 21), (26, 18), (26, 3), (16, 9), (7, 20), (26, 23), (4, 19), (8, 8), (13, 15), (17, 0), (27, 10), (1, 22), (24, 11), (4, 3), (24, 19), (15, 5), (5, 21), (8, 3), (8, 12), (16, 17), (14, 24), (3, 22), (1, 16), (27, 8), (19, 5), (9, 18), (24, 3), (25, 1), (9, 17), (11, 2), (8, 4), (4, 11), (4, 10), (4, 7), (1, 21), (10, 24), (16, 3), (13, 3), (9, 22), (22, 13), (25, 11), (21, 7), (12, 20), (2, 23), (27, 0), (9, 12), (12, 0), (14, 11), (0, 23), (1, 0), (17, 10), (2, 16), (7, 23), (0, 14), (15, 20), (15, 2), (26, 11), (14, 19), (21, 6), (14, 10), (20, 17), (8, 20), (4, 24), (15, 17), (1, 23), (15, 23), (15, 0), (22, 10), (7, 21), (27, 5), (7, 9), (3, 11), (1, 5), (2, 14), (10, 23), (21, 9), (26, 19), (27, 6), (6, 15), (11, 12), (14, 13), (5, 4), (27, 12), (14, 20), (11, 23), (13, 2), (20, 11), (23, 6), (18, 8), (22, 5), (24, 20), (22, 0), (17, 21), (26, 13), (1, 20), (26, 8), (11, 10), (0, 3), (12, 11), (20, 15), (22, 15), (5, 18), (13, 17), (7, 1), (19, 15), (19, 11), (1, 19), (26, 21), (18, 3), (20, 7), (8, 7), (0, 4), (20, 8), (9, 3), (6, 6), (4, 9), (5, 2), (15, 16), (1, 11), (21, 22), (19, 20), (3, 15), (19, 23), (6, 19), (1, 13), (9, 2), (3, 21), (21, 12), (17, 23), (24, 7), (17, 9), (3, 4), (3, 3), (14, 3), (20, 4), (4, 13), (6, 16), (4, 21), (27, 23), (6, 8), (15, 24), (13, 19), (0, 8), (21, 3), (23, 8), (8, 1), (7, 8), (18, 4), (21, 20), (20, 18), (0, 20), (20, 21), (12, 19), (24, 18), (20, 5), (6, 14), (24, 10), (23, 15), (20, 16), (8, 15), (0, 24), (16, 14), (16, 22), (9, 10), (15, 8), (2, 20), (20, 24), (17, 4), (11, 7), (15, 12), (24, 22), (4, 17), (5, 3), (25, 12), (27, 4), (8, 21), (20, 22), (2, 6), (9, 15), (7, 0), (23, 24), (15, 6), (21, 1), (9, 14), (25, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "461125", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), 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), (15, 17), (24, 25), (4, 16), (5, 14), (11, 2), (8, 9), (1, 7), (24, 2), (12, 13), (24, 14), (7, 13), (20, 18), (14, 16), (2, 8), (5, 25), (1, 12), (13, 1), (15, 20), (7, 24), (4, 23), (19, 4), (20, 21), (15, 10), (15, 9), (0, 19), (22, 15), (3, 11), (9, 10), (15, 16), (17, 7), (8, 4), (18, 3), (3, 20), (21, 3), (21, 8), (21, 12), (15, 12), (13, 9), (21, 20), (10, 28), (9, 28), (7, 22), (1, 25), (1, 5), (12, 27), (14, 17), (6, 7), (6, 25), (5, 21), (10, 21), (21, 25), (10, 5), (11, 20), (24, 12), (24, 15), (7, 18), (10, 15), (15, 26), (24, 24), (4, 24), (1, 23), (1, 1), (9, 4), (12, 3), (23, 4), (11, 22), (14, 28), (15, 6), (22, 24), (19, 21), (8, 14), (2, 27), (20, 5), (2, 18), (17, 3), (22, 22), (5, 8), (21, 10), (0, 24), (19, 9), (17, 8), (12, 0), (20, 27), (15, 24), (22, 8), (3, 0), (15, 18), (18, 11), (7, 11), (3, 15), (15, 0), (24, 20), (9, 20), (5, 9), (6, 20), (15, 19), (19, 3), (13, 0), (18, 14), (9, 13), (9, 15), (14, 20), (5, 3), (12, 25), (21, 9), (8, 25), (14, 12), (2, 2), (1, 14), (6, 26), (12, 7), (7, 9), (6, 6), (16, 16), (10, 19), (23, 21), (13, 3), (11, 6), (24, 7), (6, 4), (12, 24), (23, 12), (15, 21), (5, 24), (17, 2), (24, 19), (2, 5), (11, 3), (1, 22), (12, 18), (15, 15), (22, 17), (7, 5), (0, 1), (2, 26), (3, 21), (9, 8), (14, 9), (14, 25), (23, 26), (3, 17), (22, 19), (11, 24), (10, 4), (4, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96187", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 4), (8, 6), (13, 9), (15, 19), (15, 11), (17, 10), (14, 6), (8, 1), (10, 17), (8, 5), (21, 12), (8, 3), (19, 8), (11, 13), (9, 2), (22, 4), (0, 18), (8, 20), (19, 11), (0, 3), (8, 17), (6, 13), (6, 12), (4, 7), (8, 12), (16, 1), (5, 8), (14, 25), (9, 4), (22, 0), (6, 25), (5, 23), (5, 6), (13, 1), (2, 23), (10, 23), (18, 6), (7, 3), (6, 10), (7, 11), (10, 12), (6, 4), (7, 25), (14, 9), (11, 17), (3, 13), (22, 19), (14, 13), (11, 23), (21, 11), (14, 10), (15, 21), (2, 22), (4, 14), (1, 7), (13, 22), (3, 9), (5, 25), (3, 5), (1, 11), (20, 10), (18, 20), (17, 4), (16, 18), (20, 11), (4, 16), (9, 1), (2, 19), (4, 9), (20, 22), (12, 23), (3, 20), (22, 10), (18, 16), (11, 8), (18, 19), (4, 11), (22, 3), (18, 25), (11, 3), (0, 23), (12, 25), (20, 17), (20, 24), (16, 4), (10, 14), (18, 3), (8, 8), (19, 5), (5, 21), (13, 6), (10, 7), (21, 19), (12, 17), (7, 6), (5, 3), (18, 14), (8, 22), (5, 5), (2, 17), (20, 7), (22, 6), (0, 10), (20, 14), (3, 19), (18, 23), (10, 11), (6, 24), (6, 14), (19, 23), (12, 8), (14, 0), (12, 2), (11, 7), (16, 22), (17, 16), (17, 2), (17, 0), (8, 14), (4, 24), (0, 22), (17, 7), (22, 9), (1, 15), (10, 8), (3, 7), (10, 25), (7, 9), (7, 14), (12, 5), (0, 5), (20, 25), (20, 12), (19, 1), (2, 24), (6, 3), (12, 6), (9, 10), (0, 15), (6, 7), (0, 11), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14682", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (10, 18), (6, 7), (14, 5), (4, 16), (7, 6), (1, 17), (19, 17), (7, 1), (7, 5), (11, 12), (11, 1), (6, 17), (9, 16), (5, 0), (1, 0), (6, 16), (6, 13), (5, 15), (0, 11), (15, 15), (5, 16), (13, 17), (8, 19), (17, 6), (11, 2), (12, 12), (19, 6), (13, 6), (6, 1), (4, 6), (15, 18), (13, 16), (7, 16), (14, 16), (1, 13), (8, 14), (4, 5), (15, 0), (17, 8), (7, 13), (7, 9), (12, 11), (2, 10), (8, 5), (1, 2), (3, 11), (17, 19), (17, 16), (5, 9), (0, 15), (16, 20), (3, 0), (17, 20), (6, 20), (0, 9), (5, 13), (8, 4), (4, 8), (0, 16), (8, 7), (0, 20), (1, 6), (7, 2), (8, 1), (2, 13), (14, 20), (3, 5), (2, 20), (9, 7), (10, 16), (11, 7), (14, 18), (17, 3), (11, 11), (19, 10), (13, 5), (9, 19), (1, 16), (8, 16), (13, 1), (5, 11), (9, 5), (4, 15), (15, 17), (6, 19), (17, 10), (8, 3), (1, 14), (19, 14), (19, 3), (6, 5), (19, 4), (9, 4), (9, 10), (10, 17), (3, 14), (12, 2), (6, 18), (4, 11), (7, 14), (1, 4), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932778", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 19), (7, 12), (1, 16), (16, 4), (21, 14), (3, 19), (10, 18), (14, 13), (4, 10), (17, 1), (22, 9), (16, 3), (0, 4), (0, 10), (9, 15), (21, 13), (16, 12), (1, 0), (13, 0), (14, 6), (1, 15), (3, 11), (10, 10), (9, 18), (7, 5), (2, 3), (13, 18), (14, 1), (13, 5), (18, 2), (4, 9), (7, 16), (4, 3), (14, 5), (18, 7), (2, 15), (2, 17), (20, 1), (7, 15), (0, 13), (7, 8), (6, 7), (19, 5), (2, 10), (9, 3), (0, 9), (23, 1), (22, 13), (24, 3), (7, 2), (11, 8), (15, 7), (2, 19), (8, 5), (20, 17), (17, 15), (13, 12), (8, 13), (5, 3), (0, 8), (14, 17), (6, 15), (19, 11), (13, 17), (6, 14), (12, 5), (10, 3), (18, 4), (12, 2), (19, 6), (10, 13), (12, 1), (4, 17), (23, 16), (4, 19), (23, 7), (15, 10), (11, 12), (5, 5), (24, 15), (18, 1), (16, 11), (16, 5), (13, 14), (11, 19), (10, 11), (15, 6), (20, 3), (18, 19), (12, 17), (23, 9), (5, 16), (16, 10), (13, 11), (12, 11), (19, 15), (6, 19), (1, 12), (15, 2), (15, 3), (24, 5), (15, 16), (11, 3), (2, 12), (19, 8), (1, 19), (18, 18), (22, 12), (24, 14), (3, 3), (12, 4), (5, 11), (9, 7), (21, 15), (22, 5), (1, 1), (6, 3), (2, 16), (2, 13), (23, 5), (3, 15), (11, 1), (12, 18), (23, 8), (15, 12), (12, 15), (22, 3), (10, 15), (21, 8), (11, 14), (4, 8), (24, 12), (18, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888384", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 22), (7, 14), (7, 2), (4, 2), (0, 8), (14, 17), (19, 17), (11, 4), (5, 5), (9, 3), (6, 15), (9, 12), (2, 10), (19, 5), (11, 10), (20, 10), (17, 25), (19, 7), (13, 22), (21, 4), (4, 18), (15, 9), (13, 6), (6, 8), (1, 18), (2, 2), (18, 13), (10, 24), (16, 21), (10, 6), (13, 23), (0, 14), (8, 2), (12, 21), (19, 13), (9, 6), (2, 8), (20, 18), (17, 15), (15, 13), (22, 5), (14, 1), (0, 25), (21, 13), (5, 14), (4, 5), (15, 26), (21, 26), (15, 28), (18, 4), (2, 27), (8, 19), (21, 1), (22, 4), (11, 0), (13, 18), (18, 26), (13, 5), (16, 17), (20, 24), (12, 4), (4, 19), (0, 5), (4, 25), (16, 2), (20, 16), (11, 21), (11, 18), (21, 21), (15, 14), (10, 1), (19, 0), (20, 3), (3, 6), (15, 22), (16, 27), (7, 10), (22, 2), (7, 8), (9, 5), (8, 3), (7, 11), (16, 9), (19, 25), (21, 9), (11, 13), (21, 16), (21, 7), (10, 2), (18, 28), (17, 0), (3, 19), (17, 12), (14, 15), (19, 20), (1, 15), (8, 6), (19, 16), (19, 15), (13, 27), (22, 10), (7, 5), (13, 14), (13, 3), (6, 11), (2, 12), (14, 0), (4, 3), (11, 3), (19, 6), (4, 28), (1, 0), (1, 2), (22, 15), (18, 0), (12, 13), (21, 24), (6, 17), (6, 21), (0, 11), (12, 7), (6, 16), (20, 9), (14, 24), (21, 5), (20, 5), (18, 18), (12, 22), (0, 24), (17, 26), (22, 18), (2, 19), (4, 10), (21, 15), (20, 23), (4, 8), (18, 16), (8, 15), (3, 2), (3, 5), (2, 11), (19, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774940", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), 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, 13), (15, 17), (4, 17), (3, 3), (11, 14), (14, 12), (18, 20), (7, 15), (3, 12), (13, 3), (4, 18), (10, 8), (19, 20), (13, 2), (17, 11), (11, 5), (16, 13), (3, 13), (17, 20), (13, 6), (10, 10), (4, 1), (9, 18), (2, 11), (20, 15), (15, 7), (16, 12), (9, 8), (10, 16), (10, 5), (16, 1), (4, 10), (12, 7), (11, 13), (3, 2), (12, 18), (13, 0), (8, 8), (5, 15), (1, 3), (18, 11), (1, 20), (11, 8), (13, 13), (14, 6), (4, 9), (11, 9), (19, 12), (2, 17), (15, 6), (12, 15), (14, 4), (18, 1), (9, 15), (12, 0), (7, 14), (11, 3), (12, 4), (8, 5), (5, 10), (10, 7), (1, 12), (1, 5), (15, 20), (6, 9), (18, 16), (19, 4), (5, 0), (15, 1), (2, 0), (7, 12), (19, 9), (0, 7), (14, 11), (4, 3), (15, 11), (4, 6), (1, 14), (14, 19), (17, 8), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906517", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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, 18), (8, 11), (11, 2), (13, 4), (0, 16), (14, 17), (7, 10), (1, 5), (10, 11), (11, 14), (2, 9), (2, 3), (1, 8), (10, 10), (5, 20), (7, 20), (17, 14), (17, 4), (18, 6), (7, 0), (19, 4), (3, 14), (5, 17), (1, 15), (3, 5), (10, 0), (13, 8), (4, 8), (4, 3), (4, 14), (14, 0), (19, 14), (7, 13), (5, 16), (2, 21), (3, 10), (8, 2), (18, 8), (8, 19), (13, 5), (1, 14), (7, 17), (15, 18), (19, 2), (16, 15), (5, 13), (8, 3), (19, 6), (8, 13), (6, 10), (11, 10), (17, 7), (3, 16), (17, 9), (15, 2), (0, 11), (11, 0), (16, 3), (9, 9), (12, 4), (12, 10), (19, 13), (6, 19), (5, 5), (9, 1), (2, 20), (6, 8), (18, 17), (4, 9), (1, 2), (17, 21), (16, 9), (1, 9), (0, 3), (6, 1), (10, 12), (5, 1), (5, 12), (11, 17), (12, 2), (1, 21), (7, 18), (15, 11), (13, 11), (13, 3), (11, 16), (0, 20), (7, 4), (16, 18), (7, 3), (10, 2), (2, 17), (7, 6), (18, 0), (19, 12), (4, 13), (4, 0), (15, 4), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552963", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 12), (12, 7), (7, 22), (11, 0), (14, 14), (14, 13), (14, 12), (7, 19), (10, 8), (1, 21), (15, 16), (8, 16), (8, 13), (2, 21), (1, 20), (12, 8), (0, 5), (2, 2), (7, 12), (9, 4), (13, 4), (18, 2), (6, 22), (18, 20), (17, 21), (13, 0), (16, 22), (3, 17), (9, 10), (9, 8), (0, 17), (12, 3), (6, 4), (11, 19), (13, 12), (11, 18), (3, 7), (11, 2), (4, 6), (10, 16), (12, 20), (13, 19), (12, 9), (15, 21), (10, 0), (4, 19), (18, 8), (16, 4), (18, 12), (4, 11), (6, 8), (4, 2), (7, 17), (5, 7), (18, 21), (12, 21), (8, 15), (12, 22), (2, 7), (10, 6), (17, 15), (19, 17), (19, 12), (3, 9), (16, 5), (6, 19), (13, 7), (16, 11), (17, 7), (16, 1), (0, 10), (8, 0), (9, 1), (3, 3), (7, 15), (19, 11), (2, 0), (12, 0), (4, 18), (7, 5), (13, 2), (6, 1), (7, 20), (16, 19), (17, 13), (16, 10), (4, 10), (16, 0), (11, 6), (8, 11), (17, 22), (3, 16), (5, 21), (13, 5), (15, 4), (15, 11), (1, 7), (19, 3), (1, 13), (18, 14), (2, 10), (11, 8), (4, 0), (6, 17), (7, 18), (0, 8), (14, 3), (16, 14), (1, 0), (8, 12), (19, 9), (12, 1), (17, 5), (2, 16), (3, 1), (18, 17), (5, 17), (15, 8), (5, 18), (13, 6), (6, 10), (16, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556416", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (1, 1), (18, 9), (6, 7), (10, 10), (19, 9), (16, 3), (5, 5), (7, 6), (7, 22), (7, 13), (5, 3), (5, 12), (17, 11), (0, 13), (8, 4), (4, 11), (8, 16), (4, 22), (16, 11), (13, 3), (11, 17), (19, 10), (11, 12), (6, 2), (17, 19), (16, 5), (4, 7), (4, 20), (4, 14), (14, 10), (3, 12), (18, 12), (18, 8), (1, 8), (5, 4), (8, 2), (10, 8), (4, 17), (2, 17), (3, 13), (13, 16), (5, 9), (9, 22), (9, 18), (15, 20), (16, 15), (11, 4), (15, 9), (11, 14), (1, 7), (0, 1), (9, 17), (6, 21), (13, 19), (11, 5), (3, 22), (14, 12), (10, 18), (14, 8), (6, 12), (13, 6), (12, 9), (4, 0), (11, 20), (0, 10), (19, 11), (12, 1), (7, 2), (15, 15), (4, 13), (1, 5), (1, 14), (5, 11), (2, 13), (6, 16), (3, 4), (11, 7), (17, 20), (19, 0), (8, 14), (6, 22), (6, 6), (11, 9), (13, 13), (19, 3), (7, 16), (19, 20), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "952863", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), 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), (17, 14), (15, 3), (7, 17), (8, 21), (21, 22), (18, 14), (22, 4), (4, 13), (0, 5), (17, 3), (22, 14), (22, 18), (12, 20), (9, 9), (20, 11), (15, 9), (19, 15), (19, 21), (21, 3), (4, 16), (17, 17), (0, 4), (11, 9), (2, 3), (18, 7), (5, 18), (2, 20), (6, 12), (9, 14), (20, 6), (6, 22), (21, 19), (17, 12), (11, 0), (11, 14), (19, 2), (8, 0), (22, 10), (13, 4), (18, 8), (21, 16), (20, 19), (20, 2), (13, 5), (17, 11), (17, 13), (16, 19), (22, 5), (21, 8), (3, 0), (16, 20), (14, 12), (15, 11), (12, 0), (10, 10), (22, 15), (11, 22), (7, 3), (18, 22), (22, 2), (22, 11), (19, 12), (8, 17), (13, 10), (4, 3), (22, 1), (8, 15), (5, 9), (4, 14), (5, 20), (6, 17), (12, 14), (11, 11), (13, 3), (15, 14), (10, 16), (14, 3), (15, 0), (13, 0), (6, 9), (5, 14), (8, 10), (6, 8), (3, 10), (1, 20), (14, 7), (11, 17), (18, 15), (20, 17), (1, 8), (11, 4), (4, 22), (0, 14), (10, 20), (5, 3), (16, 13), (17, 20), (11, 1), (16, 22), (17, 2), (9, 1), (3, 9), (10, 3), (12, 21), (2, 11), (1, 14), (17, 1), (8, 12), (10, 0), (7, 6), (21, 0), (18, 16), (20, 15), (7, 13), (12, 16), (4, 7), (8, 18), (12, 17), (8, 4), (21, 4), (11, 16), (13, 21), (21, 15), (4, 17), (16, 3), (3, 6), (15, 22), (5, 22), (2, 16), (20, 14), (13, 16), (16, 14), (12, 15), (8, 19), (21, 6), (12, 9), (18, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299808", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (19, 5), (5, 3), (25, 12), (17, 9), (2, 7), (7, 5), (5, 16), (6, 17), (17, 2), (0, 15), (18, 5), (15, 9), (6, 10), (17, 1), (18, 19), (23, 17), (1, 15), (14, 10), (6, 14), (19, 7), (9, 6), (15, 7), (26, 19), (6, 3), (9, 8), (19, 0), (19, 2), (16, 11), (5, 10), (13, 6), (21, 4), (8, 9), (27, 6), (13, 19), (10, 13), (12, 9), (4, 19), (22, 15), (11, 3), (10, 0), (0, 16), (14, 20), (12, 4), (8, 12), (17, 20), (18, 0), (24, 10), (6, 1), (2, 18), (2, 10), (3, 3), (3, 0), (22, 18), (20, 6), (13, 0), (0, 10), (11, 19), (24, 11), (17, 5), (27, 1), (12, 6), (6, 19), (5, 15), (19, 4), (3, 8), (20, 1), (23, 18), (9, 17), (25, 10), (22, 11), (4, 20), (20, 2), (24, 5), (13, 2), (14, 5), (14, 18), (24, 3), (22, 13), (22, 8), (0, 19), (24, 4), (7, 19), (14, 11), (8, 19), (7, 15), (18, 13), (26, 7), (6, 7), (25, 20), (21, 0), (27, 14), (0, 4), (2, 3), (20, 15), (11, 16), (4, 14), (7, 11), (23, 7), (3, 17), (22, 3), (8, 5), (10, 19), (6, 0), (6, 11), (7, 14), (23, 1), (9, 16), (13, 12), (10, 14), (18, 17), (26, 0), (1, 9), (14, 4), (8, 7), (14, 6), (15, 11), (11, 12), (12, 8), (21, 12), (26, 18), (16, 14), (0, 20), (20, 9), (1, 12), (19, 16), (15, 17), (12, 13), (13, 5), (3, 11), (3, 10), (26, 4), (23, 15), (10, 1), (9, 19), (17, 17), (12, 18), (19, 18), (20, 0), (3, 13), (5, 14), (9, 5), (0, 14), (23, 3), (10, 16), (24, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763374", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), 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), (8, 24), (13, 12), (14, 17), (19, 16), (9, 14), (10, 13), (12, 26), (14, 27), (1, 4), (1, 16), (7, 15), (16, 9), (15, 5), (10, 20), (14, 2), (7, 20), (15, 27), (18, 27), (18, 18), (4, 4), (9, 22), (16, 23), (17, 18), (12, 5), (1, 11), (16, 5), (3, 12), (10, 11), (3, 8), (14, 21), (15, 8), (1, 10), (14, 18), (18, 13), (7, 12), (4, 16), (17, 9), (8, 5), (18, 2), (0, 4), (15, 3), (9, 26), (2, 8), (10, 27), (1, 15), (8, 21), (15, 26), (19, 5), (0, 2), (18, 11), (17, 21), (0, 13), (4, 11), (14, 13), (5, 22), (13, 23), (13, 14), (1, 26), (5, 7), (4, 5), (5, 26), (0, 24), (6, 25), (11, 20), (0, 12), (14, 22), (4, 10), (4, 17), (19, 1), (8, 12), (4, 7), (13, 0), (14, 3), (17, 8), (18, 7), (14, 23), (15, 17), (3, 27), (4, 27), (6, 12), (2, 2), (14, 20), (1, 13), (4, 0), (2, 15), (1, 5), (10, 2), (3, 13), (5, 2), (8, 13), (8, 14), (10, 3), (9, 2), (13, 9), (0, 9), (7, 0), (10, 25), (11, 7), (19, 2), (19, 8), (15, 0), (11, 5), (13, 20), (5, 18), (4, 22), (5, 15), (12, 23), (1, 7), (8, 23), (15, 9), (14, 12), (5, 5), (12, 0), (3, 24), (19, 13), (13, 4), (10, 15), (10, 17), (10, 23), (11, 10), (19, 0), (1, 23), (3, 16), (15, 13), (6, 16), (9, 24), (7, 9), (16, 19), (3, 21), (7, 17), (17, 16), (14, 8), (8, 4), (0, 18), (15, 25), (5, 14), (15, 23), (5, 0), (16, 2), (16, 10), (11, 21), (3, 9), (9, 9), (7, 2), (15, 6), (10, 9), (0, 19), (19, 19), (6, 9), (9, 5), (11, 19), (13, 24), (5, 12), (9, 19), (8, 3), (7, 4), (18, 0), (6, 1), (15, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614504", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 6), (14, 12), (12, 24), (13, 0), (5, 17), (20, 19), (22, 5), (8, 21), (0, 3), (9, 10), (7, 16), (8, 17), (11, 18), (3, 19), (22, 21), (7, 12), (10, 11), (18, 24), (21, 24), (16, 18), (22, 8), (8, 3), (8, 12), (22, 10), (6, 23), (13, 1), (5, 6), (9, 12), (1, 6), (21, 5), (19, 5), (20, 9), (4, 7), (12, 12), (18, 2), (20, 23), (18, 3), (17, 7), (20, 13), (5, 21), (10, 16), (1, 7), (1, 24), (4, 25), (16, 23), (13, 15), (4, 13), (19, 25), (10, 15), (19, 20), (17, 5), (13, 12), (22, 19), (11, 2), (19, 3), (18, 16), (7, 9), (12, 18), (1, 21), (3, 3), (11, 3), (1, 18), (20, 3), (1, 22), (16, 0), (10, 4), (15, 1), (21, 11), (19, 4), (10, 1), (7, 11), (22, 3), (14, 1), (9, 1), (12, 10), (9, 7), (22, 7), (1, 17), (4, 8), (5, 24), (15, 6), (11, 0), (4, 15), (8, 20), (8, 24), (9, 11), (8, 11), (14, 13), (11, 5), (7, 19), (15, 13), (0, 23), (2, 2), (14, 5), (12, 13), (7, 0), (14, 7), (20, 10), (19, 9), (10, 24), (1, 8), (11, 24), (13, 24), (16, 8), (1, 16), (3, 13), (2, 14), (17, 13), (18, 23), (20, 16), (10, 25), (19, 11), (5, 5), (17, 22), (21, 22), (16, 21), (4, 14), (10, 0), (12, 19), (18, 1), (22, 9), (13, 11), (11, 14), (12, 25), (16, 7), (5, 16), (11, 21), (12, 3), (2, 25), (6, 17), (1, 13), (17, 19), (13, 4), (2, 13), (21, 4), (17, 16), (16, 13), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139360", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (23, 3), (10, 1), (17, 18), (0, 14), (25, 6), (20, 10), (10, 8), (24, 11), (24, 0), (17, 3), (15, 9), (17, 7), (8, 17), (17, 15), (7, 4), (8, 15), (13, 13), (0, 2), (14, 7), (20, 3), (10, 12), (15, 13), (13, 19), (14, 15), (4, 12), (10, 16), (26, 12), (1, 7), (17, 2), (25, 18), (7, 19), (18, 10), (1, 15), (2, 12), (7, 2), (9, 14), (19, 10), (19, 1), (16, 7), (6, 14), (4, 15), (8, 8), (12, 18), (7, 17), (14, 1), (9, 3), (21, 17), (23, 2), (12, 8), (14, 10), (7, 14), (15, 11), (20, 11), (17, 19), (18, 18), (20, 2), (17, 1), (2, 17), (10, 3), (1, 5), (23, 0), (18, 8), (4, 9), (19, 14), (18, 2), (5, 3), (26, 17), (22, 9), (20, 17), (9, 4), (25, 12), (24, 13), (18, 13), (4, 6), (0, 6), (26, 0), (21, 10), (7, 6), (18, 19), (1, 4), (7, 0), (3, 3), (24, 7), (5, 12), (15, 5), (4, 18), (23, 1), (11, 16), (15, 16), (15, 10), (16, 12), (8, 11), (3, 5), (9, 1), (12, 1), (16, 2), (2, 0), (19, 18), (16, 15), (11, 7), (16, 14), (25, 3), (8, 4), (5, 4), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649880", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 8), (3, 7), (21, 13), (18, 9), (1, 5), (14, 1), (9, 8), (18, 4), (20, 21), (24, 6), (18, 21), (16, 4), (0, 16), (26, 16), (2, 12), (6, 4), (22, 12), (15, 2), (13, 7), (0, 22), (21, 2), (11, 22), (1, 15), (6, 8), (21, 15), (2, 2), (8, 18), (1, 0), (16, 21), (12, 8), (7, 5), (3, 18), (6, 12), (1, 1), (26, 21), (4, 13), (7, 11), (23, 4), (23, 6), (24, 12), (27, 16), (9, 13), (19, 18), (7, 18), (19, 21), (16, 20), (7, 6), (20, 19), (19, 2), (27, 12), (13, 19), (9, 19), (25, 1), (17, 7), (9, 4), (2, 20), (23, 15), (0, 3), (19, 1), (7, 16), (27, 10), (19, 12), (0, 14), (5, 4), (20, 0), (25, 20), (5, 5), (21, 1), (12, 15), (16, 14), (14, 3), (6, 5), (23, 21), (8, 19), (6, 18), (27, 13), (23, 9), (5, 8), (14, 2), (15, 13), (11, 13), (6, 9), (14, 7), (2, 16), (20, 4), (18, 14), (8, 22), (3, 15), (8, 1), (23, 0), (27, 20), (16, 12), (26, 9), (12, 18), (10, 17), (19, 13), (10, 11), (23, 20), (3, 20), (3, 16), (15, 22), (2, 21), (11, 6), (15, 1), (8, 10), (15, 4), (13, 18), (23, 22), (21, 0), (27, 14), (19, 14), (24, 13), (12, 16), (15, 3), (9, 6), (20, 3), (18, 3), (3, 14), (10, 20), (0, 7), (12, 2), (10, 1), (15, 10), (21, 20), (27, 17), (9, 7), (25, 5), (4, 3), (20, 18), (24, 11), (0, 15), (9, 9), (4, 16), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789360", "dataset": "MATH"}
{"messages": [{"content": "In a 27x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 23), (22, 22), (16, 15), (18, 19), (8, 4), (20, 24), (0, 19), (7, 6), (15, 20), (8, 7), (5, 3), (4, 9), (15, 4), (3, 16), (25, 1), (18, 21), (1, 16), (16, 8), (5, 9), (4, 22), (8, 14), (14, 21), (26, 19), (21, 6), (13, 13), (7, 19), (7, 2), (14, 9), (23, 10), (13, 15), (26, 22), (1, 10), (5, 0), (20, 14), (4, 10), (15, 21), (13, 16), (10, 2), (6, 17), (6, 23), (0, 8), (6, 4), (8, 10), (11, 0), (21, 11), (4, 1), (7, 5), (13, 9), (25, 11), (10, 10), (23, 11), (6, 19), (15, 5), (7, 16), (22, 9), (25, 8), (6, 1), (3, 19), (0, 24), (10, 16), (16, 1), (5, 22), (24, 7), (2, 15), (14, 16), (22, 18), (2, 14), (10, 23), (23, 18), (26, 21), (24, 21), (22, 23), (12, 15), (1, 20), (2, 12), (6, 22), (9, 11), (24, 6), (23, 12), (2, 23), (12, 20), (3, 4), (7, 13), (10, 12), (12, 7), (10, 18), (15, 22), (4, 15), (0, 6), (18, 4), (18, 20), (25, 10), (15, 10), (20, 11), (17, 16), (10, 20), (11, 3), (17, 14), (10, 6), (4, 14), (17, 21), (5, 15), (15, 3), (1, 17), (6, 2), (7, 1), (19, 6), (17, 3), (14, 5), (8, 18), (14, 4), (1, 23), (19, 17), (7, 12), (21, 1), (10, 14), (20, 19), (7, 4), (20, 12), (4, 0), (22, 12), (16, 12), (15, 16), (3, 1), (15, 2), (14, 14), (25, 18), (21, 23), (6, 21), (2, 20), (4, 5), (16, 16), (10, 24), (3, 24), (11, 4), (7, 24), (26, 0), (17, 17), (24, 15), (8, 20), (18, 7), (6, 5), (5, 13), (6, 8), (17, 0), (5, 4), (26, 4), (0, 16), (13, 3), (9, 24), (25, 12), (5, 14), (13, 14), (21, 8), (11, 1), (8, 13), (5, 23), (22, 7), (18, 14), (16, 4), (16, 6), (8, 0), (12, 12), (13, 18), (18, 1), (19, 16), (0, 15), (26, 18), (1, 13), (16, 0), (3, 15), (4, 18), (21, 18), (21, 0), (13, 22), (20, 3), (9, 16), (2, 16), (21, 24), (7, 18), (26, 7), (25, 6), (26, 9), (0, 5), (21, 12), (9, 2), (10, 17), (7, 17), (23, 0), (15, 1), (11, 9), (14, 17), (7, 3), (4, 2), (4, 16), (22, 4), (14, 7), (14, 20), (13, 8), (25, 3), (7, 20), (10, 22), (2, 8), (10, 19), (10, 3), (17, 24), (5, 10), (13, 7), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628680", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), 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, 11), (6, 11), (1, 11), (11, 10), (5, 2), (10, 14), (19, 15), (8, 19), (20, 4), (3, 21), (21, 5), (21, 3), (5, 8), (9, 15), (14, 18), (8, 8), (18, 20), (14, 17), (11, 17), (8, 6), (18, 10), (2, 11), (16, 17), (15, 10), (0, 8), (19, 18), (11, 13), (0, 3), (17, 21), (1, 23), (10, 12), (10, 8), (11, 6), (10, 1), (5, 19), (19, 23), (1, 6), (21, 12), (13, 18), (18, 0), (9, 20), (14, 16), (14, 1), (11, 8), (21, 0), (3, 7), (1, 19), (2, 18), (11, 21), (6, 21), (21, 6), (12, 20), (11, 2), (20, 23), (20, 21), (6, 3), (10, 11), (9, 13), (19, 17), (6, 7), (4, 10), (0, 5), (4, 16), (15, 11), (1, 9), (17, 20), (21, 15), (18, 14), (15, 8), (4, 18), (13, 4), (14, 5), (17, 13), (18, 8), (12, 11), (7, 21), (12, 4), (12, 14), (8, 23), (5, 10), (0, 10), (17, 12), (13, 23), (18, 11), (18, 18), (2, 16), (0, 14), (14, 2), (17, 11), (20, 13), (18, 15), (6, 20), (5, 1), (1, 21), (8, 18), (15, 4), (14, 9), (7, 12), (10, 15), (4, 2), (3, 15), (1, 22), (17, 2), (20, 17), (15, 6), (3, 5), (6, 10), (15, 0), (18, 2), (3, 18), (19, 10), (5, 5), (13, 3), (17, 22), (6, 15), (3, 4), (16, 7), (10, 18), (2, 15), (15, 5), (11, 19), (13, 2), (13, 14), (11, 15), (19, 9), (20, 2), (16, 8), (9, 2), (5, 7), (7, 18), (11, 20), (10, 4), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901108", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (0, 6), (0, 10), (13, 21), (13, 10), (18, 6), (8, 24), (13, 6), (13, 5), (1, 3), (4, 24), (7, 7), (13, 8), (8, 6), (14, 20), (0, 9), (20, 2), (6, 22), (2, 5), (16, 20), (0, 17), (4, 22), (10, 24), (7, 18), (20, 17), (10, 7), (1, 10), (12, 20), (3, 20), (17, 2), (9, 11), (18, 20), (18, 7), (16, 12), (13, 18), (13, 24), (4, 16), (18, 14), (9, 8), (15, 6), (17, 7), (9, 20), (0, 16), (8, 25), (17, 6), (13, 3), (19, 5), (15, 12), (17, 13), (2, 3), (10, 11), (12, 13), (1, 2), (2, 6), (7, 11), (19, 13), (19, 10), (2, 18), (20, 15), (3, 15), (4, 9), (8, 21), (4, 12), (11, 8), (8, 1), (3, 14), (11, 13), (15, 5), (2, 13), (20, 21), (3, 24), (11, 2), (9, 10), (2, 17), (2, 12), (18, 13), (0, 25), (20, 0), (0, 24), (17, 12), (16, 18), (1, 16), (6, 8), (12, 17), (14, 24), (16, 23), (5, 13), (10, 20), (9, 16), (8, 22), (0, 22), (5, 7), (19, 0), (13, 23), (7, 4), (15, 15), (7, 6), (3, 4), (16, 8), (8, 7), (5, 22), (16, 9), (9, 22), (18, 9), (2, 10), (18, 11), (14, 5), (10, 15), (14, 12), (20, 8), (13, 22), (19, 24), (17, 16), (4, 19), (11, 5), (16, 21), (20, 13), (5, 0), (3, 10), (16, 6), (19, 2), (6, 3), (2, 15), (6, 20), (7, 2), (12, 12), (2, 11), (13, 14), (4, 15), (12, 4), (17, 17), (8, 4), (0, 11), (18, 25), (16, 17), (6, 23), (16, 0), (14, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721215", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 3), (21, 14), (6, 12), (4, 8), (14, 19), (13, 20), (5, 18), (7, 15), (10, 19), (10, 9), (3, 12), (23, 18), (19, 5), (19, 7), (25, 1), (21, 3), (21, 7), (21, 10), (12, 18), (23, 11), (20, 3), (10, 8), (18, 18), (6, 3), (4, 15), (15, 2), (21, 8), (16, 6), (12, 10), (0, 16), (8, 8), (1, 17), (0, 2), (15, 4), (16, 11), (8, 2), (23, 16), (3, 20), (4, 17), (15, 20), (17, 7), (4, 19), (25, 15), (5, 16), (5, 13), (0, 12), (7, 13), (24, 11), (18, 0), (17, 11), (13, 0), (14, 13), (2, 12), (17, 8), (5, 7), (0, 6), (20, 13), (2, 8), (17, 3), (24, 0), (16, 15), (6, 8), (11, 7), (18, 10), (1, 15), (2, 16), (20, 14), (0, 19), (16, 1), (24, 10), (24, 19), (4, 20), (11, 0), (19, 17), (15, 15), (6, 15), (25, 6), (25, 0), (18, 11), (1, 1), (21, 5), (2, 14), (11, 4), (12, 14), (16, 13), (1, 18), (4, 16), (8, 6), (25, 12), (20, 9), (3, 8), (10, 3), (9, 7), (10, 7), (22, 17), (22, 1), (16, 10), (19, 10), (23, 20), (10, 15), (10, 5), (12, 6), (7, 4), (5, 17), (15, 11), (8, 13), (7, 19), (12, 3), (5, 14), (5, 6), (14, 8), (9, 13), (17, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541335", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (20, 10), (0, 4), (16, 4), (25, 9), (6, 7), (19, 5), (0, 10), (1, 12), (11, 9), (0, 6), (22, 9), (25, 12), (15, 9), (3, 7), (18, 12), (18, 14), (9, 6), (6, 18), (25, 1), (26, 10), (19, 0), (27, 0), (23, 4), (18, 15), (21, 11), (5, 5), (19, 4), (3, 1), (4, 14), (8, 4), (16, 19), (26, 1), (7, 7), (25, 3), (16, 3), (22, 13), (18, 3), (20, 17), (7, 15), (26, 16), (17, 10), (19, 11), (25, 7), (0, 13), (17, 9), (24, 7), (4, 1), (15, 5), (12, 2), (14, 0), (2, 19), (5, 9), (7, 3), (6, 16), (13, 16), (19, 3), (5, 1), (20, 11), (20, 12), (14, 14), (1, 11), (18, 17), (27, 12), (13, 8), (4, 16), (15, 14), (6, 0), (11, 7), (17, 11), (21, 19), (22, 16), (3, 16), (9, 0), (5, 10), (24, 19), (17, 3), (2, 16), (26, 18), (7, 11), (24, 14), (14, 17), (3, 4), (19, 19), (27, 3), (2, 4), (22, 6), (7, 9), (0, 3), (18, 9), (9, 3), (14, 19), (26, 11), (14, 8), (16, 5), (6, 8), (25, 0), (3, 0), (16, 6), (2, 17), (21, 14), (17, 2), (20, 16), (19, 10), (18, 13), (1, 10), (10, 15), (4, 12), (12, 1), (23, 19), (19, 2), (8, 3), (18, 5), (24, 2), (26, 0), (6, 13), (20, 2), (12, 8), (3, 17), (14, 15), (2, 3), (4, 19), (2, 1), (17, 4), (1, 17), (14, 10), (4, 11), (25, 13), (27, 18), (8, 18), (2, 14), (21, 10), (14, 7), (21, 12), (6, 2), (26, 13), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758808", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), 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), (15, 22), (20, 9), (19, 11), (17, 13), (8, 22), (4, 26), (19, 13), (5, 24), (0, 22), (13, 0), (9, 16), (12, 11), (6, 26), (17, 19), (20, 19), (12, 15), (5, 3), (11, 26), (15, 5), (16, 6), (14, 25), (7, 10), (20, 12), (4, 14), (2, 5), (16, 8), (14, 2), (6, 13), (11, 18), (16, 16), (1, 15), (12, 6), (7, 13), (18, 11), (6, 3), (4, 22), (3, 23), (9, 13), (8, 2), (9, 24), (11, 13), (17, 1), (12, 13), (12, 17), (15, 10), (20, 21), (7, 26), (0, 14), (13, 1), (6, 19), (12, 4), (9, 23), (17, 14), (9, 2), (17, 3), (17, 20), (0, 21), (14, 14), (18, 4), (10, 18), (1, 12), (4, 7), (14, 23), (15, 11), (5, 23), (17, 25), (11, 14), (1, 21), (14, 0), (13, 17), (5, 9), (19, 18), (1, 23), (14, 9), (0, 8), (6, 15), (11, 7), (12, 1), (17, 21), (0, 24), (15, 21), (1, 17), (19, 9), (13, 18), (7, 19), (10, 4), (7, 1), (9, 21), (3, 18), (4, 9), (14, 16), (8, 9), (1, 8), (0, 13), (6, 5), (11, 23), (19, 12), (17, 2), (16, 19), (1, 16), (8, 12), (20, 24), (7, 17), (12, 19), (16, 5), (14, 18), (14, 24), (2, 12), (16, 17), (5, 17), (2, 23), (13, 4), (20, 6), (8, 26), (4, 23), (13, 12), (7, 5), (4, 25), (4, 1), (12, 5), (18, 14), (8, 4), (4, 20), (3, 17), (12, 2), (7, 22), (1, 2), (7, 14), (16, 1), (17, 24), (1, 6), (11, 9), (12, 8), (1, 13), (20, 23), (11, 19), (11, 2), (19, 16), (5, 0), (20, 7), (15, 13), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972214", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 9), (12, 15), (9, 2), (11, 11), (17, 10), (1, 12), (17, 0), (0, 6), (7, 18), (5, 8), (21, 11), (1, 14), (7, 14), (8, 13), (0, 5), (6, 8), (7, 16), (19, 17), (12, 0), (15, 15), (10, 18), (12, 19), (16, 3), (4, 5), (13, 17), (14, 6), (4, 6), (6, 3), (19, 0), (17, 6), (5, 0), (2, 15), (20, 8), (9, 5), (12, 3), (3, 7), (11, 13), (21, 1), (17, 16), (2, 13), (7, 5), (10, 5), (12, 14), (17, 11), (20, 11), (7, 7), (21, 16), (4, 10), (19, 16), (8, 8), (0, 8), (20, 1), (22, 6), (7, 11), (17, 15), (10, 12), (6, 17), (19, 3), (18, 18), (13, 12), (10, 7), (6, 0), (2, 0), (15, 9), (19, 10), (12, 1), (0, 12), (16, 7), (17, 19), (13, 13), (20, 4), (21, 2), (10, 13), (22, 12), (3, 15), (12, 2), (1, 2), (14, 12), (13, 19), (1, 1), (17, 12), (14, 3), (12, 7), (8, 16), (15, 7), (6, 1), (3, 13), (4, 0), (10, 1), (0, 11), (9, 7), (7, 1), (13, 15), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "603072", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 20), (12, 18), (23, 6), (20, 15), (0, 19), (12, 16), (19, 10), (7, 10), (21, 11), (20, 11), (14, 0), (10, 5), (5, 11), (10, 23), (16, 20), (10, 11), (5, 6), (9, 1), (12, 7), (7, 1), (7, 4), (11, 11), (8, 14), (3, 5), (16, 2), (5, 14), (17, 12), (17, 9), (14, 20), (9, 9), (5, 1), (15, 21), (8, 19), (8, 9), (10, 15), (2, 1), (23, 21), (9, 3), (20, 2), (0, 5), (3, 6), (13, 10), (10, 1), (6, 9), (15, 7), (7, 15), (13, 2), (4, 21), (21, 0), (0, 14), (6, 7), (1, 13), (2, 19), (13, 20), (4, 8), (2, 12), (1, 18), (5, 9), (23, 19), (18, 19), (19, 14), (4, 14), (8, 3), (2, 8), (0, 22), (15, 10), (1, 4), (11, 17), (14, 22), (8, 4), (14, 3), (14, 21), (3, 2), (23, 0), (22, 7), (14, 4), (1, 8), (21, 9), (12, 22), (19, 8), (13, 15), (10, 3), (8, 20), (10, 22), (14, 7), (22, 18), (8, 17), (3, 8), (2, 18), (16, 5), (13, 11), (4, 17), (10, 18), (7, 18), (14, 16), (20, 17), (17, 23), (13, 14), (1, 3), (19, 11), (22, 5), (23, 8), (0, 16), (20, 19), (23, 2), (16, 4), (5, 5), (13, 1), (18, 4), (0, 1), (18, 17), (19, 18), (0, 20), (0, 23), (22, 17), (3, 18), (0, 7), (0, 9), (3, 21), (13, 3), (20, 18), (17, 3), (22, 22), (0, 3), (17, 18), (5, 21), (11, 22), (10, 0), (15, 23), (18, 9), (9, 23), (9, 20), (9, 0), (18, 1), (13, 17), (20, 12), (14, 14), (15, 16), (6, 15), (4, 22), (17, 7), (23, 10), (12, 4), (8, 23), (22, 9), (0, 12), (19, 13), (4, 7), (5, 20), (12, 13), (17, 16), (22, 14), (5, 16), (6, 12), (22, 10), (21, 2), (20, 23), (8, 15), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946294", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 21), (11, 4), (21, 12), (20, 18), (16, 9), (12, 21), (2, 5), (11, 12), (11, 6), (1, 24), (7, 7), (0, 24), (19, 13), (4, 5), (1, 5), (15, 13), (7, 14), (15, 0), (21, 14), (20, 8), (8, 15), (1, 17), (20, 21), (4, 20), (11, 7), (20, 12), (8, 18), (12, 7), (12, 3), (3, 3), (7, 2), (18, 17), (13, 22), (4, 15), (4, 6), (18, 5), (10, 13), (6, 7), (20, 9), (10, 22), (3, 18), (21, 13), (15, 9), (0, 22), (18, 12), (3, 8), (14, 3), (17, 19), (15, 19), (4, 23), (5, 24), (11, 11), (5, 9), (6, 3), (14, 8), (4, 7), (21, 16), (8, 11), (16, 1), (12, 12), (9, 16), (18, 3), (20, 19), (4, 13), (3, 19), (9, 3), (18, 6), (5, 23), (9, 21), (16, 10), (20, 16), (18, 22), (18, 23), (7, 20), (18, 10), (1, 7), (15, 14), (3, 11), (17, 8), (5, 2), (2, 19), (11, 14), (6, 10), (2, 22), (5, 15), (10, 3), (19, 14), (16, 12), (1, 10), (2, 6), (10, 0), (3, 7), (8, 19), (16, 0), (4, 12), (13, 16), (12, 2), (18, 13), (21, 19), (2, 18), (21, 15), (9, 10), (2, 12), (0, 9), (17, 22), (1, 3), (13, 11), (0, 12), (7, 19), (3, 15), (8, 24), (9, 15), (2, 11), (14, 21), (8, 20), (1, 16), (20, 1), (12, 23), (19, 17), (10, 8), (6, 14), (1, 21), (18, 16), (21, 18), (10, 19), (11, 21), (5, 6), (16, 14), (14, 20), (7, 21), (13, 1), (10, 1), (3, 20), (10, 6), (9, 8), (19, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338400", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (16, 6), (5, 18), (7, 16), (20, 14), (17, 7), (23, 16), (5, 12), (23, 13), (24, 15), (6, 3), (8, 9), (23, 11), (9, 3), (10, 15), (8, 19), (18, 7), (16, 11), (7, 18), (23, 17), (26, 17), (18, 13), (21, 6), (5, 8), (23, 2), (25, 9), (7, 7), (19, 9), (22, 11), (15, 5), (12, 14), (15, 7), (19, 17), (2, 17), (13, 2), (4, 10), (3, 4), (16, 17), (6, 5), (2, 2), (13, 7), (19, 4), (19, 2), (14, 6), (10, 19), (12, 10), (2, 14), (24, 14), (17, 14), (26, 15), (4, 16), (7, 10), (16, 13), (17, 2), (5, 3), (23, 9), (20, 3), (22, 7), (6, 20), (25, 17), (10, 10), (2, 8), (20, 7), (17, 6), (10, 8), (7, 11), (15, 4), (7, 13), (14, 12), (15, 12), (24, 11), (18, 16), (2, 7), (20, 15), (21, 3), (10, 14), (2, 9), (19, 1), (7, 6), (4, 17), (1, 7), (0, 12), (3, 9), (21, 2), (19, 16), (14, 17), (10, 3), (9, 20), (23, 20), (2, 11), (12, 7), (0, 16), (20, 19), (1, 13), (1, 9), (15, 10), (2, 13), (18, 20), (22, 0), (10, 5), (4, 7), (24, 2), (0, 8), (23, 19), (1, 4), (4, 3), (1, 16), (24, 5), (12, 3), (22, 14), (8, 11), (21, 0), (0, 13), (2, 15), (9, 17), (22, 19), (10, 16), (12, 17), (15, 2), (22, 15), (26, 6), (11, 2), (16, 19), (22, 3), (6, 17), (17, 13), (22, 1), (11, 12), (25, 16), (5, 4), (19, 19), (19, 5), (14, 4), (7, 20), (14, 19), (20, 10), (17, 16), (13, 8), (21, 1), (12, 8), (26, 16), (13, 16), (25, 20), (13, 18), (15, 19), (11, 4), (14, 14), (8, 18), (5, 5), (22, 5), (21, 8), (17, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367956", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 18), (12, 5), (13, 7), (11, 25), (9, 11), (13, 9), (14, 20), (5, 19), (3, 9), (20, 14), (4, 12), (3, 23), (11, 16), (8, 0), (17, 2), (17, 12), (4, 24), (0, 15), (19, 5), (5, 15), (12, 10), (17, 0), (5, 0), (3, 11), (4, 9), (0, 18), (2, 14), (3, 18), (18, 22), (10, 0), (8, 4), (1, 19), (12, 17), (1, 5), (8, 23), (13, 17), (7, 12), (19, 19), (2, 3), (19, 9), (14, 18), (9, 25), (15, 21), (4, 4), (7, 23), (12, 24), (13, 21), (17, 11), (1, 0), (10, 1), (7, 21), (15, 22), (9, 7), (16, 16), (16, 0), (11, 6), (9, 21), (15, 1), (20, 13), (10, 16), (13, 24), (17, 24), (12, 20), (10, 6), (9, 9), (19, 17), (9, 5), (12, 11), (19, 1), (12, 1), (1, 18), (20, 5), (7, 2), (4, 0), (16, 25), (20, 4), (3, 17), (20, 18), (17, 5), (14, 4), (18, 3), (7, 4), (13, 13), (13, 10), (8, 22), (11, 2), (9, 2), (17, 22), (1, 6), (12, 21), (0, 14), (18, 11), (0, 3), (4, 16), (13, 5), (19, 16), (15, 18), (9, 12), (19, 7), (5, 9), (15, 0), (2, 18), (10, 25), (8, 17), (12, 25), (0, 2), (15, 11), (17, 15), (12, 2), (8, 2), (1, 16), (17, 13), (0, 7), (1, 13), (11, 21), (2, 5), (5, 24), (12, 16), (5, 18), (15, 24), (5, 8), (19, 3), (6, 11), (5, 11), (18, 0), (12, 9), (4, 20), (3, 16), (10, 11), (4, 14), (19, 18), (0, 20), (15, 8), (1, 7), (13, 14), (17, 8), (15, 23), (1, 24), (18, 13), (5, 17), (5, 1), (11, 17), (17, 23), (14, 7), (2, 17), (0, 10), (0, 13), (13, 6), (11, 10), (20, 16), (3, 10), (0, 8), (4, 19), (19, 15), (9, 22), (10, 12), (13, 23), (1, 14), (2, 9), (12, 23), (9, 6), (14, 0), (6, 23), (15, 25), (14, 10), (6, 2), (4, 13), (8, 21), (14, 8), (16, 14), (9, 19), (9, 8), (16, 11), (3, 6), (6, 5), (12, 7), (10, 14), (16, 20), (7, 9), (15, 6), (14, 23), (15, 13), (2, 12), (16, 9), (15, 20), (0, 19), (7, 19), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751338", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 20), (12, 18), (7, 17), (15, 9), (3, 9), (1, 6), (19, 11), (5, 20), (0, 11), (19, 12), (12, 7), (7, 20), (8, 11), (3, 20), (18, 19), (11, 8), (11, 6), (16, 5), (1, 14), (9, 7), (12, 17), (2, 3), (0, 4), (1, 9), (2, 18), (4, 11), (0, 13), (6, 9), (19, 21), (0, 8), (20, 13), (13, 19), (14, 20), (20, 19), (11, 7), (10, 20), (2, 11), (17, 15), (20, 0), (17, 20), (9, 0), (13, 5), (7, 5), (16, 15), (5, 6), (4, 1), (15, 8), (2, 9), (4, 5), (19, 9), (0, 3), (15, 11), (19, 3), (5, 4), (5, 8), (2, 10), (19, 6), (3, 7), (11, 17), (9, 9), (20, 21), (12, 13), (7, 15), (18, 10), (9, 15), (20, 16), (6, 10), (11, 15), (2, 16), (11, 10), (18, 1), (0, 18), (12, 9), (2, 14), (10, 15), (14, 1), (1, 15), (18, 17), (4, 0), (21, 17), (16, 10), (14, 11), (16, 3), (1, 5), (10, 0), (14, 9), (21, 13), (16, 1), (15, 7), (12, 10), (13, 3), (6, 4), (9, 13), (7, 2), (11, 19), (0, 2), (6, 19), (15, 19), (8, 1), (19, 4), (19, 8), (16, 0), (5, 7), (1, 20), (11, 9), (17, 10), (6, 12), (15, 16), (2, 4), (21, 5), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445326", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 21), (16, 16), (10, 7), (16, 18), (10, 13), (2, 3), (15, 2), (0, 10), (11, 10), (17, 9), (8, 24), (4, 24), (15, 21), (12, 17), (12, 23), (6, 5), (8, 12), (20, 11), (11, 18), (7, 10), (4, 1), (12, 7), (19, 2), (15, 4), (15, 16), (4, 6), (11, 8), (21, 11), (13, 23), (16, 10), (15, 18), (1, 3), (18, 21), (16, 24), (0, 14), (19, 1), (12, 13), (10, 0), (15, 5), (6, 3), (2, 12), (13, 20), (0, 16), (13, 12), (3, 19), (5, 10), (9, 11), (20, 18), (4, 2), (1, 11), (2, 4), (6, 16), (10, 23), (18, 11), (6, 6), (16, 20), (14, 23), (16, 14), (18, 6), (0, 21), (8, 1), (0, 13), (0, 24), (16, 23), (19, 12), (14, 5), (21, 8), (15, 11), (19, 19), (14, 22), (17, 24), (18, 2), (11, 3), (19, 4), (11, 4), (5, 21), (13, 5), (7, 24), (17, 3), (22, 3), (5, 22), (14, 3), (5, 23), (7, 5), (0, 2), (9, 6), (16, 1), (4, 3), (13, 16), (5, 17), (19, 13), (7, 3), (3, 8), (12, 9), (14, 7), (7, 1), (8, 22), (6, 22), (13, 18), (16, 7), (16, 11), (5, 20), (3, 5), (1, 8), (21, 3), (3, 22), (13, 2), (17, 2), (16, 17), (6, 9), (10, 3), (16, 4), (5, 15), (5, 13), (22, 2), (20, 21), (0, 23), (21, 14), (21, 18), (3, 6), (8, 9), (4, 8), (4, 22), (15, 10), (18, 18), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492877", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 3), (1, 11), (0, 7), (23, 8), (15, 1), (13, 0), (15, 14), (19, 21), (10, 12), (9, 14), (4, 4), (5, 9), (18, 2), (10, 16), (8, 9), (0, 22), (4, 2), (19, 1), (15, 17), (10, 23), (1, 24), (18, 4), (4, 1), (10, 5), (8, 18), (9, 23), (1, 23), (13, 14), (23, 19), (7, 2), (17, 9), (5, 19), (4, 23), (20, 20), (16, 9), (6, 22), (11, 20), (17, 6), (15, 5), (2, 5), (6, 20), (11, 21), (1, 1), (18, 17), (14, 14), (2, 3), (8, 10), (20, 7), (7, 21), (11, 17), (18, 21), (23, 11), (23, 4), (6, 2), (15, 23), (6, 19), (3, 2), (0, 26), (8, 13), (10, 8), (11, 0), (12, 13), (12, 4), (21, 7), (19, 17), (9, 25), (1, 17), (8, 3), (21, 0), (0, 25), (13, 6), (1, 21), (13, 2), (9, 24), (11, 18), (3, 3), (8, 23), (4, 14), (11, 5), (14, 22), (22, 15), (12, 9), (1, 0), (0, 8), (21, 24), (20, 6), (14, 16), (7, 12), (2, 18), (21, 17), (17, 23), (2, 4), (9, 1), (0, 20), (5, 3), (14, 13), (15, 10), (6, 4), (6, 13), (7, 7), (9, 19), (3, 14), (21, 22), (15, 3), (1, 22), (5, 22), (10, 20), (7, 13), (9, 21), (10, 18), (0, 16), (13, 26), (6, 5), (17, 7), (7, 10), (22, 3), (7, 22), (23, 2), (23, 20), (0, 11), (22, 4), (7, 15), (0, 24), (10, 11), (16, 1), (15, 12), (14, 5), (19, 13), (18, 10), (11, 23), (10, 26), (2, 13), (21, 5), (19, 24), (18, 12), (17, 19), (15, 26), (11, 16), (6, 10), (10, 9), (19, 19), (10, 25), (9, 15), (16, 20), (16, 24), (20, 25), (18, 13), (15, 21), (0, 3), (14, 20), (9, 8), (11, 24), (23, 6), (22, 11), (22, 19), (22, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "819440", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 9), (10, 6), (2, 0), (27, 10), (23, 13), (15, 17), (14, 7), (7, 4), (28, 2), (3, 11), (1, 14), (22, 2), (13, 12), (16, 9), (18, 13), (6, 4), (20, 6), (26, 7), (24, 13), (25, 0), (20, 15), (18, 9), (27, 14), (2, 13), (26, 4), (28, 14), (6, 16), (25, 9), (9, 7), (8, 3), (25, 19), (24, 16), (8, 7), (18, 3), (7, 17), (0, 11), (26, 18), (7, 6), (6, 14), (9, 8), (22, 17), (26, 8), (21, 2), (19, 18), (5, 4), (19, 20), (10, 11), (23, 17), (14, 14), (0, 8), (28, 1), (25, 6), (22, 16), (24, 0), (7, 2), (9, 2), (13, 19), (20, 17), (2, 14), (13, 3), (1, 6), (0, 6), (19, 19), (21, 17), (10, 7), (16, 20), (3, 20), (2, 6), (14, 9), (8, 19), (20, 14), (3, 1), (12, 10), (18, 17), (16, 13), (12, 17), (19, 3), (26, 20), (28, 17), (10, 13), (11, 18), (2, 19), (26, 6), (14, 10), (17, 5), (11, 11), (22, 9), (3, 2), (10, 10), (1, 1), (4, 17), (12, 2), (1, 8), (15, 7), (9, 11), (24, 1), (5, 8), (11, 20), (19, 16), (8, 17), (9, 0), (20, 16), (11, 5), (17, 11), (11, 8), (7, 19), (10, 15), (6, 2), (9, 1), (25, 12), (13, 20), (6, 15), (10, 1), (11, 6), (1, 7), (10, 2), (15, 4), (17, 14), (3, 3), (23, 5), (9, 16), (1, 15), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890514", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (0, 20), (10, 21), (4, 15), (9, 21), (17, 22), (9, 10), (17, 8), (15, 4), (8, 8), (2, 4), (18, 2), (1, 14), (19, 18), (16, 10), (19, 11), (10, 3), (13, 10), (4, 7), (7, 15), (16, 12), (5, 6), (7, 6), (14, 12), (9, 15), (11, 13), (16, 18), (9, 4), (7, 18), (0, 19), (14, 11), (1, 15), (14, 9), (0, 11), (1, 21), (6, 4), (1, 19), (3, 8), (19, 7), (8, 0), (5, 9), (2, 11), (11, 11), (14, 5), (5, 3), (15, 1), (5, 22), (16, 11), (0, 16), (16, 17), (11, 9), (9, 20), (3, 10), (6, 14), (8, 7), (19, 20), (7, 11), (12, 10), (18, 4), (13, 6), (2, 13), (12, 14), (9, 6), (8, 13), (2, 12), (12, 18), (16, 3), (3, 11), (2, 7), (13, 16), (12, 5), (5, 18), (11, 6), (13, 9), (4, 4), (7, 10), (2, 21), (7, 8), (9, 13), (4, 2), (2, 16), (5, 8), (8, 22), (19, 13), (1, 16), (17, 12), (11, 5), (3, 1), (15, 11), (7, 2), (9, 16), (12, 12), (18, 9), (9, 2), (15, 20), (9, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954776", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 22), (22, 22), (16, 5), (18, 25), (19, 2), (2, 17), (17, 14), (10, 26), (17, 2), (15, 25), (17, 25), (26, 17), (2, 14), (16, 10), (22, 16), (3, 22), (17, 4), (2, 19), (18, 3), (21, 4), (14, 13), (1, 11), (5, 12), (1, 8), (26, 16), (10, 20), (4, 3), (22, 25), (10, 24), (25, 10), (0, 26), (5, 22), (17, 10), (26, 11), (16, 16), (9, 25), (24, 16), (26, 19), (0, 5), (8, 11), (4, 6), (21, 3), (26, 26), (21, 7), (4, 20), (18, 9), (25, 18), (9, 12), (11, 25), (3, 19), (9, 15), (11, 15), (26, 13), (16, 17), (8, 15), (9, 13), (3, 5), (9, 8), (24, 20), (15, 21), (27, 3), (0, 2), (6, 2), (2, 6), (13, 2), (27, 6), (8, 24), (8, 2), (11, 9), (13, 0), (1, 6), (22, 13), (5, 13), (22, 15), (0, 20), (19, 4), (13, 14), (15, 6), (1, 5), (11, 22), (17, 19), (26, 1), (10, 6), (9, 19), (18, 4), (23, 26), (11, 23), (10, 9), (23, 16), (15, 17), (2, 2), (1, 21), (13, 22), (15, 11), (8, 4), (15, 10), (3, 21), (10, 21), (23, 23), (11, 2), (22, 2), (20, 7), (8, 23), (7, 9), (22, 14), (1, 22), (21, 17), (7, 12), (6, 13), (8, 26), (6, 9), (9, 14), (19, 12), (7, 10), (27, 9), (6, 25), (0, 11), (3, 24), (7, 1), (14, 5), (1, 19), (3, 12), (27, 15), (16, 2), (9, 7), (16, 7), (9, 21), (17, 26), (25, 5), (4, 15), (23, 0), (12, 10), (10, 2), (23, 18), (15, 22), (9, 23), (16, 26), (18, 24), (20, 13), (0, 24), (25, 9), (8, 7), (0, 1), (1, 13), (6, 24), (12, 11), (10, 15), (6, 11), (4, 22), (27, 24), (14, 14), (8, 8), (22, 19), (23, 21), (10, 19), (7, 3), (23, 11), (7, 4), (21, 24), (24, 26), (18, 10), (12, 16), (16, 18), (16, 21), (5, 11), (16, 12), (18, 18), (10, 7), (4, 24), (25, 8), (10, 4), (20, 11), (6, 16), (0, 12), (19, 26), (6, 26), (24, 3), (9, 9), (3, 26), (17, 20), (21, 19), (16, 1), (19, 0), (13, 21), (25, 3), (25, 17), (16, 25), (27, 17), (16, 13), (21, 11), (22, 18), (23, 13), (17, 9), (0, 16), (6, 8), (2, 23), (6, 23), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907920", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), 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, 16), (16, 19), (15, 1), (3, 12), (9, 7), (23, 2), (22, 3), (2, 7), (19, 5), (4, 5), (5, 9), (7, 6), (12, 8), (4, 13), (1, 3), (22, 18), (12, 1), (21, 0), (5, 0), (9, 17), (12, 13), (15, 20), (19, 12), (24, 19), (10, 19), (17, 10), (11, 18), (23, 17), (11, 3), (15, 14), (0, 2), (1, 6), (6, 7), (10, 6), (6, 4), (21, 4), (17, 19), (10, 21), (14, 18), (25, 16), (3, 14), (6, 0), (25, 9), (18, 6), (17, 9), (4, 16), (3, 5), (17, 7), (0, 3), (13, 11), (14, 12), (23, 6), (8, 11), (19, 9), (25, 6), (4, 3), (6, 1), (0, 20), (17, 12), (24, 14), (18, 19), (3, 11), (22, 0), (0, 18), (20, 18), (24, 6), (22, 8), (12, 18), (2, 4), (16, 10), (25, 12), (0, 16), (13, 10), (0, 8), (18, 3), (11, 21), (22, 14), (10, 17), (6, 3), (5, 5), (1, 1), (0, 15), (18, 1), (12, 2), (7, 10), (23, 18), (19, 0), (17, 3), (16, 13), (11, 2), (25, 18), (9, 14), (4, 17), (18, 17), (25, 0), (11, 9), (8, 13), (25, 19), (4, 8), (14, 16), (17, 13), (18, 14), (2, 10), (15, 15), (7, 3), (18, 13), (8, 12), (22, 2), (5, 13), (24, 11), (18, 2), (10, 9), (16, 18), (2, 20), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278154", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 25), (7, 15), (5, 22), (14, 25), (1, 8), (3, 20), (8, 20), (22, 22), (11, 18), (20, 9), (8, 11), (15, 23), (3, 27), (2, 9), (8, 2), (18, 21), (15, 11), (21, 3), (6, 16), (13, 25), (0, 4), (16, 5), (16, 3), (22, 1), (14, 8), (22, 18), (4, 24), (11, 19), (4, 9), (1, 27), (13, 0), (9, 13), (7, 25), (11, 15), (9, 17), (15, 2), (7, 16), (4, 3), (11, 1), (17, 7), (16, 22), (18, 6), (2, 20), (22, 3), (14, 5), (11, 11), (11, 20), (21, 6), (6, 10), (3, 12), (21, 22), (13, 16), (2, 7), (18, 2), (14, 21), (7, 21), (19, 5), (6, 8), (17, 9), (11, 8), (7, 7), (8, 15), (22, 15), (3, 4), (11, 12), (20, 14), (21, 16), (17, 3), (14, 26), (3, 19), (18, 13), (22, 26), (10, 12), (2, 23), (0, 1), (2, 19), (5, 14), (21, 15), (19, 6), (20, 15), (12, 21), (21, 25), (2, 26), (1, 22), (20, 17), (20, 23), (14, 9), (3, 25), (13, 3), (21, 5), (19, 18), (15, 7), (15, 12), (1, 20), (4, 11), (16, 25), (14, 10), (13, 18), (14, 24), (6, 19), (10, 19), (17, 15), (9, 27), (15, 9), (4, 19), (12, 9), (11, 22), (18, 20), (6, 22), (1, 21), (15, 18), (22, 25), (9, 24), (7, 1), (16, 11), (16, 24), (6, 11), (19, 22), (0, 16), (0, 11), (18, 22), (19, 12), (0, 2), (18, 1), (18, 18), (19, 25), (2, 18), (9, 12), (4, 15), (3, 6), (19, 2), (14, 13), (10, 7), (2, 15), (12, 24), (5, 24), (15, 10), (17, 13), (18, 8), (14, 17), (12, 16), (20, 6), (6, 25), (13, 5), (3, 14), (2, 3), (17, 8), (8, 9), (8, 10), (5, 10), (4, 13), (5, 17), (19, 27), (9, 23), (20, 10), (8, 12), (19, 20), (3, 15), (19, 19), (16, 23), (19, 7), (8, 27), (3, 22), (19, 0), (4, 6), (16, 14), (11, 2), (6, 13), (0, 19), (1, 4), (13, 13), (12, 1), (18, 10), (11, 27), (16, 0), (21, 1), (14, 20), (5, 4), (19, 14), (21, 4), (17, 11), (18, 5), (8, 1), (0, 15), (15, 24), (4, 2), (0, 20), (18, 4), (4, 21), (15, 20), (11, 0), (14, 23), (22, 11), (10, 1), (18, 17), (16, 20), (9, 20), (17, 12), (2, 11), (10, 25), (7, 5), (4, 23), (20, 1), (15, 25), (14, 12), (17, 27), (14, 6), (21, 11), (6, 7), (18, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830700", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 7), (1, 15), (17, 6), (6, 1), (10, 18), (20, 12), (20, 13), (5, 16), (19, 6), (6, 10), (16, 11), (15, 6), (7, 4), (12, 0), (17, 0), (17, 4), (12, 4), (3, 12), (0, 8), (9, 18), (18, 7), (15, 0), (5, 1), (17, 3), (8, 22), (14, 9), (1, 20), (19, 3), (11, 14), (0, 20), (12, 8), (16, 15), (0, 23), (9, 14), (16, 10), (15, 12), (16, 16), (19, 9), (17, 2), (21, 21), (14, 20), (16, 13), (12, 20), (9, 5), (20, 0), (12, 2), (18, 11), (11, 13), (2, 0), (11, 16), (19, 1), (17, 1), (16, 23), (6, 13), (16, 21), (12, 16), (7, 20), (11, 12), (11, 7), (12, 12), (19, 8), (4, 11), (7, 19), (7, 3), (13, 21), (2, 16), (13, 12), (14, 1), (9, 8), (8, 3), (18, 5), (18, 13), (17, 13), (14, 11), (5, 11), (5, 22), (7, 14), (5, 14), (5, 7), (8, 6), (17, 10), (15, 15), (2, 20), (13, 15), (7, 1), (3, 6), (11, 0), (4, 15), (19, 22), (17, 11), (7, 12), (19, 7), (6, 8), (14, 3), (4, 5), (6, 11), (7, 23), (6, 15), (1, 12), (13, 20), (18, 6), (14, 18), (21, 18), (19, 12), (21, 12), (16, 2), (6, 4), (10, 10), (11, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680009", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), 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), (13, 21), (14, 10), (22, 8), (8, 18), (15, 5), (8, 9), (8, 0), (8, 3), (8, 19), (18, 12), (14, 2), (0, 5), (13, 9), (11, 21), (27, 9), (20, 15), (12, 9), (22, 21), (1, 14), (13, 7), (2, 15), (25, 12), (3, 5), (9, 0), (24, 18), (14, 16), (1, 20), (3, 3), (18, 10), (9, 15), (8, 2), (12, 11), (5, 15), (3, 21), (15, 10), (14, 14), (12, 0), (11, 5), (25, 11), (15, 9), (3, 15), (22, 17), (11, 17), (13, 8), (23, 2), (24, 22), (1, 7), (17, 14), (4, 16), (6, 17), (9, 12), (10, 22), (13, 11), (13, 4), (10, 2), (7, 22), (7, 0), (20, 3), (5, 2), (21, 10), (2, 1), (13, 2), (27, 19), (16, 12), (19, 12), (18, 21), (6, 11), (23, 20), (25, 1), (13, 10), (11, 16), (15, 4), (8, 14), (1, 2), (11, 11), (7, 1), (7, 10), (10, 19), (7, 5), (16, 7), (6, 22), (0, 16), (23, 12), (16, 4), (1, 4), (9, 6), (4, 20), (5, 11), (3, 2), (0, 20), (15, 21), (26, 8), (21, 19), (5, 7), (19, 1), (5, 13), (21, 3), (26, 14), (27, 20), (12, 8), (19, 10), (5, 20), (23, 13), (6, 14), (14, 20), (24, 20), (3, 1), (9, 18), (4, 13), (2, 12), (15, 14), (23, 10), (10, 12), (1, 0), (7, 4), (26, 16), (4, 8), (0, 7), (12, 1), (5, 18), (10, 16), (24, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "261261", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), 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), (8, 21), (15, 3), (21, 13), (1, 0), (23, 17), (15, 17), (19, 12), (5, 11), (13, 17), (6, 19), (2, 19), (2, 10), (21, 9), (13, 7), (0, 16), (2, 5), (8, 2), (8, 15), (5, 17), (7, 0), (10, 7), (11, 22), (20, 21), (23, 7), (14, 3), (4, 15), (16, 2), (23, 16), (3, 20), (19, 20), (21, 0), (9, 13), (5, 4), (20, 3), (9, 17), (1, 5), (19, 18), (10, 10), (0, 19), (20, 1), (19, 10), (7, 7), (4, 22), (18, 9), (10, 9), (13, 22), (19, 14), (17, 7), (1, 3), (21, 18), (20, 0), (23, 4), (20, 7), (13, 9), (4, 6), (5, 9), (4, 20), (12, 13), (2, 14), (19, 0), (19, 4), (0, 10), (13, 6), (2, 18), (6, 16), (11, 3), (3, 14), (18, 13), (2, 21), (21, 19), (7, 10), (14, 13), (12, 9), (22, 21), (21, 2), (17, 1), (17, 19), (13, 8), (6, 0), (14, 11), (9, 10), (5, 18), (15, 12), (18, 5), (6, 18), (19, 15), (22, 20), (10, 17), (17, 15), (1, 15), (17, 13), (3, 3), (20, 11), (1, 17), (0, 2), (11, 12), (6, 20), (1, 7), (10, 8), (11, 15), (16, 0), (13, 11), (8, 13), (4, 13), (17, 14), (14, 2), (7, 19), (9, 18), (21, 1), (11, 0), (9, 14), (18, 16), (5, 19), (8, 5), (15, 10), (11, 2), (17, 21), (10, 22), (22, 2), (2, 17), (16, 13), (2, 2), (15, 11), (19, 5), (12, 5), (22, 12), (15, 8), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865638", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), 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), (24, 10), (7, 12), (20, 8), (15, 24), (14, 15), (9, 19), (20, 19), (1, 4), (17, 23), (14, 2), (23, 20), (18, 20), (6, 11), (10, 8), (11, 19), (5, 13), (21, 12), (9, 9), (5, 12), (21, 22), (13, 19), (26, 14), (20, 9), (16, 5), (9, 5), (3, 25), (4, 19), (2, 15), (7, 11), (10, 19), (15, 22), (19, 26), (13, 26), (7, 3), (7, 19), (19, 16), (16, 7), (13, 0), (6, 2), (5, 15), (21, 2), (5, 21), (6, 17), (9, 10), (23, 14), (4, 12), (16, 24), (8, 24), (12, 10), (5, 10), (21, 26), (11, 6), (1, 14), (7, 13), (5, 5), (26, 1), (7, 5), (20, 13), (17, 16), (16, 19), (26, 5), (22, 18), (18, 14), (20, 26), (22, 23), (26, 6), (21, 19), (9, 25), (12, 26), (16, 4), (6, 25), (24, 17), (2, 7), (0, 21), (10, 26), (22, 17), (23, 0), (0, 2), (17, 7), (23, 2), (8, 18), (4, 11), (24, 16), (8, 7), (22, 4), (13, 25), (14, 9), (9, 11), (18, 0), (2, 2), (4, 23), (21, 15), (20, 10), (11, 2), (19, 1), (5, 2), (12, 15), (10, 7), (23, 23), (13, 3), (20, 21), (5, 23), (11, 20), (11, 5), (18, 6), (7, 16), (22, 19), (22, 11), (20, 16), (10, 13), (0, 23), (6, 23), (3, 20), (6, 1), (19, 2), (26, 13), (12, 3), (15, 0), (7, 18), (11, 9), (20, 23), (11, 8), (6, 7), (24, 26), (25, 21), (17, 1), (1, 26), (24, 19), (23, 26), (22, 0), (0, 19), (23, 15), (16, 9), (12, 17), (22, 20), (3, 1), (14, 10), (5, 1), (15, 1), (23, 17), (1, 12), (6, 24), (1, 10), (10, 0), (19, 18), (14, 22), (8, 21), (24, 18), (26, 20), (6, 18), (5, 7), (0, 11), (25, 24), (1, 22), (25, 0), (1, 2), (13, 17), (19, 12), (24, 20), (10, 5), (10, 25), (10, 3), (4, 4), (24, 7), (15, 8), (17, 0), (8, 14), (11, 23), (25, 23), (17, 2), (22, 6), (9, 13), (11, 10), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956088", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (0, 20), (8, 23), (0, 13), (8, 4), (5, 24), (1, 21), (21, 24), (11, 17), (15, 2), (2, 10), (4, 8), (19, 12), (10, 11), (2, 6), (8, 15), (4, 16), (22, 11), (13, 20), (7, 11), (4, 0), (22, 8), (19, 21), (8, 24), (11, 10), (1, 3), (17, 24), (9, 6), (20, 22), (7, 6), (19, 6), (14, 3), (12, 18), (18, 13), (18, 11), (4, 24), (22, 10), (17, 13), (18, 22), (20, 14), (12, 6), (17, 14), (9, 13), (1, 5), (2, 2), (21, 4), (1, 19), (15, 13), (12, 10), (10, 8), (1, 8), (2, 9), (8, 11), (22, 0), (6, 1), (6, 22), (11, 2), (13, 5), (16, 12), (18, 2), (11, 20), (18, 19), (16, 8), (23, 1), (23, 14), (4, 19), (20, 12), (8, 10), (2, 23), (4, 9), (18, 10), (18, 15), (17, 23), (22, 5), (3, 13), (20, 5), (9, 14), (22, 4), (22, 12), (6, 6), (22, 18), (8, 5), (8, 8), (12, 0), (13, 19), (9, 18), (10, 5), (22, 24), (23, 8), (20, 24), (21, 9), (3, 21), (1, 10), (0, 6), (21, 15), (0, 5), (20, 13), (19, 7), (16, 21), (4, 14), (1, 12), (6, 3), (7, 23), (4, 18), (7, 15), (0, 8), (21, 7), (0, 12), (18, 3), (4, 5), (14, 17), (3, 12), (1, 24), (10, 21), (6, 17), (19, 0), (2, 20), (23, 4), (12, 11), (5, 9), (0, 23), (5, 16), (19, 13), (2, 21), (11, 6), (11, 24), (11, 22), (22, 16), (19, 19), (5, 14), (18, 9), (13, 18), (13, 16), (5, 10), (10, 10), (3, 16), (8, 17), (12, 8), (4, 13), (17, 12), (5, 4), (12, 7), (16, 11), (15, 16), (4, 3), (10, 7), (9, 0), (9, 5), (3, 18), (6, 13), (4, 12), (12, 23), (23, 10), (23, 9), (9, 7), (2, 14), (15, 10), (17, 4), (3, 0), (6, 7), (2, 13), (12, 16), (22, 17), (7, 7), (9, 2), (17, 9), (7, 12), (8, 1), (14, 19), (11, 3), (14, 20), (20, 17), (14, 2), (23, 6), (18, 7), (6, 11), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "868896", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), 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), (15, 27), (15, 26), (10, 9), (19, 12), (8, 23), (14, 5), (10, 14), (3, 3), (9, 24), (17, 6), (13, 17), (3, 13), (4, 11), (12, 6), (9, 4), (8, 27), (18, 4), (22, 13), (22, 25), (22, 7), (17, 15), (0, 12), (17, 20), (13, 16), (3, 16), (21, 13), (4, 12), (18, 14), (11, 21), (21, 0), (18, 1), (21, 25), (12, 4), (16, 12), (19, 5), (5, 25), (20, 23), (13, 12), (20, 6), (12, 11), (9, 6), (11, 2), (2, 9), (22, 26), (10, 11), (11, 24), (8, 21), (5, 20), (3, 4), (18, 8), (23, 6), (7, 2), (14, 27), (19, 4), (15, 0), (9, 20), (19, 6), (2, 11), (18, 15), (4, 19), (0, 4), (16, 1), (4, 10), (19, 0), (23, 11), (16, 2), (22, 20), (12, 25), (23, 4), (16, 6), (22, 1), (24, 1), (20, 9), (0, 2), (24, 16), (15, 25), (8, 13), (6, 14), (7, 3), (2, 6), (20, 15), (6, 20), (5, 16), (22, 2), (4, 2), (17, 18), (14, 4), (11, 14), (8, 20), (7, 4), (16, 27), (12, 21), (2, 23), (2, 17), (4, 9), (11, 17), (13, 27), (2, 27), (15, 1), (17, 24), (7, 25), (0, 27), (16, 5), (16, 8), (3, 14), (2, 0), (4, 0), (8, 5), (16, 0), (3, 21), (1, 0), (12, 9), (15, 6), (15, 5), (0, 3), (7, 12), (6, 12), (23, 24), (9, 22), (2, 24), (18, 11), (13, 18), (17, 7), (20, 0), (9, 27), (20, 2), (22, 6), (19, 11), (18, 17), (0, 11), (14, 14), (15, 11), (19, 2), (14, 3), (14, 21), (3, 17), (2, 7), (24, 2), (17, 12), (5, 4), (18, 23), (2, 25), (22, 5), (7, 11), (1, 19), (11, 9), (7, 26), (1, 12), (9, 14), (13, 13), (6, 18), (19, 23), (10, 4), (22, 9), (6, 13), (16, 9), (9, 15), (3, 23), (5, 14), (2, 18), (4, 6), (6, 17), (20, 18), (12, 15), (4, 8), (4, 17), (13, 21), (6, 0), (12, 13), (23, 23), (21, 21), (0, 9), (16, 23), (1, 8), (23, 10), (16, 21), (22, 23), (23, 7), (10, 25), (8, 9), (24, 0), (6, 22), (17, 22), (0, 13), (21, 9), (20, 16), (23, 20), (13, 24), (18, 18), (10, 0), (4, 3), (6, 26), (4, 23), (16, 11), (16, 22), (18, 9), (20, 22), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682254", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), 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), (24, 4), (24, 8), (0, 20), (3, 7), (6, 12), (16, 17), (25, 8), (25, 2), (25, 17), (25, 12), (10, 20), (19, 10), (13, 21), (11, 23), (5, 21), (7, 5), (7, 6), (13, 1), (24, 2), (13, 5), (15, 10), (4, 15), (1, 21), (17, 23), (7, 8), (16, 13), (14, 4), (22, 14), (18, 22), (24, 23), (11, 3), (4, 4), (17, 13), (25, 20), (19, 9), (23, 0), (17, 11), (25, 4), (0, 5), (1, 14), (10, 12), (13, 4), (20, 18), (9, 19), (19, 19), (14, 1), (10, 2), (8, 9), (25, 21), (9, 5), (12, 23), (13, 8), (3, 18), (8, 20), (22, 5), (20, 20), (10, 14), (19, 15), (12, 12), (13, 2), (12, 2), (23, 9), (5, 11), (19, 5), (21, 14), (6, 14), (5, 7), (15, 18), (8, 4), (11, 4), (21, 1), (12, 13), (8, 3), (14, 7), (21, 9), (1, 18), (7, 21), (25, 1), (23, 11), (22, 20), (12, 7), (17, 19), (2, 22), (0, 19), (24, 14), (14, 5), (13, 18), (23, 1), (19, 3), (1, 23), (23, 5), (0, 18), (22, 16), (22, 11), (24, 17), (20, 16), (8, 22), (17, 2), (19, 8), (19, 17), (4, 3), (24, 7), (25, 19), (0, 13), (1, 11), (5, 15), (23, 14), (10, 0), (24, 1), (25, 6), (5, 13), (24, 18), (1, 7), (11, 18), (19, 11), (19, 6), (9, 20), (17, 9), (25, 18), (16, 0), (21, 6), (19, 1), (6, 3), (21, 2), (21, 16), (19, 2), (20, 13), (5, 6), (15, 22), (1, 5), (17, 12), (7, 10), (4, 19), (0, 10), (13, 14), (8, 15), (2, 15), (6, 2), (2, 1), (10, 21), (18, 18), (12, 11), (16, 8), (22, 0), (22, 21), (13, 9), (0, 3), (4, 11), (21, 5), (11, 21), (14, 17), (4, 2), (22, 8), (21, 4), (2, 0), (9, 9), (22, 7), (7, 20), (9, 4), (14, 6), (19, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29484", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), 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), (0, 4), (22, 5), (12, 9), (17, 7), (21, 4), (0, 11), (11, 21), (23, 1), (22, 14), (22, 19), (15, 10), (14, 21), (7, 12), (14, 10), (19, 3), (12, 5), (23, 12), (5, 3), (21, 12), (4, 6), (21, 3), (1, 16), (14, 4), (16, 21), (11, 14), (11, 4), (7, 22), (6, 18), (11, 5), (18, 14), (20, 0), (8, 22), (15, 8), (13, 7), (12, 22), (4, 4), (14, 16), (13, 9), (19, 20), (5, 15), (11, 11), (18, 16), (9, 18), (12, 7), (2, 8), (7, 6), (17, 10), (7, 0), (5, 5), (18, 17), (21, 6), (15, 17), (14, 2), (15, 3), (8, 5), (0, 19), (1, 17), (12, 16), (4, 2), (9, 7), (14, 7), (21, 16), (3, 15), (21, 15), (15, 13), (12, 20), (7, 5), (2, 21), (17, 16), (8, 17), (10, 1), (1, 19), (4, 20), (18, 6), (8, 20), (13, 21), (6, 7), (13, 19), (3, 20), (22, 4), (4, 19), (20, 22), (20, 10), (16, 10), (3, 9), (16, 17), (19, 7), (23, 18), (4, 17), (21, 8), (2, 19), (13, 1), (3, 6), (6, 16), (6, 5), (9, 3), (0, 8), (3, 7), (23, 7), (5, 14), (17, 14), (23, 5), (21, 22), (22, 15), (21, 5), (20, 21), (11, 2), (17, 9), (1, 5), (20, 11), (9, 15), (18, 13), (0, 21), (16, 9), (1, 6), (0, 5), (12, 2), (3, 1), (18, 22), (9, 14), (4, 11), (20, 7), (18, 21), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142100", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), 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), (9, 2), (11, 13), (14, 11), (20, 7), (4, 1), (7, 10), (4, 21), (3, 6), (19, 21), (0, 4), (27, 8), (5, 10), (24, 11), (20, 20), (2, 21), (11, 10), (8, 0), (8, 1), (17, 18), (22, 19), (21, 10), (10, 14), (17, 1), (21, 20), (26, 0), (20, 6), (17, 7), (23, 15), (25, 12), (16, 19), (17, 14), (25, 1), (9, 4), (6, 19), (3, 9), (5, 6), (13, 9), (19, 8), (19, 15), (2, 13), (7, 22), (15, 7), (19, 11), (14, 2), (10, 8), (25, 4), (26, 14), (16, 6), (22, 21), (21, 4), (11, 0), (22, 0), (12, 18), (18, 18), (12, 13), (4, 7), (18, 8), (21, 8), (16, 17), (5, 13), (6, 21), (11, 8), (21, 13), (1, 21), (9, 18), (1, 11), (17, 13), (5, 2), (11, 2), (14, 3), (6, 7), (21, 11), (22, 14), (3, 22), (4, 19), (27, 0), (22, 20), (27, 3), (7, 19), (21, 6), (7, 15), (17, 15), (17, 20), (1, 8), (7, 17), (19, 20), (14, 4), (5, 16), (6, 18), (18, 17), (14, 1), (0, 15), (12, 16), (23, 1), (25, 14), (1, 10), (23, 19), (24, 20), (8, 15), (19, 12), (19, 3), (9, 12), (2, 22), (12, 7), (14, 22), (25, 15), (1, 4), (6, 17), (25, 8), (23, 13), (4, 12), (9, 14), (12, 6), (17, 8), (8, 3), (2, 2), (1, 1), (8, 12), (5, 19), (14, 10), (26, 13), (19, 13), (11, 12), (27, 11), (25, 21), (1, 12), (7, 21), (23, 0), (24, 21), (11, 7), (18, 16), (5, 12), (16, 14), (10, 10), (20, 15), (14, 14), (21, 0), (4, 20), (22, 8), (26, 9), (17, 6), (24, 3), (19, 14), (20, 17), (13, 8), (17, 0), (23, 14), (15, 17), (9, 21), (10, 5), (16, 13), (7, 12), (0, 6), (3, 14), (9, 6), (9, 0), (1, 15), (23, 4), (16, 11), (17, 17), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810242", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (18, 10), (4, 0), (18, 21), (9, 18), (11, 13), (7, 17), (13, 16), (21, 13), (17, 23), (5, 7), (2, 21), (18, 9), (20, 24), (17, 17), (21, 6), (15, 3), (19, 14), (14, 17), (17, 18), (18, 20), (6, 14), (8, 24), (1, 6), (20, 9), (19, 15), (20, 25), (15, 7), (0, 10), (20, 22), (9, 4), (17, 7), (17, 25), (2, 12), (20, 5), (2, 17), (1, 12), (13, 12), (1, 18), (16, 15), (4, 1), (0, 24), (4, 15), (4, 17), (7, 25), (15, 5), (21, 15), (8, 17), (4, 7), (16, 0), (1, 3), (5, 4), (19, 22), (18, 5), (12, 15), (20, 11), (16, 17), (0, 22), (11, 1), (11, 12), (16, 16), (17, 5), (7, 13), (3, 19), (0, 15), (16, 21), (11, 6), (5, 0), (9, 21), (19, 7), (17, 2), (12, 9), (1, 16), (8, 6), (11, 20), (4, 10), (16, 7), (10, 3), (16, 3), (9, 19), (18, 16), (3, 13), (15, 18), (11, 16), (15, 6), (12, 13), (11, 0), (13, 19), (6, 20), (5, 17), (4, 24), (4, 23), (19, 5), (17, 3), (6, 19), (2, 0), (7, 2), (1, 14), (8, 25), (14, 2), (15, 17), (3, 5), (11, 21), (2, 5), (2, 24), (2, 20), (17, 14), (10, 4), (16, 19), (14, 12), (10, 19), (11, 19), (21, 9), (3, 12), (13, 9), (4, 19), (7, 15), (19, 19), (6, 1), (13, 14), (17, 6), (19, 2), (8, 1), (20, 15), (10, 15), (12, 21), (17, 19), (12, 10), (11, 4), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918292", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (23, 13), (16, 15), (26, 13), (9, 19), (25, 4), (23, 0), (13, 11), (6, 9), (25, 1), (13, 3), (2, 11), (21, 13), (16, 23), (11, 2), (11, 5), (12, 7), (3, 19), (9, 4), (3, 9), (19, 21), (18, 6), (18, 3), (23, 27), (12, 13), (10, 21), (20, 3), (11, 27), (2, 23), (19, 9), (2, 5), (21, 25), (6, 15), (21, 8), (15, 13), (8, 7), (2, 14), (20, 4), (9, 5), (12, 16), (16, 24), (3, 27), (2, 17), (17, 11), (3, 7), (17, 1), (1, 5), (5, 21), (2, 27), (24, 10), (1, 16), (0, 8), (26, 5), (23, 12), (8, 12), (0, 11), (9, 0), (8, 14), (0, 27), (26, 6), (4, 1), (10, 7), (8, 20), (0, 6), (14, 5), (12, 8), (23, 16), (24, 15), (17, 3), (19, 23), (26, 2), (22, 21), (15, 16), (21, 4), (21, 2), (8, 3), (15, 22), (11, 17), (12, 15), (23, 25), (5, 20), (13, 13), (18, 14), (2, 16), (21, 23), (7, 2), (15, 14), (12, 11), (15, 12), (9, 9), (1, 14), (7, 24), (20, 9), (9, 16), (23, 19), (9, 2), (21, 18), (22, 24), (21, 17), (7, 23), (20, 22), (25, 12), (15, 18), (13, 4), (10, 17), (4, 3), (8, 2), (19, 3), (24, 8), (6, 5), (3, 15), (4, 16), (20, 21), (14, 16), (6, 11), (9, 23), (17, 13), (8, 16), (17, 5), (16, 5), (26, 9), (24, 25), (24, 27), (26, 22), (1, 10), (19, 7), (20, 17), (15, 19), (21, 9), (2, 26), (6, 8), (23, 22), (25, 9), (4, 26), (5, 9), (25, 6), (14, 20), (0, 22), (14, 13), (24, 1), (9, 7), (20, 19), (8, 15), (5, 12), (23, 2), (11, 26), (8, 5), (10, 8), (10, 25), (26, 16), (22, 2), (1, 1), (2, 20), (14, 25), (14, 8), (2, 0), (14, 27), (8, 1), (10, 12), (6, 0), (13, 12), (26, 0), (18, 8), (7, 11), (22, 8), (0, 23), (6, 14), (12, 17), (16, 22), (21, 22), (22, 0), (19, 27), (11, 8), (4, 20), (6, 12), (4, 4), (9, 10), (10, 27), (3, 4), (12, 0), (19, 14), (0, 18), (20, 14), (26, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299922", "dataset": "MATH"}
{"messages": [{"content": "In a 22x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 18), (5, 8), (7, 10), (13, 19), (3, 5), (18, 19), (5, 2), (18, 9), (9, 16), (10, 1), (8, 12), (7, 11), (6, 3), (9, 9), (16, 18), (18, 16), (12, 15), (9, 6), (1, 17), (6, 8), (3, 1), (11, 5), (20, 15), (11, 12), (8, 1), (0, 2), (8, 17), (19, 13), (4, 4), (21, 5), (15, 11), (9, 18), (15, 15), (12, 17), (3, 13), (2, 17), (10, 13), (13, 17), (21, 11), (14, 11), (10, 0), (20, 8), (15, 14), (1, 4), (5, 10), (16, 6), (17, 19), (11, 16), (9, 0), (3, 10), (14, 0), (1, 13), (2, 14), (13, 3), (7, 2), (6, 11), (7, 7), (17, 3), (14, 18), (0, 13), (2, 11), (6, 19), (2, 16), (15, 5), (8, 5), (3, 2), (11, 15), (16, 11), (13, 15), (12, 1), (20, 18), (1, 10), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743099", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 24), (20, 10), (1, 2), (14, 18), (16, 13), (0, 2), (11, 13), (14, 15), (20, 24), (11, 1), (13, 3), (10, 3), (7, 2), (17, 12), (13, 13), (7, 5), (9, 7), (3, 18), (7, 0), (3, 3), (21, 14), (18, 23), (15, 10), (23, 5), (10, 14), (14, 11), (7, 15), (7, 3), (6, 1), (16, 11), (14, 13), (13, 17), (20, 18), (15, 8), (1, 9), (19, 1), (23, 8), (21, 15), (9, 2), (16, 14), (5, 23), (8, 8), (20, 21), (23, 6), (9, 8), (12, 11), (0, 24), (19, 14), (0, 12), (12, 8), (18, 2), (20, 26), (8, 25), (2, 10), (11, 23), (9, 5), (4, 13), (15, 22), (22, 24), (2, 12), (20, 15), (8, 4), (20, 12), (18, 11), (10, 0), (10, 5), (11, 14), (22, 4), (13, 22), (5, 26), (0, 9), (10, 2), (1, 23), (2, 15), (22, 11), (13, 12), (5, 17), (6, 16), (8, 16), (2, 14), (0, 22), (10, 8), (10, 15), (0, 26), (6, 26), (15, 24), (23, 2), (15, 18), (4, 9), (15, 1), (14, 24), (22, 0), (1, 1), (12, 7), (3, 14), (0, 21), (17, 20), (14, 8), (0, 7), (10, 1), (22, 14), (9, 14), (7, 26), (13, 4), (1, 25), (4, 18), (0, 13), (0, 3), (11, 18), (12, 13), (5, 19), (19, 23), (6, 22), (9, 26), (20, 3), (17, 17), (20, 0), (5, 6), (21, 4), (3, 25), (19, 12), (12, 20), (21, 13), (6, 19), (20, 9), (22, 21), (18, 21), (23, 13), (17, 1), (17, 0), (20, 11), (5, 15), (22, 8), (13, 0), (15, 3), (13, 15), (10, 13), (11, 9), (18, 12), (3, 12), (7, 1), (21, 17), (11, 2), (23, 11), (9, 3), (14, 12), (22, 9), (17, 24), (7, 9), (10, 22), (19, 4), (13, 6), (5, 1), (3, 9), (15, 12), (20, 13), (2, 19), (8, 7), (6, 25), (20, 4), (16, 5), (2, 7), (12, 9), (23, 18), (1, 7), (14, 26), (4, 20), (8, 11), (11, 16), (17, 16), (6, 4), (13, 19), (11, 4), (12, 5), (0, 6), (13, 10), (3, 10), (23, 21), (0, 10), (22, 19), (13, 24), (21, 3), (20, 14), (20, 2), (17, 8), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "678321", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 10), (11, 27), (26, 4), (12, 5), (1, 19), (7, 3), (26, 7), (20, 15), (16, 2), (26, 15), (10, 4), (6, 13), (23, 9), (15, 27), (21, 12), (4, 2), (3, 25), (10, 20), (3, 10), (9, 10), (24, 14), (22, 22), (14, 0), (18, 27), (13, 14), (9, 15), (14, 25), (22, 12), (26, 2), (10, 26), (9, 3), (15, 28), (18, 26), (13, 8), (21, 5), (6, 18), (23, 22), (3, 0), (20, 1), (20, 9), (2, 16), (26, 1), (22, 24), (24, 28), (25, 1), (6, 22), (10, 25), (8, 8), (20, 13), (6, 20), (9, 7), (25, 21), (2, 25), (6, 6), (18, 11), (5, 27), (18, 16), (16, 9), (20, 8), (17, 19), (16, 8), (12, 9), (9, 16), (22, 1), (8, 15), (25, 0), (25, 19), (25, 6), (11, 11), (11, 3), (13, 2), (9, 1), (7, 26), (17, 8), (11, 1), (4, 28), (15, 10), (13, 10), (5, 10), (11, 25), (12, 22), (2, 8), (24, 9), (9, 12), (17, 20), (0, 28), (4, 20), (17, 25), (23, 6), (18, 19), (26, 22), (15, 25), (10, 16), (8, 24), (23, 0), (22, 0), (21, 14), (1, 1), (2, 20), (22, 3), (26, 6), (22, 10), (7, 12), (4, 15), (5, 19), (7, 24), (21, 24), (17, 22), (19, 2), (8, 11), (7, 1), (15, 6), (24, 15), (7, 11), (23, 23), (16, 4), (1, 22), (1, 28), (25, 11), (26, 27), (16, 23), (7, 6), (23, 15), (2, 13), (7, 2), (23, 26), (26, 25), (16, 15), (1, 10), (5, 21), (14, 26), (0, 9), (1, 16), (17, 24), (6, 28), (8, 13), (8, 3), (6, 8), (1, 15), (10, 12), (6, 10), (4, 26), (10, 10), (7, 25), (23, 8), (3, 11), (6, 1), (10, 24), (19, 15), (4, 17), (8, 0), (0, 14), (23, 25), (15, 22), (16, 7), (13, 20), (7, 4), (25, 13), (15, 15), (16, 24), (10, 14), (3, 5), (21, 8), (17, 4), (15, 5), (1, 12), (2, 22), (0, 17), (26, 10), (2, 26), (6, 25), (23, 27), (0, 5), (22, 18), (22, 21), (9, 22), (22, 2), (16, 17), (16, 16), (3, 6), (20, 22), (11, 20), (0, 23), (20, 4), (18, 0), (8, 12), (8, 9), (18, 7), (9, 2), (24, 8), (7, 0), (1, 9), (23, 4), (25, 3), (16, 0), (13, 26), (21, 10), (4, 16), (8, 14), (20, 14), (17, 13), (11, 4), (23, 2), (20, 3), (4, 10), (4, 14), (12, 23), (10, 15), (14, 23), (13, 1), (4, 18), (21, 19), (21, 3), (11, 0), (19, 4), (20, 27), (18, 2), (11, 8), (12, 24), (19, 24), (2, 9), (10, 0), (22, 7), (19, 11), (11, 10), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763800", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (24, 0), (19, 14), (0, 15), (20, 15), (8, 4), (15, 10), (10, 4), (5, 9), (6, 15), (16, 7), (4, 8), (4, 18), (4, 16), (4, 7), (4, 15), (1, 7), (8, 14), (8, 15), (0, 7), (25, 2), (4, 9), (25, 19), (13, 19), (25, 8), (7, 11), (26, 2), (24, 11), (27, 11), (5, 10), (7, 8), (20, 9), (23, 2), (7, 4), (2, 3), (7, 1), (8, 1), (17, 11), (16, 14), (20, 19), (3, 11), (24, 8), (16, 11), (9, 11), (19, 8), (20, 0), (13, 0), (5, 19), (10, 5), (21, 5), (28, 2), (12, 16), (16, 15), (12, 18), (19, 3), (23, 4), (15, 5), (23, 12), (21, 2), (15, 2), (7, 0), (20, 1), (19, 9), (26, 9), (15, 9), (8, 13), (5, 0), (13, 7), (10, 13), (8, 16), (23, 9), (10, 12), (23, 14), (21, 0), (4, 1), (15, 3), (17, 12), (22, 16), (9, 19), (16, 10), (17, 14), (5, 5), (12, 11), (13, 3), (0, 9), (14, 1), (11, 3), (5, 2), (17, 13), (3, 1), (28, 14), (11, 7), (22, 13), (6, 13), (23, 19), (15, 14), (3, 15), (8, 6), (22, 7), (18, 14), (5, 8), (14, 5), (21, 15), (22, 4), (5, 4), (25, 0), (9, 10), (2, 7), (4, 10), (28, 16), (14, 8), (18, 11), (11, 6), (18, 1), (7, 6), (6, 19), (28, 12), (27, 16), (9, 7), (27, 1), (16, 9), (20, 3), (28, 15), (16, 3), (13, 15), (6, 18), (3, 12), (12, 3), (24, 12), (11, 14), (15, 16), (27, 13), (3, 0), (2, 12), (18, 0), (10, 3), (21, 13), (2, 4), (26, 5), (25, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217920", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), 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), (22, 3), (11, 9), (24, 16), (2, 3), (14, 9), (20, 5), (22, 19), (21, 25), (27, 21), (9, 12), (13, 27), (19, 13), (8, 9), (18, 17), (27, 24), (10, 14), (25, 23), (5, 5), (20, 4), (15, 4), (19, 11), (11, 0), (12, 2), (19, 20), (25, 11), (14, 20), (1, 6), (2, 10), (22, 16), (13, 21), (27, 23), (26, 2), (27, 22), (20, 20), (25, 1), (5, 27), (8, 0), (21, 8), (7, 22), (18, 19), (22, 5), (2, 6), (13, 19), (0, 22), (6, 3), (23, 23), (17, 8), (20, 14), (24, 26), (6, 23), (21, 18), (19, 26), (17, 4), (15, 8), (20, 6), (14, 14), (3, 19), (13, 10), (19, 19), (9, 18), (1, 19), (25, 22), (12, 26), (12, 23), (6, 24), (12, 18), (11, 21), (27, 26), (4, 0), (8, 13), (23, 6), (21, 23), (16, 0), (12, 7), (19, 5), (17, 19), (16, 15), (23, 9), (25, 16), (14, 19), (17, 2), (15, 22), (10, 13), (15, 23), (10, 21), (26, 0), (10, 25), (7, 13), (14, 27), (4, 11), (11, 7), (16, 3), (20, 25), (4, 8), (27, 8), (10, 24), (4, 15), (1, 15), (22, 18), (20, 26), (17, 6), (14, 12), (13, 0), (7, 23), (15, 5), (7, 5), (2, 0), (13, 11), (23, 0), (8, 15), (6, 13), (8, 20), (17, 26), (9, 7), (27, 10), (14, 6), (3, 8), (2, 22), (21, 22), (9, 4), (26, 4), (8, 26), (8, 21), (21, 4), (16, 10), (18, 14), (6, 1), (8, 23), (9, 22), (6, 9), (3, 2), (19, 12), (15, 6), (18, 10), (7, 11), (1, 18), (14, 23), (23, 5), (25, 2), (21, 19), (3, 18), (22, 15), (0, 4), (22, 23), (4, 26), (14, 25), (11, 20), (14, 21), (2, 24), (5, 10), (12, 14), (3, 13), (6, 12), (25, 5), (17, 27), (11, 3), (16, 17), (8, 8), (20, 23), (4, 3), (2, 23), (16, 20), (9, 21), (17, 9), (22, 11), (7, 16), (25, 3), (10, 8), (8, 16), (9, 1), (22, 21), (23, 12), (15, 13), (2, 25), (13, 3), (23, 25), (11, 25), (2, 4), (25, 14), (21, 5), (2, 5), (20, 17), (13, 25), (13, 14), (20, 3), (26, 15), (26, 3), (23, 8), (11, 14), (6, 19), (27, 7), (23, 20), (11, 11), (7, 7), (21, 2), (0, 9), (2, 12), (21, 20), (1, 23), (19, 22), (25, 9), (13, 9), (13, 20), (26, 5), (18, 8), (13, 1), (10, 26), (8, 6), (9, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "881920", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 27), (14, 16), (17, 19), (1, 8), (1, 21), (17, 17), (8, 4), (16, 21), (25, 15), (5, 26), (19, 18), (5, 23), (5, 27), (11, 11), (10, 26), (3, 11), (23, 16), (21, 23), (20, 20), (12, 13), (0, 1), (10, 18), (25, 20), (14, 5), (12, 17), (24, 26), (19, 21), (23, 12), (25, 4), (0, 15), (24, 9), (9, 9), (15, 6), (6, 5), (12, 16), (8, 5), (20, 8), (1, 6), (26, 15), (5, 1), (4, 2), (9, 22), (15, 11), (12, 14), (15, 12), (23, 1), (14, 15), (0, 17), (8, 13), (0, 10), (16, 14), (16, 0), (15, 23), (10, 22), (9, 24), (23, 25), (23, 20), (8, 21), (14, 8), (15, 22), (2, 5), (13, 8), (11, 14), (6, 10), (17, 0), (24, 15), (26, 0), (19, 7), (9, 2), (9, 14), (15, 1), (26, 12), (14, 10), (5, 16), (17, 14), (2, 23), (16, 11), (12, 7), (9, 13), (20, 21), (19, 16), (17, 18), (17, 8), (22, 10), (21, 27), (5, 20), (12, 11), (7, 6), (0, 8), (12, 10), (18, 8), (15, 18), (24, 7), (22, 14), (14, 7), (23, 17), (7, 0), (10, 15), (2, 20), (13, 23), (16, 8), (16, 7), (0, 16), (16, 2), (1, 1), (21, 22), (26, 2), (15, 3), (11, 18), (0, 20), (13, 21), (20, 13), (13, 9), (24, 14), (21, 10), (22, 4), (0, 6), (5, 12), (6, 18), (0, 24), (26, 8), (22, 6), (8, 26), (25, 0), (20, 15), (1, 26), (7, 27), (14, 20), (15, 0), (2, 7), (26, 19), (17, 25), (20, 23), (25, 23), (13, 16), (22, 12), (8, 6), (7, 26), (4, 13), (17, 15), (12, 1), (9, 5), (26, 26), (3, 1), (6, 2), (12, 24), (9, 25), (25, 7), (1, 25), (7, 7), (13, 12), (12, 0), (3, 7), (10, 1), (10, 25), (25, 18), (6, 0), (19, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836072", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), 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), (20, 24), (20, 10), (0, 20), (21, 25), (5, 25), (17, 17), (2, 25), (9, 21), (7, 17), (2, 6), (15, 12), (13, 22), (18, 15), (14, 5), (17, 6), (1, 17), (10, 11), (20, 18), (8, 12), (5, 17), (13, 9), (12, 8), (8, 4), (9, 4), (20, 16), (18, 3), (0, 5), (18, 7), (3, 23), (16, 17), (7, 18), (7, 23), (1, 24), (10, 4), (10, 5), (24, 12), (11, 8), (18, 12), (8, 13), (15, 0), (12, 10), (4, 6), (10, 3), (19, 19), (15, 14), (19, 0), (24, 20), (7, 22), (10, 13), (19, 10), (9, 6), (10, 20), (1, 8), (13, 11), (13, 0), (18, 8), (21, 21), (0, 25), (12, 23), (23, 20), (9, 18), (4, 21), (13, 14), (6, 22), (12, 11), (0, 22), (1, 3), (2, 11), (3, 3), (19, 14), (14, 20), (13, 6), (1, 12), (22, 9), (20, 7), (8, 15), (22, 21), (0, 11), (15, 18), (18, 17), (16, 9), (0, 3), (23, 17), (13, 1), (1, 2), (0, 14), (20, 19), (13, 5), (2, 2), (4, 4), (18, 9), (13, 17), (17, 2), (12, 18), (3, 20), (5, 4), (22, 24), (8, 9), (22, 18), (6, 25), (10, 23), (15, 11), (0, 18), (22, 1), (20, 13), (21, 10), (4, 9), (0, 15), (2, 18), (14, 22), (12, 19), (5, 9), (6, 2), (11, 22), (17, 22), (22, 12), (24, 11), (12, 15), (15, 10), (4, 25), (0, 9), (8, 8), (11, 9), (17, 8), (19, 15), (20, 21), (10, 24), (6, 18), (2, 19), (9, 22), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268554", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 19), (19, 19), (19, 15), (8, 17), (8, 12), (2, 18), (13, 18), (9, 0), (8, 0), (6, 6), (16, 18), (6, 5), (3, 1), (15, 18), (19, 1), (2, 8), (1, 0), (20, 15), (1, 8), (17, 7), (19, 13), (1, 11), (8, 14), (9, 10), (6, 8), (0, 8), (19, 2), (4, 9), (6, 1), (6, 2), (6, 18), (0, 3), (13, 0), (3, 10), (6, 4), (3, 14), (19, 10), (15, 13), (16, 19), (3, 13), (1, 2), (0, 7), (1, 6), (3, 9), (0, 12), (9, 16), (17, 13), (15, 11), (14, 17), (8, 15), (3, 5), (10, 8), (14, 13), (10, 16), (5, 7), (7, 8), (18, 17), (8, 1), (12, 10), (15, 5), (3, 11), (5, 15), (3, 3), (14, 7), (1, 9), (9, 4), (8, 8), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "855995", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 7), (25, 18), (4, 20), (6, 14), (17, 5), (26, 19), (22, 7), (10, 17), (3, 12), (0, 8), (17, 11), (17, 15), (12, 20), (16, 13), (5, 12), (9, 10), (9, 17), (14, 2), (4, 2), (12, 12), (9, 15), (5, 5), (13, 3), (7, 9), (3, 18), (7, 11), (22, 8), (17, 18), (24, 11), (13, 8), (9, 12), (16, 3), (26, 15), (6, 2), (2, 17), (2, 13), (2, 10), (2, 0), (4, 17), (11, 14), (19, 18), (26, 1), (8, 19), (19, 1), (1, 13), (6, 5), (18, 15), (9, 5), (7, 8), (16, 11), (2, 1), (12, 8), (19, 5), (10, 8), (7, 10), (26, 2), (24, 7), (14, 16), (3, 8), (0, 3), (22, 3), (12, 7), (12, 17), (4, 11), (3, 11), (5, 20), (25, 6), (19, 19), (0, 17), (16, 6), (7, 4), (3, 2), (16, 18), (15, 19), (5, 9), (13, 17), (16, 14), (26, 16), (2, 6), (23, 1), (14, 0), (23, 5), (12, 15), (23, 4), (4, 3), (10, 19), (17, 14), (24, 16), (22, 10), (8, 6), (7, 0), (5, 15), (26, 6), (11, 1), (0, 10), (2, 9), (17, 17), (2, 14), (10, 3), (15, 6), (25, 16), (26, 13), (18, 12), (16, 1), (24, 1), (15, 2), (23, 14), (6, 0), (17, 3), (16, 7), (21, 0), (26, 4), (16, 12), (24, 9), (24, 5), (20, 14), (17, 7), (21, 17), (5, 14), (2, 20), (13, 20), (14, 13), (12, 10), (12, 0), (13, 5), (3, 3), (17, 9), (25, 11), (18, 1), (10, 15), (1, 19), (24, 3), (19, 12), (25, 7), (1, 1), (5, 11), (16, 2), (23, 11), (19, 0), (3, 6), (1, 6), (16, 15), (17, 2), (12, 19), (17, 0), (26, 10), (7, 3), (19, 10), (20, 10), (20, 9), (18, 5), (11, 19), (20, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719780", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 6), (15, 0), (22, 4), (5, 0), (3, 6), (4, 6), (16, 27), (4, 15), (24, 2), (18, 13), (9, 13), (4, 1), (10, 21), (22, 7), (4, 22), (9, 19), (21, 20), (12, 6), (2, 14), (3, 0), (6, 13), (5, 21), (15, 20), (2, 1), (19, 4), (6, 5), (12, 13), (19, 27), (10, 16), (21, 21), (4, 0), (16, 20), (17, 3), (2, 21), (17, 27), (15, 21), (5, 4), (2, 0), (12, 24), (14, 0), (15, 5), (24, 26), (18, 18), (11, 19), (5, 7), (4, 19), (6, 21), (8, 13), (1, 0), (5, 10), (11, 22), (4, 13), (23, 16), (22, 17), (2, 22), (6, 11), (8, 22), (4, 5), (17, 12), (24, 11), (14, 25), (16, 0), (10, 6), (12, 2), (22, 3), (24, 8), (10, 26), (22, 8), (8, 19), (14, 7), (15, 16), (11, 9), (20, 3), (11, 8), (18, 5), (22, 10), (20, 9), (2, 17), (23, 4), (5, 1), (7, 24), (2, 10), (20, 0), (9, 5), (18, 2), (0, 10), (15, 23), (5, 24), (3, 19), (2, 26), (17, 4), (15, 19), (20, 13), (21, 19), (22, 21), (14, 8), (17, 18), (11, 3), (0, 23), (9, 21), (5, 9), (15, 18), (19, 13), (13, 6), (0, 27), (17, 26), (13, 9), (14, 26), (2, 5), (0, 13), (14, 22), (7, 21), (22, 26), (11, 2), (20, 1), (21, 4), (17, 0), (21, 13), (16, 12), (2, 13), (10, 12), (7, 11), (13, 25), (23, 3), (8, 21), (16, 15), (6, 9), (11, 0), (9, 2), (15, 11), (1, 22), (6, 4), (2, 25), (7, 9), (6, 7), (15, 17), (2, 2), (1, 6), (9, 15), (1, 15), (7, 10), (19, 0), (4, 23), (11, 24), (24, 24), (10, 17), (8, 15), (6, 8), (23, 11), (9, 11), (9, 6), (9, 17), (22, 23), (10, 18), (9, 14), (23, 25), (18, 12), (1, 16), (7, 15), (24, 7), (8, 5), (21, 16), (1, 2), (15, 25), (10, 20), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401040", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (25, 21), (15, 0), (16, 24), (15, 16), (20, 7), (2, 18), (7, 27), (15, 10), (14, 13), (18, 14), (4, 5), (2, 5), (3, 17), (3, 5), (23, 23), (7, 19), (0, 12), (14, 27), (19, 4), (16, 25), (12, 2), (10, 23), (16, 20), (19, 11), (8, 3), (15, 11), (13, 0), (24, 18), (24, 11), (12, 21), (14, 19), (14, 22), (25, 11), (13, 14), (22, 18), (5, 19), (14, 16), (8, 7), (6, 9), (0, 1), (16, 16), (2, 14), (6, 2), (24, 5), (8, 21), (7, 2), (12, 26), (0, 25), (13, 24), (10, 22), (15, 9), (16, 8), (0, 18), (9, 3), (10, 7), (2, 7), (25, 13), (22, 26), (14, 6), (3, 27), (5, 8), (6, 4), (18, 18), (5, 17), (2, 17), (23, 22), (21, 19), (21, 15), (17, 17), (3, 20), (12, 11), (18, 24), (4, 15), (10, 9), (6, 20), (1, 1), (17, 7), (13, 10), (6, 13), (3, 8), (7, 15), (21, 17), (22, 25), (7, 13), (0, 5), (22, 5), (1, 6), (11, 1), (18, 21), (24, 25), (24, 10), (10, 24), (9, 11), (2, 12), (1, 7), (2, 20), (17, 5), (2, 26), (8, 17), (9, 5), (25, 2), (1, 23), (10, 8), (5, 15), (9, 12), (23, 7), (24, 19), (20, 0), (8, 14), (6, 7), (13, 17), (11, 17), (5, 12), (1, 21), (24, 12), (19, 10), (4, 3), (12, 23), (13, 12), (5, 22), (0, 21), (15, 22), (11, 26), (15, 5), (3, 14), (20, 1), (0, 3), (21, 25), (17, 4), (1, 15), (2, 3), (19, 7), (20, 8), (14, 4), (15, 13), (4, 27), (25, 27), (16, 7), (1, 17), (0, 2), (21, 18), (12, 1), (6, 25), (7, 6), (15, 19), (15, 7), (6, 16), (21, 20), (17, 2), (21, 13), (15, 20), (11, 11), (14, 7), (25, 16), (11, 14), (7, 12), (19, 15), (17, 19), (3, 1), (0, 9), (19, 13), (12, 8), (1, 16), (13, 21), (14, 23), (4, 25), (26, 7), (1, 3), (6, 24), (10, 21), (2, 13), (5, 16), (10, 5), (11, 27), (14, 1), (3, 26), (18, 25), (12, 5), (15, 6), (4, 10), (10, 19), (21, 6), (10, 14), (22, 17), (14, 17), (8, 19), (26, 17), (2, 2), (4, 17), (17, 13), (5, 27), (20, 24), (0, 27), (3, 13), (2, 16), (7, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870381", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), 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, 4), (7, 9), (19, 7), (1, 0), (21, 1), (21, 26), (6, 19), (13, 20), (7, 18), (23, 20), (18, 14), (20, 10), (13, 5), (20, 21), (0, 25), (20, 15), (14, 9), (0, 17), (12, 25), (3, 12), (24, 22), (12, 26), (4, 12), (11, 3), (8, 1), (6, 2), (21, 24), (10, 25), (19, 13), (3, 11), (5, 15), (17, 10), (25, 4), (1, 2), (23, 25), (23, 21), (24, 14), (16, 17), (2, 17), (10, 1), (0, 22), (14, 8), (15, 23), (21, 20), (4, 26), (14, 19), (17, 18), (24, 6), (8, 10), (18, 12), (1, 14), (19, 4), (19, 1), (21, 15), (24, 4), (17, 7), (19, 2), (13, 23), (3, 23), (5, 2), (22, 23), (18, 5), (12, 8), (0, 12), (8, 11), (21, 13), (16, 11), (8, 6), (18, 1), (5, 14), (5, 7), (15, 20), (23, 3), (20, 22), (19, 23), (2, 16), (3, 24), (1, 13), (0, 20), (12, 17), (15, 11), (17, 12), (25, 25), (17, 5), (0, 4), (20, 20), (9, 19), (25, 14), (17, 0), (6, 7), (24, 3), (13, 9), (22, 18), (8, 22), (1, 15), (20, 19), (6, 5), (0, 26), (1, 1), (13, 10), (21, 14), (13, 1), (9, 5), (18, 21), (11, 14), (14, 3), (19, 16), (17, 14), (7, 13), (6, 24), (6, 13), (18, 26), (4, 5), (7, 23), (11, 22), (8, 20), (7, 2), (8, 21), (14, 17), (10, 8), (5, 0), (10, 11), (17, 3), (16, 0), (4, 6), (3, 10), (25, 13), (20, 1), (7, 17), (5, 21), (25, 15), (12, 3), (24, 13), (14, 10), (11, 18), (20, 24), (1, 24), (25, 18), (14, 20), (20, 18), (7, 25), (6, 16), (17, 21), (5, 12), (24, 17), (23, 18), (17, 11), (4, 24), (24, 7), (21, 19), (5, 18), (24, 16), (10, 15), (15, 4), (9, 16), (11, 9), (13, 12), (19, 15), (11, 25), (3, 14), (11, 21), (2, 23), (10, 6), (10, 22), (23, 19), (23, 5), (12, 12), (15, 14), (3, 4), (17, 2), (23, 8), (9, 0), (13, 11), (12, 5), (16, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758637", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 19), (13, 16), (5, 17), (20, 14), (21, 5), (4, 20), (12, 18), (2, 16), (4, 18), (12, 17), (14, 1), (10, 21), (9, 13), (6, 4), (5, 11), (16, 6), (19, 15), (3, 0), (9, 10), (17, 22), (8, 18), (20, 1), (7, 21), (16, 17), (7, 13), (3, 14), (1, 9), (8, 0), (14, 20), (11, 18), (0, 16), (1, 14), (3, 13), (2, 12), (0, 18), (12, 21), (5, 0), (8, 12), (12, 10), (17, 16), (17, 20), (12, 13), (16, 12), (16, 2), (3, 6), (17, 18), (21, 8), (19, 10), (15, 4), (14, 14), (9, 3), (4, 2), (1, 11), (14, 13), (15, 5), (21, 13), (5, 14), (4, 0), (16, 14), (8, 4), (0, 20), (12, 3), (2, 17), (21, 12), (8, 20), (4, 13), (11, 5), (0, 10), (6, 6), (20, 20), (17, 19), (10, 7), (5, 20), (1, 7), (5, 10), (12, 15), (5, 5), (18, 11), (14, 18), (8, 14), (19, 4), (1, 6), (3, 1), (13, 11), (2, 13), (5, 13), (0, 3), (11, 22), (20, 18), (11, 16), (16, 1), (9, 8), (19, 13), (3, 12), (12, 16), (13, 6), (18, 12), (4, 6), (15, 16), (18, 2), (17, 10), (14, 12), (20, 16), (19, 20), (11, 20), (6, 18), (9, 12), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933600", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 1), (4, 24), (0, 7), (17, 2), (20, 11), (4, 15), (5, 17), (8, 5), (20, 2), (14, 3), (18, 8), (19, 20), (4, 3), (7, 24), (15, 16), (16, 6), (5, 13), (9, 12), (2, 16), (12, 1), (2, 8), (19, 7), (12, 12), (14, 17), (10, 22), (9, 0), (15, 18), (10, 5), (5, 23), (20, 0), (2, 21), (0, 10), (8, 7), (21, 17), (0, 8), (3, 18), (6, 10), (5, 14), (0, 13), (20, 7), (17, 10), (22, 18), (20, 16), (2, 14), (14, 8), (22, 21), (4, 13), (5, 10), (9, 18), (20, 6), (14, 22), (8, 17), (21, 2), (19, 13), (16, 19), (7, 12), (5, 11), (4, 19), (18, 4), (13, 20), (8, 6), (15, 19), (8, 24), (5, 2), (6, 2), (15, 8), (12, 24), (7, 22), (7, 18), (9, 3), (1, 17), (8, 19), (22, 6), (11, 7), (1, 18), (14, 20), (3, 17), (6, 4), (6, 13), (15, 14), (14, 24), (12, 22), (2, 13), (14, 14), (19, 22), (15, 13), (14, 13), (20, 10), (13, 0), (20, 24), (21, 8), (3, 19), (21, 16), (5, 24), (0, 9), (11, 20), (7, 14), (1, 24), (20, 3), (13, 14), (19, 21), (8, 20), (11, 23), (20, 1), (9, 17), (7, 8), (13, 15), (3, 15), (4, 9), (18, 9), (5, 8), (1, 3), (1, 16), (13, 11), (22, 8), (9, 19), (9, 24), (16, 3), (19, 15), (21, 19), (15, 15), (6, 14), (17, 12), (8, 3), (0, 14), (12, 2), (13, 17), (8, 22), (1, 12), (15, 0), (5, 16), (20, 20), (1, 14), (11, 5), (1, 7), (18, 6), (16, 4), (4, 8), (8, 2), (17, 9), (3, 5), (10, 9), (15, 22), (3, 23), (21, 12), (12, 4), (5, 12), (22, 19), (20, 14), (21, 13), (10, 0), (14, 10), (18, 18), (7, 3), (5, 19), (8, 12), (6, 15), (17, 16), (16, 20), (1, 22), (17, 17), (8, 1), (22, 0), (11, 21), (15, 7), (16, 10), (4, 0), (21, 4), (0, 22), (13, 1), (7, 23), (14, 4), (17, 19), (9, 5), (19, 9), (22, 12), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804384", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), 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, 8), (6, 5), (19, 10), (20, 5), (17, 10), (10, 15), (11, 6), (10, 18), (21, 18), (1, 17), (11, 18), (0, 21), (4, 16), (14, 13), (5, 15), (21, 6), (9, 21), (2, 9), (7, 11), (13, 18), (3, 8), (9, 5), (16, 15), (11, 8), (20, 20), (5, 12), (18, 11), (17, 14), (14, 1), (20, 10), (19, 7), (14, 8), (10, 8), (4, 12), (3, 4), (4, 13), (21, 14), (14, 20), (17, 1), (9, 16), (3, 12), (15, 20), (5, 20), (18, 19), (4, 21), (15, 7), (7, 7), (10, 17), (17, 17), (7, 0), (21, 4), (3, 14), (2, 6), (7, 21), (7, 2), (15, 4), (8, 15), (5, 13), (0, 15), (8, 12), (8, 9), (1, 20), (9, 4), (12, 6), (8, 16), (9, 1), (14, 6), (8, 5), (15, 15), (10, 11), (5, 17), (1, 13), (6, 9), (14, 14), (6, 6), (2, 20), (6, 18), (20, 11), (0, 9), (15, 16), (8, 11), (16, 19), (6, 4), (6, 11), (1, 14), (1, 9), (16, 20), (20, 1), (20, 8), (2, 21), (7, 19), (12, 1), (20, 2), (1, 0), (0, 19), (10, 14), (9, 19), (19, 1), (15, 3), (13, 10), (20, 0), (8, 0), (6, 13), (5, 21), (2, 14), (14, 4), (7, 5), (12, 16), (3, 16), (13, 11), (15, 6), (21, 0), (3, 18), (3, 3), (11, 16), (7, 15), (16, 21), (1, 1), (9, 20), (19, 20), (17, 11), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "693056", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), 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), (12, 21), (6, 18), (4, 17), (9, 17), (22, 16), (21, 15), (20, 3), (16, 3), (11, 19), (19, 19), (17, 15), (12, 10), (2, 3), (17, 17), (9, 19), (23, 20), (14, 4), (21, 6), (23, 4), (10, 16), (4, 13), (1, 9), (21, 1), (1, 12), (1, 16), (12, 2), (7, 7), (18, 18), (20, 12), (4, 6), (12, 6), (0, 5), (20, 9), (4, 9), (22, 3), (6, 0), (11, 4), (19, 9), (16, 8), (2, 2), (22, 13), (2, 9), (23, 7), (11, 3), (9, 9), (12, 5), (1, 0), (20, 13), (23, 12), (3, 2), (15, 13), (10, 1), (1, 8), (4, 14), (23, 5), (22, 18), (5, 13), (18, 6), (18, 8), (22, 9), (17, 3), (20, 20), (11, 14), (6, 1), (22, 6), (7, 20), (0, 21), (7, 11), (10, 9), (11, 16), (6, 19), (8, 1), (7, 3), (8, 2), (7, 2), (15, 0), (24, 16), (10, 20), (5, 17), (16, 12), (0, 10), (13, 1), (10, 8), (9, 20), (8, 15), (11, 5), (3, 12), (8, 14), (21, 16), (23, 21), (17, 11), (0, 18), (15, 2), (6, 11), (22, 15), (19, 3), (22, 11), (15, 12), (18, 0), (17, 21), (13, 13), (7, 15), (1, 3), (22, 0), (8, 0), (7, 18), (23, 18), (12, 9), (11, 7), (14, 7), (4, 18), (7, 21), (21, 20), (17, 2), (1, 6), (23, 10), (20, 0), (19, 17), (9, 12), (18, 17), (23, 1), (19, 1), (0, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785003", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 6), (6, 21), (2, 4), (16, 1), (13, 3), (7, 2), (5, 10), (9, 4), (18, 17), (16, 19), (16, 6), (12, 2), (21, 18), (14, 17), (15, 8), (3, 17), (3, 4), (11, 17), (20, 13), (2, 14), (17, 9), (11, 19), (15, 5), (9, 13), (13, 2), (10, 15), (17, 16), (6, 19), (21, 2), (15, 2), (19, 18), (19, 20), (11, 7), (15, 15), (5, 11), (12, 0), (5, 4), (19, 1), (1, 16), (5, 20), (10, 21), (19, 10), (9, 18), (22, 6), (9, 20), (14, 3), (15, 1), (9, 14), (4, 8), (16, 8), (1, 15), (2, 13), (1, 7), (21, 21), (8, 2), (8, 10), (11, 13), (14, 13), (8, 5), (8, 16), (9, 6), (14, 20), (4, 13), (19, 16), (20, 6), (17, 5), (1, 1), (17, 21), (4, 21), (19, 19), (19, 15), (18, 19), (9, 15), (19, 3), (14, 12), (2, 7), (4, 4), (1, 11), (14, 16), (4, 12), (20, 8), (8, 18), (15, 19), (0, 12), (10, 7), (16, 3), (16, 15), (21, 15), (10, 20), (16, 2), (19, 21), (22, 19), (13, 5), (12, 18), (11, 14), (2, 2), (3, 8), (5, 18), (7, 18), (21, 16), (18, 2), (16, 13), (4, 6), (6, 6), (16, 14), (20, 12), (22, 11), (21, 11), (16, 17), (2, 0), (5, 1), (2, 16), (5, 2), (20, 7), (4, 10), (19, 9), (13, 13), (18, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459088", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), 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, 6), (15, 21), (21, 13), (16, 5), (18, 13), (21, 12), (11, 3), (21, 22), (22, 1), (3, 15), (22, 15), (14, 15), (14, 16), (20, 12), (0, 2), (21, 2), (6, 7), (7, 11), (16, 12), (6, 17), (18, 9), (7, 2), (11, 9), (8, 0), (3, 7), (15, 13), (18, 20), (18, 10), (16, 7), (20, 15), (4, 2), (9, 16), (1, 11), (14, 9), (21, 10), (19, 19), (13, 4), (11, 10), (17, 5), (9, 6), (9, 8), (3, 17), (13, 9), (6, 14), (12, 13), (4, 7), (1, 6), (0, 13), (2, 10), (16, 1), (3, 21), (22, 19), (18, 16), (9, 7), (1, 12), (5, 4), (16, 22), (17, 16), (5, 16), (12, 3), (2, 17), (3, 2), (12, 14), (14, 10), (19, 21), (0, 6), (9, 5), (2, 22), (11, 16), (22, 6), (17, 13), (11, 22), (21, 5), (18, 3), (23, 6), (7, 10), (14, 8), (1, 0), (17, 3), (13, 5), (19, 10), (23, 1), (15, 7), (13, 12), (15, 12), (13, 20), (21, 1), (12, 2), (11, 18), (0, 5), (9, 3), (18, 11), (2, 6), (22, 22), (20, 10), (5, 13), (8, 17), (9, 10), (16, 6), (10, 16), (23, 0), (18, 12), (1, 3), (1, 13), (12, 20), (7, 12), (4, 8), (5, 5), (14, 5), (17, 6), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874158", "dataset": "MATH"}
{"messages": [{"content": "In a 25x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 23), 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), (5, 20), (1, 14), (18, 13), (19, 6), (8, 5), (0, 7), (7, 5), (24, 21), (9, 17), (5, 13), (8, 23), (21, 21), (13, 8), (23, 7), (10, 19), (4, 17), (22, 17), (19, 5), (16, 21), (15, 14), (1, 12), (21, 5), (10, 23), (19, 17), (2, 3), (16, 22), (17, 10), (24, 7), (12, 3), (22, 1), (5, 1), (3, 14), (17, 17), (5, 0), (11, 8), (24, 5), (16, 1), (1, 17), (12, 7), (15, 13), (13, 1), (9, 6), (6, 20), (11, 13), (17, 21), (7, 16), (13, 3), (2, 15), (4, 19), (8, 11), (22, 2), (12, 17), (2, 19), (6, 4), (9, 7), (22, 19), (12, 12), (3, 18), (23, 16), (0, 10), (16, 16), (11, 7), (18, 22), (14, 6), (7, 22), (17, 14), (1, 23), (15, 3), (14, 20), (2, 10), (13, 11), (20, 18), (1, 9), (6, 23), (24, 2), (8, 20), (14, 8), (5, 16), (20, 22), (19, 12), (17, 16), (20, 8), (10, 13), (9, 18), (6, 14), (23, 19), (5, 21), (1, 11), (7, 7), (19, 13), (9, 22), (24, 17), (16, 4), (23, 21), (17, 23), (1, 6), (0, 22), (13, 9), (14, 14), (8, 9), (19, 4), (9, 14), (7, 18), (11, 1), (14, 10), (24, 16), (10, 8), (2, 21), (22, 9), (9, 12), (15, 8), (9, 23), (3, 8), (8, 0), (9, 11), (17, 2), (6, 11), (17, 0), (15, 21), (21, 17), (19, 10), (16, 9), (23, 2), (2, 20), (9, 13), (15, 10), (1, 8), (11, 4), (18, 18), (23, 10), (24, 11), (10, 9), (7, 3), (7, 20), (10, 7), (12, 16), (14, 18), (20, 6), (23, 9), (13, 2), (15, 9), (11, 3), (7, 4), (11, 12), (14, 19), (11, 17), (5, 11), (8, 14), (4, 8), (22, 4), (22, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "927828", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 8), (23, 14), (22, 19), (11, 4), (12, 14), (23, 9), (7, 1), (15, 5), (14, 6), (9, 10), (10, 11), (4, 0), (8, 15), (5, 18), (16, 6), (8, 2), (14, 3), (17, 7), (16, 2), (19, 16), (17, 18), (4, 9), (0, 14), (19, 1), (12, 11), (7, 2), (22, 4), (22, 16), (1, 19), (19, 5), (5, 2), (10, 4), (2, 18), (7, 11), (3, 1), (19, 18), (1, 8), (7, 5), (0, 5), (8, 10), (16, 14), (5, 0), (6, 10), (4, 8), (5, 19), (17, 0), (3, 11), (3, 16), (21, 13), (7, 19), (18, 6), (4, 3), (22, 6), (9, 18), (8, 16), (17, 4), (4, 14), (20, 3), (12, 10), (11, 8), (22, 13), (21, 3), (17, 1), (18, 19), (1, 16), (5, 1), (14, 1), (10, 13), (8, 19), (3, 7), (24, 4), (21, 19), (20, 16), (9, 11), (11, 16), (14, 0), (20, 2), (9, 3), (14, 10), (17, 11), (3, 19), (16, 16), (18, 15), (22, 11), (15, 16), (23, 13), (18, 10), (2, 15), (9, 9), (12, 18), (2, 19), (18, 13), (3, 0), (18, 11), (18, 2), (8, 12), (12, 9), (5, 8), (2, 7), (24, 14), (10, 8), (20, 17), (9, 0), (0, 3), (22, 2), (19, 4), (21, 0), (15, 0), (15, 8), (24, 9), (18, 17), (4, 11), (4, 18), (21, 14), (15, 14), (15, 2), (15, 6), (10, 10), (11, 15), (8, 8), (6, 14), (0, 16), (21, 5), (24, 1), (15, 1), (13, 9), (13, 7), (9, 8), (21, 18), (12, 4), (1, 11), (7, 3), (10, 19), (24, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426195", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), 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), (20, 4), (6, 2), (1, 20), (16, 0), (7, 5), (1, 11), (16, 4), (23, 12), (14, 8), (21, 7), (20, 13), (4, 9), (4, 22), (14, 5), (1, 21), (14, 26), (4, 16), (11, 4), (5, 13), (1, 26), (1, 3), (25, 3), (0, 3), (23, 4), (8, 26), (23, 5), (15, 13), (25, 19), (21, 10), (8, 9), (22, 20), (12, 22), (6, 4), (14, 25), (18, 9), (7, 7), (26, 14), (1, 6), (7, 4), (24, 10), (24, 7), (21, 12), (10, 15), (25, 14), (21, 18), (21, 0), (22, 23), (20, 3), (23, 25), (1, 25), (5, 8), (9, 26), (0, 2), (26, 4), (7, 0), (17, 24), (10, 7), (23, 24), (17, 13), (19, 11), (18, 18), (6, 3), (25, 6), (23, 22), (10, 22), (3, 14), (5, 5), (16, 15), (16, 1), (5, 1), (11, 14), (4, 1), (19, 21), (15, 19), (17, 26), (14, 20), (12, 11), (4, 23), (14, 24), (15, 2), (24, 5), (13, 2), (17, 12), (18, 26), (10, 2), (8, 14), (20, 18), (14, 17), (3, 2), (24, 4), (26, 24), (8, 4), (17, 16), (25, 1), (6, 17), (6, 15), (21, 13), (4, 19), (14, 2), (1, 14), (1, 17), (2, 5), (7, 2), (21, 2), (17, 19), (6, 10), (5, 18), (6, 0), (1, 12), (22, 1), (5, 20), (20, 25), (14, 0), (4, 17), (14, 10), (18, 25), (2, 23), (23, 20), (23, 9), (11, 17), (14, 7), (10, 12), (11, 13), (20, 24), (10, 0), (5, 19), (15, 4), (25, 16), (26, 6), (24, 22), (7, 20), (22, 24), (7, 17), (21, 16), (24, 17), (17, 7), (26, 23), (3, 18), (5, 15), (5, 0), (4, 25), (5, 2), (4, 7), (20, 20), (17, 0), (19, 25), (24, 1), (12, 5), (14, 4), (9, 9), (12, 4), (26, 7), (13, 6), (21, 1), (25, 10), (16, 23), (3, 4), (17, 20), (15, 20), (26, 25), (15, 8), (14, 13), (24, 16), (2, 9), (16, 7), (18, 16), (26, 13), (8, 0), (8, 3), (15, 10), (14, 19), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "835545", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (22, 4), (21, 5), (7, 19), (24, 13), (19, 4), (27, 1), (27, 9), (19, 18), (4, 9), (26, 13), (11, 11), (13, 1), (8, 5), (6, 17), (9, 7), (11, 0), (17, 6), (6, 14), (15, 19), (22, 2), (19, 9), (14, 19), (23, 15), (22, 8), (23, 7), (7, 1), (13, 3), (18, 10), (15, 9), (8, 0), (8, 8), (0, 7), (3, 16), (13, 0), (9, 10), (7, 4), (24, 10), (26, 10), (11, 1), (6, 19), (18, 15), (16, 10), (18, 0), (25, 8), (12, 9), (0, 16), (25, 1), (20, 19), (10, 15), (24, 14), (21, 4), (26, 3), (4, 16), (14, 13), (25, 5), (10, 19), (21, 2), (2, 10), (13, 2), (20, 18), (19, 1), (27, 6), (4, 14), (7, 10), (17, 4), (8, 15), (24, 5), (0, 6), (3, 18), (13, 6), (10, 5), (2, 5), (9, 11), (7, 2), (15, 17), (12, 10), (7, 11), (21, 7), (19, 15), (15, 0), (25, 11), (26, 18), (5, 9), (16, 2), (7, 3), (19, 14), (14, 6), (12, 8), (15, 2), (21, 14), (7, 14), (2, 17), (0, 11), (5, 10), (10, 0), (2, 6), (0, 17), (11, 13), (12, 2), (24, 19), (7, 5), (27, 4), (5, 3), (27, 15), (0, 10), (8, 16), (13, 15), (16, 8), (19, 7), (4, 8), (22, 17), (16, 11), (24, 15), (17, 2), (9, 2), (11, 3), (11, 15), (26, 11), (3, 3), (11, 6), (10, 7), (10, 1), (26, 0), (23, 8), (17, 18), (4, 12), (26, 17), (1, 19), (0, 14), (14, 16), (13, 7), (8, 18), (1, 11), (21, 0), (12, 7), (15, 10), (15, 11), (26, 6), (12, 1), (12, 15), (12, 11), (25, 15), (19, 13), (8, 10), (15, 5), (4, 1), (23, 1), (11, 10), (10, 3), (14, 2), (7, 6), (7, 16), (22, 0), (5, 4), (27, 5), (6, 1), (22, 13), (0, 8), (8, 3), (2, 9), (7, 18), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "669682", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 22), (16, 3), (23, 0), (22, 22), (19, 6), (14, 4), (10, 20), (8, 5), (5, 14), (4, 18), (16, 16), (23, 5), (21, 15), (22, 9), (23, 13), (22, 21), (23, 12), (12, 3), (1, 1), (8, 14), (20, 6), (19, 16), (1, 25), (12, 18), (5, 7), (23, 11), (8, 0), (9, 11), (20, 14), (3, 4), (16, 14), (4, 6), (13, 15), (19, 9), (23, 19), (16, 6), (5, 10), (22, 7), (19, 12), (4, 12), (14, 5), (17, 4), (0, 16), (13, 2), (20, 2), (19, 14), (22, 25), (19, 18), (3, 15), (14, 16), (10, 21), (19, 22), (11, 18), (1, 5), (8, 13), (3, 18), (13, 19), (7, 5), (10, 25), (10, 18), (7, 15), (6, 8), (16, 21), (8, 19), (2, 22), (17, 15), (20, 10), (1, 22), (10, 24), (3, 17), (2, 12), (15, 19), (11, 0), (21, 4), (16, 2), (9, 16), (16, 8), (17, 25), (23, 16), (2, 13), (1, 20), (17, 0), (12, 12), (1, 2), (20, 5), (13, 18), (7, 0), (4, 15), (13, 13), (17, 5), (11, 2), (19, 19), (5, 11), (8, 25), (21, 14), (22, 19), (4, 20), (2, 14), (7, 12), (10, 3), (4, 22), (1, 12), (13, 21), (7, 10), (23, 22), (7, 2), (4, 9), (11, 13), (3, 14), (3, 7), (15, 7), (9, 4), (5, 19), (18, 0), (13, 14), (14, 9), (5, 25), (9, 21), (15, 0), (13, 10), (5, 23), (18, 12), (10, 8), (0, 1), (20, 23), (16, 23), (15, 15), (9, 9), (9, 2), (8, 8), (3, 23), (17, 18), (0, 18), (11, 19), (10, 9), (6, 15), (11, 8), (2, 4), (3, 12), (17, 11), (3, 6), (11, 5), (6, 17), (14, 22), (20, 19), (22, 23), (13, 1), (11, 12), (16, 15), (0, 4), (10, 5), (19, 5), (14, 7), (15, 12), (1, 10), (2, 11), (17, 9), (11, 23), (11, 16), (3, 3), (13, 6), (3, 13), (1, 16), (6, 12), (17, 3), (11, 4), (6, 14), (23, 17), (6, 23), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209280", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), 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), (13, 18), (13, 15), (5, 8), (9, 6), (19, 16), (1, 18), (8, 2), (15, 10), (9, 10), (15, 8), (14, 14), (14, 17), (1, 0), (15, 6), (14, 1), (0, 18), (11, 15), (7, 6), (8, 8), (1, 1), (10, 15), (17, 6), (3, 16), (5, 17), (2, 4), (8, 16), (5, 18), (12, 7), (14, 12), (0, 6), (7, 4), (5, 1), (20, 1), (20, 7), (5, 19), (17, 16), (20, 14), (15, 16), (4, 16), (19, 6), (16, 4), (18, 9), (1, 2), (8, 10), (8, 6), (12, 12), (0, 9), (10, 18), (13, 9), (3, 1), (16, 9), (14, 10), (10, 6), (13, 8), (16, 19), (7, 19), (20, 10), (19, 19), (0, 4), (7, 15), (10, 9), (16, 11), (1, 19), (4, 6), (11, 6), (13, 7), (9, 19), (11, 4), (14, 0), (3, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964516", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 21), (12, 1), (1, 6), (2, 13), (10, 16), (3, 9), (11, 16), (10, 19), (16, 10), (15, 3), (7, 1), (15, 2), (10, 18), (10, 3), (11, 6), (19, 4), (15, 8), (8, 1), (11, 21), (13, 0), (5, 14), (11, 12), (0, 10), (9, 4), (6, 20), (5, 9), (3, 19), (14, 13), (9, 15), (13, 22), (8, 19), (15, 21), (6, 7), (14, 7), (3, 4), (14, 8), (16, 7), (2, 9), (7, 21), (18, 8), (15, 10), (12, 23), (13, 11), (2, 10), (16, 5), (9, 9), (14, 14), (4, 15), (17, 13), (5, 15), (18, 10), (17, 19), (15, 22), (12, 2), (16, 18), (13, 12), (4, 10), (10, 10), (3, 15), (11, 18), (11, 7), (1, 7), (7, 19), (13, 19), (8, 18), (11, 9), (9, 0), (9, 20), (11, 23), (10, 23), (11, 2), (15, 0), (13, 16), (16, 21), (0, 6), (2, 20), (18, 1), (12, 22), (3, 10), (6, 15), (15, 13), (3, 23), (9, 12), (3, 7), (0, 17), (15, 16), (14, 19), (0, 3), (8, 13), (10, 0), (12, 5), (5, 17), (7, 22), (14, 15), (10, 1), (4, 2), (0, 22), (14, 9), (1, 4), (9, 3), (11, 13), (13, 17), (18, 14), (4, 5), (19, 1), (19, 6), (14, 5), (8, 4), (5, 16), (15, 7), (7, 10), (17, 21), (18, 12), (6, 22), (4, 20), (0, 11), (0, 2), (6, 13), (5, 10), (6, 1), (7, 18), (19, 12), (19, 0), (7, 13), (18, 4), (6, 4), (9, 14), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724023", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), 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), (9, 19), (0, 19), (3, 19), (4, 16), (6, 8), (5, 3), (15, 0), (18, 1), (15, 18), (15, 9), (18, 13), (7, 15), (1, 7), (14, 5), (8, 15), (19, 17), (14, 16), (18, 12), (18, 6), (3, 13), (12, 19), (12, 11), (6, 15), (2, 17), (0, 2), (14, 4), (17, 18), (12, 16), (16, 19), (10, 13), (16, 5), (5, 13), (10, 12), (5, 11), (16, 16), (12, 6), (0, 18), (4, 4), (18, 0), (17, 9), (17, 11), (2, 7), (11, 15), (17, 6), (11, 4), (10, 9), (7, 11), (0, 4), (13, 2), (7, 8), (5, 19), (9, 1), (15, 11), (8, 12), (8, 8), (16, 1), (1, 14), (3, 11), (17, 0), (15, 17), (0, 17), (19, 9), (4, 1), (15, 1), (6, 13), (1, 1), (9, 13), (4, 13), (3, 1), (11, 8), (15, 4), (15, 5), (3, 6), (12, 8), (9, 11), (13, 4), (7, 7), (7, 16), (16, 10), (9, 14), (13, 0), (2, 3), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "819488", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 1), (3, 20), (15, 25), (21, 3), (21, 12), (17, 11), (3, 1), (20, 12), (20, 18), (3, 21), (17, 15), (0, 12), (14, 4), (18, 26), (9, 20), (17, 16), (2, 2), (15, 19), (2, 22), (13, 23), (4, 5), (15, 2), (12, 1), (12, 22), (8, 5), (9, 22), (7, 21), (1, 9), (10, 23), (18, 25), (16, 8), (0, 19), (18, 21), (14, 19), (6, 17), (9, 6), (2, 0), (1, 21), (18, 1), (13, 26), (7, 4), (20, 14), (10, 15), (11, 6), (15, 26), (5, 9), (10, 1), (9, 8), (15, 23), (6, 20), (6, 1), (7, 13), (7, 17), (21, 9), (20, 25), (17, 22), (5, 0), (6, 3), (19, 21), (12, 24), (15, 17), (14, 20), (21, 14), (7, 5), (5, 10), (9, 7), (3, 8), (16, 12), (8, 25), (16, 16), (17, 6), (16, 14), (13, 0), (10, 12), (20, 21), (7, 9), (0, 23), (10, 26), (1, 5), (0, 16), (20, 22), (14, 16), (5, 8), (17, 14), (14, 23), (9, 14), (5, 23), (14, 12), (6, 8), (21, 16), (3, 18), (4, 16), (21, 1), (6, 16), (1, 25), (19, 5), (2, 16), (12, 2), (3, 17), (13, 11), (18, 9), (17, 4), (16, 9), (5, 18), (14, 14), (14, 0), (11, 13), (16, 24), (3, 2), (17, 1), (2, 4), (17, 9), (1, 17), (10, 14), (17, 0), (8, 3), (15, 4), (16, 1), (20, 3), (2, 7), (19, 4), (1, 11), (15, 21), (16, 4), (0, 10), (8, 13), (20, 8), (6, 21), (12, 15), (20, 2), (18, 11), (4, 18), (14, 10), (10, 19), (12, 5), (20, 15), (4, 7), (1, 12), (5, 4), (13, 4), (4, 19), (13, 14), (19, 8), (9, 18), (19, 13), (0, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37128", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 11), (8, 19), (4, 19), (4, 4), (14, 1), (9, 8), (10, 2), (8, 6), (1, 17), (4, 3), (17, 3), (4, 2), (2, 4), (2, 19), (9, 3), (19, 11), (7, 22), (17, 17), (20, 5), (10, 10), (10, 19), (18, 6), (9, 18), (23, 22), (23, 12), (3, 9), (5, 12), (3, 19), (9, 21), (6, 22), (19, 13), (24, 9), (3, 6), (11, 8), (2, 1), (1, 9), (7, 4), (0, 16), (22, 9), (21, 22), (12, 13), (20, 17), (14, 6), (18, 5), (23, 10), (7, 7), (23, 11), (14, 23), (23, 23), (7, 19), (23, 15), (6, 0), (4, 20), (22, 3), (24, 15), (2, 3), (23, 18), (14, 24), (11, 7), (0, 26), (8, 4), (13, 15), (5, 9), (12, 16), (12, 9), (21, 4), (10, 5), (17, 1), (21, 2), (10, 24), (22, 19), (20, 11), (1, 24), (10, 1), (5, 8), (16, 13), (4, 10), (22, 7), (6, 12), (3, 20), (2, 20), (15, 6), (18, 19), (4, 24), (13, 18), (7, 8), (17, 8), (4, 0), (3, 14), (2, 10), (11, 25), (2, 14), (2, 5), (14, 11), (13, 12), (11, 24), (6, 17), (8, 16), (17, 26), (12, 10), (16, 1), (23, 13), (15, 12), (15, 18), (4, 17), (10, 11), (6, 15), (11, 16), (13, 26), (20, 19), (20, 2), (10, 4), (3, 25), (13, 25), (9, 13), (24, 1), (0, 6), (12, 4), (0, 24), (24, 21), (10, 16), (8, 7), (16, 14), (9, 12), (19, 20), (14, 7), (20, 13), (8, 15), (4, 13), (19, 6), (5, 3), (0, 13), (3, 24), (19, 9), (17, 6), (17, 25), (10, 23), (5, 6), (16, 5), (21, 23), (11, 9), (16, 23), (0, 3), (14, 14), (12, 11), (10, 3), (8, 22), (8, 26), (15, 19), (16, 25), (20, 20), (23, 16), (22, 10), (18, 18), (3, 26), (13, 9), (0, 10), (24, 12), (24, 3), (14, 12), (22, 8), (3, 0), (11, 11), (23, 24), (3, 11), (19, 4), (13, 20), (9, 10), (11, 6), (5, 24), (9, 15), (24, 18), (21, 8), (19, 0), (0, 9), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564372", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 23), (23, 7), (7, 7), (13, 0), (5, 18), (27, 1), (5, 2), (9, 0), (24, 16), (24, 17), (12, 23), (3, 18), (18, 13), (14, 15), (21, 7), (15, 1), (0, 4), (21, 9), (7, 8), (1, 1), (23, 15), (23, 13), (5, 5), (4, 19), (12, 3), (25, 1), (11, 6), (26, 12), (1, 5), (16, 11), (13, 21), (25, 3), (9, 2), (11, 3), (14, 7), (26, 15), (1, 9), (5, 25), (1, 23), (7, 3), (22, 22), (25, 14), (2, 24), (16, 0), (2, 22), (9, 14), (23, 16), (6, 23), (19, 7), (14, 2), (20, 19), (12, 25), (26, 4), (13, 25), (19, 2), (25, 23), (0, 9), (23, 10), (9, 24), (3, 8), (10, 17), (22, 11), (9, 12), (24, 22), (20, 11), (9, 15), (0, 15), (23, 17), (8, 11), (23, 5), (17, 22), (5, 13), (4, 9), (26, 24), (20, 20), (14, 22), (22, 3), (21, 6), (22, 24), (20, 16), (8, 1), (7, 1), (18, 10), (11, 23), (2, 15), (26, 22), (23, 24), (9, 6), (22, 5), (18, 19), (9, 11), (2, 8), (19, 13), (12, 24), (18, 20), (22, 15), (26, 18), (22, 13), (3, 5), (25, 5), (27, 16), (18, 22), (15, 16), (23, 8), (11, 1), (21, 5), (18, 8), (17, 6), (23, 0), (3, 12), (6, 5), (5, 9), (0, 21), (26, 0), (26, 5), (10, 1), (13, 9), (13, 6), (7, 25), (0, 10), (2, 3), (27, 21), (21, 16), (4, 21), (14, 23), (1, 8), (22, 7), (16, 6), (8, 14), (3, 13), (26, 2), (6, 11), (20, 13), (6, 25), (5, 20), (11, 10), (6, 2), (6, 12), (22, 2), (16, 4), (17, 21), (10, 11), (19, 8), (16, 10), (10, 12), (21, 22), (14, 25), (11, 19), (16, 3), (12, 5), (8, 7), (5, 24), (5, 4), (19, 18), (10, 19), (23, 3), (22, 16), (13, 15), (13, 2), (7, 24), (5, 12), (11, 9), (24, 13), (22, 18), (15, 14), (1, 6), (4, 2), (9, 5), (26, 20), (22, 17), (22, 21), (12, 11), (26, 19), (23, 6), (20, 0), (23, 18), (16, 16), (0, 25), (13, 17), (1, 21), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170016", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 5), (2, 7), (7, 20), (20, 19), (15, 0), (4, 7), (4, 2), (23, 9), (10, 7), (9, 8), (20, 21), (12, 3), (19, 20), (8, 9), (21, 24), (21, 5), (4, 11), (4, 17), (0, 2), (23, 17), (10, 16), (9, 14), (9, 26), (18, 7), (4, 18), (19, 3), (23, 24), (21, 21), (18, 12), (14, 22), (18, 14), (19, 2), (23, 20), (4, 16), (21, 26), (19, 22), (2, 12), (0, 8), (3, 12), (10, 14), (4, 26), (18, 6), (19, 4), (3, 2), (12, 5), (7, 8), (18, 24), (6, 0), (14, 5), (17, 1), (2, 25), (13, 18), (14, 17), (10, 4), (11, 18), (3, 19), (0, 16), (7, 3), (20, 11), (15, 20), (13, 17), (20, 22), (21, 25), (1, 5), (11, 16), (9, 16), (7, 21), (20, 14), (11, 7), (11, 8), (18, 17), (16, 22), (5, 3), (9, 19), (20, 17), (22, 16), (16, 19), (16, 5), (20, 10), (7, 17), (3, 23), (9, 20), (8, 1), (10, 3), (20, 18), (0, 11), (18, 20), (11, 11), (12, 16), (12, 25), (13, 5), (8, 4), (12, 14), (3, 24), (8, 22), (10, 25), (22, 19), (22, 6), (6, 11), (21, 8), (23, 16), (0, 15), (15, 21), (5, 26), (17, 23), (16, 7), (13, 16), (15, 2), (3, 17), (0, 4), (16, 4), (9, 24), (13, 1), (19, 12), (0, 17), (11, 13), (4, 13), (17, 4), (8, 16), (14, 3), (15, 13), (6, 4), (0, 26), (17, 10), (9, 21), (19, 5), (15, 10), (1, 20), (9, 4), (20, 12), (2, 4), (4, 8), (11, 17), (14, 20), (5, 25), (4, 3), (23, 19), (6, 17), (17, 21), (13, 22), (19, 17), (16, 24), (8, 6), (18, 2), (1, 11), (7, 11), (23, 2), (7, 25), (20, 15), (18, 23), (22, 1), (16, 16), (17, 19), (21, 15), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "834798", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 22), (1, 15), (10, 9), (3, 17), (13, 27), (5, 23), (0, 15), (1, 25), (1, 24), (13, 26), (13, 13), (19, 19), (9, 26), (2, 18), (5, 5), (7, 12), (18, 11), (5, 13), (19, 22), (13, 18), (15, 15), (3, 9), (7, 26), (11, 27), (18, 9), (4, 3), (7, 14), (15, 14), (14, 24), (6, 4), (0, 22), (11, 20), (8, 2), (6, 26), (5, 15), (19, 16), (3, 4), (12, 8), (1, 1), (12, 5), (10, 2), (8, 10), (4, 14), (7, 5), (9, 4), (1, 5), (3, 12), (2, 13), (4, 8), (13, 6), (2, 22), (7, 25), (16, 4), (8, 25), (11, 6), (16, 25), (1, 27), (10, 19), (15, 4), (15, 16), (6, 10), (11, 5), (19, 6), (5, 14), (3, 13), (7, 7), (9, 5), (9, 18), (2, 27), (5, 12), (13, 2), (17, 23), (9, 0), (12, 13), (9, 6), (9, 20), (13, 7), (12, 4), (18, 0), (4, 24), (11, 15), (1, 20), (11, 25), (8, 8), (7, 24), (5, 6), (17, 26), (0, 7), (1, 9), (11, 3), (18, 10), (3, 8), (17, 4), (17, 9), (2, 11), (2, 2), (13, 0), (18, 4), (3, 6), (18, 6), (1, 23), (0, 19), (8, 15), (11, 21), (16, 15), (1, 0), (18, 24), (11, 4), (5, 26), (11, 19), (2, 20), (11, 8), (18, 2), (10, 18), (4, 22), (7, 27), (14, 21), (10, 6), (16, 13), (18, 13), (7, 2), (10, 22), (1, 18), (8, 9), (6, 25), (18, 27), (7, 0), (18, 14), (11, 26), (10, 12), (15, 19), (3, 18), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565992", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 12), (8, 2), (6, 12), (1, 18), (19, 8), (7, 2), (24, 18), (27, 10), (12, 17), (10, 15), (17, 3), (25, 1), (2, 8), (0, 16), (20, 2), (8, 14), (16, 7), (6, 7), (3, 13), (27, 9), (2, 12), (22, 4), (13, 10), (13, 12), (15, 4), (16, 2), (1, 2), (25, 9), (18, 7), (15, 18), (19, 7), (9, 12), (8, 13), (0, 5), (8, 0), (22, 11), (25, 11), (2, 15), (5, 3), (4, 10), (8, 12), (12, 12), (10, 6), (20, 4), (19, 1), (27, 2), (7, 6), (18, 17), (17, 5), (6, 17), (20, 18), (23, 13), (2, 9), (20, 16), (5, 4), (10, 10), (5, 11), (7, 1), (5, 5), (10, 2), (21, 12), (21, 18), (18, 1), (1, 19), (21, 1), (14, 13), (6, 8), (26, 18), (24, 1), (17, 2), (14, 4), (17, 14), (22, 10), (25, 4), (24, 5), (10, 18), (16, 18), (27, 15), (1, 16), (5, 12), (25, 5), (5, 15), (20, 17), (4, 7), (27, 8), (23, 1), (13, 19), (15, 12), (10, 19), (24, 10), (2, 17), (17, 15), (5, 16), (8, 6), (9, 13), (8, 4), (13, 14), (23, 2), (2, 5), (24, 9), (17, 17), (4, 6), (4, 5), (23, 16), (23, 8), (8, 16), (3, 4), (14, 11), (1, 3), (3, 12), (8, 1), (26, 13), (12, 11), (27, 4), (2, 4), (18, 3), (5, 8), (16, 19), (13, 17), (10, 11), (11, 0), (13, 1), (14, 10), (19, 13), (25, 14), (14, 3), (7, 0), (23, 10), (14, 19), (1, 5), (4, 14), (25, 8), (4, 9), (21, 8), (6, 4), (9, 2), (1, 11), (18, 11), (26, 3), (0, 10), (21, 15), (25, 2), (6, 19), (2, 18), (9, 16), (3, 9), (20, 14), (9, 6), (18, 5), (2, 16), (26, 8), (19, 19), (26, 1), (17, 12), (18, 16), (10, 1), (27, 7), (24, 6), (13, 5), (4, 11), (27, 17), (5, 0), (24, 0), (7, 7), (12, 6), (11, 11), (9, 5), (24, 7), (10, 16), (23, 4), (9, 0), (14, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657800", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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), (1, 0), (2, 13), (10, 21), (20, 20), (13, 6), (11, 19), (12, 11), (5, 10), (13, 1), (5, 6), (9, 13), (8, 8), (16, 18), (15, 5), (19, 12), (22, 3), (11, 9), (15, 14), (22, 1), (3, 22), (19, 0), (18, 21), (5, 20), (20, 6), (10, 15), (6, 5), (4, 7), (13, 9), (16, 3), (4, 3), (6, 16), (16, 10), (12, 15), (10, 24), (8, 5), (17, 4), (2, 6), (16, 24), (15, 19), (0, 5), (16, 21), (13, 8), (19, 16), (12, 22), (6, 4), (18, 4), (9, 21), (14, 1), (18, 20), (7, 2), (18, 25), (1, 11), (19, 13), (14, 14), (22, 15), (20, 12), (14, 6), (2, 26), (12, 26), (11, 11), (11, 20), (0, 24), (14, 20), (17, 22), (17, 23), (20, 24), (1, 16), (5, 2), (16, 4), (20, 18), (4, 21), (1, 25), (9, 5), (19, 5), (21, 4), (0, 16), (19, 18), (9, 2), (12, 8), (5, 21), (19, 22), (11, 16), (17, 9), (3, 26), (6, 3), (17, 25), (22, 24), (4, 17), (9, 4), (21, 16), (9, 17), (18, 2), (15, 24), (9, 18), (1, 1), (10, 20), (13, 20), (22, 25), (11, 10), (7, 14), (8, 11), (9, 20), (7, 9), (8, 10), (22, 20), (19, 11), (5, 8), (5, 19), (21, 0), (15, 16), (15, 25), (8, 23), (4, 8), (14, 24), (10, 3), (11, 24), (20, 22), (2, 24), (2, 9), (21, 7), (6, 25), (7, 26), (7, 21), (18, 10), (0, 19), (22, 6), (16, 7), (9, 7), (6, 9), (13, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920056", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 24), (7, 21), (17, 0), (20, 20), (4, 5), (1, 27), (24, 20), (0, 9), (21, 19), (3, 9), (18, 4), (8, 0), (15, 2), (2, 4), (24, 1), (8, 4), (13, 4), (12, 27), (7, 12), (6, 25), (2, 21), (21, 20), (10, 6), (5, 7), (4, 3), (21, 22), (24, 4), (9, 2), (21, 8), (21, 5), (14, 8), (3, 14), (10, 26), (15, 13), (2, 16), (10, 23), (12, 5), (15, 20), (22, 22), (16, 26), (8, 12), (19, 21), (12, 8), (24, 3), (24, 24), (2, 15), (6, 15), (3, 19), (0, 21), (2, 26), (23, 22), (10, 27), (10, 16), (23, 5), (0, 18), (23, 21), (13, 10), (15, 14), (19, 16), (19, 19), (3, 16), (3, 1), (10, 5), (18, 9), (14, 22), (11, 5), (15, 21), (18, 5), (22, 12), (1, 2), (13, 21), (10, 8), (8, 22), (11, 23), (12, 20), (20, 21), (18, 25), (13, 27), (2, 9), (21, 12), (18, 6), (0, 15), (18, 11), (23, 9), (14, 6), (12, 25), (18, 17), (21, 23), (11, 2), (24, 19), (3, 22), (19, 6), (18, 24), (12, 11), (4, 17), (5, 14), (18, 3), (22, 15), (5, 24), (19, 12), (21, 9), (12, 12), (18, 19), (0, 24), (23, 13), (16, 6), (9, 3), (23, 6), (19, 4), (11, 14), (14, 15), (10, 18), (0, 4), (13, 17), (0, 11), (4, 15), (16, 3), (24, 17), (21, 7), (6, 22), (9, 25), (14, 17), (16, 20), (3, 21), (13, 20), (1, 19), (2, 8), (19, 9), (14, 25), (7, 17), (5, 18), (5, 12), (15, 24), (23, 14), (11, 25), (10, 0), (16, 14), (14, 10), (8, 3), (20, 19), (14, 5), (17, 2), (9, 20), (0, 16), (6, 9), (1, 0), (21, 24), (1, 12), (0, 22), (22, 11), (22, 10), (22, 16), (0, 17), (2, 24), (14, 7), (1, 4), (7, 4), (22, 20), (7, 10), (1, 10), (10, 2), (19, 3), (8, 8), (17, 18), (4, 22), (14, 2), (24, 0), (4, 13), (2, 18), (14, 19), (20, 16), (16, 25), (1, 26), (11, 8), (3, 26), (14, 16), (4, 16), (9, 16), (1, 1), (16, 21), (16, 7), (0, 12), (16, 12), (16, 24), (24, 26), (8, 1), (19, 5), (14, 11), (12, 13), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947370", "dataset": "MATH"}
{"messages": [{"content": "In a 29x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 3), (1, 14), (21, 6), (15, 7), (27, 11), (27, 9), (7, 5), (16, 1), (0, 10), (4, 4), (14, 2), (1, 1), (2, 12), (24, 16), (2, 21), (12, 20), (11, 9), (26, 0), (22, 2), (20, 9), (13, 21), (0, 6), (18, 18), (11, 16), (24, 12), (12, 22), (28, 0), (28, 19), (6, 21), (1, 2), (26, 18), (11, 15), (0, 22), (21, 2), (17, 18), (8, 20), (28, 7), (16, 22), (14, 5), (14, 19), (10, 1), (20, 14), (11, 11), (13, 13), (22, 11), (16, 16), (18, 8), (27, 20), (24, 2), (27, 1), (11, 14), (27, 10), (11, 2), (19, 22), (6, 0), (20, 7), (9, 15), (23, 10), (23, 21), (16, 17), (21, 7), (13, 7), (21, 0), (5, 16), (22, 0), (24, 21), (20, 15), (15, 5), (28, 15), (9, 19), (1, 22), (3, 1), (28, 16), (26, 5), (7, 15), (5, 15), (10, 19), (8, 13), (17, 15), (25, 13), (5, 0), (10, 2), (28, 18), (10, 8), (8, 2), (3, 18), (7, 18), (22, 20), (13, 3), (6, 7), (18, 10), (16, 4), (12, 19), (17, 17), (5, 12), (8, 1), (13, 4), (8, 17), (9, 11), (23, 2), (18, 5), (3, 14), (1, 8), (0, 19), (8, 15), (11, 1), (10, 7), (22, 18), (19, 8), (10, 3), (28, 13), (6, 11), (14, 16), (2, 14), (19, 11), (23, 4), (12, 8), (20, 1), (6, 1), (2, 15), (17, 21), (17, 3), (8, 6), (6, 20), (13, 15), (4, 9), (15, 6), (24, 14), (24, 4), (4, 10), (25, 8), (3, 17), (19, 5), (14, 3), (13, 12), (11, 19), (4, 22), (4, 8), (9, 4), (15, 9), (18, 2), (16, 21), (26, 14), (10, 0), (19, 6), (11, 6), (10, 22), (15, 17), (18, 7), (6, 2), (3, 5), (14, 12), (23, 17), (10, 12), (8, 9), (11, 3), (25, 19), (24, 19), (18, 16), (3, 15), (10, 9), (10, 4), (22, 10), (16, 13), (4, 11), (19, 21), (14, 11), (8, 12), (7, 0), (11, 5), (17, 5), (5, 17), (11, 21), (9, 22), (4, 1), (21, 22), (22, 1), (11, 0), (16, 0), (4, 6), (11, 20), (20, 13), (28, 1), (28, 2), (23, 0), (6, 5), (28, 20), (11, 18), (3, 12), (25, 5), (17, 20), (5, 5), (18, 21), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130240", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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, 18), (21, 23), (1, 1), (16, 20), (20, 17), (14, 20), (0, 10), (14, 26), (19, 7), (17, 21), (18, 18), (9, 24), (10, 4), (1, 17), (10, 17), (13, 3), (1, 22), (3, 14), (0, 3), (1, 7), (7, 24), (11, 3), (20, 7), (8, 19), (16, 4), (2, 18), (4, 2), (5, 14), (19, 15), (8, 10), (17, 7), (2, 2), (3, 1), (6, 8), (3, 15), (12, 7), (2, 25), (3, 26), (20, 21), (6, 26), (16, 25), (16, 24), (22, 19), (6, 2), (19, 3), (9, 0), (5, 11), (9, 11), (10, 19), (4, 13), (4, 12), (20, 23), (14, 2), (11, 24), (12, 17), (5, 9), (21, 20), (0, 21), (10, 18), (12, 0), (10, 13), (9, 2), (9, 5), (8, 7), (20, 18), (15, 4), (14, 13), (1, 21), (15, 21), (1, 2), (17, 0), (2, 20), (18, 20), (0, 17), (16, 15), (2, 8), (16, 1), (5, 20), (20, 0), (7, 18), (22, 22), (6, 18), (2, 22), (13, 18), (22, 7), (1, 12), (8, 12), (8, 23), (11, 21), (15, 16), (9, 9), (6, 19), (22, 10), (17, 8), (17, 4), (14, 5), (16, 5), (20, 4), (16, 7), (6, 1), (7, 26), (20, 25), (19, 20), (22, 2), (17, 5), (1, 20), (9, 23), (18, 5), (15, 9), (18, 22), (19, 4), (20, 10), (9, 22), (3, 12), (6, 15), (21, 12), (2, 21), (9, 8), (4, 25), (6, 9), (10, 10), (11, 22), (5, 24), (20, 9), (14, 15), (14, 10), (11, 9), (16, 17), (13, 20), (4, 20), (6, 11), (9, 12), (15, 5), (22, 4), (14, 24), (8, 8), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993736", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (2, 6), (22, 12), (11, 10), (24, 15), (18, 15), (5, 6), (23, 1), (11, 0), (16, 0), (2, 8), (19, 15), (15, 5), (17, 11), (17, 0), (18, 1), (9, 1), (9, 14), (11, 9), (14, 17), (2, 15), (1, 5), (1, 15), (21, 3), (22, 3), (10, 12), (26, 4), (9, 6), (15, 3), (11, 16), (15, 14), (15, 10), (18, 12), (19, 19), (25, 0), (17, 19), (18, 7), (7, 7), (13, 19), (0, 19), (26, 16), (25, 9), (13, 14), (2, 10), (1, 0), (0, 18), (23, 8), (26, 15), (21, 7), (19, 13), (4, 10), (5, 7), (3, 1), (15, 12), (5, 3), (12, 10), (2, 16), (19, 4), (24, 1), (21, 8), (11, 12), (6, 13), (1, 7), (15, 18), (8, 5), (14, 2), (25, 6), (24, 14), (22, 4), (7, 0), (24, 11), (26, 17), (17, 2), (21, 9), (6, 5), (14, 16), (1, 9), (22, 0), (7, 12), (22, 2), (22, 8), (12, 5), (13, 18), (8, 18), (7, 10), (22, 19), (9, 11), (19, 6), (24, 9), (15, 6), (11, 3), (25, 16), (23, 16), (2, 14), (16, 18), (11, 8), (7, 9), (16, 15), (4, 5), (12, 11), (17, 4), (23, 15), (6, 4), (5, 18), (0, 3), (21, 11), (26, 8), (10, 6), (16, 6), (12, 7), (14, 18), (12, 19), (0, 12), (3, 8), (20, 17), (16, 2), (12, 18), (26, 0), (5, 5), (12, 9), (9, 19), (17, 13), (2, 11), (19, 10), (17, 16), (26, 3), (8, 6), (21, 18), (5, 17), (16, 8), (25, 1), (10, 9), (22, 9), (4, 6), (26, 9), (18, 5), (15, 7), (24, 2), (23, 11), (22, 7), (12, 16), (24, 12), (9, 8), (6, 8), (13, 17), (15, 13), (8, 14), (18, 9), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "737919", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 11), (10, 4), (24, 10), (6, 22), (23, 4), (9, 15), (9, 5), (25, 24), (5, 11), (21, 21), (14, 5), (15, 15), (18, 1), (8, 19), (0, 4), (7, 17), (20, 16), (15, 3), (7, 0), (2, 22), (0, 26), (12, 7), (8, 1), (16, 19), (7, 2), (4, 16), (11, 11), (12, 19), (17, 23), (23, 0), (14, 9), (8, 12), (6, 9), (3, 7), (22, 5), (6, 25), (10, 5), (0, 11), (10, 15), (20, 22), (7, 5), (27, 4), (14, 20), (6, 17), (23, 10), (25, 19), (12, 14), (5, 18), (8, 0), (17, 15), (13, 9), (25, 3), (14, 26), (24, 17), (19, 12), (16, 8), (21, 8), (24, 14), (24, 6), (20, 21), (25, 23), (25, 20), (17, 21), (2, 9), (10, 23), (18, 13), (15, 8), (0, 12), (15, 13), (10, 14), (16, 1), (21, 24), (1, 13), (2, 5), (24, 26), (15, 20), (9, 26), (19, 21), (18, 24), (27, 6), (14, 24), (13, 8), (25, 9), (1, 14), (4, 12), (19, 18), (27, 21), (17, 10), (9, 12), (24, 3), (25, 11), (10, 1), (3, 14), (19, 4), (17, 4), (16, 9), (14, 6), (6, 5), (22, 23), (6, 24), (25, 0), (26, 5), (18, 11), (3, 17), (19, 20), (19, 14), (2, 4), (13, 18), (14, 0), (16, 16), (11, 0), (20, 13), (5, 19), (20, 2), (4, 13), (23, 14), (19, 16), (9, 17), (10, 12), (18, 20), (25, 16), (27, 20), (22, 18), (27, 18), (8, 2), (23, 6), (1, 15), (5, 15), (2, 3), (20, 0), (13, 10), (15, 7), (1, 9), (15, 21), (21, 3), (20, 10), (26, 19), (14, 3), (7, 25), (26, 26), (24, 12), (24, 1), (11, 6), (11, 22), (7, 26), (2, 2), (23, 17), (4, 14), (17, 8), (12, 12), (16, 17), (2, 17), (22, 7), (22, 3), (15, 17), (21, 11), (11, 10), (17, 25), (2, 7), (13, 23), (22, 4), (17, 20), (25, 6), (4, 11), (1, 8), (27, 22), (9, 23), (7, 6), (10, 25), (8, 16), (4, 17), (27, 12), (0, 16), (15, 0), (17, 17), (6, 11), (23, 21), (18, 6), (22, 25), (6, 2), (25, 7), (19, 15), (15, 11), (13, 1), (22, 21), (10, 13), (23, 1), (11, 18), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114240", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 15), (0, 14), (0, 2), (10, 7), (3, 9), (2, 0), (2, 19), (12, 15), (21, 9), (2, 4), (4, 0), (14, 4), (18, 8), (18, 11), (21, 19), (9, 8), (0, 20), (19, 10), (1, 16), (14, 5), (15, 0), (12, 17), (11, 12), (3, 19), (6, 7), (4, 22), (12, 13), (5, 21), (3, 17), (14, 12), (1, 24), (15, 2), (15, 1), (14, 3), (11, 23), (15, 24), (6, 11), (8, 15), (9, 4), (7, 17), (15, 5), (3, 23), (17, 21), (9, 11), (19, 24), (17, 16), (18, 14), (7, 12), (8, 3), (14, 6), (21, 4), (15, 12), (9, 1), (5, 3), (7, 0), (8, 10), (6, 3), (15, 16), (8, 17), (4, 6), (18, 7), (3, 16), (4, 20), (9, 17), (5, 4), (1, 2), (9, 2), (20, 4), (6, 15), (6, 23), (13, 10), (14, 13), (20, 23), (10, 19), (4, 5), (1, 20), (12, 7), (7, 19), (5, 15), (5, 18), (2, 11), (5, 7), (2, 14), (8, 7), (20, 15), (5, 0), (0, 6), (12, 1), (3, 1), (15, 13), (2, 13), (16, 18), (0, 16), (2, 18), (17, 8), (11, 22), (6, 5), (6, 20), (5, 8), (9, 19), (10, 3), (0, 1), (9, 9), (21, 21), (17, 17), (12, 6), (17, 6), (15, 4), (12, 12), (16, 3), (17, 10), (18, 19), (9, 10), (0, 7), (5, 22), (10, 12), (2, 10), (6, 1), (5, 1), (3, 20), (7, 8), (11, 11), (15, 10), (11, 24), (6, 6), (8, 21), (19, 9), (6, 8), (20, 3), (21, 12), (17, 13), (21, 18), (18, 23), (16, 19), (17, 2), (7, 3), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766468", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), 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), (1, 22), (16, 20), (23, 7), (5, 9), (17, 17), (1, 3), (20, 14), (21, 16), (15, 7), (9, 5), (14, 15), (10, 23), (17, 6), (17, 19), (23, 16), (5, 5), (0, 3), (15, 23), (18, 9), (19, 9), (23, 9), (15, 12), (15, 2), (7, 9), (22, 21), (4, 8), (9, 13), (24, 3), (21, 20), (10, 13), (18, 15), (3, 3), (4, 1), (12, 1), (17, 16), (13, 2), (4, 17), (7, 2), (21, 0), (14, 5), (6, 14), (25, 10), (19, 23), (15, 4), (9, 3), (18, 7), (25, 14), (19, 15), (8, 10), (7, 19), (2, 15), (20, 20), (7, 17), (11, 5), (18, 21), (11, 10), (9, 6), (17, 14), (25, 9), (6, 8), (19, 21), (16, 17), (20, 15), (20, 10), (1, 12), (20, 18), (24, 21), (22, 11), (0, 4), (14, 18), (11, 4), (4, 19), (7, 18), (9, 18), (24, 22), (18, 10), (1, 10), (10, 22), (12, 12), (16, 9), (21, 1), (6, 17), (6, 12), (22, 10), (22, 22), (4, 5), (5, 0), (10, 19), (20, 0), (11, 15), (3, 22), (22, 15), (0, 2), (10, 15), (17, 1), (13, 7), (2, 4), (8, 20), (16, 8), (12, 15), (8, 5), (19, 16), (15, 16), (18, 17), (17, 0), (21, 5), (11, 19), (10, 5), (11, 6), (0, 21), (2, 8), (25, 19), (9, 7), (3, 14), (20, 12), (5, 3), (20, 9), (17, 12), (8, 17), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "837825", "dataset": "MATH"}
{"messages": [{"content": "In a 25x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 23), 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), (4, 3), (5, 3), (22, 8), (23, 14), (4, 0), (3, 1), (11, 1), (3, 3), (12, 6), (3, 5), (0, 21), (16, 15), (20, 16), (17, 2), (22, 11), (4, 19), (12, 4), (19, 8), (18, 0), (0, 15), (2, 2), (0, 20), (0, 16), (12, 17), (16, 12), (20, 20), (21, 14), (20, 2), (15, 0), (5, 9), (24, 8), (9, 22), (13, 17), (17, 8), (9, 14), (8, 14), (19, 14), (4, 22), (13, 3), (5, 2), (14, 16), (20, 15), (16, 22), (11, 10), (13, 7), (8, 20), (22, 1), (12, 1), (24, 10), (15, 14), (24, 5), (1, 15), (12, 2), (10, 7), (15, 10), (6, 7), (2, 18), (13, 1), (16, 1), (7, 17), (0, 11), (13, 4), (10, 6), (19, 5), (10, 23), (15, 16), (6, 15), (19, 9), (12, 8), (19, 17), (15, 19), (9, 8), (14, 5), (18, 2), (18, 20), (18, 16), (22, 17), (13, 0), (12, 3), (4, 17), (16, 21), (21, 1), (22, 16), (8, 1), (12, 16), (7, 14), (16, 2), (7, 11), (9, 6), (14, 12), (10, 12), (0, 19), (18, 9), (20, 1), (11, 17), (8, 16), (20, 8), (17, 1), (24, 17), (24, 14), (19, 13), (5, 4), (15, 9), (8, 9), (2, 17), (22, 4), (10, 1), (0, 5), (15, 8), (12, 10), (8, 7), (12, 7), (15, 2), (21, 15), (9, 21), (14, 8), (21, 12), (11, 23), (1, 19), (4, 4), (11, 3), (24, 22), (15, 12), (10, 2), (8, 17), (5, 11), (0, 10), (11, 8), (14, 2), (24, 4), (8, 23), (1, 7), (2, 20), (17, 23), (21, 17), (11, 19), (16, 23), (15, 6), (24, 1), (14, 9), (18, 13), (8, 4), (24, 3), (19, 21), (20, 12), (19, 2), (21, 5), (13, 9), (18, 8), (5, 15), (17, 3), (15, 13), (22, 15), (3, 8), (21, 0), (16, 19), (5, 7), (15, 4), (22, 2), (8, 15), (14, 6), (14, 19), (22, 0), (17, 16), (7, 23), (16, 14), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791559", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), 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), (20, 5), (2, 17), (7, 17), (1, 17), (13, 20), (16, 18), (6, 5), (4, 19), (19, 6), (14, 13), (21, 20), (19, 15), (7, 4), (16, 13), (19, 12), (5, 2), (21, 17), (5, 0), (10, 0), (12, 12), (17, 17), (8, 15), (14, 10), (11, 18), (4, 21), (9, 20), (15, 4), (6, 18), (14, 0), (0, 1), (5, 14), (10, 8), (21, 10), (16, 16), (19, 17), (1, 6), (12, 17), (2, 8), (14, 5), (20, 8), (14, 1), (21, 4), (7, 9), (21, 16), (12, 6), (16, 3), (18, 20), (16, 15), (14, 4), (8, 0), (19, 11), (18, 9), (19, 2), (13, 17), (3, 6), (20, 1), (7, 7), (20, 20), (4, 6), (6, 11), (2, 14), (3, 8), (18, 12), (0, 14), (2, 10), (8, 14), (13, 14), (2, 5), (17, 20), (11, 16), (14, 3), (13, 16), (10, 14), (17, 0), (17, 14), (2, 9), (14, 20), (12, 3), (7, 5), (19, 9), (0, 4), (2, 1), (5, 10), (15, 6), (6, 19), (21, 15), (17, 10), (11, 14), (4, 4), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "837896", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 14), (19, 0), (18, 19), (10, 11), (11, 17), (17, 24), (11, 22), (18, 0), (15, 26), (12, 9), (11, 8), (5, 20), (6, 2), (11, 10), (15, 10), (11, 7), (13, 8), (21, 5), (18, 12), (15, 12), (18, 13), (1, 1), (8, 4), (20, 7), (5, 21), (20, 5), (1, 20), (8, 12), (7, 11), (13, 13), (13, 3), (0, 9), (7, 6), (6, 12), (4, 1), (14, 6), (11, 1), (15, 14), (0, 14), (7, 22), (17, 13), (7, 7), (9, 17), (14, 20), (2, 25), (4, 11), (9, 19), (19, 21), (15, 9), (10, 21), (18, 6), (21, 7), (14, 13), (4, 23), (19, 5), (12, 18), (0, 5), (7, 8), (17, 3), (11, 13), (8, 2), (13, 23), (14, 12), (3, 24), (16, 0), (9, 13), (10, 17), (18, 16), (1, 6), (6, 0), (1, 17), (8, 18), (12, 25), (15, 17), (1, 26), (6, 9), (12, 15), (9, 16), (8, 25), (13, 19), (6, 15), (4, 14), (20, 8), (17, 0), (5, 15), (13, 0), (16, 8), (9, 24), (21, 24), (9, 15), (2, 13), (4, 21), (14, 8), (18, 11), (2, 8), (12, 23), (17, 7), (13, 12), (10, 9), (12, 10), (17, 22), (5, 4), (4, 6), (4, 18), (5, 24), (16, 23), (2, 6), (4, 22), (1, 7), (5, 7), (1, 16), (19, 6), (1, 5), (20, 2), (17, 26), (18, 20), (18, 21), (21, 14), (2, 12), (19, 25), (10, 0), (8, 6), (14, 9), (19, 4), (9, 21), (8, 0), (16, 1), (11, 26), (18, 26), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358416", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 23), (12, 11), (7, 16), (18, 4), (4, 17), (0, 4), (3, 15), (6, 4), (18, 8), (16, 2), (10, 22), (23, 5), (17, 9), (25, 23), (23, 3), (15, 12), (8, 23), (18, 14), (8, 16), (23, 6), (22, 4), (5, 6), (20, 2), (26, 20), (2, 22), (10, 11), (8, 12), (9, 19), (12, 18), (14, 15), (5, 10), (14, 4), (19, 20), (11, 13), (24, 19), (15, 18), (11, 15), (8, 2), (17, 19), (25, 17), (23, 15), (26, 10), (18, 7), (13, 12), (9, 17), (0, 7), (6, 8), (18, 6), (22, 0), (12, 3), (7, 9), (13, 16), (21, 9), (14, 18), (1, 3), (3, 0), (8, 8), (20, 6), (9, 2), (0, 3), (5, 18), (23, 23), (3, 9), (24, 11), (23, 10), (7, 20), (10, 13), (17, 3), (13, 6), (22, 17), (25, 13), (4, 13), (8, 14), (24, 13), (23, 19), (24, 8), (20, 13), (18, 5), (11, 12), (6, 23), (0, 12), (12, 10), (12, 23), (6, 16), (10, 15), (23, 0), (13, 7), (10, 5), (9, 3), (22, 18), (1, 17), (14, 19), (9, 5), (16, 16), (2, 6), (6, 22), (13, 3), (5, 2), (23, 18), (1, 4), (12, 13), (16, 1), (10, 23), (20, 9), (3, 20), (21, 13), (11, 14), (11, 0), (13, 2), (25, 11), (18, 16), (13, 19), (6, 17), (15, 10), (14, 5), (21, 2), (17, 13), (13, 11), (14, 21), (13, 21), (13, 15), (21, 8), (14, 8), (22, 15), (7, 19), (24, 22), (3, 5), (24, 6), (3, 11), (19, 14), (1, 22), (2, 16), (4, 20), (25, 15), (15, 6), (8, 1), (16, 9), (6, 0), (4, 12), (16, 3), (17, 15), (14, 14), (26, 0), (1, 15), (18, 1), (4, 18), (21, 22), (15, 2), (8, 17), (26, 2), (25, 8), (8, 19), (15, 5), (0, 19), (8, 13), (12, 2), (9, 15), (11, 19), (4, 3), (15, 7), (1, 11), (9, 11), (20, 19), (8, 18), (22, 10), (25, 4), (8, 4), (18, 22), (26, 11), (25, 3), (10, 9), (23, 4), (21, 14), (3, 7), (12, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578592", "dataset": "MATH"}
{"messages": [{"content": "In a 22x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 19), 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), (21, 14), (5, 6), (20, 4), (19, 10), (19, 0), (5, 7), (15, 3), (17, 6), (2, 1), (15, 6), (13, 16), (1, 8), (21, 0), (16, 10), (21, 10), (15, 14), (4, 11), (21, 11), (2, 5), (5, 17), (21, 7), (4, 17), (8, 16), (2, 4), (15, 13), (14, 7), (12, 14), (14, 9), (10, 19), (13, 15), (4, 13), (21, 9), (17, 9), (9, 14), (9, 2), (4, 6), (13, 19), (5, 14), (14, 19), (20, 1), (4, 12), (21, 8), (6, 8), (19, 5), (6, 19), (17, 14), (10, 13), (3, 8), (6, 17), (15, 15), (10, 9), (6, 7), (14, 17), (10, 0), (4, 15), (1, 1), (6, 14), (17, 12), (0, 1), (12, 8), (10, 16), (1, 6), (3, 13), (0, 5), (21, 6), (6, 1), (17, 11), (0, 7), (4, 1), (12, 4), (20, 2), (11, 16), (4, 4), (21, 2), (19, 15), (17, 0), (3, 5), (17, 5), (7, 9), (0, 8), (10, 10), (16, 14), (21, 3), (6, 16), (16, 5), (16, 8), (8, 1), (11, 15), (1, 18), (8, 0), (8, 15), (14, 0), (8, 9), (11, 10), (19, 12), (0, 10), (12, 13), (16, 18), (11, 19), (12, 7), (14, 15), (5, 16), (2, 6), (19, 9), (2, 8), (19, 14), (8, 13), (10, 3), (7, 1), (18, 19), (16, 7), (18, 17), (14, 2), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626160", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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), (4, 21), (2, 12), (14, 4), (19, 12), (16, 22), (26, 26), (14, 17), (0, 11), (2, 17), (26, 11), (21, 24), (5, 21), (1, 13), (11, 11), (21, 13), (20, 15), (22, 13), (20, 17), (26, 21), (18, 3), (21, 4), (17, 13), (13, 22), (16, 23), (6, 1), (1, 22), (6, 20), (13, 18), (16, 12), (2, 11), (21, 3), (18, 8), (16, 0), (2, 5), (19, 6), (24, 22), (18, 14), (0, 20), (24, 0), (21, 14), (16, 19), (4, 17), (12, 25), (9, 1), (16, 17), (18, 2), (4, 18), (7, 9), (15, 18), (2, 15), (22, 18), (10, 21), (3, 4), (6, 17), (10, 18), (0, 25), (27, 11), (26, 12), (13, 17), (4, 0), (8, 21), (15, 7), (18, 17), (24, 17), (11, 6), (7, 0), (12, 5), (5, 4), (22, 24), (3, 20), (25, 18), (6, 2), (15, 11), (14, 20), (15, 6), (9, 9), (22, 1), (4, 1), (17, 23), (22, 26), (2, 14), (25, 13), (8, 26), (24, 16), (20, 7), (2, 25), (15, 24), (12, 10), (10, 16), (26, 23), (12, 20), (17, 17), (8, 20), (4, 23), (8, 15), (22, 15), (26, 14), (15, 26), (26, 22), (6, 19), (16, 2), (22, 14), (17, 6), (5, 11), (19, 10), (20, 6), (24, 12), (4, 20), (9, 17), (23, 17), (23, 9), (7, 8), (15, 13), (25, 8), (27, 18), (11, 13), (12, 9), (27, 4), (27, 21), (17, 0), (26, 4), (15, 3), (16, 5), (14, 5), (2, 8), (2, 20), (15, 0), (17, 16), (23, 18), (7, 25), (25, 14), (11, 7), (4, 8), (5, 6), (10, 4), (8, 16), (9, 4), (13, 9), (12, 19), (16, 18), (12, 18), (24, 13), (14, 16), (19, 19), (20, 23), (26, 2), (3, 1), (15, 2), (14, 18), (16, 7), (22, 23), (8, 22), (3, 9), (10, 8), (11, 24), (0, 7), (9, 10), (2, 7), (18, 24), (7, 13), (17, 2), (3, 5), (5, 5), (26, 3), (25, 17), (4, 25), (24, 18), (0, 21), (22, 8), (9, 12), (22, 0), (27, 10), (16, 4), (15, 12), (27, 7), (10, 24), (11, 16), (5, 2), (14, 6), (9, 16), (20, 1), (14, 7), (17, 20), (1, 0), (23, 0), (13, 3), (4, 24), (14, 1), (11, 1), (23, 1), (12, 26), (0, 3), (1, 9), (11, 23), (20, 3), (12, 6), (27, 9), (6, 24), (19, 13), (7, 5), (6, 9), (16, 24), (12, 22), (26, 10), (9, 6), (9, 3), (0, 9), (17, 1), (2, 26), (3, 2), (10, 20), (18, 7), (15, 20), (9, 19), (12, 15), (9, 8), (4, 11), (14, 21), (1, 25), (15, 1), (8, 6), (7, 11), (21, 17), (19, 3), (9, 24), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973440", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), 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), (24, 19), (9, 1), (10, 13), (2, 12), (9, 11), (7, 25), (4, 25), (12, 2), (7, 16), (17, 8), (4, 24), (15, 6), (19, 17), (16, 0), (23, 25), (17, 2), (2, 11), (23, 5), (11, 23), (12, 23), (10, 21), (22, 25), (20, 21), (3, 11), (19, 9), (11, 17), (6, 16), (9, 10), (13, 4), (22, 10), (16, 21), (11, 24), (3, 4), (14, 23), (16, 4), (17, 17), (7, 26), (5, 21), (4, 23), (12, 26), (11, 5), (8, 18), (1, 26), (12, 6), (22, 19), (6, 14), (19, 22), (3, 5), (1, 17), (1, 15), (1, 12), (12, 24), (17, 11), (23, 3), (17, 10), (6, 9), (22, 9), (21, 17), (11, 11), (15, 5), (23, 4), (21, 23), (18, 11), (19, 12), (0, 22), (23, 24), (18, 18), (11, 22), (6, 13), (20, 25), (12, 17), (19, 11), (8, 25), (4, 6), (5, 13), (10, 2), (13, 15), (25, 24), (25, 18), (0, 14), (7, 24), (13, 8), (6, 21), (6, 3), (7, 6), (9, 15), (22, 11), (21, 15), (17, 19), (18, 6), (12, 3), (1, 7), (8, 21), (6, 17), (15, 25), (15, 14), (25, 4), (2, 20), (25, 21), (22, 15), (6, 15), (19, 7), (8, 17), (3, 1), (8, 24), (2, 7), (25, 6), (21, 4), (17, 3), (14, 20), (13, 20), (20, 6), (6, 11), (15, 4), (14, 13), (22, 5), (12, 7), (8, 0), (16, 11), (24, 3), (6, 20), (18, 26), (4, 21), (25, 7), (22, 4), (8, 10), (9, 14), (20, 4), (19, 19), (10, 12), (25, 14), (22, 22), (4, 22), (12, 18), (22, 1), (9, 21), (15, 23), (2, 9), (14, 1), (1, 14), (14, 22), (23, 16), (11, 12), (22, 17), (14, 0), (6, 12), (23, 21), (22, 14), (0, 3), (20, 19), (14, 18), (14, 14), (4, 11), (10, 4), (5, 7), (25, 16), (8, 4), (1, 16), (10, 22), (0, 18), (16, 25), (3, 13), (24, 21), (17, 9), (11, 3), (21, 22), (13, 26), (14, 8), (20, 1), (24, 6), (18, 12), (3, 17), (25, 2), (5, 15), (25, 3), (10, 3), (3, 7), (2, 22), (21, 3), (0, 19), (13, 5), (7, 18), (11, 15), (23, 18), (3, 12), (1, 20), (19, 14), (12, 14), (5, 0), (8, 11), (14, 24), (16, 2), (21, 21), (10, 25), (24, 20), (11, 10), (23, 23), (19, 10), (25, 8), (13, 11), (1, 5), (16, 8), (7, 23), (4, 12), (8, 2), (3, 14), (1, 1), (1, 13), (18, 8), (6, 10), (19, 5), (8, 13), (15, 18), (2, 26), (0, 26), (8, 7), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440464", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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), (27, 2), (3, 7), (1, 15), (26, 8), (24, 19), (16, 17), (16, 4), (20, 9), (24, 13), (26, 7), (6, 16), (15, 11), (25, 1), (0, 17), (27, 25), (26, 9), (22, 12), (22, 24), (6, 8), (7, 14), (11, 13), (2, 3), (21, 6), (12, 25), (3, 9), (14, 0), (20, 6), (18, 1), (23, 21), (12, 20), (11, 22), (4, 3), (19, 18), (25, 7), (16, 24), (2, 19), (9, 12), (11, 20), (12, 24), (9, 9), (11, 24), (5, 8), (9, 0), (27, 9), (13, 3), (27, 20), (10, 11), (6, 12), (20, 0), (15, 9), (15, 16), (9, 7), (8, 19), (15, 3), (17, 11), (6, 3), (11, 0), (28, 13), (0, 10), (13, 8), (15, 20), (24, 12), (4, 1), (3, 2), (0, 22), (19, 23), (18, 26), (11, 5), (15, 26), (8, 0), (18, 19), (1, 20), (7, 24), (13, 1), (0, 26), (25, 24), (20, 19), (5, 10), (14, 9), (10, 20), (1, 22), (28, 22), (10, 10), (17, 14), (20, 3), (5, 13), (4, 14), (11, 25), (9, 17), (21, 19), (3, 14), (22, 21), (12, 21), (17, 5), (8, 24), (21, 0), (21, 14), (13, 22), (12, 11), (22, 7), (1, 21), (1, 13), (3, 18), (22, 2), (0, 20), (19, 0), (14, 8), (2, 26), (23, 16), (23, 9), (22, 1), (16, 21), (19, 26), (23, 6), (22, 11), (26, 11), (26, 14), (10, 13), (15, 7), (14, 3), (4, 19), (12, 15), (9, 11), (16, 0), (8, 9), (15, 24), (25, 13), (6, 15), (5, 18), (3, 23), (18, 2), (3, 6), (14, 1), (24, 11), (7, 2), (9, 23), (24, 1), (0, 6), (24, 17), (1, 10), (24, 2), (22, 25), (17, 13), (8, 13), (8, 17), (14, 25), (20, 5), (8, 1), (10, 16), (26, 18), (19, 21), (18, 10), (18, 13), (20, 10), (7, 12), (2, 16), (18, 5), (14, 13), (14, 10), (16, 10), (2, 22), (3, 16), (16, 14), (25, 0), (22, 8), (12, 3), (21, 3), (3, 11), (20, 15), (25, 20), (26, 1), (24, 16), (1, 26), (5, 21), (17, 9), (20, 12), (6, 14), (8, 11), (24, 23), (4, 23), (18, 18), (18, 8), (14, 17), (8, 7), (23, 3), (2, 7), (10, 25), (12, 0), (19, 1), (16, 9), (0, 9), (2, 11), (21, 23), (27, 17), (21, 15), (19, 15), (1, 5), (11, 1), (6, 26), (2, 9), (23, 22), (22, 5), (22, 10), (8, 21), (17, 0), (25, 6), (0, 19), (19, 16), (19, 19), (12, 14), (18, 20), (26, 6), (15, 2), (3, 10), (27, 14), (28, 3), (3, 8), (17, 3), (20, 23), (20, 20), (2, 1), (14, 26), (18, 12), (28, 14), (26, 26), (1, 19), (25, 11), (26, 24), (1, 0), (13, 11), (16, 22), (23, 19), (17, 23), (12, 2), (19, 8), (20, 26), (18, 24), (25, 15), (27, 7), (17, 21), (24, 7), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887040", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 23), (20, 5), (1, 14), (14, 16), (1, 15), (6, 3), (14, 7), (16, 24), (3, 4), (4, 25), (9, 15), (8, 14), (1, 25), (9, 19), (22, 9), (0, 11), (0, 22), (6, 18), (1, 1), (5, 22), (4, 0), (1, 26), (7, 26), (13, 8), (18, 9), (2, 17), (12, 22), (8, 1), (8, 12), (17, 4), (17, 15), (11, 21), (4, 1), (5, 4), (22, 13), (9, 7), (11, 16), (5, 16), (12, 17), (10, 13), (9, 24), (7, 13), (4, 12), (6, 22), (9, 27), (12, 16), (15, 6), (5, 14), (13, 12), (19, 20), (18, 7), (10, 25), (0, 19), (0, 26), (17, 16), (19, 27), (0, 15), (4, 26), (13, 6), (2, 3), (1, 4), (2, 15), (12, 20), (8, 10), (21, 7), (7, 24), (10, 3), (18, 23), (17, 17), (14, 20), (15, 0), (8, 13), (16, 25), (15, 19), (19, 7), (17, 8), (6, 23), (11, 13), (12, 19), (18, 1), (7, 17), (7, 27), (4, 2), (8, 0), (7, 11), (14, 5), (18, 26), (12, 11), (10, 19), (16, 26), (13, 24), (2, 1), (22, 6), (2, 21), (21, 5), (9, 0), (16, 14), (4, 4), (11, 18), (14, 2), (22, 23), (10, 20), (19, 19), (18, 25), (16, 27), (10, 14), (17, 7), (17, 27), (17, 6), (17, 21), (13, 13), (15, 16), (7, 21), (22, 8), (22, 25), (0, 14), (10, 23), (14, 13), (3, 18), (5, 1), (7, 12), (21, 22), (13, 20), (19, 3), (15, 12), (20, 24), (5, 19), (6, 13), (13, 16), (3, 2), (21, 20), (20, 1), (19, 12), (1, 20), (5, 10), (2, 8), (8, 22), (1, 0), (15, 21), (19, 16), (5, 17), (20, 25), (10, 7), (6, 9), (1, 24), (19, 24), (19, 17), (15, 22), (3, 17), (17, 26), (2, 20), (16, 15), (18, 12), (3, 23), (15, 7), (9, 17), (18, 21), (14, 18), (17, 10), (13, 26), (15, 3), (8, 15), (1, 16), (11, 14), (0, 6), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867136", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 4), (13, 3), (7, 1), (2, 4), (0, 1), (16, 4), (21, 13), (21, 11), (6, 3), (23, 16), (4, 16), (1, 7), (15, 18), (14, 9), (11, 7), (2, 13), (13, 18), (11, 17), (5, 4), (14, 10), (23, 9), (17, 6), (13, 13), (1, 13), (16, 1), (3, 18), (15, 14), (11, 1), (5, 15), (18, 18), (9, 5), (16, 17), (19, 9), (8, 0), (3, 4), (13, 1), (19, 4), (23, 3), (16, 5), (9, 9), (21, 6), (14, 12), (6, 4), (0, 5), (23, 14), (7, 7), (5, 19), (5, 3), (10, 4), (6, 9), (13, 12), (8, 11), (1, 9), (2, 19), (7, 19), (22, 17), (19, 10), (19, 19), (10, 3), (21, 3), (6, 19), (14, 4), (0, 11), (21, 16), (13, 19), (14, 17), (11, 6), (19, 12), (12, 15), (0, 9), (8, 14), (17, 7), (2, 7), (4, 2), (23, 11), (10, 16), (7, 16), (15, 10), (3, 17), (9, 3), (3, 15), (16, 11), (15, 17), (22, 2), (18, 1), (7, 3), (21, 18), (12, 3), (22, 18), (14, 16), (15, 6), (4, 5), (1, 8), (22, 6), (10, 13), (0, 4), (14, 6), (6, 8), (17, 8), (13, 6), (12, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777268", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (15, 5), (9, 9), (0, 8), (20, 13), (22, 9), (13, 12), (13, 18), (2, 17), (17, 14), (10, 5), (19, 10), (0, 16), (14, 13), (18, 0), (20, 1), (8, 6), (1, 10), (10, 0), (8, 17), (15, 18), (18, 2), (23, 3), (21, 6), (2, 14), (13, 16), (8, 16), (20, 19), (24, 8), (9, 5), (2, 7), (8, 2), (10, 14), (11, 18), (24, 3), (15, 19), (23, 12), (3, 19), (20, 18), (11, 2), (23, 7), (4, 9), (26, 9), (16, 6), (11, 5), (23, 10), (4, 14), (3, 17), (23, 13), (11, 19), (2, 18), (21, 2), (23, 17), (20, 11), (26, 8), (26, 11), (25, 1), (4, 13), (12, 3), (12, 5), (10, 9), (22, 11), (5, 11), (19, 2), (22, 10), (0, 2), (16, 10), (0, 11), (3, 7), (6, 8), (0, 17), (9, 10), (25, 2), (25, 13), (22, 5), (0, 14), (18, 13), (14, 18), (19, 3), (13, 8), (13, 17), (0, 3), (15, 7), (12, 0), (21, 5), (7, 14), (25, 5), (24, 4), (8, 12), (12, 10), (4, 8), (13, 9), (15, 10), (3, 1), (14, 16), (13, 14), (5, 13), (9, 14), (21, 10), (21, 7), (9, 16), (18, 3), (4, 10), (0, 7), (16, 16), (23, 8), (18, 8), (14, 17), (20, 0), (3, 2), (17, 3), (7, 5), (22, 15), (11, 4), (26, 15), (12, 1), (9, 2), (1, 14), (4, 0), (11, 15), (11, 13), (12, 13), (6, 15), (13, 7), (26, 18), (26, 13), (16, 1), (25, 10), (11, 8), (17, 18), (26, 1), (9, 15), (6, 18), (17, 16), (7, 9), (17, 13), (8, 7), (17, 12), (14, 2), (1, 17), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609124", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (3, 20), (9, 18), (19, 14), (10, 1), (17, 2), (15, 9), (12, 7), (12, 15), (18, 7), (10, 4), (4, 7), (19, 17), (16, 19), (0, 4), (16, 8), (4, 20), (4, 21), (11, 1), (15, 13), (17, 20), (17, 12), (18, 18), (13, 7), (14, 0), (18, 16), (8, 7), (11, 17), (8, 1), (15, 19), (16, 14), (19, 8), (9, 10), (3, 1), (0, 12), (3, 21), (14, 4), (14, 13), (15, 17), (8, 18), (7, 12), (18, 14), (17, 15), (16, 11), (1, 11), (10, 13), (10, 16), (16, 12), (5, 10), (8, 10), (3, 15), (8, 3), (0, 3), (18, 0), (9, 16), (19, 5), (14, 3), (8, 14), (1, 0), (4, 17), (8, 9), (19, 1), (17, 11), (12, 18), (12, 2), (3, 4), (4, 15), (9, 20), (2, 13), (3, 11), (6, 9), (14, 7), (13, 18), (1, 8), (19, 11), (10, 19), (15, 8), (3, 14), (2, 21), (19, 9), (17, 9), (10, 20), (13, 15), (3, 17), (1, 13), (4, 5), (8, 15), (14, 19), (15, 4), (6, 15), (16, 17), (9, 9), (3, 13), (5, 19), (5, 12), (16, 3), (8, 0), (17, 16), (16, 16), (2, 7), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684996", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 10), (16, 12), (21, 19), (1, 15), (22, 17), (5, 5), (18, 10), (9, 3), (16, 19), (2, 21), (18, 21), (23, 16), (12, 10), (22, 19), (14, 7), (23, 8), (18, 19), (19, 16), (5, 18), (4, 0), (15, 14), (14, 11), (0, 6), (0, 14), (19, 7), (0, 4), (6, 4), (12, 6), (0, 10), (23, 0), (1, 10), (14, 13), (2, 22), (10, 16), (19, 9), (3, 2), (13, 16), (7, 5), (20, 3), (16, 10), (12, 15), (25, 15), (21, 2), (3, 17), (21, 7), (18, 4), (24, 3), (13, 10), (20, 19), (7, 18), (8, 5), (11, 16), (10, 19), (4, 12), (3, 8), (11, 5), (1, 1), (7, 14), (0, 21), (19, 18), (21, 21), (18, 14), (17, 22), (3, 18), (2, 8), (8, 20), (11, 3), (18, 18), (23, 2), (2, 2), (17, 8), (13, 17), (2, 7), (9, 12), (7, 8), (13, 7), (5, 1), (3, 6), (8, 17), (17, 16), (3, 12), (24, 9), (19, 4), (25, 3), (5, 15), (22, 2), (15, 18), (0, 3), (0, 19), (5, 7), (4, 10), (22, 20), (4, 1), (10, 6), (8, 11), (2, 0), (10, 20), (9, 19), (16, 3), (4, 14), (1, 5), (19, 12), (20, 10), (22, 6), (17, 20), (9, 16), (11, 20), (22, 14), (7, 3), (25, 20), (22, 4), (17, 17), (11, 17), (6, 21), (10, 4), (20, 7), (22, 15), (22, 1), (16, 15), (2, 11), (14, 16), (7, 1), (25, 4), (10, 0), (15, 10), (7, 17), (24, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "678699", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), 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, 18), (18, 14), (2, 21), (7, 0), (15, 10), (13, 11), (1, 25), (14, 25), (8, 20), (3, 8), (12, 22), (15, 8), (12, 24), (13, 12), (9, 6), (10, 22), (13, 13), (9, 24), (11, 5), (7, 18), (19, 9), (17, 1), (7, 17), (15, 3), (0, 4), (13, 4), (9, 22), (10, 5), (9, 14), (11, 9), (1, 9), (14, 6), (1, 3), (6, 17), (6, 5), (2, 8), (3, 6), (6, 7), (14, 26), (4, 18), (9, 17), (2, 10), (16, 22), (15, 14), (6, 11), (17, 8), (14, 19), (3, 10), (17, 14), (11, 11), (17, 3), (14, 3), (9, 25), (0, 20), (12, 19), (6, 9), (18, 23), (0, 6), (17, 25), (0, 1), (17, 16), (19, 4), (4, 19), (14, 16), (2, 1), (19, 0), (8, 16), (7, 21), (0, 10), (19, 23), (19, 22), (9, 11), (9, 2), (2, 19), (6, 6), (18, 13), (17, 13), (19, 5), (17, 24), (18, 24), (3, 7), (18, 9), (11, 15), (2, 25), (8, 2), (3, 5), (11, 1), (17, 0), (12, 25), (13, 1), (0, 7), (10, 3), (16, 7), (16, 10), (8, 8), (9, 7), (19, 17), (11, 17), (4, 21), (2, 13), (13, 18), (0, 22), (17, 15), (5, 14), (1, 5), (3, 1), (4, 16), (1, 15), (18, 7), (7, 13), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640135", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 17), (4, 6), (19, 4), (17, 24), (14, 20), (20, 5), (3, 1), (8, 0), (16, 18), (9, 2), (5, 27), (14, 1), (13, 5), (1, 16), (7, 28), (14, 26), (15, 14), (2, 24), (4, 15), (12, 0), (8, 18), (4, 5), (2, 9), (3, 14), (14, 27), (4, 24), (20, 26), (4, 27), (17, 9), (19, 11), (4, 18), (1, 13), (9, 14), (1, 26), (22, 25), (18, 26), (20, 11), (11, 11), (1, 25), (18, 13), (23, 20), (8, 19), (15, 11), (12, 15), (1, 3), (6, 14), (16, 17), (21, 7), (9, 16), (6, 21), (10, 18), (11, 12), (13, 27), (12, 23), (8, 6), (23, 2), (19, 1), (18, 20), (19, 6), (13, 24), (16, 6), (5, 7), (4, 3), (1, 7), (23, 14), (9, 1), (19, 26), (8, 12), (23, 25), (18, 10), (17, 6), (20, 13), (12, 14), (20, 3), (14, 21), (15, 22), (11, 1), (21, 9), (22, 1), (4, 14), (17, 19), (10, 12), (11, 27), (15, 25), (1, 11), (15, 15), (9, 20), (16, 26), (19, 15), (17, 10), (18, 12), (16, 8), (3, 5), (19, 14), (2, 23), (1, 21), (21, 15), (15, 12), (20, 2), (9, 7), (1, 0), (1, 18), (20, 12), (19, 13), (6, 5), (23, 4), (3, 7), (11, 17), (1, 6), (12, 10), (20, 22), (19, 25), (12, 7), (4, 28), (2, 1), (7, 27), (15, 28), (1, 19), (4, 22), (6, 1), (8, 24), (1, 27), (3, 20), (12, 26), (19, 22), (0, 18), (6, 8), (4, 8), (9, 23), (11, 19), (13, 13), (1, 20), (13, 6), (19, 21), (20, 27), (7, 14), (3, 3), (21, 19), (4, 11), (21, 25), (18, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612672", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 17), (20, 7), (9, 20), (10, 23), (15, 16), (11, 9), (23, 12), (13, 18), (1, 4), (27, 7), (21, 5), (3, 3), (14, 23), (16, 19), (15, 11), (12, 23), (1, 2), (20, 18), (13, 3), (27, 18), (11, 2), (6, 14), (9, 2), (22, 19), (23, 9), (23, 1), (7, 7), (26, 7), (9, 15), (24, 19), (20, 2), (9, 10), (2, 2), (0, 5), (14, 17), (27, 16), (8, 11), (21, 11), (0, 9), (21, 7), (19, 3), (3, 9), (2, 21), (22, 24), (25, 6), (26, 12), (21, 24), (15, 4), (16, 24), (17, 13), (4, 16), (17, 2), (25, 21), (1, 24), (11, 5), (16, 11), (18, 16), (21, 4), (27, 23), (10, 19), (23, 18), (11, 0), (14, 18), (21, 13), (13, 4), (5, 6), (1, 9), (20, 23), (21, 0), (17, 1), (1, 21), (2, 1), (24, 16), (11, 14), (4, 20), (24, 24), (23, 3), (21, 15), (15, 1), (22, 17), (10, 17), (6, 11), (2, 11), (5, 20), (10, 24), (13, 24), (0, 21), (22, 13), (26, 22), (16, 4), (5, 1), (5, 14), (24, 15), (13, 11), (7, 18), (10, 21), (4, 12), (24, 9), (26, 9), (1, 0), (22, 3), (3, 2), (21, 17), (15, 9), (0, 15), (17, 22), (18, 9), (0, 11), (19, 0), (9, 14), (2, 17), (27, 21), (27, 13), (19, 8), (5, 17), (20, 17), (15, 2), (21, 3), (5, 21), (4, 23), (13, 21), (20, 10), (24, 6), (12, 1), (23, 15), (5, 18), (16, 1), (20, 14), (26, 14), (16, 9), (25, 24), (0, 8), (20, 24), (4, 11), (8, 10), (8, 15), (0, 16), (8, 12), (6, 5), (16, 5), (15, 3), (21, 8), (19, 15), (4, 17), (8, 14), (5, 16), (14, 1), (1, 8), (18, 1), (18, 6), (4, 1), (19, 24), (7, 1), (0, 14), (10, 6), (3, 4), (3, 14), (7, 2), (0, 19), (15, 7), (16, 14), (9, 7), (5, 5), (11, 19), (22, 16), (14, 21), (5, 13), (19, 19), (22, 5), (8, 0), (6, 13), (21, 1), (12, 17), (2, 13), (4, 14), (21, 2), (10, 8), (19, 22), (2, 0), (8, 24), (7, 6), (7, 0), (3, 1), (26, 21), (11, 4), (24, 20), (22, 0), (22, 23), (17, 16), (25, 8), (14, 9), (1, 22), (6, 4), (23, 13), (16, 21), (13, 8), (9, 13), (23, 16), (25, 1), (21, 6), (3, 23), (17, 12), (12, 0), (16, 2), (20, 1), (26, 13), (21, 10), (20, 8), (0, 18), (4, 4), (22, 20), (26, 5), (16, 23), (24, 14), (0, 22), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205824", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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), (17, 12), (5, 24), (16, 18), (2, 3), (18, 13), (10, 9), (14, 3), (0, 6), (5, 15), (1, 21), (1, 22), (14, 0), (13, 3), (18, 22), (17, 15), (8, 23), (10, 13), (4, 6), (10, 2), (1, 16), (1, 10), (11, 23), (4, 21), (12, 5), (4, 5), (15, 14), (9, 1), (19, 15), (16, 21), (10, 6), (17, 0), (16, 11), (0, 20), (18, 15), (3, 5), (8, 15), (14, 8), (11, 14), (3, 23), (0, 14), (1, 4), (19, 4), (3, 21), (18, 0), (6, 16), (17, 19), (0, 16), (3, 7), (7, 5), (0, 22), (11, 15), (14, 13), (18, 2), (19, 1), (5, 4), (14, 6), (6, 5), (15, 15), (7, 9), (3, 16), (10, 12), (7, 19), (8, 6), (6, 12), (16, 4), (14, 15), (6, 9), (2, 8), (18, 11), (15, 6), (11, 10), (17, 21), (13, 10), (1, 12), (8, 12), (14, 14), (19, 10), (9, 8), (9, 17), (11, 4), (12, 12), (5, 10), (8, 18), (0, 13), (13, 24), (15, 5), (2, 14), (9, 16), (16, 9), (18, 18), (4, 19), (12, 23), (11, 9), (18, 12), (13, 12), (2, 4), (2, 2), (12, 8), (16, 13), (15, 18), (19, 16), (4, 15), (14, 11), (5, 17), (10, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13242", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 3), (18, 13), (25, 18), (19, 6), (20, 25), (12, 10), (12, 28), (26, 0), (13, 8), (9, 21), (5, 17), (17, 18), (24, 3), (26, 14), (7, 26), (4, 21), (13, 27), (10, 24), (21, 24), (13, 14), (0, 7), (7, 9), (6, 6), (17, 13), (15, 19), (22, 1), (6, 9), (18, 4), (7, 0), (0, 5), (11, 2), (8, 15), (18, 3), (4, 8), (24, 0), (8, 6), (3, 2), (23, 4), (21, 27), (10, 9), (14, 28), (27, 6), (17, 27), (25, 13), (20, 24), (6, 11), (17, 1), (7, 8), (18, 18), (6, 4), (24, 19), (14, 17), (19, 28), (16, 18), (3, 10), (6, 10), (17, 21), (20, 1), (22, 24), (5, 6), (11, 16), (23, 2), (9, 2), (20, 12), (16, 25), (24, 27), (20, 6), (0, 18), (11, 20), (18, 0), (1, 13), (5, 9), (10, 10), (16, 5), (0, 20), (0, 19), (12, 20), (26, 11), (14, 3), (19, 19), (19, 5), (7, 28), (9, 20), (6, 21), (2, 5), (12, 22), (2, 14), (21, 16), (0, 3), (23, 18), (19, 1), (15, 17), (15, 9), (5, 19), (21, 20), (22, 13), (8, 5), (17, 23), (4, 17), (22, 5), (16, 2), (12, 3), (0, 10), (20, 19), (27, 4), (12, 25), (9, 12), (10, 0), (1, 9), (9, 1), (24, 5), (22, 28), (24, 8), (18, 11), (1, 18), (5, 12), (6, 1), (15, 21), (14, 14), (25, 28), (2, 13), (20, 14), (23, 8), (16, 11), (18, 8), (2, 2), (26, 9), (4, 15), (10, 11), (13, 11), (18, 26), (16, 6), (7, 3), (21, 8), (14, 20), (19, 14), (2, 16), (6, 17), (7, 5), (11, 13), (3, 17), (12, 1), (17, 20), (14, 10), (1, 23), (15, 4), (14, 0), (7, 10), (25, 25), (3, 13), (17, 9), (23, 10), (0, 12), (23, 19), (21, 0), (15, 26), (9, 4), (11, 5), (7, 25), (9, 26), (27, 22), (10, 4), (19, 10), (26, 17), (1, 22), (27, 0), (2, 19), (12, 24), (1, 12), (5, 3), (24, 23), (26, 19), (6, 14), (4, 22), (13, 9), (8, 9), (4, 18), (22, 16), (18, 28), (3, 14), (11, 28), (27, 16), (2, 18), (15, 16), (22, 18), (13, 16), (14, 8), (9, 3), (4, 20), (17, 2), (25, 24), (15, 18), (26, 7), (3, 23), (19, 4), (25, 0), (3, 9), (5, 4), (21, 25), (15, 5), (0, 2), (25, 20), (13, 22), (19, 15), (10, 27), (13, 6), (13, 20), (16, 21), (22, 21), (12, 5), (25, 10), (26, 16), (10, 2), (3, 3), (8, 16), (1, 4), (16, 9), (25, 17), (6, 8), (0, 16), (10, 3), (19, 26), (12, 17), (11, 7), (10, 25), (16, 15), (17, 26), (5, 21), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824499", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 14), (9, 8), (20, 15), (15, 3), (21, 11), (6, 6), (25, 2), (11, 9), (9, 17), (18, 12), (14, 19), (17, 13), (26, 12), (15, 12), (15, 14), (11, 19), (18, 18), (20, 0), (0, 10), (19, 10), (26, 13), (11, 16), (2, 19), (8, 4), (16, 11), (23, 12), (9, 1), (9, 3), (11, 0), (16, 15), (1, 18), (12, 1), (11, 15), (8, 12), (10, 7), (6, 2), (0, 20), (7, 19), (9, 19), (4, 10), (12, 13), (24, 6), (13, 1), (21, 4), (0, 18), (19, 9), (9, 13), (7, 7), (13, 18), (18, 15), (15, 7), (13, 8), (15, 16), (14, 4), (18, 17), (4, 3), (0, 2), (15, 2), (22, 15), (26, 4), (22, 7), (18, 1), (3, 14), (22, 12), (4, 14), (20, 1), (24, 15), (12, 15), (14, 18), (7, 10), (21, 15), (14, 16), (6, 8), (11, 13), (26, 6), (20, 10), (26, 18), (21, 3), (21, 5), (22, 13), (7, 2), (23, 13), (13, 19), (1, 15), (21, 0), (19, 0), (17, 11), (16, 6), (12, 17), (23, 4), (2, 1), (10, 5), (27, 9), (15, 20), (22, 5), (7, 17), (13, 7), (8, 3), (20, 3), (15, 5), (7, 11), (21, 2), (1, 12), (17, 20), (13, 16), (0, 19), (6, 15), (0, 11), (13, 2), (16, 17), (25, 12), (7, 18), (24, 4), (19, 16), (16, 0), (23, 3), (8, 10), (25, 8), (26, 0), (1, 0), (15, 9), (5, 8), (18, 0), (23, 6), (15, 10), (4, 18), (22, 6), (8, 20), (25, 10), (5, 19), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753228", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 22), (19, 4), (14, 7), (15, 9), (19, 6), (10, 19), (7, 10), (12, 20), (11, 10), (10, 4), (1, 21), (6, 13), (3, 11), (17, 5), (5, 0), (0, 11), (10, 21), (13, 12), (12, 10), (11, 9), (15, 2), (20, 13), (3, 20), (20, 20), (7, 8), (3, 8), (16, 15), (7, 13), (18, 9), (1, 6), (8, 22), (8, 0), (8, 19), (17, 18), (20, 19), (9, 15), (4, 14), (8, 10), (0, 10), (14, 23), (19, 3), (15, 4), (17, 8), (2, 16), (0, 8), (5, 11), (6, 14), (4, 19), (16, 1), (10, 20), (20, 7), (20, 14), (11, 16), (12, 4), (14, 10), (15, 11), (7, 7), (13, 23), (11, 11), (18, 20), (18, 4), (16, 10), (16, 3), (13, 18), (20, 22), (15, 20), (6, 15), (9, 9), (6, 17), (3, 10), (10, 5), (1, 0), (14, 5), (17, 1), (5, 2), (7, 15), (5, 21), (8, 3), (8, 20), (20, 15), (20, 21), (15, 19), (12, 2), (15, 7), (20, 17), (19, 0), (0, 18), (13, 9), (4, 0), (19, 17), (16, 5), (20, 2), (6, 4), (18, 15), (16, 14), (14, 15), (12, 9), (10, 7), (8, 11), (9, 19), (13, 2), (15, 18), (12, 8), (6, 11), (5, 8), (13, 6), (5, 17), (13, 4), (1, 13), (11, 7), (14, 8), (10, 0), (4, 7), (17, 7), (6, 23), (8, 15), (19, 14), (4, 21), (6, 20), (18, 13), (3, 1), (13, 7), (18, 12), (9, 7), (3, 0), (13, 19), (11, 20), (2, 3), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "460491", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 16), (16, 26), (0, 2), (13, 14), (2, 21), (13, 10), (12, 2), (3, 11), (21, 25), (3, 0), (9, 25), (9, 5), (26, 5), (7, 6), (14, 6), (7, 23), (10, 24), (22, 10), (13, 8), (18, 10), (7, 4), (0, 20), (19, 3), (25, 0), (3, 22), (2, 9), (20, 5), (7, 0), (8, 24), (0, 3), (19, 26), (3, 6), (2, 10), (22, 26), (24, 14), (5, 25), (8, 0), (15, 21), (17, 13), (10, 14), (28, 24), (13, 21), (18, 3), (9, 21), (18, 22), (8, 7), (7, 25), (4, 8), (27, 11), (2, 16), (8, 23), (25, 23), (27, 10), (14, 2), (6, 22), (20, 8), (4, 7), (20, 25), (20, 2), (20, 10), (4, 2), (24, 11), (13, 26), (9, 26), (26, 18), (12, 16), (9, 9), (6, 25), (20, 14), (3, 12), (11, 26), (12, 20), (9, 19), (27, 12), (7, 18), (16, 20), (9, 17), (6, 1), (6, 18), (27, 18), (0, 14), (5, 13), (9, 7), (18, 13), (11, 6), (16, 19), (12, 4), (15, 9), (26, 2), (11, 17), (16, 2), (13, 23), (3, 23), (26, 20), (3, 20), (10, 9), (11, 22), (20, 11), (4, 16), (9, 10), (3, 17), (22, 12), (20, 1), (23, 16), (9, 11), (16, 1), (6, 16), (21, 8), (0, 1), (22, 8), (26, 12), (2, 22), (12, 15), (27, 7), (23, 26), (25, 2), (11, 0), (3, 25), (19, 25), (27, 25), (8, 25), (22, 25), (5, 10), (11, 3), (18, 20), (5, 1), (3, 26), (23, 13), (13, 18), (27, 23), (4, 18), (21, 5), (13, 17), (21, 0), (7, 17), (25, 21), (14, 22), (17, 10), (25, 4), (5, 16), (9, 18), (19, 2), (1, 4), (1, 24), (6, 23), (10, 5), (7, 13), (15, 4), (5, 7), (15, 19), (4, 9), (27, 16), (28, 9), (19, 0), (11, 8), (19, 20), (12, 14), (22, 7), (15, 2), (23, 7), (6, 26), (22, 0), (22, 22), (16, 8), (2, 15), (25, 24), (18, 4), (20, 20), (4, 6), (11, 2), (16, 11), (11, 9), (20, 13), (15, 24), (14, 1), (19, 4), (8, 13), (23, 20), (6, 13), (18, 1), (21, 7), (1, 3), (15, 25), (18, 14), (2, 12), (11, 15), (9, 20), (2, 5), (8, 5), (23, 22), (12, 10), (14, 17), (2, 24), (27, 5), (24, 20), (7, 9), (26, 4), (28, 21), (2, 19), (5, 15), (12, 0), (4, 12), (5, 2), (10, 11), (9, 6), (21, 3), (10, 10), (23, 19), (25, 10), (17, 21), (11, 7), (26, 13), (1, 26), (13, 1), (25, 13), (17, 3), (21, 19), (25, 17), (15, 15), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907008", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), 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), (3, 16), (0, 7), (3, 4), (2, 0), (10, 5), (5, 6), (17, 2), (15, 18), (9, 13), (15, 12), (12, 3), (11, 19), (1, 20), (1, 10), (8, 7), (20, 22), (16, 16), (18, 18), (7, 9), (15, 14), (20, 8), (14, 6), (20, 12), (17, 15), (17, 17), (9, 19), (17, 5), (16, 3), (0, 4), (7, 1), (14, 11), (7, 13), (6, 13), (2, 8), (15, 7), (11, 12), (18, 0), (15, 19), (4, 23), (14, 8), (9, 22), (5, 4), (5, 9), (5, 0), (8, 14), (18, 15), (18, 7), (19, 5), (5, 18), (4, 8), (13, 17), (17, 0), (12, 20), (19, 2), (2, 15), (1, 15), (17, 7), (11, 10), (16, 15), (2, 20), (10, 0), (8, 6), (9, 12), (18, 3), (7, 17), (20, 20), (5, 19), (6, 2), (0, 5), (11, 17), (0, 20), (11, 11), (8, 22), (18, 19), (17, 14), (13, 0), (12, 8), (6, 5), (7, 20), (16, 9), (7, 22), (20, 3), (6, 15), (17, 6), (14, 3), (4, 9), (0, 22), (14, 21), (2, 12), (3, 22), (5, 11), (19, 8), (6, 22), (7, 23), (8, 11), (2, 6), (1, 8), (14, 2), (15, 2), (11, 0), (12, 23), (9, 23), (17, 13), (8, 15), (12, 11), (10, 14), (13, 20), (11, 8), (16, 7), (20, 4), (11, 6), (8, 21), (19, 14), (8, 10), (1, 7), (11, 21), (11, 2), (9, 3), (19, 22), (3, 0), (6, 19), (8, 0), (6, 1), (13, 9), (1, 5), (1, 2), (15, 8), (18, 10), (19, 1), (17, 21), (6, 10), (0, 13), (3, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984624", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 6), (10, 19), (13, 16), (21, 14), (7, 19), (20, 2), (7, 12), (20, 16), (2, 10), (11, 15), (10, 11), (12, 16), (9, 4), (13, 3), (17, 9), (2, 9), (0, 9), (8, 18), (19, 15), (20, 11), (17, 5), (4, 11), (17, 6), (16, 20), (17, 8), (17, 16), (6, 10), (17, 3), (3, 14), (14, 3), (17, 0), (19, 11), (20, 13), (15, 9), (7, 13), (9, 8), (16, 8), (7, 6), (9, 17), (5, 9), (13, 12), (17, 7), (3, 18), (2, 15), (11, 10), (1, 16), (13, 18), (12, 10), (4, 1), (10, 14), (3, 6), (12, 11), (21, 3), (12, 6), (10, 12), (16, 11), (5, 3), (12, 20), (6, 18), (8, 17), (19, 19), (4, 13), (4, 19), (5, 10), (8, 15), (14, 19), (0, 2), (13, 14), (13, 4), (14, 8), (6, 4), (18, 15), (0, 14), (11, 8), (9, 13), (1, 13), (1, 5), (14, 7), (1, 7), (17, 2), (17, 10), (11, 19), (16, 1), (16, 6), (6, 7), (14, 6), (15, 13), (7, 0), (8, 10), (7, 5), (11, 1), (9, 16), (16, 9), (6, 6), (21, 17), (14, 5), (21, 2), (11, 9), (0, 18), (2, 5), (2, 3), (13, 15), (13, 5), (10, 18), (3, 15), (19, 7), (4, 12), (12, 4), (15, 12), (18, 13), (9, 11), (5, 11), (8, 14), (10, 6), (10, 13), (14, 18), (5, 5), (9, 2), (17, 15), (17, 4), (8, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967680", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), 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), (8, 1), (11, 4), (9, 7), (12, 0), (15, 18), (4, 14), (18, 12), (4, 9), (16, 19), (19, 0), (17, 10), (2, 13), (6, 3), (12, 16), (18, 14), (3, 12), (10, 15), (19, 4), (12, 6), (16, 14), (17, 5), (20, 13), (3, 1), (11, 18), (15, 12), (8, 4), (10, 4), (12, 17), (3, 14), (17, 12), (12, 11), (18, 4), (12, 5), (20, 12), (0, 15), (2, 8), (16, 13), (6, 11), (0, 19), (3, 2), (13, 16), (4, 5), (12, 13), (3, 11), (7, 17), (2, 7), (7, 7), (8, 8), (16, 0), (1, 10), (17, 1), (2, 10), (13, 13), (20, 16), (18, 5), (16, 9), (4, 2), (17, 7), (5, 8), (15, 15), (9, 16), (1, 11), (16, 16), (2, 0), (14, 9), (7, 0), (20, 4), (9, 2), (10, 1), (10, 18), (4, 18), (1, 5), (0, 1), (17, 2), (17, 3), (0, 10), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177894", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 5), (4, 12), (10, 17), (7, 22), (9, 13), (6, 1), (11, 7), (27, 16), (10, 3), (4, 5), (0, 18), (26, 18), (25, 8), (17, 10), (24, 8), (22, 20), (12, 7), (16, 1), (8, 3), (8, 20), (26, 8), (23, 10), (23, 13), (11, 14), (26, 10), (23, 11), (10, 6), (4, 3), (2, 0), (7, 18), (15, 15), (25, 17), (12, 4), (20, 2), (19, 2), (0, 11), (19, 17), (2, 7), (17, 22), (17, 18), (20, 4), (4, 7), (8, 17), (19, 12), (15, 4), (16, 9), (5, 9), (4, 21), (6, 14), (8, 6), (24, 3), (27, 8), (5, 5), (2, 22), (18, 13), (21, 4), (18, 21), (4, 1), (2, 1), (8, 8), (2, 11), (16, 8), (13, 8), (23, 8), (4, 2), (22, 14), (18, 10), (3, 3), (3, 19), (9, 6), (26, 19), (22, 0), (10, 0), (3, 10), (24, 7), (6, 20), (10, 19), (20, 0), (19, 13), (9, 14), (5, 3), (11, 18), (24, 15), (27, 1), (22, 2), (2, 14), (1, 22), (27, 12), (21, 17), (18, 5), (22, 1), (6, 2), (5, 8), (5, 12), (6, 16), (24, 20), (25, 4), (12, 16), (8, 7), (16, 18), (18, 8), (17, 3), (11, 5), (23, 22), (15, 1), (27, 11), (5, 13), (27, 20), (11, 21), (10, 1), (19, 19), (6, 9), (20, 10), (3, 18), (3, 9), (4, 19), (5, 17), (5, 11), (22, 21), (11, 15), (24, 1), (19, 20), (22, 4), (1, 9), (1, 19), (20, 15), (25, 16), (12, 15), (19, 6), (1, 18), (2, 19), (4, 15), (16, 4), (15, 17), (10, 20), (15, 14), (26, 21), (23, 7), (17, 9), (19, 16), (13, 4), (5, 1), (14, 16), (20, 3), (25, 20), (13, 22), (13, 10), (0, 3), (12, 21), (13, 1), (9, 8), (7, 19), (26, 2), (17, 19), (1, 11), (27, 10), (7, 4), (0, 16), (5, 6), (16, 22), (26, 14), (26, 6), (17, 20), (17, 5), (27, 14), (18, 17), (25, 14), (20, 13), (9, 4), (25, 10), (17, 7), (0, 12), (9, 20), (14, 7), (3, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "871560", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 24), (13, 8), (3, 3), (11, 6), (23, 0), (23, 4), (8, 4), (17, 11), (3, 17), (5, 3), (7, 18), (10, 10), (21, 5), (10, 17), (0, 6), (23, 13), (0, 25), (0, 14), (8, 16), (22, 7), (17, 8), (9, 2), (10, 15), (3, 18), (9, 19), (23, 1), (4, 15), (21, 21), (22, 0), (18, 5), (10, 25), (13, 24), (16, 14), (10, 22), (7, 24), (16, 9), (11, 21), (16, 25), (5, 9), (23, 21), (5, 28), (19, 6), (13, 16), (2, 8), (13, 2), (23, 3), (15, 19), (20, 17), (17, 22), (15, 4), (8, 5), (22, 23), (7, 26), (14, 0), (22, 9), (3, 5), (11, 19), (19, 19), (4, 19), (10, 6), (1, 9), (17, 28), (0, 19), (2, 11), (7, 20), (1, 5), (10, 3), (14, 15), (20, 23), (7, 27), (1, 18), (19, 13), (23, 20), (12, 11), (0, 21), (2, 27), (18, 20), (14, 18), (9, 6), (14, 10), (1, 24), (8, 1), (3, 27), (16, 16), (15, 1), (12, 21), (7, 15), (4, 20), (17, 1), (5, 16), (18, 26), (18, 21), (7, 9), (1, 0), (17, 16), (21, 26), (4, 16), (8, 18), (4, 5), (22, 28), (4, 13), (11, 11), (19, 11), (15, 10), (4, 7), (11, 26), (12, 16), (7, 0), (21, 8), (3, 9), (1, 28), (9, 27), (23, 17), (4, 1), (9, 3), (17, 23), (1, 23), (17, 5), (6, 6), (9, 9), (14, 13), (9, 10), (14, 19), (15, 18), (14, 23), (20, 11), (21, 3), (20, 13), (8, 19), (6, 9), (13, 12), (23, 8), (9, 26), (11, 0), (4, 11), (22, 26), (20, 18), (5, 14), (12, 24), (19, 2), (3, 11), (6, 27), (1, 3), (14, 8), (5, 8), (5, 0), (4, 22), (20, 1), (13, 10), (10, 8), (23, 11), (6, 26), (19, 27), (4, 3), (2, 6), (13, 1), (22, 20), (5, 11), (5, 20), (21, 12), (7, 8), (7, 22), (10, 19), (3, 6), (21, 16), (17, 19), (18, 15), (10, 28), (17, 9), (22, 11), (16, 7), (13, 9), (8, 21), (15, 6), (20, 22), (4, 21), (17, 2), (19, 22), (10, 23), (6, 17), (6, 13), (3, 19), (21, 20), (21, 0), (0, 11), (14, 6), (12, 8), (12, 9), (18, 8), (8, 25), (17, 27), (7, 11), (1, 1), (20, 6), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822668", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), 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), (11, 8), (6, 18), (21, 15), (16, 12), (12, 17), (3, 8), (17, 1), (13, 13), (4, 13), (11, 10), (20, 7), (5, 12), (10, 11), (11, 18), (7, 3), (11, 16), (5, 2), (17, 3), (16, 9), (13, 1), (17, 2), (13, 18), (1, 2), (19, 7), (4, 3), (23, 12), (6, 15), (7, 5), (14, 11), (12, 13), (19, 18), (13, 0), (13, 9), (18, 8), (6, 17), (17, 16), (3, 11), (10, 0), (12, 9), (0, 15), (3, 1), (1, 3), (22, 15), (9, 9), (18, 9), (24, 10), (10, 18), (9, 13), (12, 18), (8, 14), (14, 10), (16, 15), (15, 8), (14, 7), (11, 11), (14, 5), (23, 8), (4, 14), (0, 4), (8, 11), (24, 9), (5, 16), (0, 1), (23, 2), (21, 18), (5, 11), (24, 1), (7, 10), (14, 19), (23, 17), (12, 3), (8, 1), (11, 3), (17, 4), (21, 6), (1, 10), (0, 10), (9, 3), (24, 12), (8, 19), (1, 18), (0, 19), (22, 19), (19, 12), (21, 1), (8, 7), (11, 19), (8, 6), (22, 5), (14, 13), (22, 6), (22, 3), (5, 7), (7, 2), (16, 0), (1, 1), (16, 6), (24, 11), (20, 12), (22, 4), (11, 13), (15, 16), (23, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818884", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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), (18, 3), (16, 16), (18, 9), (12, 9), (20, 1), (19, 18), (5, 17), (7, 14), (8, 0), (13, 2), (15, 0), (9, 19), (5, 12), (11, 12), (2, 6), (4, 16), (8, 3), (19, 17), (11, 0), (1, 3), (9, 10), (7, 16), (6, 10), (13, 5), (10, 10), (17, 14), (14, 6), (7, 0), (3, 19), (5, 8), (12, 4), (13, 16), (7, 19), (6, 8), (4, 10), (11, 19), (3, 15), (5, 4), (18, 11), (8, 16), (12, 0), (12, 21), (9, 5), (16, 7), (5, 1), (10, 3), (16, 14), (4, 18), (16, 18), (13, 15), (19, 6), (17, 20), (14, 0), (6, 15), (8, 9), (5, 0), (10, 17), (1, 1), (9, 20), (4, 0), (20, 16), (18, 13), (1, 20), (12, 20), (5, 19), (20, 10), (18, 17), (19, 0), (10, 21), (16, 0), (14, 7), (12, 16), (6, 7), (16, 1), (13, 19), (17, 13), (9, 1), (6, 2), (2, 0), (0, 9), (3, 7), (3, 9), (12, 10), (5, 7), (1, 5), (16, 11), (1, 21), (8, 1), (18, 18), (18, 12), (3, 16), (15, 8), (4, 11), (0, 12), (13, 18), (11, 6), (14, 1), (11, 8), (19, 9), (1, 0), (14, 15), (1, 6), (12, 13), (5, 13), (13, 3), (5, 20), (6, 17), (13, 8), (14, 19), (10, 0), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563658", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 16), (13, 12), (15, 14), (7, 19), (11, 11), (2, 2), (9, 4), (12, 15), (1, 18), (21, 11), (20, 8), (6, 8), (10, 12), (17, 10), (16, 10), (19, 14), (12, 8), (23, 4), (2, 10), (5, 5), (8, 5), (22, 6), (0, 11), (18, 3), (8, 19), (4, 7), (8, 4), (11, 3), (13, 9), (10, 17), (15, 8), (24, 1), (25, 6), (12, 18), (16, 19), (23, 0), (7, 13), (11, 19), (22, 15), (8, 3), (16, 18), (1, 11), (21, 15), (6, 11), (5, 13), (14, 2), (2, 18), (5, 14), (13, 20), (24, 7), (24, 13), (6, 3), (16, 17), (17, 15), (1, 15), (16, 9), (22, 5), (5, 1), (17, 2), (12, 4), (8, 20), (4, 13), (19, 16), (15, 12), (25, 3), (18, 20), (4, 9), (4, 12), (17, 0), (7, 18), (21, 18), (10, 6), (8, 12), (16, 14), (5, 6), (10, 3), (10, 0), (6, 7), (24, 17), (25, 4), (5, 0), (7, 10), (1, 8), (17, 7), (25, 2), (13, 8), (24, 8), (15, 4), (11, 12), (23, 9), (0, 3), (5, 3), (5, 20), (14, 18), (19, 6), (8, 9), (16, 3), (7, 16), (19, 1), (20, 13), (23, 8), (25, 5), (22, 11), (21, 6), (13, 15), (14, 8), (21, 4), (25, 14), (22, 14), (22, 4), (11, 15), (23, 13), (5, 7), (5, 2), (11, 0), (20, 5), (18, 6), (1, 12), (6, 13), (7, 17), (2, 4), (0, 10), (25, 18), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34314", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 22), (24, 15), (13, 22), (21, 11), (18, 6), (9, 26), (1, 5), (4, 6), (26, 21), (11, 7), (10, 8), (17, 28), (2, 12), (0, 2), (25, 8), (24, 21), (4, 15), (9, 16), (16, 28), (23, 17), (8, 4), (13, 17), (19, 10), (2, 14), (24, 24), (11, 19), (10, 2), (1, 13), (9, 9), (19, 11), (15, 6), (10, 4), (20, 17), (1, 27), (8, 12), (10, 1), (7, 10), (12, 5), (14, 16), (7, 21), (22, 3), (7, 23), (17, 10), (25, 1), (6, 6), (12, 26), (10, 0), (20, 23), (12, 28), (16, 21), (11, 27), (7, 24), (18, 28), (0, 24), (25, 4), (1, 28), (22, 2), (26, 20), (15, 7), (6, 17), (3, 16), (10, 11), (12, 6), (25, 15), (3, 20), (6, 19), (18, 22), (22, 24), (24, 16), (3, 15), (21, 28), (20, 1), (17, 22), (3, 8), (24, 19), (13, 8), (25, 3), (6, 8), (8, 19), (23, 13), (1, 17), (24, 0), (13, 3), (23, 25), (5, 10), (0, 18), (15, 2), (8, 27), (8, 2), (3, 12), (5, 4), (12, 11), (18, 24), (16, 19), (23, 8), (9, 12), (26, 5), (2, 0), (25, 11), (3, 19), (20, 15), (4, 13), (3, 21), (1, 16), (4, 20), (13, 10), (17, 6), (15, 13), (22, 21), (0, 22), (4, 25), (1, 4), (3, 28), (1, 3), (3, 27), (12, 25), (20, 9), (16, 13), (24, 11), (0, 8), (16, 0), (20, 25), (23, 22), (11, 17), (6, 7), (7, 22), (0, 19), (0, 21), (16, 18), (26, 13), (1, 9), (23, 26), (13, 21), (18, 5), (11, 4), (4, 2), (10, 16), (8, 9), (18, 8), (22, 27), (5, 14), (5, 13), (13, 9), (12, 15), (1, 15), (12, 21), (24, 1), (6, 26), (21, 9), (18, 10), (1, 0), (24, 9), (2, 17), (15, 22), (21, 16), (5, 24), (25, 10), (0, 26), (19, 8), (16, 2), (20, 28), (0, 17), (7, 14), (21, 3), (26, 22), (16, 17), (4, 18), (15, 27), (19, 19), (16, 8), (20, 2), (6, 18), (2, 6), (14, 2), (15, 19), (18, 19), (24, 6), (14, 27), (4, 11), (15, 21), (5, 26), (0, 5), (25, 24), (3, 4), (16, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732841", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 17), (5, 12), (18, 7), (21, 19), (17, 6), (19, 2), (9, 17), (25, 23), (1, 14), (7, 5), (27, 20), (14, 7), (1, 11), (10, 21), (24, 7), (12, 16), (8, 16), (3, 20), (26, 7), (5, 3), (11, 24), (15, 4), (23, 0), (21, 24), (22, 11), (8, 18), (9, 8), (19, 12), (22, 10), (9, 24), (4, 19), (21, 23), (5, 8), (22, 3), (24, 0), (13, 16), (11, 5), (18, 0), (27, 22), (11, 9), (12, 13), (19, 13), (9, 3), (25, 15), (15, 24), (16, 15), (9, 16), (14, 13), (18, 23), (25, 12), (13, 21), (17, 24), (24, 15), (18, 16), (12, 2), (25, 5), (10, 4), (16, 2), (20, 20), (7, 10), (2, 18), (6, 0), (11, 15), (13, 3), (20, 9), (4, 12), (25, 1), (26, 9), (26, 17), (4, 18), (8, 5), (25, 14), (17, 3), (20, 17), (5, 7), (20, 1), (2, 12), (7, 9), (11, 16), (21, 13), (21, 14), (27, 19), (19, 23), (5, 0), (14, 20), (23, 2), (16, 1), (0, 21), (9, 9), (21, 8), (24, 9), (12, 14), (7, 0), (24, 21), (10, 13), (10, 8), (8, 24), (11, 10), (13, 11), (19, 7), (22, 21), (15, 18), (17, 2), (21, 21), (13, 14), (10, 12), (20, 18), (21, 16), (13, 17), (20, 23), (4, 22), (0, 18), (1, 24), (6, 14), (7, 24), (5, 22), (26, 4), (2, 10), (12, 10), (15, 15), (18, 15), (0, 12), (6, 19), (3, 6), (23, 16), (13, 2), (27, 12), (14, 8), (10, 11), (17, 16), (23, 24), (27, 0), (8, 21), (26, 20), (1, 9), (4, 0), (9, 7), (3, 17), (7, 3), (3, 3), (12, 21), (12, 4), (24, 6), (15, 13), (11, 13), (3, 7), (16, 24), (27, 6), (1, 4), (22, 7), (17, 14), (14, 18), (24, 16), (14, 11), (27, 13), (8, 23), (3, 15), (27, 3), (26, 2), (21, 7), (27, 11), (9, 13), (14, 10), (16, 19), (16, 4), (2, 3), (11, 14), (23, 8), (1, 19), (13, 5), (25, 2), (16, 0), (15, 6), (25, 21), (24, 24), (17, 13), (3, 11), (1, 13), (23, 12), (4, 21), (8, 13), (6, 2), (10, 1), (4, 14), (13, 12), (15, 1), (6, 17), (20, 12), (12, 8), (18, 13), (16, 10), (12, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717526", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 15), (0, 24), (11, 17), (19, 12), (19, 25), (5, 17), (5, 6), (12, 3), (6, 3), (18, 19), (19, 19), (15, 20), (20, 12), (5, 11), (8, 10), (15, 21), (1, 8), (10, 18), (0, 25), (11, 22), (10, 5), (5, 4), (17, 27), (14, 25), (11, 0), (18, 8), (11, 5), (3, 21), (20, 26), (8, 9), (20, 8), (8, 8), (21, 0), (6, 27), (4, 24), (6, 7), (18, 24), (11, 18), (8, 4), (1, 5), (15, 17), (10, 23), (7, 2), (16, 13), (14, 7), (5, 25), (2, 3), (13, 6), (16, 18), (3, 12), (2, 16), (20, 6), (0, 2), (1, 28), (11, 7), (4, 6), (16, 0), (16, 21), (12, 19), (16, 14), (13, 24), (19, 21), (18, 27), (4, 26), (9, 19), (13, 22), (18, 15), (14, 18), (20, 9), (3, 23), (5, 23), (20, 16), (5, 15), (4, 9), (6, 0), (4, 7), (18, 18), (0, 3), (9, 16), (9, 2), (12, 20), (15, 11), (2, 21), (7, 14), (10, 13), (0, 8), (1, 18), (12, 24), (6, 15), (5, 13), (4, 0), (12, 10), (16, 6), (17, 19), (5, 5), (20, 10), (6, 28), (16, 5), (8, 3), (20, 7), (20, 27), (15, 13), (2, 5), (11, 23), (20, 21), (5, 27), (5, 28), (10, 16), (21, 22), (10, 28), (8, 21), (9, 4), (1, 16), (11, 27), (6, 10), (17, 15), (7, 4), (20, 0), (10, 27), (9, 13), (2, 18), (14, 16), (15, 8), (8, 5), (5, 8), (13, 11), (13, 16), (14, 12), (14, 23), (9, 5), (12, 15), (8, 18), (3, 0), (19, 1), (15, 0), (9, 28), (7, 16), (6, 4), (17, 8), (13, 12), (2, 24), (16, 9), (18, 26), (7, 1), (0, 27), (9, 14), (0, 9), (11, 4), (21, 12), (2, 14), (6, 9), (4, 23), (16, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55760", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 22), (24, 5), (25, 3), (3, 11), (0, 11), (15, 22), (6, 21), (7, 18), (26, 13), (8, 23), (0, 9), (2, 23), (17, 13), (17, 10), (27, 16), (20, 3), (4, 2), (14, 2), (0, 17), (11, 23), (13, 11), (15, 3), (12, 0), (26, 19), (1, 13), (26, 16), (20, 4), (18, 0), (16, 20), (8, 21), (24, 21), (24, 4), (4, 3), (18, 5), (7, 2), (1, 7), (17, 16), (5, 6), (17, 8), (13, 15), (13, 21), (19, 7), (9, 2), (16, 1), (9, 11), (11, 4), (19, 20), (21, 3), (15, 7), (26, 6), (15, 6), (23, 8), (21, 1), (18, 1), (7, 20), (18, 15), (8, 2), (12, 5), (5, 1), (25, 12), (23, 1), (0, 12), (5, 5), (22, 15), (20, 7), (13, 6), (21, 5), (10, 2), (5, 3), (20, 22), (11, 10), (15, 10), (3, 20), (10, 22), (25, 16), (24, 7), (18, 23), (5, 15), (19, 15), (9, 4), (16, 14), (10, 7), (14, 21), (2, 15), (13, 20), (12, 8), (4, 22), (21, 11), (5, 22), (4, 1), (8, 9), (10, 16), (27, 5), (19, 19), (22, 7), (4, 13), (25, 5), (2, 11), (24, 14), (27, 6), (7, 9), (1, 2), (23, 23), (17, 1), (5, 4), (4, 11), (18, 20), (1, 20), (17, 7), (1, 3), (22, 20), (18, 11), (21, 13), (12, 12), (17, 3), (4, 14), (19, 2), (12, 2), (5, 10), (26, 7), (6, 11), (5, 13), (10, 9), (13, 18), (3, 9), (23, 19), (18, 7), (8, 10), (1, 5), (22, 12), (14, 1), (5, 12), (11, 17), (0, 16), (7, 1), (21, 0), (12, 21), (14, 9), (5, 16), (0, 7), (23, 9), (21, 7), (21, 14), (26, 12), (23, 11), (10, 1), (4, 0), (12, 4), (22, 11), (15, 5), (7, 8), (22, 8), (7, 12), (21, 8), (22, 3), (5, 20), (10, 10), (25, 19), (18, 18), (24, 17), (3, 14), (6, 19), (24, 15), (22, 22), (27, 9), (14, 0), (23, 21), (25, 23), (24, 19), (7, 4), (5, 2), (3, 18), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341832", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 14), (8, 23), (16, 10), (3, 11), (3, 16), (2, 2), (5, 1), (7, 6), (15, 13), (13, 1), (18, 24), (6, 12), (12, 23), (1, 0), (9, 19), (9, 15), (15, 22), (10, 10), (12, 22), (10, 12), (9, 9), (6, 2), (1, 18), (14, 0), (9, 6), (20, 18), (3, 13), (21, 10), (1, 7), (13, 7), (10, 19), (10, 13), (5, 3), (17, 21), (21, 24), (10, 0), (2, 5), (12, 21), (4, 5), (16, 5), (2, 21), (3, 22), (17, 1), (20, 3), (2, 14), (4, 7), (4, 25), (18, 13), (20, 5), (5, 11), (19, 3), (7, 4), (12, 25), (1, 6), (10, 23), (5, 9), (7, 9), (20, 10), (19, 6), (16, 9), (9, 8), (17, 3), (4, 13), (8, 15), (14, 15), (12, 19), (14, 23), (16, 12), (4, 18), (20, 1), (16, 21), (17, 17), (3, 14), (16, 0), (17, 23), (9, 22), (12, 16), (15, 20), (11, 19), (13, 15), (20, 12), (8, 24), (13, 20), (0, 8), (7, 13), (18, 5), (20, 13), (16, 11), (13, 6), (20, 22), (3, 9), (3, 17), (15, 17), (6, 20), (20, 16), (4, 16), (12, 11), (10, 18), (16, 6), (3, 4), (8, 14), (6, 9), (11, 11), (5, 14), (4, 23), (11, 8), (16, 24), (21, 15), (9, 18), (11, 22), (1, 20), (6, 18), (7, 8), (15, 1), (2, 25), (19, 17), (14, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717336", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 9), (22, 19), (22, 16), (18, 27), (21, 12), (17, 24), (12, 2), (2, 8), (4, 26), (14, 8), (21, 15), (11, 4), (11, 19), (19, 1), (10, 9), (19, 16), (14, 4), (20, 5), (2, 14), (4, 8), (7, 19), (5, 7), (4, 19), (9, 23), (19, 6), (18, 9), (14, 24), (11, 20), (9, 16), (8, 7), (21, 21), (13, 11), (22, 14), (3, 25), (15, 13), (4, 11), (16, 27), (4, 10), (2, 5), (5, 16), (12, 22), (11, 22), (11, 21), (3, 8), (12, 12), (8, 8), (2, 18), (2, 6), (12, 9), (6, 22), (16, 15), (22, 15), (18, 3), (19, 0), (11, 24), (8, 16), (18, 18), (8, 25), (8, 21), (20, 8), (21, 25), (10, 15), (12, 14), (17, 21), (21, 27), (4, 1), (19, 2), (4, 22), (0, 22), (5, 6), (22, 1), (10, 17), (11, 14), (10, 5), (17, 14), (4, 13), (19, 19), (7, 1), (11, 18), (14, 17), (17, 0), (17, 10), (12, 20), (10, 10), (21, 22), (12, 4), (2, 17), (11, 23), (2, 0), (8, 26), (6, 1), (11, 11), (18, 6), (7, 18), (7, 10), (14, 7), (3, 2), (10, 11), (0, 5), (9, 0), (4, 6), (19, 8), (6, 20), (7, 22), (1, 27), (21, 13), (20, 3), (22, 20), (9, 20), (23, 22), (3, 1), (18, 8), (22, 5), (7, 13), (19, 24), (11, 17), (8, 10), (10, 8), (17, 2), (6, 15), (21, 2), (6, 21), (19, 22), (10, 6), (22, 11), (3, 24), (20, 20), (8, 0), (18, 20), (23, 24), (21, 17), (16, 9), (20, 14), (0, 1), (20, 24), (14, 12), (20, 9), (9, 15), (22, 24), (18, 23), (18, 26), (15, 2), (2, 25), (22, 21), (3, 15), (17, 23), (12, 0), (1, 23), (8, 22), (18, 19), (2, 22), (7, 2), (19, 4), (23, 20), (13, 0), (9, 17), (16, 0), (19, 18), (7, 14), (4, 15), (6, 10), (6, 8), (14, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814692", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 17), (23, 9), (21, 4), (17, 1), (2, 7), (7, 15), (4, 19), (22, 3), (12, 6), (12, 21), (1, 18), (22, 2), (13, 17), (19, 13), (3, 17), (22, 19), (16, 12), (5, 10), (21, 14), (14, 19), (11, 0), (18, 13), (23, 5), (23, 18), (0, 9), (7, 8), (25, 21), (21, 2), (9, 14), (22, 15), (13, 15), (25, 9), (14, 5), (10, 10), (12, 17), (1, 10), (18, 3), (23, 20), (23, 1), (6, 4), (20, 9), (4, 0), (22, 12), (15, 21), (19, 11), (14, 22), (25, 18), (2, 23), (25, 6), (23, 19), (23, 15), (11, 21), (16, 20), (4, 23), (21, 21), (14, 14), (25, 11), (9, 5), (16, 21), (2, 8), (0, 23), (18, 20), (6, 8), (25, 3), (12, 5), (21, 17), (22, 6), (1, 6), (18, 9), (24, 13), (3, 6), (19, 5), (23, 2), (0, 2), (25, 7), (19, 9), (15, 2), (16, 13), (15, 1), (17, 2), (8, 10), (7, 23), (13, 11), (14, 9), (8, 23), (1, 1), (14, 23), (11, 11), (16, 22), (19, 14), (9, 6), (9, 22), (23, 10), (19, 0), (9, 9), (20, 23), (20, 17), (4, 2), (1, 19), (18, 8), (6, 1), (8, 8), (6, 15), (5, 15), (10, 5), (26, 5), (6, 5), (21, 16), (3, 3), (23, 7), (26, 2), (11, 1), (26, 20), (16, 2), (21, 13), (4, 16), (13, 0), (19, 15), (8, 16), (2, 4), (1, 17), (10, 4), (0, 6), (20, 2), (24, 9), (6, 20), (9, 7), (23, 17), (17, 7), (18, 18), (12, 2), (5, 8), (2, 11), (11, 13), (13, 19), (15, 16), (21, 15), (7, 22), (23, 13), (8, 0), (9, 15), (2, 15), (15, 5), (12, 9), (8, 11), (8, 20), (7, 9), (20, 6), (26, 6), (8, 9), (10, 15), (14, 3), (5, 5), (9, 4), (0, 21), (1, 21), (21, 10), (6, 16), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528024", "dataset": "MATH"}
{"messages": [{"content": "In a 26x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 19), 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), (21, 18), (24, 11), (16, 17), (23, 7), (11, 0), (1, 1), (22, 1), (8, 14), (15, 17), (16, 18), (9, 17), (18, 19), (13, 1), (3, 0), (15, 8), (18, 10), (22, 18), (8, 12), (12, 12), (8, 11), (8, 6), (6, 0), (15, 9), (3, 13), (5, 13), (20, 0), (24, 9), (17, 17), (8, 4), (19, 5), (10, 15), (11, 8), (4, 11), (4, 17), (23, 5), (7, 12), (2, 12), (1, 17), (8, 9), (12, 11), (20, 14), (19, 6), (23, 8), (8, 5), (13, 7), (13, 16), (14, 1), (12, 6), (9, 7), (14, 2), (4, 16), (11, 14), (19, 9), (1, 13), (18, 0), (24, 13), (17, 11), (0, 17), (2, 8), (16, 15), (12, 19), (2, 19), (6, 15), (0, 10), (10, 12), (9, 5), (18, 8), (11, 17), (11, 12), (18, 2), (10, 1), (0, 9), (16, 5), (23, 14), (17, 12), (25, 18), (1, 11), (5, 6), (25, 10), (21, 1), (21, 12), (25, 5), (18, 1), (16, 13), (12, 16), (0, 12), (19, 16), (13, 4), (23, 13), (15, 14), (5, 16), (3, 9), (1, 15), (8, 17), (5, 17), (0, 5), (6, 4), (1, 19), (24, 4), (8, 1), (11, 7), (7, 0), (20, 13), (17, 13), (8, 7), (23, 17), (12, 10), (21, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785516", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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), (16, 12), (17, 19), (12, 11), (15, 20), (11, 14), (0, 14), (3, 7), (23, 2), (6, 4), (12, 14), (16, 20), (21, 14), (4, 12), (0, 4), (18, 0), (0, 19), (11, 7), (20, 5), (23, 1), (8, 0), (10, 1), (20, 15), (16, 5), (20, 12), (5, 2), (18, 7), (8, 7), (15, 19), (18, 5), (22, 14), (3, 8), (2, 15), (12, 13), (20, 10), (23, 3), (1, 15), (13, 15), (23, 16), (13, 18), (22, 12), (14, 11), (1, 11), (0, 1), (22, 19), (20, 18), (20, 8), (20, 7), (6, 0), (8, 2), (8, 16), (14, 4), (10, 6), (2, 9), (20, 1), (7, 10), (11, 3), (11, 10), (17, 2), (8, 11), (9, 1), (21, 16), (11, 2), (13, 9), (3, 15), (4, 8), (18, 8), (5, 4), (4, 18), (23, 10), (22, 17), (6, 12), (1, 8), (4, 1), (4, 19), (22, 1), (11, 19), (6, 20), (16, 11), (10, 9), (15, 13), (16, 2), (16, 10), (2, 16), (0, 13), (3, 10), (7, 18), (11, 8), (16, 15), (12, 20), (19, 7), (10, 0), (8, 19), (5, 0), (19, 19), (20, 14), (8, 3), (22, 4), (3, 4), (22, 16), (15, 15), (0, 7), (19, 4), (10, 11), (21, 11), (2, 8), (7, 5), (12, 18), (18, 3), (13, 12), (1, 2), (7, 16), (10, 20), (3, 1), (6, 1), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967392", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), 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, 4), (3, 2), (19, 9), (8, 28), (15, 3), (1, 21), (4, 13), (7, 7), (20, 6), (8, 9), (23, 10), (15, 17), (19, 4), (21, 28), (17, 20), (12, 15), (9, 8), (11, 10), (11, 2), (24, 10), (26, 7), (18, 4), (26, 13), (8, 7), (3, 21), (25, 2), (11, 24), (14, 13), (16, 20), (17, 28), (25, 25), (9, 25), (0, 24), (12, 26), (9, 16), (26, 8), (16, 16), (26, 16), (2, 26), (11, 22), (26, 2), (5, 16), (13, 11), (20, 2), (11, 17), (7, 22), (26, 17), (13, 9), (16, 14), (14, 12), (3, 27), (20, 11), (5, 2), (0, 2), (14, 27), (12, 21), (3, 9), (25, 12), (23, 5), (21, 13), (9, 3), (8, 5), (21, 26), (5, 13), (25, 28), (5, 18), (14, 22), (7, 10), (6, 24), (1, 22), (25, 6), (0, 1), (10, 19), (0, 6), (16, 27), (1, 15), (13, 22), (1, 12), (21, 0), (24, 6), (10, 7), (22, 28), (5, 28), (18, 5), (19, 11), (6, 23), (12, 25), (18, 14), (18, 0), (26, 23), (4, 19), (18, 12), (0, 10), (1, 25), (8, 11), (15, 20), (19, 13), (26, 20), (15, 1), (25, 18), (22, 14), (16, 13), (25, 4), (4, 22), (25, 0), (2, 0), (20, 8), (15, 21), (5, 26), (12, 28), (11, 12), (2, 14), (17, 24), (22, 17), (0, 4), (12, 6), (2, 11), (13, 18), (9, 26), (5, 7), (16, 6), (26, 24), (19, 24), (12, 12), (4, 27), (19, 14), (7, 8), (22, 22), (6, 12), (5, 11), (19, 26), (6, 20), (19, 25), (17, 13), (13, 8), (9, 22), (14, 6), (10, 21), (6, 6), (8, 15), (26, 15), (24, 0), (16, 9), (23, 1), (20, 12), (7, 23), (11, 19), (3, 4), (17, 5), (19, 6), (19, 16), (25, 7), (20, 25), (26, 10), (0, 19), (23, 12), (16, 4), (12, 18), (24, 11), (1, 6), (24, 4), (12, 23), (5, 27), (10, 23), (11, 20), (24, 1), (15, 2), (26, 3), (22, 2), (15, 16), (21, 18), (8, 17), (9, 24), (21, 3), (20, 9), (5, 6), (0, 15), (23, 28), (17, 2), (15, 27), (18, 7), (25, 15), (7, 6), (8, 23), (4, 28), (21, 7), (26, 21), (5, 20), (2, 5), (23, 0), (26, 0), (0, 12), (15, 6), (2, 10), (5, 21), (13, 19), (1, 23), (3, 5), (12, 10), (10, 25), (0, 11), (3, 22), (4, 16), (3, 10), (7, 19), (21, 19), (5, 19), (14, 5), (17, 8), (12, 7), (7, 13), (17, 15), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28380", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (13, 22), (25, 16), (4, 22), (13, 28), (12, 2), (22, 19), (12, 18), (10, 13), (2, 3), (17, 21), (0, 26), (9, 27), (23, 9), (23, 18), (19, 22), (12, 13), (21, 14), (0, 5), (1, 10), (14, 18), (6, 0), (2, 14), (25, 11), (1, 5), (15, 11), (4, 26), (21, 26), (20, 22), (12, 4), (1, 18), (20, 16), (4, 24), (7, 13), (17, 28), (4, 19), (4, 28), (18, 12), (7, 25), (16, 25), (25, 6), (4, 1), (25, 1), (16, 5), (8, 6), (16, 11), (14, 12), (7, 17), (7, 22), (7, 2), (13, 15), (13, 2), (3, 27), (1, 24), (11, 4), (10, 11), (8, 1), (6, 13), (3, 7), (25, 17), (8, 26), (13, 8), (14, 16), (9, 15), (19, 12), (1, 11), (19, 20), (23, 7), (20, 24), (24, 27), (19, 1), (10, 28), (9, 21), (2, 11), (5, 19), (5, 3), (6, 5), (4, 27), (19, 16), (7, 10), (6, 18), (21, 17), (4, 5), (2, 25), (0, 4), (11, 2), (9, 12), (0, 21), (4, 10), (9, 6), (8, 20), (24, 4), (14, 21), (1, 14), (21, 4), (24, 21), (19, 8), (4, 25), (11, 23), (14, 22), (5, 18), (8, 21), (23, 1), (25, 20), (22, 18), (15, 10), (25, 8), (6, 14), (3, 15), (7, 9), (21, 10), (20, 14), (11, 13), (16, 10), (16, 15), (21, 19), (22, 27), (17, 13), (1, 19), (14, 26), (11, 14), (5, 14), (17, 10), (1, 13), (18, 13), (20, 11), (12, 16), (10, 20), (21, 22), (4, 20), (18, 24), (17, 4), (18, 6), (4, 4), (7, 6), (11, 6), (6, 3), (14, 17), (14, 25), (19, 4), (16, 0), (9, 4), (20, 0), (9, 25), (4, 23), (17, 16), (3, 6), (7, 23), (6, 1), (0, 16), (21, 12), (13, 27), (22, 20), (15, 24), (25, 22), (21, 24), (3, 20), (17, 23), (1, 21), (5, 15), (19, 28), (11, 19), (24, 19), (0, 2), (18, 26), (4, 9), (2, 26), (2, 23), (13, 10), (12, 7), (0, 25), (7, 16), (0, 6), (8, 2), (16, 8), (24, 6), (13, 11), (17, 25), (20, 15), (5, 24), (15, 25), (17, 17), (1, 27), (7, 19), (25, 13), (19, 19), (25, 24), (7, 21), (6, 25), (10, 7), (20, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787912", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), 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, 24), (18, 19), (23, 17), (18, 2), (0, 15), (24, 12), (19, 15), (2, 4), (13, 19), (3, 15), (20, 4), (24, 1), (3, 16), (3, 20), (20, 25), (4, 0), (22, 23), (9, 22), (6, 18), (10, 0), (18, 11), (20, 2), (19, 11), (0, 18), (7, 17), (9, 10), (7, 16), (7, 6), (13, 20), (0, 17), (5, 15), (13, 23), (23, 24), (19, 9), (22, 7), (8, 16), (1, 19), (13, 18), (9, 5), (6, 0), (18, 22), (22, 0), (5, 23), (10, 14), (3, 12), (18, 5), (5, 9), (7, 13), (14, 3), (2, 2), (20, 18), (2, 12), (13, 24), (22, 25), (16, 19), (5, 3), (18, 4), (22, 20), (9, 16), (1, 6), (5, 24), (14, 12), (14, 11), (4, 3), (4, 21), (4, 11), (8, 20), (3, 11), (6, 22), (5, 19), (0, 5), (10, 5), (2, 21), (9, 11), (17, 21), (6, 10), (23, 10), (15, 1), (19, 20), (14, 25), (20, 9), (15, 5), (17, 14), (4, 12), (2, 6), (17, 24), (22, 14), (1, 7), (13, 22), (6, 4), (7, 1), (2, 10), (1, 24), (4, 20), (1, 12), (8, 3), (16, 18), (20, 13), (18, 7), (7, 2), (16, 3), (21, 25), (4, 18), (6, 19), (5, 20), (24, 9), (16, 23), (23, 14), (4, 7), (19, 19), (4, 9), (13, 25), (7, 12), (19, 12), (11, 0), (2, 24), (8, 25), (1, 20), (9, 4), (17, 19), (15, 20), (18, 20), (10, 4), (1, 25), (11, 25), (9, 14), (6, 5), (24, 18), (5, 8), (9, 19), (16, 20), (21, 8), (20, 1), (10, 7), (8, 22), (12, 7), (10, 22), (14, 17), (9, 12), (17, 23), (14, 19), (6, 2), (4, 1), (6, 1), (15, 6), (17, 4), (14, 22), (15, 23), (7, 15), (0, 8), (20, 3), (11, 12), (7, 5), (19, 17), (16, 10), (15, 24), (11, 8), (24, 20), (16, 2), (6, 21), (21, 3), (0, 16), (20, 16), (11, 21), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179928", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), 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), (14, 2), (17, 6), (12, 6), (16, 16), (20, 19), (1, 8), (27, 18), (13, 0), (5, 17), (10, 0), (10, 8), (24, 17), (22, 12), (16, 7), (23, 10), (18, 4), (23, 6), (12, 4), (3, 8), (25, 13), (21, 11), (18, 10), (25, 8), (26, 16), (22, 1), (21, 15), (11, 19), (19, 18), (1, 4), (27, 13), (9, 19), (21, 4), (17, 15), (17, 18), (17, 10), (27, 7), (25, 0), (2, 8), (18, 6), (10, 17), (22, 9), (3, 15), (14, 10), (25, 14), (23, 13), (10, 5), (6, 10), (6, 17), (4, 7), (6, 2), (3, 0), (9, 4), (12, 13), (22, 5), (9, 7), (9, 18), (14, 13), (2, 17), (15, 1), (25, 3), (23, 16), (19, 12), (8, 12), (18, 14), (26, 8), (16, 8), (7, 2), (8, 19), (16, 2), (27, 16), (15, 11), (22, 3), (21, 2), (11, 3), (20, 18), (25, 7), (17, 19), (27, 8), (17, 2), (13, 12), (28, 1), (22, 13), (5, 18), (20, 1), (20, 12), (22, 8), (1, 10), (28, 14), (26, 4), (13, 8), (24, 3), (11, 8), (26, 19), (25, 11), (22, 14), (20, 13), (16, 6), (28, 13), (3, 2), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892635", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 2), (2, 8), (11, 2), (8, 10), (8, 16), (9, 21), (11, 10), (10, 7), (3, 18), (4, 7), (7, 4), (15, 20), (19, 12), (11, 4), (20, 15), (10, 19), (2, 12), (5, 3), (18, 13), (4, 0), (19, 5), (10, 20), (14, 14), (1, 13), (19, 17), (11, 19), (12, 12), (11, 8), (10, 3), (20, 20), (11, 6), (4, 10), (15, 7), (2, 11), (2, 9), (2, 19), (15, 16), (16, 14), (10, 14), (8, 3), (12, 14), (11, 15), (0, 6), (12, 7), (4, 8), (18, 2), (19, 1), (10, 11), (19, 20), (4, 16), (20, 13), (5, 6), (1, 5), (3, 16), (9, 12), (7, 0), (4, 9), (13, 21), (12, 16), (5, 13), (14, 5), (14, 6), (16, 21), (10, 10), (6, 11), (9, 1), (8, 11), (8, 20), (5, 19), (7, 14), (20, 19), (5, 4), (17, 13), (16, 8), (2, 6), (7, 8), (4, 19), (15, 13), (3, 13), (12, 5), (13, 12), (4, 6), (15, 14), (3, 14), (13, 7), (1, 3), (19, 11), (4, 21), (13, 15), (19, 7), (7, 15), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738330", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 11), (15, 0), (10, 7), (11, 22), (17, 4), (5, 13), (11, 14), (8, 12), (6, 7), (2, 7), (0, 12), (4, 23), (7, 2), (18, 18), (17, 1), (6, 0), (6, 22), (3, 21), (12, 22), (10, 9), (6, 9), (20, 10), (10, 4), (20, 13), (14, 23), (5, 8), (16, 21), (10, 2), (0, 18), (7, 8), (12, 7), (14, 5), (18, 7), (14, 9), (20, 4), (16, 17), (18, 20), (4, 8), (16, 13), (17, 2), (9, 21), (16, 22), (8, 21), (19, 8), (4, 9), (20, 6), (6, 1), (14, 14), (12, 12), (10, 21), (9, 16), (14, 0), (14, 15), (11, 17), (3, 14), (0, 11), (15, 8), (5, 9), (1, 6), (12, 8), (9, 6), (19, 15), (15, 9), (1, 22), (11, 20), (6, 11), (8, 13), (10, 0), (7, 20), (20, 17), (16, 15), (0, 20), (7, 0), (1, 3), (17, 22), (6, 2), (13, 18), (17, 14), (17, 17), (0, 19), (0, 10), (6, 23), (8, 7), (10, 5), (11, 12), (13, 12), (7, 13), (11, 15), (1, 9), (19, 7), (2, 5), (11, 9), (16, 7), (3, 13), (5, 7), (17, 15), (16, 19), (3, 1), (4, 19), (8, 15), (14, 20), (5, 22), (17, 12), (15, 22), (11, 18), (21, 18), (13, 10), (18, 23), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895442", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 22), (3, 17), (6, 8), (6, 2), (13, 20), (14, 11), (4, 12), (7, 3), (20, 15), (8, 10), (5, 22), (7, 1), (11, 7), (6, 21), (10, 6), (17, 11), (20, 12), (2, 8), (0, 15), (17, 13), (5, 20), (0, 10), (0, 4), (9, 1), (17, 17), (3, 6), (0, 1), (16, 18), (18, 11), (16, 9), (17, 7), (1, 2), (18, 2), (14, 13), (6, 10), (12, 11), (15, 0), (20, 10), (2, 6), (4, 11), (13, 13), (1, 16), (17, 20), (5, 17), (19, 15), (11, 11), (18, 3), (10, 4), (10, 1), (1, 18), (15, 13), (4, 19), (19, 19), (5, 13), (17, 2), (16, 10), (1, 21), (12, 13), (5, 10), (13, 19), (12, 8), (7, 13), (16, 12), (0, 16), (5, 19), (10, 15), (9, 7), (16, 15), (6, 4), (5, 18), (10, 16), (1, 17), (12, 18), (2, 20), (10, 20), (14, 5), (1, 14), (13, 14), (11, 10), (7, 22), (1, 20), (1, 15), (11, 22), (3, 9), (16, 20), (14, 6), (3, 19), (6, 5), (1, 6), (11, 2), (15, 3), (10, 5), (15, 20), (2, 12), (7, 21), (17, 9), (12, 5), (6, 22), (19, 5), (15, 17), (2, 18), (16, 11), (5, 16), (15, 12), (0, 9), (2, 11), (3, 21), (2, 19), (19, 21), (12, 1), (11, 19), (8, 6), (9, 17), (8, 3), (10, 2), (15, 9), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36512", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (17, 11), (4, 3), (9, 13), (1, 21), (12, 18), (13, 17), (12, 2), (14, 16), (2, 4), (4, 9), (17, 13), (16, 18), (10, 19), (12, 16), (19, 16), (5, 3), (9, 5), (6, 19), (14, 20), (10, 15), (15, 13), (12, 5), (5, 5), (1, 3), (8, 10), (2, 7), (14, 0), (18, 13), (15, 1), (11, 16), (6, 10), (2, 10), (16, 10), (17, 20), (3, 9), (12, 11), (10, 7), (18, 22), (10, 9), (12, 7), (12, 15), (10, 10), (7, 7), (13, 22), (5, 10), (4, 0), (6, 14), (3, 7), (17, 10), (1, 20), (14, 15), (8, 1), (17, 4), (7, 13), (8, 20), (16, 20), (17, 1), (18, 16), (13, 21), (5, 18), (10, 14), (10, 22), (19, 8), (3, 19), (17, 16), (8, 9), (1, 2), (13, 13), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887448", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (0, 5), (19, 7), (19, 1), (15, 9), (16, 16), (23, 14), (16, 12), (4, 16), (11, 11), (18, 3), (2, 10), (14, 2), (8, 17), (0, 13), (17, 0), (18, 17), (11, 19), (12, 18), (10, 2), (1, 15), (7, 19), (21, 10), (11, 4), (1, 19), (21, 11), (13, 1), (21, 7), (14, 6), (10, 15), (12, 16), (23, 3), (18, 13), (1, 11), (21, 3), (0, 8), (16, 0), (10, 16), (1, 1), (5, 0), (19, 0), (15, 17), (10, 11), (12, 2), (6, 17), (6, 6), (18, 19), (23, 10), (20, 10), (7, 17), (17, 19), (17, 15), (17, 3), (15, 2), (2, 7), (17, 17), (9, 18), (17, 4), (18, 15), (8, 4), (11, 3), (1, 13), (0, 14), (21, 16), (2, 9), (2, 11), (14, 5), (13, 13), (12, 12), (17, 7), (22, 4), (9, 16), (7, 7), (14, 11), (16, 19), (13, 0), (5, 4), (20, 19), (11, 6), (12, 4), (1, 7), (2, 13), (23, 1), (17, 6), (14, 12), (15, 6), (6, 19), (5, 10), (13, 8), (13, 12), (7, 12), (5, 11), (5, 3), (6, 3), (0, 6), (2, 12), (9, 13), (3, 14), (22, 14), (4, 2), (21, 6), (11, 1), (1, 3), (1, 18), (22, 16), (19, 3), (9, 11), (17, 2), (15, 19), (13, 4), (6, 1), (16, 1), (18, 10), (19, 2), (5, 7), (22, 6), (23, 7), (20, 3), (7, 5), (3, 8), (15, 4), (19, 6), (17, 5), (7, 15), (23, 4), (3, 19), (4, 10), (21, 5), (21, 12), (10, 12), (1, 9), (15, 11), (8, 14), (14, 0), (5, 19), (21, 0), (21, 17), (14, 18), (16, 5), (21, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "903798", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 4), (20, 21), (2, 8), (24, 3), (19, 0), (9, 5), (0, 24), (4, 27), (20, 5), (25, 12), (26, 16), (8, 11), (14, 21), (20, 6), (6, 18), (14, 16), (18, 0), (2, 25), (8, 9), (20, 27), (22, 13), (15, 17), (15, 0), (12, 1), (6, 13), (18, 9), (25, 4), (25, 25), (4, 8), (23, 9), (14, 18), (12, 18), (15, 8), (8, 3), (19, 11), (5, 10), (6, 27), (25, 19), (14, 6), (25, 1), (24, 11), (24, 9), (3, 6), (19, 24), (10, 9), (13, 3), (4, 10), (4, 23), (9, 10), (8, 12), (23, 11), (6, 24), (16, 16), (11, 6), (12, 27), (23, 21), (6, 20), (8, 27), (23, 2), (22, 9), (22, 16), (19, 25), (21, 21), (4, 2), (11, 26), (15, 22), (1, 12), (27, 18), (26, 1), (5, 27), (4, 4), (17, 15), (19, 15), (0, 21), (26, 17), (1, 14), (14, 11), (1, 25), (8, 5), (17, 2), (24, 18), (0, 23), (11, 11), (22, 8), (21, 25), (2, 27), (9, 0), (9, 6), (3, 18), (8, 2), (18, 17), (0, 14), (21, 1), (22, 14), (13, 15), (11, 20), (5, 16), (21, 2), (27, 21), (14, 26), (10, 12), (19, 7), (21, 11), (17, 4), (4, 26), (6, 26), (4, 14), (3, 2), (2, 7), (23, 6), (24, 21), (2, 19), (18, 13), (14, 24), (17, 10), (6, 3), (7, 12), (15, 12), (7, 5), (21, 8), (4, 6), (21, 5), (11, 13), (15, 14), (16, 12), (0, 19), (13, 11), (13, 18), (12, 3), (18, 12), (16, 15), (10, 27), (3, 26), (21, 27), (11, 21), (10, 8), (20, 12), (27, 1), (9, 16), (14, 15), (16, 18), (17, 1), (26, 2), (2, 17), (10, 10), (18, 6), (23, 5), (5, 18), (20, 14), (26, 5), (3, 13), (17, 24), (9, 12), (8, 13), (17, 20), (10, 26), (8, 26), (21, 17), (3, 27), (16, 27), (3, 19), (27, 4), (7, 21), (6, 0), (12, 26), (14, 2), (4, 11), (18, 3), (24, 16), (5, 2), (6, 5), (3, 3), (0, 8), (17, 21), (26, 27), (5, 6), (25, 27), (21, 19), (25, 8), (16, 6), (12, 15), (3, 9), (9, 13), (17, 14), (9, 9), (4, 1), (14, 4), (18, 2), (0, 13), (7, 26), (4, 18), (16, 24), (18, 20), (17, 17), (2, 18), (17, 22), (22, 2), (3, 14), (11, 25), (9, 25), (1, 1), (24, 27), (14, 0), (2, 3), (27, 6), (19, 12), (11, 8), (5, 7), (15, 24), (23, 27), (27, 0), (7, 20), (11, 16), (6, 4), (10, 19), (11, 12), (15, 19), (22, 23), (14, 20), (4, 15), (2, 11), (18, 24), (22, 17), (25, 9), (2, 16), (17, 3), (5, 9), (5, 17), (12, 11), (20, 2), (18, 10), (4, 13), (8, 7), (9, 14), (15, 10), (0, 27), (24, 15), (13, 16), (11, 5), (20, 15), (10, 24), (3, 23), (10, 6), (12, 12), (21, 16), (17, 9), (14, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915744", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 20), (15, 21), (4, 8), (4, 0), (15, 2), (7, 16), (16, 6), (6, 15), (6, 19), (2, 20), (1, 5), (17, 1), (9, 5), (3, 21), (6, 8), (19, 9), (6, 1), (13, 14), (10, 3), (7, 12), (8, 10), (11, 6), (13, 1), (18, 21), (3, 20), (19, 7), (7, 7), (15, 10), (0, 15), (8, 17), (15, 20), (1, 18), (9, 7), (8, 2), (6, 3), (7, 17), (2, 8), (9, 15), (5, 17), (18, 11), (8, 4), (19, 11), (12, 2), (14, 14), (18, 19), (17, 0), (12, 0), (11, 8), (19, 10), (15, 0), (0, 4), (2, 17), (7, 21), (0, 6), (3, 6), (15, 3), (6, 2), (15, 15), (1, 12), (10, 16), (13, 7), (2, 16), (17, 21), (11, 21), (11, 16), (15, 16), (6, 12), (3, 16), (1, 11), (10, 10), (6, 18), (5, 9), (12, 8), (2, 11), (12, 6), (11, 12), (19, 17), (0, 13), (4, 14), (3, 2), (16, 12), (14, 3), (2, 6), (11, 18), (2, 15), (0, 16), (8, 19), (5, 12), (3, 3), (0, 19), (9, 19), (6, 0), (14, 2), (11, 0), (19, 2), (16, 16), (14, 7), (6, 6), (1, 16), (17, 19), (10, 12), (14, 22), (14, 17), (16, 2), (9, 4), (14, 15), (0, 9), (13, 10), (0, 21), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "809276", "dataset": "MATH"}
{"messages": [{"content": "In a 25x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 22), 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), (21, 19), (18, 18), (22, 19), (12, 8), (3, 17), (13, 7), (11, 5), (11, 10), (20, 18), (10, 2), (6, 3), (22, 14), (1, 15), (10, 15), (5, 19), (24, 4), (21, 8), (17, 4), (21, 4), (2, 13), (18, 12), (17, 14), (8, 14), (20, 14), (20, 6), (7, 20), (23, 4), (15, 4), (22, 1), (2, 16), (1, 8), (2, 10), (17, 9), (2, 9), (22, 9), (18, 2), (19, 17), (9, 12), (1, 10), (3, 9), (12, 9), (2, 0), (23, 14), (5, 22), (6, 2), (21, 10), (24, 15), (8, 17), (16, 19), (6, 22), (4, 13), (24, 5), (19, 18), (14, 1), (18, 19), (22, 16), (19, 3), (1, 21), (0, 7), (2, 2), (21, 22), (7, 8), (8, 19), (7, 10), (21, 11), (14, 2), (4, 10), (20, 21), (14, 4), (6, 4), (17, 3), (23, 7), (6, 13), (3, 16), (1, 14), (2, 18), (22, 18), (12, 21), (2, 4), (10, 9), (7, 3), (19, 0), (4, 8), (13, 16), (17, 20), (12, 6), (20, 20), (20, 8), (6, 0), (15, 18), (11, 16), (14, 10), (23, 8), (16, 5), (13, 8), (12, 13), (5, 6), (14, 3), (21, 2), (15, 22), (3, 5), (3, 18), (24, 1), (6, 18), (8, 12), (23, 18), (4, 3), (1, 17), (0, 14), (20, 5), (3, 6), (8, 9), (12, 18), (10, 7), (9, 19), (2, 6), (17, 11), (13, 4), (20, 13), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940302", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 22), (4, 18), (19, 17), (16, 17), (10, 9), (5, 16), (9, 5), (17, 24), (2, 26), (10, 24), (18, 17), (8, 22), (18, 21), (12, 8), (13, 17), (18, 8), (16, 11), (3, 13), (1, 19), (4, 9), (16, 13), (5, 6), (2, 20), (9, 18), (11, 13), (7, 6), (4, 25), (9, 16), (15, 16), (13, 23), (16, 0), (16, 8), (6, 3), (8, 2), (16, 19), (0, 1), (0, 26), (2, 6), (15, 4), (6, 22), (5, 12), (15, 2), (16, 2), (10, 20), (17, 12), (5, 17), (2, 18), (9, 15), (18, 19), (8, 8), (0, 12), (4, 4), (17, 16), (12, 20), (9, 10), (8, 5), (6, 17), (10, 6), (12, 26), (1, 21), (15, 8), (17, 20), (1, 22), (3, 23), (2, 1), (13, 4), (6, 15), (14, 24), (10, 4), (13, 5), (10, 25), (5, 19), (7, 9), (8, 17), (17, 26), (6, 0), (12, 23), (18, 2), (11, 8), (13, 20), (11, 10), (3, 4), (11, 23), (18, 10), (3, 7), (2, 23), (4, 8), (12, 6), (12, 7), (1, 7), (7, 22), (1, 15), (15, 1), (16, 16), (13, 25), (14, 12), (7, 11), (0, 21), (9, 9), (18, 1), (19, 22), (16, 18), (12, 12), (17, 19), (12, 17), (18, 12), (5, 9), (14, 1), (2, 2), (6, 12), (4, 22), (1, 20), (17, 2), (12, 18), (10, 0), (16, 26), (1, 16), (4, 3), (19, 12), (10, 22), (13, 22), (5, 1), (2, 13), (3, 12), (9, 22), (7, 25), (4, 1), (10, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672656", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), 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), (3, 15), (5, 17), (15, 16), (15, 5), (9, 13), (18, 11), (1, 14), (8, 10), (17, 18), (3, 13), (17, 6), (12, 5), (3, 4), (5, 9), (3, 17), (25, 10), (11, 18), (9, 7), (18, 12), (7, 20), (17, 7), (11, 9), (20, 9), (24, 3), (1, 12), (1, 16), (1, 4), (17, 11), (11, 6), (24, 14), (22, 6), (19, 17), (4, 1), (6, 8), (17, 12), (5, 3), (7, 18), (5, 12), (14, 4), (8, 4), (20, 11), (13, 20), (8, 11), (16, 6), (4, 0), (13, 1), (5, 20), (16, 15), (19, 3), (2, 12), (16, 17), (23, 14), (24, 2), (3, 2), (17, 5), (11, 2), (23, 7), (9, 15), (23, 2), (7, 13), (5, 16), (4, 15), (22, 17), (20, 7), (2, 0), (13, 6), (4, 12), (7, 2), (16, 3), (18, 10), (25, 16), (20, 20), (18, 2), (6, 15), (19, 20), (8, 3), (11, 8), (15, 12), (18, 17), (22, 11), (13, 7), (6, 13), (12, 15), (19, 1), (20, 3), (4, 11), (6, 14), (15, 0), (0, 19), (24, 18), (23, 5), (22, 1), (6, 11), (23, 10), (19, 12), (1, 18), (24, 15), (11, 14), (21, 5), (16, 7), (19, 9), (2, 13), (23, 8), (4, 13), (22, 12), (10, 10), (4, 6), (18, 7), (0, 1), (5, 4), (21, 9), (0, 17), (7, 1), (11, 10), (20, 2), (10, 20), (15, 8), (22, 4), (11, 4), (11, 5), (22, 9), (13, 11), (20, 4), (19, 0), (20, 18), (9, 10), (25, 14), (17, 1), (0, 18), (13, 4), (21, 3), (23, 4), (25, 4), (25, 15), (18, 5), (20, 1), (10, 7), (9, 1), (10, 15), (1, 3), (8, 7), (9, 0), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31020", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (4, 4), (13, 10), (10, 28), (3, 22), (16, 17), (17, 9), (2, 18), (4, 15), (11, 10), (15, 12), (13, 12), (19, 23), (5, 11), (3, 27), (19, 4), (0, 6), (18, 5), (20, 24), (2, 4), (4, 12), (19, 6), (9, 26), (4, 14), (23, 17), (18, 3), (6, 23), (7, 10), (2, 17), (5, 12), (13, 18), (19, 21), (14, 14), (12, 24), (12, 4), (7, 13), (20, 25), (23, 0), (4, 22), (12, 19), (8, 6), (19, 19), (4, 21), (15, 14), (22, 20), (21, 12), (20, 6), (21, 21), (17, 6), (6, 15), (16, 0), (1, 5), (18, 4), (1, 24), (7, 25), (13, 13), (18, 18), (19, 0), (0, 5), (12, 6), (20, 0), (13, 19), (1, 7), (1, 19), (14, 4), (15, 7), (12, 18), (21, 22), (9, 5), (11, 23), (3, 10), (20, 3), (23, 21), (17, 8), (1, 18), (20, 19), (22, 1), (7, 2), (4, 9), (8, 24), (17, 3), (6, 24), (15, 21), (11, 13), (1, 22), (12, 25), (12, 23), (17, 23), (17, 17), (22, 11), (15, 20), (8, 10), (13, 1), (23, 5), (7, 7), (5, 26), (17, 14), (1, 12), (1, 20), (20, 13), (22, 10), (12, 15), (13, 15), (8, 2), (1, 3), (12, 27), (5, 22), (2, 1), (22, 6), (9, 17), (1, 0), (22, 24), (21, 10), (5, 23), (3, 0), (7, 14), (11, 18), (8, 4), (8, 5), (15, 10), (9, 7), (5, 16), (14, 23), (23, 25), (12, 5), (5, 27), (10, 0), (19, 9), (13, 2), (2, 16), (17, 15), (9, 10), (18, 15), (4, 28), (19, 20), (4, 8), (23, 8), (6, 14), (11, 16), (22, 14), (22, 21), (0, 16), (23, 12), (11, 19), (4, 25), (14, 5), (12, 10), (1, 11), (0, 14), (14, 10), (21, 16), (5, 0), (23, 19), (1, 16), (22, 26), (9, 0), (9, 3), (2, 0), (15, 11), (21, 14), (20, 21), (11, 7), (18, 21), (5, 3), (21, 23), (21, 3), (15, 2), (17, 2), (4, 13), (18, 0), (0, 8), (8, 26), (23, 9), (2, 5), (0, 22), (12, 21), (10, 26), (22, 2), (14, 19), (9, 12), (18, 2), (6, 10), (20, 11), (7, 5), (19, 25), (4, 26), (1, 17), (14, 21), (11, 9), (23, 23), (12, 17), (20, 16), (20, 4), (22, 25), (12, 8), (6, 18), (21, 25), (3, 17), (16, 13), (5, 10), (4, 19), (2, 27), (2, 21), (7, 17), (23, 14), (14, 0), (4, 17), (3, 21), (8, 1), (17, 1), (17, 25), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380688", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 26), (4, 11), (0, 5), (25, 10), (26, 19), (2, 27), (8, 24), (2, 16), (24, 27), (14, 4), (27, 2), (2, 17), (17, 27), (22, 5), (6, 11), (0, 23), (23, 10), (5, 27), (20, 19), (22, 20), (26, 1), (10, 2), (23, 27), (5, 23), (1, 25), (4, 17), (15, 16), (23, 2), (2, 8), (6, 23), (12, 24), (6, 16), (15, 27), (12, 18), (21, 25), (4, 16), (27, 25), (6, 9), (8, 14), (12, 27), (6, 10), (7, 0), (26, 8), (27, 12), (21, 18), (0, 3), (1, 23), (7, 3), (1, 17), (11, 19), (13, 18), (20, 7), (6, 7), (7, 11), (10, 16), (24, 24), (17, 3), (18, 14), (4, 7), (23, 16), (17, 21), (0, 22), (12, 21), (2, 0), (6, 26), (3, 21), (5, 25), (12, 9), (21, 13), (2, 13), (9, 27), (8, 26), (5, 8), (23, 7), (23, 19), (22, 25), (15, 20), (4, 12), (2, 15), (16, 26), (18, 17), (26, 7), (20, 27), (27, 21), (8, 1), (19, 26), (10, 24), (13, 12), (22, 12), (19, 9), (18, 5), (22, 0), (21, 12), (2, 26), (8, 0), (11, 18), (19, 15), (7, 12), (20, 4), (26, 26), (4, 23), (6, 27), (22, 7), (3, 11), (7, 22), (2, 11), (18, 10), (25, 25), (24, 1), (21, 9), (12, 4), (3, 4), (19, 18), (14, 18), (9, 21), (19, 20), (4, 22), (23, 5), (21, 5), (2, 22), (25, 9), (4, 18), (18, 20), (18, 13), (15, 2), (20, 24), (27, 19), (1, 22), (19, 5), (26, 5), (7, 17), (7, 26), (23, 14), (12, 23), (9, 11), (0, 21), (4, 26), (20, 5), (24, 0), (2, 10), (14, 22), (27, 15), (27, 23), (22, 27), (6, 25), (21, 10), (13, 10), (13, 1), (7, 9), (6, 18), (5, 26), (12, 26), (6, 6), (18, 19), (8, 11), (26, 3), (26, 17), (9, 7), (25, 2), (26, 2), (3, 12), (17, 15), (22, 14), (25, 19), (3, 15), (11, 11), (0, 26), (0, 17), (11, 2), (16, 22), (3, 14), (24, 23), (22, 3), (26, 4), (19, 8), (7, 4), (12, 12), (10, 14), (15, 26), (8, 10), (23, 12), (14, 9), (3, 25), (17, 2), (11, 0), (16, 5), (0, 1), (15, 1), (23, 21), (22, 17), (7, 5), (8, 19), (8, 15), (12, 0), (3, 23), (26, 0), (14, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767901", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 20), (0, 4), (11, 11), (13, 23), (13, 24), (9, 26), (14, 27), (12, 14), (0, 23), (14, 17), (15, 19), (12, 20), (0, 19), (6, 16), (7, 14), (5, 3), (14, 25), (6, 26), (10, 18), (1, 12), (10, 9), (4, 27), (6, 4), (12, 18), (0, 24), (7, 18), (5, 13), (12, 21), (5, 10), (10, 13), (8, 12), (11, 22), (4, 16), (2, 18), (17, 25), (11, 8), (16, 19), (0, 22), (10, 0), (18, 18), (14, 15), (10, 24), (17, 20), (17, 5), (15, 15), (12, 0), (19, 17), (0, 15), (7, 21), (11, 7), (11, 26), (8, 15), (16, 5), (12, 12), (9, 27), (8, 17), (13, 17), (9, 13), (5, 5), (19, 7), (15, 13), (16, 22), (11, 23), (15, 21), (12, 8), (9, 15), (10, 11), (18, 9), (12, 3), (8, 8), (0, 6), (13, 8), (8, 20), (18, 0), (7, 0), (13, 1), (4, 22), (12, 22), (4, 20), (8, 2), (8, 18), (2, 25), (7, 10), (12, 27), (3, 22), (3, 10), (7, 8), (3, 20), (18, 7), (5, 17), (9, 19), (10, 15), (13, 22), (13, 6), (8, 25), (17, 7), (17, 11), (15, 0), (15, 16), (8, 0), (12, 23), (7, 11), (3, 0), (8, 27), (7, 26), (11, 18), (19, 21), (16, 15), (3, 4), (11, 12), (2, 10), (18, 8), (2, 20), (0, 18), (16, 14), (3, 24), (13, 18), (6, 10), (4, 5), (7, 20), (7, 22), (16, 0), (17, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899990", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), 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), (12, 22), (25, 20), (19, 14), (16, 23), (25, 13), (18, 5), (6, 17), (6, 13), (14, 14), (9, 14), (23, 21), (5, 20), (22, 23), (9, 16), (10, 3), (5, 25), (14, 25), (8, 22), (6, 14), (14, 24), (4, 16), (22, 22), (8, 7), (0, 21), (2, 4), (15, 27), (25, 9), (13, 27), (4, 13), (9, 5), (6, 27), (1, 12), (13, 3), (15, 22), (23, 26), (2, 16), (24, 25), (9, 12), (16, 25), (15, 23), (17, 22), (7, 7), (5, 12), (17, 10), (0, 4), (24, 13), (14, 2), (18, 12), (24, 6), (20, 18), (24, 17), (14, 21), (6, 18), (25, 16), (23, 18), (19, 10), (17, 21), (18, 22), (13, 15), (2, 10), (19, 19), (3, 3), (14, 12), (8, 16), (22, 13), (9, 3), (8, 12), (21, 9), (11, 14), (22, 24), (5, 10), (14, 19), (19, 7), (1, 26), (19, 13), (21, 5), (6, 21), (18, 8), (23, 16), (16, 16), (0, 1), (10, 16), (11, 19), (11, 4), (3, 13), (15, 16), (20, 10), (14, 13), (4, 11), (3, 12), (21, 6), (14, 9), (11, 22), (9, 27), (24, 4), (24, 21), (19, 20), (2, 26), (24, 15), (12, 24), (2, 12), (22, 21), (22, 1), (11, 20), (12, 13), (18, 15), (13, 20), (21, 27), (6, 25), (16, 6), (17, 9), (19, 25), (2, 17), (24, 8), (7, 16), (10, 4), (7, 6), (2, 7), (3, 9), (16, 26), (24, 16), (2, 13), (9, 20), (13, 6), (12, 11), (9, 13), (9, 25), (17, 3), (24, 10), (2, 20), (6, 7), (3, 7), (20, 22), (1, 13), (7, 2), (8, 15), (16, 10), (16, 17), (2, 2), (23, 5), (11, 7), (8, 11), (13, 23), (24, 9), (15, 20), (5, 2), (0, 20), (20, 2), (19, 8), (19, 27), (8, 27), (12, 20), (9, 1), (11, 16), (21, 11), (10, 21), (22, 2), (16, 21), (17, 26), (18, 13), (20, 19), (10, 15), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649608", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 11), (16, 15), (13, 4), (0, 16), (8, 8), (21, 20), (15, 15), (22, 2), (20, 19), (3, 15), (4, 22), (5, 22), (16, 3), (13, 7), (22, 15), (17, 3), (12, 6), (5, 4), (1, 26), (18, 21), (9, 9), (6, 25), (15, 14), (14, 18), (0, 24), (10, 24), (10, 5), (5, 2), (7, 20), (4, 14), (1, 9), (14, 9), (2, 11), (20, 14), (14, 20), (18, 0), (17, 12), (15, 7), (17, 9), (1, 21), (16, 16), (15, 19), (1, 8), (15, 28), (13, 22), (21, 10), (3, 20), (5, 0), (20, 18), (1, 4), (13, 25), (5, 10), (10, 9), (9, 26), (1, 11), (8, 28), (12, 14), (16, 17), (6, 18), (8, 25), (10, 19), (5, 19), (13, 23), (19, 20), (6, 28), (19, 23), (7, 25), (11, 2), (19, 28), (21, 16), (20, 6), (19, 5), (12, 23), (9, 8), (4, 20), (20, 11), (19, 19), (19, 2), (16, 28), (10, 27), (13, 19), (22, 26), (6, 24), (4, 26), (3, 7), (11, 15), (6, 3), (17, 4), (5, 9), (14, 5), (20, 24), (2, 12), (13, 21), (21, 4), (20, 27), (16, 1), (13, 8), (2, 23), (9, 25), (5, 28), (11, 21), (6, 0), (10, 6), (21, 8), (7, 22), (0, 18), (8, 2), (11, 25), (10, 7), (8, 4), (0, 13), (17, 25), (5, 14), (15, 22), (12, 12), (4, 24), (3, 8), (22, 0), (17, 19), (3, 16), (16, 2), (21, 18), (22, 10), (13, 3), (18, 12), (19, 10), (15, 18), (11, 0), (11, 17), (19, 22), (5, 23), (15, 21), (12, 21), (3, 23), (22, 19), (4, 13), (0, 15), (12, 19), (0, 3), (9, 22), (13, 5), (7, 11), (10, 14), (14, 6), (2, 18), (17, 13), (20, 9), (2, 3), (7, 17), (19, 15), (10, 23), (0, 1), (9, 21), (14, 10), (21, 2), (9, 2), (15, 2), (14, 22), (22, 8), (0, 27), (5, 8), (6, 15), (18, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514056", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), 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), (6, 15), (25, 15), (17, 9), (16, 10), (11, 12), (5, 26), (8, 24), (14, 19), (18, 6), (27, 7), (7, 14), (0, 18), (17, 11), (15, 6), (15, 3), (0, 11), (9, 14), (14, 23), (21, 13), (12, 27), (20, 27), (2, 16), (1, 12), (22, 10), (18, 17), (24, 7), (25, 25), (10, 6), (24, 26), (8, 11), (13, 23), (19, 27), (9, 25), (17, 5), (2, 8), (24, 3), (3, 5), (18, 2), (26, 1), (20, 28), (4, 12), (7, 23), (22, 17), (1, 27), (3, 20), (21, 16), (14, 17), (27, 2), (9, 9), (16, 24), (11, 3), (7, 0), (9, 1), (9, 0), (20, 16), (12, 3), (21, 11), (10, 8), (4, 20), (17, 10), (27, 23), (16, 1), (12, 0), (9, 27), (6, 21), (25, 26), (13, 17), (4, 0), (18, 9), (10, 3), (27, 20), (19, 13), (0, 17), (23, 15), (21, 24), (17, 17), (20, 9), (12, 23), (27, 24), (17, 3), (25, 24), (18, 10), (19, 10), (21, 12), (27, 8), (17, 16), (10, 18), (10, 19), (1, 6), (6, 9), (16, 22), (15, 7), (15, 23), (22, 28), (24, 12), (1, 18), (23, 13), (19, 26), (14, 26), (15, 8), (15, 28), (5, 12), (16, 8), (22, 3), (18, 8), (6, 12), (8, 20), (2, 15), (24, 23), (7, 15), (18, 12), (1, 14), (5, 8), (15, 12), (0, 14), (8, 1), (18, 14), (20, 12), (7, 10), (5, 11), (0, 7), (14, 27), (16, 27), (2, 6), (18, 16), (7, 12), (27, 9), (26, 4), (23, 10), (11, 18), (22, 21), (23, 2), (2, 26), (1, 22), (26, 25), (16, 26), (7, 27), (18, 13), (11, 4), (23, 23), (2, 1), (0, 10), (0, 24), (27, 26), (20, 8), (5, 4), (8, 9), (23, 12), (23, 17), (16, 25), (12, 8), (1, 4), (10, 26), (25, 13), (23, 14), (5, 14), (1, 10), (4, 2), (10, 7), (24, 28), (18, 4), (0, 28), (22, 9), (16, 2), (19, 0), (2, 11), (25, 23), (12, 13), (13, 8), (13, 21), (27, 10), (2, 9), (17, 21), (6, 11), (11, 28), (15, 17), (9, 5), (10, 9), (11, 25), (3, 24), (8, 28), (12, 7), (6, 8), (14, 12), (27, 15), (23, 16), (10, 16), (2, 27), (26, 22), (20, 0), (15, 11), (13, 28), (25, 3), (19, 9), (6, 0), (23, 9), (2, 3), (16, 4), (9, 22), (17, 6), (5, 21), (7, 18), (25, 21), (15, 14), (8, 6), (0, 9), (19, 28), (2, 23), (20, 13), (4, 14), (17, 28), (14, 8), (17, 20), (3, 6), (23, 11), (23, 18), (23, 8), (19, 14), (5, 0), (1, 9), (9, 28), (8, 4), (6, 1), (17, 2), (2, 13), (16, 3), (7, 2), (6, 4), (21, 19), (14, 20), (17, 14), (8, 17), (12, 17), (4, 4), (10, 21), (26, 13), (21, 21), (6, 19), (5, 22), (14, 9), (22, 18), (21, 17), (5, 27), (3, 19), (9, 23), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101736", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), 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), (5, 14), (12, 8), (0, 8), (12, 16), (24, 23), (15, 16), (22, 15), (16, 1), (18, 21), (4, 0), (15, 17), (0, 16), (13, 16), (5, 23), (20, 10), (7, 6), (5, 7), (20, 1), (0, 12), (2, 4), (16, 2), (25, 0), (21, 1), (8, 2), (25, 21), (9, 17), (19, 13), (23, 16), (18, 16), (25, 8), (5, 16), (2, 10), (23, 15), (15, 1), (4, 5), (2, 5), (24, 11), (0, 13), (12, 10), (22, 11), (0, 18), (25, 3), (7, 21), (22, 7), (4, 14), (14, 23), (22, 12), (21, 15), (7, 12), (9, 3), (4, 1), (1, 23), (14, 13), (23, 7), (1, 8), (14, 4), (9, 11), (18, 17), (11, 8), (5, 20), (5, 9), (0, 7), (6, 6), (12, 0), (2, 8), (22, 13), (12, 6), (3, 3), (18, 4), (25, 20), (12, 22), (20, 18), (19, 6), (8, 20), (19, 0), (2, 2), (5, 1), (3, 0), (7, 9), (21, 4), (17, 18), (7, 18), (15, 11), (11, 10), (11, 7), (24, 7), (13, 4), (1, 5), (18, 12), (17, 15), (4, 9), (1, 14), (6, 7), (15, 14), (8, 23), (7, 4), (24, 14), (6, 9), (4, 4), (21, 23), (17, 8), (22, 6), (20, 6), (3, 10), (23, 0), (2, 15), (4, 3), (19, 11), (11, 9), (16, 22), (25, 15), (4, 21), (18, 20), (0, 23), (5, 19), (10, 20), (13, 8), (9, 15), (8, 10), (13, 18), (3, 6), (8, 6), (4, 20), (1, 3), (11, 0), (24, 6), (8, 11), (10, 16), (22, 22), (16, 17), (5, 0), (23, 8), (24, 16), (6, 17), (17, 5), (11, 16), (2, 20), (16, 13), (25, 5), (24, 9), (12, 13), (2, 9), (10, 10), (18, 9), (0, 21), (5, 21), (9, 9), (11, 14), (3, 7), (5, 11), (17, 22), (2, 23), (24, 21), (25, 11), (18, 0), (0, 6), (21, 11), (5, 6), (12, 19), (17, 0), (11, 20), (9, 7), (14, 22), (15, 8), (2, 3), (13, 22), (14, 11), (5, 12), (13, 10), (7, 10), (20, 2), (18, 3), (6, 14), (24, 17), (7, 0), (22, 4), (17, 3), (24, 8), (19, 19), (14, 12), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "957600", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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), (5, 1), (8, 5), (9, 7), (16, 17), (14, 0), (5, 14), (20, 16), (22, 2), (21, 10), (1, 14), (23, 11), (19, 7), (10, 18), (13, 1), (6, 11), (18, 11), (5, 7), (17, 11), (11, 17), (7, 6), (3, 10), (24, 17), (23, 16), (3, 18), (11, 20), (3, 7), (3, 5), (13, 14), (7, 18), (2, 9), (3, 20), (1, 18), (9, 17), (22, 16), (0, 16), (22, 20), (12, 6), (20, 4), (9, 6), (21, 0), (0, 11), (0, 19), (10, 1), (0, 14), (7, 11), (12, 13), (23, 20), (20, 15), (8, 14), (20, 18), (18, 17), (15, 1), (15, 17), (11, 3), (3, 17), (18, 13), (7, 13), (24, 4), (21, 3), (23, 4), (16, 5), (13, 20), (2, 19), (1, 13), (13, 15), (18, 4), (1, 4), (1, 9), (22, 17), (9, 11), (20, 3), (2, 6), (8, 18), (0, 1), (4, 7), (23, 18), (13, 11), (9, 16), (0, 12), (1, 1), (24, 18), (9, 20), (5, 10), (6, 3), (19, 13), (24, 6), (12, 8), (22, 18), (13, 10), (18, 5), (0, 20), (0, 17), (17, 6), (7, 2), (22, 14), (13, 0), (3, 14), (4, 0), (23, 0), (14, 6), (20, 8), (15, 18), (19, 3), (5, 3), (16, 16), (5, 2), (3, 9), (6, 10), (8, 0), (1, 19), (12, 12), (14, 19), (18, 6), (4, 19), (19, 6), (6, 0), (10, 8), (22, 8), (16, 4), (8, 6), (14, 1), (23, 10), (22, 6), (17, 13), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922922", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 21), (10, 9), (9, 7), (6, 22), (6, 5), (12, 10), (3, 17), (17, 17), (20, 8), (3, 16), (10, 5), (8, 6), (3, 8), (3, 2), (7, 0), (0, 18), (19, 3), (2, 6), (7, 23), (13, 6), (17, 22), (9, 2), (8, 16), (14, 23), (14, 3), (7, 22), (1, 24), (9, 23), (6, 4), (10, 10), (13, 4), (8, 14), (18, 1), (12, 9), (7, 19), (10, 3), (12, 6), (15, 22), (12, 23), (0, 8), (5, 12), (1, 10), (12, 11), (8, 24), (18, 0), (8, 20), (8, 10), (10, 20), (19, 1), (8, 17), (11, 6), (14, 18), (3, 12), (4, 1), (11, 10), (5, 18), (11, 2), (16, 11), (3, 3), (20, 7), (8, 21), (8, 15), (9, 17), (16, 0), (9, 6), (10, 16), (11, 17), (14, 2), (13, 7), (9, 15), (2, 3), (15, 16), (4, 12), (14, 15), (9, 18), (9, 0), (3, 9), (13, 21), (19, 11), (2, 13), (18, 2), (18, 12), (8, 5), (6, 19), (18, 16), (6, 3), (19, 17), (2, 4), (6, 6), (18, 7), (9, 3), (0, 3), (12, 4), (5, 23), (14, 14), (6, 15), (14, 22), (20, 23), (19, 22), (13, 14), (12, 2), (4, 8), (0, 15), (1, 9), (19, 21), (12, 0), (7, 2), (11, 15), (11, 12), (20, 0), (11, 22), (18, 24), (5, 6), (8, 18), (9, 22), (5, 15), (16, 2), (0, 12), (7, 7), (18, 10), (5, 13), (7, 10), (14, 21), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654816", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 1), (0, 17), (14, 0), (7, 23), (17, 22), (17, 26), (7, 20), (10, 17), (17, 10), (19, 1), (1, 11), (22, 26), (3, 26), (10, 8), (17, 6), (5, 6), (11, 1), (9, 21), (14, 6), (9, 25), (19, 16), (19, 23), (22, 24), (15, 13), (12, 22), (12, 21), (10, 11), (22, 20), (15, 18), (5, 7), (18, 21), (1, 24), (7, 1), (10, 23), (7, 13), (3, 20), (24, 10), (23, 11), (0, 27), (9, 15), (6, 23), (20, 7), (20, 25), (17, 17), (19, 3), (23, 15), (18, 22), (5, 2), (6, 18), (6, 19), (5, 16), (17, 14), (23, 3), (12, 11), (19, 21), (12, 12), (2, 22), (10, 6), (3, 3), (18, 6), (7, 5), (12, 16), (17, 11), (4, 25), (15, 26), (10, 3), (15, 0), (15, 27), (14, 3), (6, 17), (19, 14), (0, 2), (5, 8), (2, 21), (20, 19), (16, 14), (14, 7), (21, 7), (20, 21), (16, 8), (2, 2), (8, 23), (13, 4), (15, 6), (7, 27), (24, 12), (11, 25), (13, 5), (20, 9), (18, 5), (14, 8), (18, 3), (15, 9), (8, 9), (21, 19), (18, 0), (14, 9), (9, 17), (23, 17), (13, 21), (10, 5), (13, 24), (23, 12), (21, 1), (9, 7), (4, 9), (11, 12), (8, 18), (21, 13), (14, 17), (2, 6), (7, 25), (14, 2), (23, 6), (17, 12), (2, 20), (4, 8), (9, 10), (4, 20), (1, 6), (13, 15), (11, 3), (24, 16), (15, 25), (13, 6), (23, 16), (0, 12), (0, 11), (14, 22), (8, 27), (14, 24), (8, 22), (16, 4), (21, 2), (10, 16), (13, 1), (13, 9), (24, 3), (21, 23), (20, 4), (0, 3), (8, 17), (5, 3), (20, 14), (9, 20), (17, 19), (15, 15), (6, 21), (16, 27), (12, 6), (4, 18), (18, 25), (21, 8), (1, 1), (5, 22), (6, 8), (19, 24), (8, 12), (23, 21), (6, 20), (7, 16), (3, 23), (15, 4), (5, 11), (7, 22), (24, 6), (16, 16), (16, 17), (17, 18), (1, 10), (19, 10), (3, 11), (9, 16), (10, 14), (22, 4), (6, 10), (22, 11), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977888", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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, 8), (16, 9), (13, 13), (5, 18), (9, 13), (9, 5), (3, 9), (19, 13), (1, 14), (7, 19), (3, 4), (8, 14), (16, 8), (10, 5), (2, 5), (19, 9), (7, 2), (7, 4), (0, 13), (11, 1), (15, 11), (17, 2), (4, 6), (14, 0), (0, 15), (9, 20), (7, 7), (1, 11), (1, 5), (19, 15), (13, 8), (8, 3), (15, 20), (1, 2), (7, 14), (7, 18), (11, 4), (16, 1), (2, 8), (11, 12), (12, 1), (1, 9), (8, 9), (18, 11), (4, 17), (16, 5), (14, 3), (18, 10), (8, 2), (8, 12), (18, 6), (4, 2), (16, 6), (13, 4), (9, 17), (3, 11), (19, 2), (13, 14), (17, 8), (13, 16), (5, 12), (16, 20), (4, 12), (13, 7), (15, 4), (7, 15), (5, 9), (17, 20), (16, 2), (10, 14), (17, 0), (1, 8), (5, 3), (16, 7), (3, 0), (2, 12), (8, 16), (14, 10), (0, 12), (10, 19), (12, 7), (2, 11), (0, 8), (12, 19), (10, 8), (5, 6), (6, 18), (1, 20), (9, 2), (4, 4), (3, 14), (18, 9), (4, 18), (18, 17), (0, 2), (3, 20), (11, 0), (2, 13), (13, 19), (16, 19), (18, 18), (17, 4), (5, 15), (3, 5), (13, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863931", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), 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, 9), (18, 20), (9, 7), (11, 16), (12, 16), (9, 1), (18, 12), (18, 4), (2, 16), (17, 7), (24, 4), (12, 11), (14, 11), (12, 18), (2, 8), (4, 9), (21, 15), (19, 14), (5, 1), (1, 2), (17, 8), (3, 0), (20, 12), (13, 5), (21, 17), (13, 18), (10, 10), (13, 17), (18, 0), (24, 14), (23, 11), (23, 6), (3, 20), (16, 11), (15, 8), (16, 19), (15, 12), (24, 19), (21, 14), (10, 5), (6, 17), (9, 9), (8, 17), (21, 9), (0, 6), (5, 10), (16, 4), (8, 13), (24, 1), (4, 5), (2, 9), (13, 13), (8, 18), (20, 2), (4, 20), (22, 14), (0, 8), (6, 12), (23, 17), (8, 2), (4, 6), (0, 18), (4, 1), (7, 12), (5, 12), (15, 7), (9, 0), (17, 9), (4, 2), (2, 13), (17, 6), (13, 16), (20, 0), (11, 1), (13, 7), (24, 7), (24, 17), (17, 5), (3, 1), (3, 19), (10, 17), (5, 8), (8, 10), (15, 10), (5, 6), (10, 1), (18, 1), (15, 15), (15, 14), (22, 11), (19, 17), (17, 15), (9, 8), (20, 1), (2, 17), (16, 16), (3, 4), (9, 10), (5, 3), (22, 12), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "756030", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 7), (4, 6), (0, 4), (4, 11), (18, 7), (12, 1), (8, 18), (2, 1), (12, 3), (5, 15), (9, 3), (11, 4), (2, 15), (22, 0), (24, 8), (13, 17), (4, 19), (16, 0), (14, 16), (18, 12), (11, 1), (23, 10), (3, 15), (7, 18), (5, 9), (1, 4), (25, 19), (13, 2), (14, 17), (11, 16), (14, 12), (25, 5), (20, 10), (15, 12), (18, 19), (15, 13), (19, 13), (13, 14), (3, 12), (16, 11), (1, 9), (2, 16), (28, 5), (24, 1), (2, 19), (17, 12), (15, 0), (23, 5), (1, 19), (27, 17), (20, 9), (19, 2), (7, 1), (23, 2), (28, 2), (22, 8), (3, 9), (11, 11), (24, 15), (28, 15), (8, 10), (22, 15), (14, 0), (11, 5), (21, 10), (1, 10), (5, 6), (13, 15), (18, 8), (9, 16), (0, 14), (6, 16), (3, 17), (19, 1), (13, 7), (10, 16), (15, 10), (1, 13), (6, 9), (21, 13), (24, 12), (10, 1), (23, 11), (20, 17), (22, 16), (15, 19), (16, 5), (9, 5), (19, 17), (21, 15), (18, 5), (16, 12), (27, 6), (23, 7), (14, 11), (0, 19), (4, 10), (27, 3), (1, 12), (26, 2), (24, 18), (10, 5), (16, 15), (22, 7), (16, 13), (22, 13), (18, 18), (12, 0), (1, 0), (21, 6), (8, 8), (19, 0), (0, 6), (25, 2), (22, 9), (6, 2), (5, 2), (11, 0), (11, 12), (21, 17), (6, 17), (2, 13), (12, 13), (10, 15), (11, 6), (10, 4), (20, 7), (3, 11), (14, 1), (6, 3), (25, 8), (15, 14), (27, 1), (8, 15), (27, 18), (23, 14), (13, 9), (9, 15), (11, 9), (17, 1), (27, 16), (21, 3), (8, 14), (20, 0), (8, 16), (7, 13), (2, 0), (25, 17), (20, 5), (17, 7), (15, 6), (14, 10), (16, 16), (22, 14), (19, 9), (18, 6), (7, 12), (17, 5), (10, 13), (6, 8), (9, 1), (3, 13), (21, 11), (13, 6), (22, 10), (20, 15), (1, 14), (24, 9), (22, 2), (4, 3), (6, 18), (15, 5), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954912", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 25), (2, 1), (5, 4), (17, 5), (18, 8), (1, 9), (8, 15), (5, 23), (1, 20), (5, 2), (2, 21), (8, 6), (16, 7), (7, 25), (3, 20), (13, 24), (12, 7), (0, 1), (17, 6), (18, 28), (18, 17), (0, 5), (4, 14), (2, 14), (4, 17), (18, 26), (3, 7), (13, 3), (4, 23), (9, 15), (2, 3), (10, 23), (7, 18), (2, 4), (1, 10), (19, 6), (16, 17), (15, 14), (19, 4), (8, 4), (10, 22), (9, 23), (16, 5), (7, 5), (5, 17), (8, 17), (2, 5), (6, 12), (15, 19), (18, 16), (4, 11), (18, 14), (19, 26), (14, 8), (5, 16), (11, 18), (2, 9), (0, 27), (11, 6), (6, 23), (3, 8), (13, 14), (11, 13), (5, 28), (16, 24), (17, 13), (4, 1), (1, 23), (11, 22), (2, 27), (6, 14), (2, 0), (18, 10), (10, 14), (18, 11), (1, 12), (14, 13), (9, 13), (17, 3), (6, 9), (13, 8), (6, 4), (12, 5), (9, 7), (1, 16), (2, 2), (5, 13), (3, 24), (11, 26), (17, 16), (16, 23), (7, 6), (8, 23), (10, 25), (15, 28), (16, 1), (15, 2), (18, 19), (3, 27), (10, 3), (7, 22), (7, 3), (14, 1), (10, 13), (7, 10), (17, 21), (15, 0), (3, 10), (0, 15), (11, 3), (10, 2), (6, 17), (3, 4), (9, 3), (8, 24), (9, 14), (4, 18), (16, 12), (17, 20), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913840", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 2), (26, 10), (14, 20), (25, 4), (27, 1), (24, 8), (27, 11), (4, 1), (9, 0), (22, 7), (0, 4), (5, 16), (8, 14), (20, 0), (28, 12), (28, 19), (20, 14), (21, 9), (19, 19), (0, 12), (21, 15), (11, 0), (18, 2), (28, 11), (7, 20), (10, 19), (21, 10), (13, 3), (7, 9), (3, 2), (12, 13), (19, 0), (14, 0), (27, 15), (8, 15), (22, 10), (1, 13), (8, 5), (3, 5), (14, 3), (18, 18), (10, 1), (20, 5), (24, 12), (23, 14), (11, 20), (28, 18), (22, 11), (8, 20), (25, 11), (9, 20), (22, 5), (17, 13), (6, 8), (17, 10), (24, 10), (1, 12), (17, 9), (22, 6), (4, 7), (5, 1), (22, 12), (25, 5), (17, 1), (17, 0), (16, 8), (19, 7), (6, 19), (14, 12), (26, 9), (4, 13), (18, 5), (18, 1), (13, 20), (28, 3), (16, 18), (3, 7), (17, 5), (3, 4), (2, 10), (22, 18), (9, 4), (26, 4), (4, 8), (6, 18), (27, 7), (19, 13), (14, 18), (13, 17), (17, 14), (26, 19), (8, 7), (23, 20), (17, 20), (7, 15), (21, 19), (1, 20), (13, 8), (5, 13), (11, 15), (19, 3), (20, 4), (25, 20), (28, 16), (7, 17), (9, 16), (1, 8), (24, 14), (27, 2), (2, 5), (1, 19), (13, 0), (8, 18), (26, 15), (20, 6), (7, 2), (25, 7), (8, 11), (19, 5), (9, 3), (26, 8), (17, 8), (28, 7), (26, 7), (23, 6), (9, 10), (14, 1), (21, 4), (9, 12), (5, 0), (27, 6), (26, 18), (26, 17), (0, 6), (5, 12), (5, 7), (3, 16), (13, 15), (18, 11), (7, 11), (9, 2), (0, 13), (1, 18), (17, 19), (15, 19), (27, 10), (14, 15), (1, 6), (26, 11), (19, 17), (12, 19), (18, 10), (23, 19), (21, 12), (27, 13), (22, 3), (15, 6), (21, 0), (20, 19), (20, 20), (15, 15), (6, 13), (18, 13), (20, 8), (16, 4), (15, 17), (18, 3), (6, 1), (2, 19), (25, 2), (22, 0), (14, 2), (18, 4), (12, 0), (13, 4), (16, 14), (12, 7), (1, 16), (1, 2), (0, 20), (8, 19), (3, 10), (3, 1), (17, 18), (26, 20), (14, 7), (1, 11), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "995040", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), 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), (7, 12), (17, 9), (6, 9), (15, 16), (7, 15), (7, 16), (16, 8), (21, 12), (7, 1), (5, 1), (7, 23), (3, 15), (22, 19), (17, 12), (4, 14), (22, 2), (6, 10), (11, 9), (5, 8), (1, 15), (2, 0), (7, 17), (19, 19), (4, 13), (9, 22), (13, 14), (20, 21), (4, 0), (13, 4), (8, 16), (14, 13), (12, 1), (11, 18), (1, 18), (14, 3), (15, 21), (10, 14), (7, 9), (17, 10), (13, 23), (4, 2), (18, 9), (11, 2), (14, 12), (9, 4), (4, 23), (3, 23), (2, 8), (17, 7), (19, 12), (15, 11), (16, 3), (14, 1), (18, 19), (12, 16), (20, 13), (9, 6), (19, 21), (0, 21), (5, 17), (21, 2), (20, 20), (6, 6), (5, 3), (1, 9), (2, 10), (11, 15), (7, 2), (2, 21), (7, 5), (4, 22), (15, 4), (12, 6), (10, 20), (5, 18), (21, 19), (21, 23), (1, 8), (3, 7), (6, 8), (1, 10), (15, 1), (22, 9), (8, 13), (4, 11), (18, 12), (14, 4), (10, 3), (5, 11), (21, 9), (12, 9), (1, 19), (0, 5), (8, 17), (0, 12), (8, 2), (5, 23), (10, 7), (21, 6), (11, 20), (13, 10), (18, 14), (21, 4), (10, 22), (6, 4), (12, 19), (14, 6), (21, 10), (9, 12), (20, 18), (3, 18), (1, 21), (15, 23), (16, 19), (2, 22), (17, 1), (19, 8), (13, 11), (0, 18), (1, 12), (9, 2), (2, 1), (20, 11), (15, 9), (16, 0), (10, 17), (10, 8), (3, 2), (5, 21), (9, 23), (2, 6), (20, 0), (3, 12), (5, 16), (4, 20), (9, 10), (16, 6), (6, 23), (1, 23), (6, 11), (1, 17), (6, 17), (1, 6), (11, 16), (11, 17), (6, 19), (0, 3), (5, 13), (16, 9), (7, 3), (18, 16), (7, 21), (15, 2), (13, 7), (21, 7), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950898", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 18), (25, 1), (11, 11), (14, 14), (27, 4), (13, 11), (6, 17), (15, 16), (6, 22), (16, 25), (11, 25), (5, 5), (0, 15), (15, 22), (10, 6), (14, 24), (0, 10), (6, 8), (25, 13), (14, 22), (15, 9), (11, 0), (4, 19), (18, 6), (9, 14), (1, 8), (19, 23), (10, 11), (6, 13), (3, 22), (26, 7), (9, 10), (4, 11), (8, 0), (25, 11), (19, 0), (6, 27), (21, 12), (18, 3), (5, 12), (15, 6), (14, 15), (18, 14), (1, 6), (12, 2), (1, 14), (1, 0), (19, 25), (3, 17), (7, 14), (11, 7), (26, 21), (20, 7), (4, 22), (22, 17), (22, 22), (7, 13), (23, 4), (25, 8), (20, 5), (7, 8), (24, 19), (23, 0), (21, 22), (19, 3), (25, 19), (8, 14), (0, 12), (22, 2), (8, 3), (23, 13), (13, 19), (20, 22), (3, 7), (25, 14), (6, 12), (12, 9), (17, 7), (24, 17), (11, 17), (10, 5), (4, 12), (22, 9), (22, 8), (20, 16), (7, 0), (4, 26), (8, 15), (22, 24), (26, 0), (9, 13), (15, 5), (26, 23), (26, 8), (12, 12), (17, 25), (25, 24), (2, 2), (26, 5), (0, 20), (18, 27), (4, 0), (23, 2), (8, 27), (20, 11), (17, 17), (20, 17), (14, 8), (15, 7), (3, 13), (18, 7), (18, 22), (19, 17), (2, 3), (20, 4), (13, 9), (10, 14), (2, 26), (0, 16), (5, 2), (4, 9), (6, 0), (13, 2), (12, 0), (20, 23), (14, 26), (16, 22), (5, 0), (1, 1), (1, 23), (0, 5), (18, 9), (8, 25), (27, 6), (13, 1), (16, 24), (25, 5), (9, 19), (21, 21), (8, 23), (19, 27), (0, 8), (27, 15), (4, 23), (23, 21), (9, 12), (4, 6), (25, 7), (1, 9), (22, 18), (22, 1), (24, 8), (18, 24), (0, 23), (10, 10), (21, 0), (18, 17), (10, 4), (11, 15), (23, 24), (10, 3), (18, 8), (21, 9), (23, 18), (25, 21), (25, 23), (17, 6), (20, 9), (17, 13), (24, 0), (1, 25), (2, 19), (26, 18), (9, 18), (27, 5), (14, 19), (19, 2), (12, 1), (25, 12), (9, 26), (1, 19), (10, 2), (18, 15), (21, 25), (24, 6), (15, 15), (17, 18), (5, 20), (21, 23), (24, 11), (20, 14), (5, 17), (14, 20), (8, 16), (11, 23), (27, 18), (3, 6), (0, 27), (27, 1), (26, 4), (23, 8), (13, 26), (23, 5), (15, 24), (11, 18), (2, 20), (18, 11), (11, 16), (21, 1), (15, 1), (4, 24), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416640", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (0, 17), (13, 11), (11, 25), (10, 10), (2, 1), (24, 20), (0, 1), (16, 12), (11, 2), (6, 1), (19, 10), (18, 22), (11, 15), (23, 24), (23, 9), (9, 3), (0, 16), (4, 16), (1, 12), (8, 20), (20, 12), (5, 3), (12, 10), (13, 12), (25, 25), (17, 1), (14, 13), (7, 14), (12, 18), (14, 17), (26, 16), (8, 6), (24, 3), (24, 6), (14, 2), (1, 17), (2, 6), (22, 19), (10, 9), (14, 25), (22, 7), (1, 23), (5, 22), (13, 26), (3, 21), (22, 17), (16, 27), (24, 12), (1, 10), (1, 8), (5, 15), (21, 27), (10, 20), (15, 13), (6, 2), (19, 11), (2, 11), (16, 7), (20, 22), (1, 11), (24, 11), (2, 5), (24, 13), (4, 21), (2, 21), (3, 25), (12, 12), (10, 14), (5, 24), (13, 9), (8, 18), (22, 20), (21, 2), (15, 15), (17, 7), (10, 5), (14, 26), (20, 11), (7, 12), (7, 13), (22, 25), (17, 0), (3, 26), (23, 20), (19, 2), (13, 1), (1, 15), (0, 14), (1, 5), (1, 4), (18, 25), (7, 10), (18, 26), (6, 26), (20, 24), (19, 16), (15, 21), (7, 15), (26, 8), (12, 13), (11, 24), (21, 26), (1, 16), (23, 23), (24, 15), (1, 21), (18, 24), (7, 16), (18, 5), (8, 2), (7, 27), (5, 5), (13, 3), (16, 21), (23, 13), (25, 6), (25, 15), (19, 4), (12, 6), (0, 18), (22, 16), (23, 26), (6, 12), (24, 23), (4, 20), (15, 25), (23, 8), (4, 8), (9, 20), (9, 0), (20, 23), (18, 15), (18, 7), (12, 4), (2, 0), (25, 4), (6, 27), (21, 1), (0, 19), (12, 23), (5, 4), (6, 4), (3, 10), (26, 10), (7, 8), (9, 18), (16, 0), (24, 16), (14, 16), (21, 15), (26, 18), (5, 16), (0, 20), (22, 5), (17, 9), (3, 24), (4, 18), (18, 3), (8, 17), (26, 15), (26, 4), (10, 11), (26, 17), (3, 2), (7, 11), (6, 3), (16, 23), (18, 10), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233280", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), 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), (23, 18), (5, 9), (13, 7), (1, 3), (13, 1), (10, 10), (6, 1), (17, 12), (9, 0), (6, 9), (17, 14), (20, 10), (15, 20), (16, 0), (9, 19), (8, 13), (18, 9), (16, 14), (3, 17), (22, 11), (2, 14), (15, 12), (23, 9), (5, 8), (9, 10), (25, 19), (3, 5), (14, 0), (23, 10), (21, 5), (25, 10), (10, 1), (15, 13), (8, 22), (20, 13), (24, 3), (12, 0), (3, 14), (2, 21), (12, 4), (4, 4), (18, 2), (4, 7), (25, 1), (20, 3), (7, 16), (13, 3), (1, 5), (3, 22), (6, 17), (19, 1), (13, 8), (8, 19), (9, 14), (2, 18), (10, 22), (5, 12), (17, 9), (15, 3), (22, 1), (23, 12), (21, 19), (14, 16), (4, 1), (18, 12), (1, 9), (15, 22), (1, 13), (20, 9), (1, 22), (22, 5), (24, 1), (21, 16), (11, 10), (18, 7), (17, 15), (11, 2), (24, 0), (19, 21), (23, 7), (12, 16), (7, 13), (13, 2), (25, 16), (5, 16), (16, 12), (8, 1), (14, 7), (17, 16), (16, 10), (9, 11), (17, 13), (17, 4), (0, 4), (1, 10), (6, 18), (21, 1), (5, 18), (7, 17), (21, 9), (8, 3), (0, 15), (10, 5), (7, 19), (25, 15), (10, 15), (2, 10), (7, 14), (8, 11), (23, 6), (20, 11), (22, 9), (21, 0), (9, 13), (13, 13), (21, 7), (3, 18), (2, 16), (19, 18), (14, 21), (6, 2), (4, 21), (14, 12), (1, 14), (20, 7), (7, 8), (11, 22), (6, 5), (16, 22), (11, 1), (19, 4), (18, 19), (11, 4), (22, 8), (8, 8), (10, 9), (9, 9), (1, 17), (25, 5), (9, 17), (9, 22), (2, 15), (2, 17), (9, 1), (4, 22), (13, 19), (6, 12), (3, 0), (23, 11), (16, 1), (10, 12), (2, 12), (6, 20), (21, 6), (22, 22), (7, 4), (15, 2), (3, 21), (22, 13), (11, 16), (21, 14), (3, 19), (19, 16), (14, 5), (15, 18), (8, 16), (1, 18), (5, 22), (16, 18), (16, 8), (25, 9), (4, 15), (20, 17), (8, 18), (20, 2), (6, 8), (10, 4), (21, 10), (6, 13), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803160", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 20), (8, 4), (15, 23), (27, 1), (16, 26), (27, 12), (13, 10), (5, 8), (21, 18), (15, 3), (9, 5), (0, 4), (8, 10), (13, 20), (27, 22), (8, 26), (22, 16), (15, 14), (1, 17), (20, 8), (19, 21), (9, 1), (10, 4), (11, 0), (16, 20), (8, 7), (4, 18), (24, 7), (6, 1), (13, 19), (4, 9), (3, 14), (26, 13), (27, 24), (3, 26), (25, 10), (10, 12), (21, 21), (23, 20), (9, 9), (25, 1), (21, 17), (26, 8), (15, 11), (16, 17), (6, 23), (13, 2), (16, 7), (20, 16), (14, 21), (28, 10), (13, 1), (26, 10), (17, 14), (11, 21), (8, 23), (25, 20), (13, 7), (2, 2), (21, 5), (13, 18), (27, 6), (1, 6), (23, 4), (7, 8), (0, 23), (11, 4), (13, 17), (16, 2), (20, 18), (8, 6), (26, 15), (16, 15), (6, 7), (5, 19), (0, 20), (28, 3), (11, 15), (4, 12), (18, 25), (5, 5), (10, 0), (18, 16), (12, 2), (14, 20), (24, 2), (5, 17), (24, 17), (2, 5), (9, 18), (16, 8), (17, 25), (1, 9), (15, 2), (7, 18), (12, 5), (8, 20), (15, 17), (7, 23), (25, 5), (13, 9), (18, 18), (2, 9), (1, 24), (23, 2), (2, 26), (2, 23), (24, 14), (0, 8), (7, 4), (19, 10), (24, 13), (18, 21), (21, 15), (2, 20), (1, 3), (0, 13), (25, 18), (6, 22), (13, 12), (0, 16), (17, 19), (4, 11), (15, 13), (11, 13), (14, 18), (5, 4), (16, 1), (3, 16), (20, 1), (6, 0), (26, 9), (2, 25), (26, 3), (20, 5), (14, 0), (15, 7), (2, 8), (19, 16), (10, 11), (4, 3), (25, 17), (15, 26), (8, 16), (10, 5), (21, 14), (14, 4), (10, 26), (21, 3), (14, 9), (19, 3), (24, 23), (20, 0), (12, 24), (9, 11), (17, 3), (6, 26), (3, 21), (4, 14), (24, 8), (16, 3), (22, 0), (8, 5), (17, 26), (13, 3), (21, 19), (21, 24), (3, 5), (28, 20), (26, 12), (15, 8), (8, 13), (27, 26), (13, 0), (7, 14), (10, 19), (19, 7), (23, 14), (0, 1), (8, 19), (7, 9), (24, 0), (5, 12), (27, 5), (5, 9), (5, 22), (5, 16), (24, 12), (13, 8), (27, 17), (11, 12), (14, 2), (16, 6), (2, 7), (20, 22), (21, 10), (14, 11), (0, 22), (4, 4), (26, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "655200", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 3), (20, 20), (5, 8), (10, 18), (3, 14), (8, 20), (14, 16), (2, 21), (16, 8), (19, 10), (1, 12), (15, 2), (15, 10), (12, 2), (16, 21), (11, 17), (5, 19), (18, 10), (9, 17), (3, 7), (21, 4), (17, 21), (7, 9), (13, 5), (6, 15), (21, 18), (10, 15), (17, 1), (6, 19), (15, 14), (15, 6), (15, 16), (20, 6), (1, 15), (4, 9), (20, 17), (3, 4), (21, 15), (2, 11), (20, 7), (13, 19), (0, 11), (19, 7), (19, 2), (18, 16), (2, 6), (8, 7), (16, 4), (19, 14), (0, 20), (10, 5), (7, 11), (3, 17), (2, 17), (17, 2), (7, 13), (14, 0), (9, 8), (21, 1), (13, 2), (16, 6), (14, 10), (11, 21), (16, 1), (12, 0), (7, 2), (11, 10), (11, 5), (18, 13), (5, 3), (20, 10), (13, 16), (20, 13), (19, 8), (12, 4), (9, 4), (8, 3), (12, 17), (13, 11), (11, 9), (20, 19), (7, 14), (8, 11), (2, 0), (3, 8), (7, 7), (17, 19), (10, 21), (11, 18), (2, 8), (7, 0), (11, 4), (0, 9), (15, 12), (17, 13), (14, 9), (9, 15), (5, 14), (17, 3), (21, 14), (2, 2), (5, 5), (10, 8), (15, 19), (5, 2), (11, 7), (0, 18), (19, 3), (11, 0), (3, 2), (11, 11), (5, 21), (4, 19), (3, 5), (5, 4), (11, 19), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976034", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (16, 19), (1, 0), (19, 21), (2, 4), (16, 8), (9, 10), (9, 4), (18, 15), (8, 0), (16, 13), (19, 15), (10, 5), (9, 12), (15, 14), (6, 4), (16, 0), (18, 1), (3, 10), (16, 7), (5, 1), (0, 15), (8, 9), (11, 11), (0, 22), (5, 13), (12, 19), (19, 17), (10, 15), (17, 11), (1, 3), (2, 12), (7, 20), (7, 18), (18, 5), (1, 22), (11, 12), (14, 6), (12, 21), (10, 9), (16, 2), (1, 7), (11, 6), (7, 5), (14, 17), (7, 12), (1, 16), (18, 3), (5, 9), (7, 11), (19, 5), (13, 6), (16, 16), (7, 3), (14, 20), (16, 4), (15, 3), (15, 11), (12, 11), (7, 7), (5, 3), (12, 4), (11, 18), (0, 13), (10, 16), (11, 9), (3, 17), (11, 17), (9, 16), (7, 6), (0, 20), (10, 13), (15, 0), (2, 7), (6, 11), (6, 10), (17, 17), (18, 2), (13, 19), (12, 6), (11, 16), (13, 15), (19, 19), (5, 22), (2, 19), (5, 2), (15, 21), (5, 16), (3, 16), (4, 22), (8, 8), (11, 1), (13, 14), (9, 8), (3, 20), (5, 8), (17, 9), (12, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624766", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), 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, 5), (1, 5), (22, 17), (10, 21), (6, 21), (25, 9), (16, 11), (5, 2), (8, 15), (11, 9), (12, 13), (7, 5), (4, 6), (9, 8), (16, 16), (25, 17), (13, 21), (7, 20), (3, 4), (14, 6), (4, 1), (23, 7), (21, 17), (14, 5), (5, 0), (18, 17), (1, 7), (12, 6), (6, 1), (5, 5), (19, 11), (3, 7), (18, 13), (20, 4), (6, 3), (13, 9), (23, 21), (3, 17), (16, 3), (25, 10), (22, 19), (22, 12), (10, 3), (15, 3), (17, 11), (18, 20), (11, 20), (20, 12), (13, 14), (8, 21), (18, 4), (24, 1), (15, 0), (19, 13), (1, 11), (11, 0), (0, 14), (16, 0), (11, 11), (2, 14), (15, 19), (24, 2), (6, 14), (16, 4), (12, 14), (3, 0), (12, 16), (25, 3), (19, 10), (20, 9), (21, 16), (19, 7), (3, 3), (22, 21), (12, 12), (22, 9), (11, 15), (2, 6), (13, 19), (2, 5), (3, 9), (8, 6), (17, 16), (24, 22), (23, 19), (2, 8), (0, 11), (13, 20), (10, 4), (2, 12), (9, 6), (21, 5), (5, 3), (10, 8), (13, 2), (20, 15), (21, 2), (25, 15), (15, 22), (14, 20), (16, 12), (22, 15), (4, 12), (12, 7), (13, 17), (14, 8), (25, 13), (16, 5), (1, 14), (3, 6), (12, 15), (4, 5), (6, 7), (9, 2), (8, 11), (19, 12), (9, 11), (5, 8), (23, 22), (17, 3), (0, 15), (19, 22), (2, 2), (11, 16), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696894", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 22), (19, 22), (4, 2), (0, 13), (8, 6), (16, 23), (17, 23), (4, 13), (19, 15), (4, 4), (5, 0), (17, 1), (14, 7), (10, 4), (4, 0), (23, 7), (26, 10), (22, 20), (9, 13), (25, 12), (23, 19), (10, 17), (26, 20), (20, 4), (8, 0), (2, 5), (25, 19), (8, 4), (18, 9), (10, 10), (21, 15), (10, 12), (22, 5), (15, 5), (10, 19), (12, 7), (3, 12), (17, 21), (2, 0), (22, 7), (18, 16), (26, 0), (22, 11), (22, 15), (25, 11), (16, 4), (15, 17), (10, 6), (13, 4), (12, 16), (5, 9), (6, 3), (7, 4), (22, 22), (7, 11), (21, 14), (14, 5), (1, 11), (0, 16), (2, 19), (21, 7), (19, 2), (4, 7), (5, 1), (22, 12), (20, 22), (20, 13), (6, 19), (9, 19), (4, 23), (6, 14), (7, 1), (21, 16), (12, 20), (9, 0), (22, 10), (8, 10), (4, 8), (7, 18), (27, 21), (15, 13), (1, 0), (18, 18), (7, 19), (25, 22), (14, 20), (8, 7), (7, 22), (21, 19), (19, 9), (11, 23), (3, 14), (17, 9), (18, 4), (20, 17), (18, 22), (10, 0), (5, 12), (11, 3), (25, 9), (17, 22), (28, 7), (23, 17), (11, 17), (10, 11), (11, 11), (9, 7), (16, 14), (22, 1), (23, 15), (7, 9), (26, 12), (5, 21), (25, 13), (5, 13), (4, 15), (13, 15), (25, 14), (24, 18), (7, 21), (25, 21), (25, 10), (12, 12), (5, 20), (28, 1), (5, 15), (9, 10), (1, 15), (26, 9), (22, 21), (15, 12), (12, 6), (13, 16), (5, 8), (14, 19), (3, 5), (6, 15), (2, 14), (4, 17), (21, 12), (12, 13), (18, 3), (9, 2), (19, 13), (26, 6), (24, 0), (27, 11), (2, 16), (17, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858360", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 2), (18, 22), (11, 11), (18, 16), (17, 24), (3, 25), (18, 25), (16, 15), (5, 17), (18, 15), (3, 10), (7, 16), (13, 21), (1, 5), (5, 22), (3, 22), (12, 7), (13, 27), (5, 5), (14, 9), (11, 4), (1, 0), (4, 3), (18, 0), (4, 0), (13, 18), (13, 4), (17, 13), (9, 20), (18, 23), (12, 18), (15, 12), (15, 26), (8, 10), (5, 7), (13, 23), (7, 4), (17, 5), (10, 24), (9, 19), (12, 21), (5, 20), (6, 10), (2, 17), (15, 14), (0, 24), (8, 22), (16, 4), (4, 9), (19, 25), (15, 16), (14, 0), (2, 18), (14, 21), (9, 27), (0, 17), (16, 9), (6, 18), (19, 1), (8, 12), (18, 14), (19, 22), (5, 9), (16, 8), (8, 18), (7, 27), (13, 1), (19, 24), (10, 7), (4, 27), (9, 8), (1, 20), (12, 13), (17, 3), (12, 23), (17, 2), (5, 27), (6, 25), (12, 17), (12, 10), (1, 19), (1, 8), (9, 21), (11, 21), (4, 15), (15, 22), (10, 17), (4, 4), (19, 6), (6, 4), (5, 8), (12, 14), (13, 5), (3, 13), (3, 8), (1, 27), (0, 6), (16, 11), (7, 19), (6, 5), (15, 23), (10, 2), (10, 20), (4, 2), (11, 8), (6, 3), (16, 7), (5, 6), (15, 11), (16, 5), (12, 1), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248820", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (4, 5), (19, 7), (20, 15), (12, 10), (25, 18), (7, 0), (20, 18), (9, 2), (16, 16), (16, 17), (15, 9), (26, 15), (26, 11), (6, 12), (22, 1), (2, 11), (24, 5), (24, 15), (0, 12), (11, 14), (27, 7), (14, 7), (17, 9), (26, 2), (19, 6), (10, 3), (14, 12), (27, 12), (9, 0), (23, 5), (3, 14), (19, 19), (12, 11), (19, 11), (20, 10), (4, 3), (1, 17), (15, 6), (4, 9), (12, 7), (1, 9), (18, 4), (1, 19), (11, 7), (21, 11), (3, 4), (10, 1), (11, 11), (6, 13), (8, 18), (21, 17), (5, 4), (20, 11), (13, 5), (16, 10), (7, 3), (11, 4), (4, 0), (13, 11), (21, 3), (17, 8), (3, 15), (8, 7), (19, 0), (16, 1), (13, 19), (14, 9), (23, 15), (8, 15), (26, 9), (14, 3), (25, 9), (21, 4), (4, 7), (17, 16), (24, 14), (0, 14), (23, 4), (25, 6), (20, 9), (6, 2), (17, 7), (10, 8), (4, 11), (11, 9), (4, 15), (27, 9), (17, 12), (7, 8), (10, 2), (13, 10), (9, 19), (23, 16), (8, 11), (21, 6), (26, 19), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436280", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 7), (12, 10), (16, 22), (2, 16), (16, 27), (17, 14), (9, 9), (0, 24), (10, 27), (9, 1), (14, 5), (21, 9), (14, 14), (17, 10), (20, 5), (4, 3), (10, 25), (1, 2), (9, 13), (15, 10), (5, 9), (12, 2), (17, 6), (2, 4), (13, 7), (10, 0), (0, 20), (15, 12), (9, 6), (12, 22), (4, 7), (15, 18), (12, 24), (15, 6), (7, 23), (11, 15), (4, 19), (3, 25), (10, 11), (12, 21), (5, 14), (14, 11), (11, 21), (11, 19), (0, 22), (17, 9), (3, 2), (21, 11), (6, 19), (17, 20), (18, 3), (18, 11), (7, 2), (9, 8), (16, 7), (17, 26), (16, 10), (15, 2), (13, 0), (16, 21), (5, 8), (2, 12), (18, 23), (18, 14), (14, 3), (14, 21), (8, 19), (1, 11), (13, 14), (11, 4), (19, 3), (3, 16), (6, 4), (9, 2), (12, 6), (9, 20), (15, 23), (21, 0), (19, 22), (10, 13), (8, 15), (17, 1), (2, 6), (3, 17), (10, 24), (19, 14), (7, 0), (19, 21), (7, 1), (9, 15), (16, 3), (10, 18), (5, 3), (1, 23), (10, 21), (8, 13), (21, 8), (8, 16), (17, 15), (20, 9), (19, 2), (6, 10), (14, 1), (1, 25), (8, 26), (12, 23), (12, 11), (21, 16), (15, 11), (7, 12), (17, 0), (15, 15), (7, 15), (10, 4), (18, 17), (11, 10), (10, 23), (9, 26), (6, 16), (5, 19), (2, 19), (16, 23), (18, 19), (18, 9), (0, 10), (13, 6), (9, 27), (16, 5), (16, 9), (11, 26), (21, 1), (13, 4), (19, 8), (14, 13), (1, 8), (5, 1), (21, 6), (4, 12), (11, 7), (10, 3), (3, 3), (14, 19), (17, 19), (13, 23), (19, 23), (20, 24), (2, 17), (11, 6), (17, 18), (14, 7), (19, 19), (6, 17), (11, 27), (4, 14), (12, 15), (1, 24), (9, 19), (19, 12), (0, 25), (8, 20), (7, 16), (0, 17), (3, 14), (1, 21), (0, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945248", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 17), (23, 14), (25, 3), (19, 0), (22, 17), (11, 7), (25, 11), (23, 3), (12, 2), (20, 4), (22, 13), (27, 18), (0, 15), (5, 11), (5, 20), (13, 18), (8, 17), (20, 10), (4, 5), (1, 7), (11, 13), (1, 14), (24, 16), (1, 15), (3, 1), (4, 1), (8, 19), (13, 16), (27, 17), (13, 14), (11, 15), (18, 13), (19, 14), (18, 15), (0, 10), (10, 17), (2, 17), (27, 8), (14, 3), (6, 3), (19, 12), (4, 16), (22, 2), (24, 2), (12, 14), (20, 0), (0, 23), (14, 9), (7, 13), (1, 16), (7, 6), (11, 2), (6, 17), (4, 13), (10, 22), (19, 23), (6, 8), (13, 5), (12, 19), (13, 7), (15, 15), (1, 5), (26, 4), (26, 0), (26, 7), (24, 10), (15, 5), (21, 10), (0, 19), (25, 23), (18, 0), (14, 4), (23, 4), (22, 11), (26, 5), (4, 10), (15, 10), (20, 16), (11, 11), (22, 8), (26, 20), (26, 10), (22, 15), (5, 1), (4, 11), (20, 18), (6, 14), (5, 9), (13, 23), (12, 13), (23, 15), (10, 8), (21, 17), (16, 11), (26, 11), (12, 18), (8, 0), (3, 21), (11, 8), (18, 17), (6, 22), (27, 1), (8, 4), (9, 8), (1, 11), (21, 4), (1, 21), (15, 16), (23, 16), (21, 19), (8, 13), (10, 11), (5, 15), (9, 9), (25, 19), (8, 22), (15, 9), (13, 20), (6, 21), (9, 11), (2, 11), (19, 7), (15, 21), (11, 4), (11, 3), (21, 16), (18, 2), (19, 10), (5, 6), (12, 12), (17, 14), (1, 6), (27, 7), (12, 16), (8, 8), (24, 8), (0, 21), (0, 16), (15, 11), (14, 8), (11, 10), (0, 18), (13, 3), (11, 5), (2, 15), (27, 0), (3, 3), (10, 4), (6, 20), (12, 5), (2, 12), (17, 7), (21, 2), (16, 3), (17, 22), (12, 0), (27, 16), (19, 8), (16, 6), (17, 15), (25, 14), (6, 12), (19, 6), (4, 23), (4, 0), (23, 8), (7, 14), (15, 13), (0, 22), (9, 6), (22, 20), (2, 13), (16, 9), (8, 6), (19, 2), (20, 5), (7, 21), (1, 3), (11, 19), (2, 8), (15, 7), (16, 5), (7, 19), (26, 19), (17, 10), (26, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660726", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 17), (8, 10), (4, 8), (2, 20), (15, 11), (4, 25), (20, 18), (18, 15), (19, 20), (12, 19), (13, 7), (7, 20), (5, 21), (17, 6), (3, 12), (3, 25), (11, 24), (5, 8), (20, 16), (11, 16), (20, 19), (17, 9), (10, 7), (3, 19), (17, 1), (8, 18), (17, 18), (12, 13), (8, 4), (0, 1), (4, 19), (19, 10), (10, 4), (12, 25), (5, 10), (13, 25), (4, 0), (3, 8), (5, 12), (0, 2), (14, 18), (7, 11), (2, 7), (20, 20), (20, 12), (21, 14), (7, 22), (13, 12), (10, 17), (18, 0), (1, 18), (14, 5), (9, 19), (10, 0), (7, 25), (20, 0), (0, 25), (14, 1), (15, 21), (18, 16), (4, 23), (0, 13), (13, 2), (16, 0), (13, 13), (12, 16), (13, 9), (13, 5), (1, 15), (9, 16), (6, 18), (4, 10), (12, 7), (4, 7), (12, 14), (11, 9), (11, 0), (2, 19), (11, 17), (7, 4), (21, 3), (13, 1), (13, 3), (11, 20), (5, 7), (5, 25), (15, 1), (2, 25), (18, 6), (17, 14), (2, 21), (5, 3), (13, 10), (21, 22), (21, 2), (16, 20), (1, 17), (14, 0), (10, 6), (5, 9), (6, 13), (9, 20), (0, 18), (4, 15), (1, 5), (11, 11), (10, 11), (19, 2), (8, 19), (9, 4), (11, 19), (2, 9), (7, 23), (9, 15), (21, 21), (17, 15), (7, 0), (14, 11), (4, 17), (8, 9), (13, 6), (2, 10), (19, 5), (19, 25), (15, 10), (10, 8), (19, 0), (6, 22), (9, 13), (6, 24), (21, 10), (6, 25), (11, 21), (1, 16), (7, 1), (12, 20), (18, 10), (7, 12), (21, 0), (12, 1), (15, 20), (19, 4), (6, 1), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239316", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 12), (10, 1), (23, 8), (25, 3), (4, 5), (12, 7), (1, 14), (26, 12), (22, 9), (24, 22), (12, 10), (17, 9), (24, 18), (18, 9), (11, 15), (16, 6), (21, 17), (4, 14), (10, 13), (2, 3), (22, 6), (14, 4), (12, 13), (22, 15), (8, 20), (2, 4), (7, 4), (16, 14), (21, 14), (1, 5), (23, 26), (19, 11), (5, 7), (4, 7), (1, 21), (9, 16), (17, 22), (20, 2), (24, 8), (7, 2), (8, 7), (26, 19), (24, 21), (0, 24), (26, 4), (12, 8), (0, 19), (9, 23), (4, 3), (15, 15), (1, 11), (18, 20), (14, 7), (20, 1), (21, 24), (26, 16), (8, 22), (15, 26), (23, 12), (19, 9), (18, 2), (13, 7), (10, 9), (23, 19), (13, 18), (10, 25), (22, 10), (7, 20), (1, 3), (3, 20), (1, 12), (25, 16), (3, 17), (25, 23), (17, 11), (25, 15), (5, 1), (10, 23), (13, 13), (11, 12), (8, 9), (12, 18), (24, 16), (26, 7), (15, 12), (5, 8), (23, 11), (4, 0), (16, 13), (24, 14), (13, 24), (21, 10), (21, 11), (16, 9), (20, 11), (22, 5), (9, 6), (2, 17), (9, 5), (4, 8), (3, 14), (19, 25), (17, 7), (13, 20), (5, 6), (25, 13), (17, 21), (4, 24), (16, 25), (25, 25), (12, 4), (20, 18), (20, 9), (3, 11), (19, 1), (5, 5), (0, 23), (4, 1), (2, 1), (17, 8), (15, 21), (4, 4), (19, 8), (7, 24), (24, 24), (3, 13), (14, 3), (19, 13), (21, 13), (16, 8), (17, 5), (20, 21), (19, 24), (17, 2), (21, 2), (9, 21), (21, 6), (11, 6), (1, 24), (21, 19), (11, 21), (6, 26), (8, 8), (19, 12), (9, 11), (15, 22), (4, 9), (21, 0), (10, 18), (7, 0), (20, 15), (17, 10), (4, 25), (23, 4), (11, 16), (3, 19), (5, 16), (21, 7), (3, 24), (5, 23), (11, 22), (22, 17), (26, 21), (7, 13), (22, 14), (4, 19), (12, 6), (26, 13), (10, 24), (20, 5), (6, 2), (9, 12), (6, 25), (7, 7), (11, 25), (11, 18), (14, 24), (4, 15), (12, 26), (21, 23), (23, 13), (5, 12), (11, 1), (22, 3), (3, 16), (7, 11), (2, 16), (25, 24), (4, 6), (24, 7), (22, 4), (11, 8), (11, 19), (0, 9), (5, 15), (24, 11), (16, 11), (15, 3), (22, 26), (2, 15), (18, 5), (13, 12), (13, 23), (2, 23), (14, 19), (20, 3), (5, 22), (19, 4), (17, 23), (22, 19), (9, 24), (8, 18), (21, 18), (4, 2), (6, 22), (24, 5), (6, 19), (9, 10), (26, 24), (1, 17), (8, 26), (25, 11), (19, 18), (12, 3), (10, 26), (10, 21), (9, 25), (17, 17), (1, 1), (15, 2), (8, 1), (20, 25), (1, 26), (24, 6), (23, 23), (8, 11), (0, 25), (15, 13), (6, 5), (21, 8), (12, 9), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840672", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 19), (13, 26), (16, 4), (15, 26), (15, 14), (11, 26), (19, 9), (19, 15), (19, 0), (0, 25), (7, 21), (18, 8), (10, 2), (10, 17), (13, 14), (11, 24), (19, 14), (10, 1), (11, 25), (13, 10), (18, 3), (16, 11), (3, 17), (12, 9), (16, 5), (20, 2), (10, 24), (12, 11), (7, 17), (7, 15), (8, 9), (20, 10), (1, 11), (8, 19), (7, 19), (9, 26), (4, 25), (7, 22), (7, 12), (11, 21), (12, 15), (20, 13), (21, 11), (14, 18), (9, 15), (9, 3), (17, 13), (12, 17), (12, 4), (6, 26), (22, 1), (18, 10), (5, 8), (16, 15), (13, 23), (1, 24), (11, 10), (12, 3), (6, 19), (14, 0), (22, 23), (1, 5), (8, 2), (11, 13), (10, 22), (10, 3), (6, 24), (18, 13), (19, 13), (18, 6), (6, 11), (7, 6), (5, 7), (13, 25), (2, 15), (8, 13), (10, 19), (13, 3), (10, 25), (7, 11), (7, 18), (8, 8), (9, 2), (11, 7), (15, 24), (10, 10), (2, 13), (2, 16), (16, 22), (3, 16), (17, 4), (22, 20), (14, 4), (20, 19), (8, 11), (17, 20), (9, 23), (15, 6), (15, 7), (19, 1), (15, 21), (3, 5), (7, 13), (18, 21), (6, 21), (11, 22), (14, 26), (17, 18), (18, 0), (1, 19), (10, 23), (5, 18), (17, 0), (19, 10), (9, 14), (13, 5), (5, 22), (2, 2), (15, 12), (0, 16), (21, 7), (5, 15), (4, 20), (15, 20), (10, 16), (2, 12), (20, 1), (12, 12), (14, 23), (22, 18), (15, 16), (22, 22), (12, 2), (4, 4), (0, 11), (8, 24), (2, 22), (12, 25), (4, 14), (6, 0), (14, 1), (1, 25), (20, 15), (21, 0), (3, 11), (13, 16), (18, 11), (13, 22), (6, 16), (1, 0), (9, 4), (17, 10), (17, 3), (21, 24), (11, 20), (3, 2), (20, 25), (19, 24), (18, 24), (19, 4), (5, 4), (6, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732804", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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, 6), (3, 0), (1, 10), (23, 14), (23, 12), (11, 2), (2, 7), (14, 18), (3, 2), (7, 14), (8, 10), (2, 2), (5, 15), (4, 4), (21, 17), (3, 11), (8, 15), (23, 3), (16, 7), (4, 3), (11, 19), (5, 0), (6, 11), (8, 7), (21, 10), (17, 13), (1, 15), (2, 12), (2, 1), (14, 12), (8, 4), (14, 7), (6, 3), (18, 10), (8, 14), (6, 12), (15, 17), (3, 6), (9, 1), (20, 13), (0, 8), (10, 5), (23, 5), (15, 6), (8, 1), (23, 9), (9, 7), (18, 18), (7, 0), (19, 2), (18, 3), (20, 17), (19, 16), (18, 2), (8, 16), (4, 2), (6, 8), (13, 7), (13, 14), (0, 18), (11, 16), (13, 5), (1, 13), (17, 0), (8, 12), (7, 12), (4, 7), (22, 19), (16, 15), (6, 16), (7, 15), (4, 1), (7, 9), (2, 15), (3, 4), (8, 11), (20, 0), (18, 8), (5, 10), (21, 11), (3, 18), (7, 3), (12, 2), (19, 6), (2, 13), (18, 4), (12, 10), (0, 1), (3, 19), (8, 17), (21, 4), (1, 17), (3, 3), (4, 14), (20, 9), (14, 10), (16, 5), (7, 7), (17, 6), (22, 3), (14, 13), (10, 2), (13, 6), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956304", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 2), (8, 21), (19, 17), (13, 0), (2, 5), (2, 14), (17, 3), (15, 18), (22, 14), (9, 3), (25, 1), (13, 15), (1, 8), (12, 19), (23, 16), (15, 3), (20, 13), (10, 20), (13, 1), (14, 19), (8, 0), (6, 7), (21, 16), (11, 21), (25, 20), (22, 16), (8, 8), (3, 18), (10, 11), (22, 4), (1, 14), (7, 2), (1, 12), (4, 3), (2, 20), (14, 14), (0, 14), (18, 19), (23, 18), (15, 10), (16, 4), (24, 8), (23, 20), (5, 6), (20, 1), (14, 15), (4, 19), (13, 7), (6, 8), (6, 15), (19, 0), (12, 3), (9, 7), (8, 16), (18, 14), (19, 10), (13, 19), (17, 20), (5, 14), (3, 20), (9, 16), (11, 10), (14, 1), (15, 8), (17, 6), (24, 1), (0, 20), (8, 2), (13, 16), (25, 0), (19, 18), (3, 4), (10, 9), (9, 1), (1, 20), (14, 8), (10, 4), (13, 12), (20, 10), (11, 8), (0, 18), (12, 0), (2, 21), (22, 13), (23, 1), (7, 7), (7, 19), (18, 13), (2, 12), (4, 20), (21, 21), (19, 21), (16, 9), (4, 13), (4, 11), (22, 8), (21, 15), (13, 18), (10, 1), (15, 17), (10, 19), (16, 3), (5, 9), (5, 17), (22, 5), (11, 7), (10, 12), (16, 14), (23, 19), (13, 2), (5, 11), (6, 19), (22, 17), (3, 15), (3, 17), (14, 10), (20, 4), (4, 6), (4, 7), (14, 9), (5, 15), (19, 2), (0, 3), (7, 1), (18, 3), (0, 19), (23, 0), (12, 5), (3, 1), (25, 3), (19, 3), (6, 9), (16, 17), (4, 9), (2, 0), (15, 15), (5, 5), (25, 17), (0, 11), (9, 2), (23, 12), (15, 16), (19, 11), (2, 13), (15, 0), (4, 5), (20, 5), (24, 14), (14, 5), (6, 18), (18, 0), (1, 21), (21, 11), (14, 2), (13, 17), (17, 4), (14, 7), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820260", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), 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), (21, 5), (7, 5), (4, 4), (19, 21), (24, 3), (19, 3), (24, 2), (8, 12), (8, 9), (5, 18), (24, 12), (23, 23), (5, 9), (0, 4), (6, 1), (18, 10), (6, 17), (17, 16), (7, 19), (2, 12), (9, 10), (18, 19), (21, 19), (10, 7), (6, 10), (22, 6), (23, 1), (16, 19), (2, 22), (8, 10), (0, 5), (2, 11), (12, 2), (8, 4), (13, 10), (25, 3), (1, 14), (25, 16), (22, 10), (2, 19), (3, 2), (0, 6), (6, 3), (16, 15), (24, 19), (21, 6), (7, 20), (3, 12), (17, 10), (7, 18), (16, 8), (16, 5), (4, 25), (19, 10), (9, 19), (17, 8), (16, 7), (8, 3), (4, 10), (15, 7), (16, 24), (1, 11), (11, 19), (9, 5), (1, 20), (13, 16), (7, 25), (12, 21), (23, 7), (3, 16), (12, 5), (3, 5), (6, 0), (13, 2), (15, 24), (10, 6), (13, 11), (22, 0), (10, 23), (18, 18), (13, 1), (4, 6), (25, 18), (10, 3), (23, 16), (9, 3), (4, 1), (9, 17), (21, 24), (11, 16), (21, 16), (17, 12), (14, 24), (22, 16), (12, 12), (6, 21), (21, 3), (10, 25), (18, 25), (22, 8), (13, 9), (24, 20), (7, 3), (20, 10), (13, 21), (14, 3), (15, 13), (3, 1), (23, 21), (0, 10), (22, 13), (20, 13), (19, 6), (17, 9), (19, 15), (4, 14), (21, 17), (18, 3), (12, 13), (13, 3), (22, 25), (23, 2), (3, 6), (12, 20), (18, 8), (21, 4), (15, 20), (5, 3), (11, 14), (13, 22), (17, 21), (13, 15), (23, 19), (16, 11), (3, 24), (0, 22), (18, 7), (11, 17), (3, 9), (20, 6), (10, 16), (3, 4), (14, 2), (24, 0), (14, 0), (4, 16), (12, 9), (0, 9), (23, 24), (5, 0), (14, 25), (11, 24), (5, 16), (15, 12), (15, 16), (5, 8), (15, 8), (17, 22), (13, 12), (18, 0), (5, 19), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947328", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), 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), (4, 13), (21, 1), (17, 17), (4, 0), (18, 1), (0, 5), (21, 4), (14, 3), (0, 20), (2, 12), (7, 5), (20, 13), (21, 0), (5, 20), (13, 19), (12, 8), (8, 7), (19, 4), (2, 13), (12, 17), (1, 20), (19, 0), (2, 10), (19, 15), (10, 1), (3, 20), (9, 20), (0, 16), (18, 0), (13, 18), (16, 6), (8, 17), (8, 13), (14, 20), (2, 9), (19, 19), (3, 16), (2, 16), (7, 13), (19, 11), (11, 12), (4, 10), (1, 3), (0, 10), (5, 12), (11, 20), (4, 8), (7, 14), (4, 20), (17, 0), (21, 11), (17, 4), (6, 3), (17, 2), (1, 6), (6, 6), (20, 2), (21, 10), (2, 8), (16, 16), (12, 18), (15, 3), (16, 5), (18, 18), (8, 18), (1, 1), (20, 17), (8, 9), (7, 7), (17, 7), (18, 12), (6, 16), (7, 4), (21, 12), (19, 10), (8, 1), (11, 15), (0, 17), (20, 3), (21, 14), (10, 11), (3, 3), (6, 8), (13, 7), (2, 17), (5, 21), (19, 5), (20, 9), (17, 8), (0, 6), (9, 2), (5, 18), (11, 4), (4, 15), (14, 1), (11, 7), (1, 13), (21, 13), (6, 15), (7, 9), (1, 2), (16, 9), (0, 1), (17, 15), (10, 10), (4, 7), (16, 21), (5, 16), (4, 17), (6, 5), (18, 21), (2, 15), (20, 1), (6, 0), (20, 19), (17, 19), (6, 14), (16, 2), (11, 1), (19, 7), (8, 21), (12, 15), (18, 10), (14, 6), (11, 0), (18, 13), (3, 18), (2, 14), (10, 13), (7, 18), (10, 16), (3, 21), (7, 16), (13, 11), (21, 9), (15, 2), (11, 5), (15, 6), (9, 8), (4, 6), (1, 17), (0, 9), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899048", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 2), (17, 7), (17, 1), (18, 3), (18, 7), (11, 12), (19, 6), (4, 12), (23, 5), (6, 3), (5, 13), (5, 1), (19, 16), (3, 1), (4, 6), (13, 1), (23, 2), (8, 13), (11, 8), (2, 15), (6, 2), (23, 11), (21, 18), (16, 6), (15, 6), (5, 21), (9, 16), (8, 20), (17, 0), (5, 12), (12, 14), (10, 12), (3, 14), (14, 1), (2, 19), (0, 2), (11, 4), (11, 7), (11, 18), (14, 2), (17, 14), (21, 5), (21, 2), (12, 5), (22, 13), (0, 20), (8, 17), (18, 21), (11, 17), (21, 14), (12, 7), (2, 0), (13, 0), (10, 20), (23, 19), (20, 19), (3, 11), (2, 3), (10, 11), (10, 16), (6, 20), (15, 4), (5, 0), (21, 13), (19, 17), (6, 5), (3, 12), (22, 12), (20, 12), (6, 15), (16, 4), (9, 9), (12, 1), (17, 4), (3, 21), (21, 19), (7, 18), (22, 5), (23, 18), (7, 3), (2, 11), (12, 13), (6, 18), (1, 0), (16, 9), (4, 3), (16, 12), (19, 5), (19, 9), (18, 19), (0, 17), (11, 0), (1, 20), (5, 6), (3, 19), (22, 3), (1, 11), (21, 9), (14, 18), (13, 18), (3, 4), (21, 11), (8, 6), (19, 8), (17, 8), (8, 8), (3, 15), (4, 11), (13, 11), (18, 11), (9, 15), (15, 21), (11, 15), (6, 11), (2, 17), (8, 7), (22, 11), (15, 16), (18, 12), (1, 18), (21, 6), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "955230", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (11, 8), (5, 17), (13, 10), (4, 0), (15, 15), (17, 2), (12, 5), (11, 4), (19, 0), (9, 12), (24, 16), (16, 4), (26, 18), (3, 19), (10, 14), (26, 15), (18, 16), (5, 6), (19, 10), (4, 12), (19, 13), (9, 6), (19, 14), (23, 15), (20, 7), (2, 19), (8, 16), (17, 3), (15, 7), (24, 9), (24, 12), (10, 5), (21, 11), (22, 9), (23, 7), (4, 1), (12, 10), (6, 7), (23, 5), (13, 2), (19, 15), (26, 14), (10, 13), (12, 8), (20, 2), (21, 10), (21, 15), (25, 5), (10, 19), (14, 8), (25, 16), (4, 8), (4, 11), (12, 17), (13, 4), (20, 8), (23, 10), (12, 2), (6, 6), (19, 7), (23, 2), (9, 0), (1, 18), (9, 16), (18, 19), (25, 4), (15, 10), (0, 7), (4, 15), (17, 14), (24, 0), (21, 5), (6, 11), (23, 6), (4, 13), (3, 1), (2, 17), (5, 3), (20, 13), (24, 11), (15, 18), (5, 4), (6, 15), (22, 17), (10, 9), (20, 17), (17, 4), (7, 11), (8, 0), (21, 16), (21, 17), (6, 14), (26, 10), (3, 13), (20, 16), (20, 6), (12, 6), (17, 13), (0, 11), (5, 13), (13, 19), (21, 14), (22, 10), (5, 0), (12, 16), (1, 9), (16, 17), (26, 2), (16, 13), (19, 11), (24, 8), (8, 10), (16, 18), (9, 3), (9, 7), (20, 18), (25, 1), (23, 4), (24, 3), (3, 16), (19, 6), (8, 5), (14, 16), (14, 19), (12, 12), (7, 18), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51696", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (23, 14), (24, 20), (1, 17), (19, 8), (10, 22), (22, 1), (24, 4), (5, 5), (24, 12), (10, 13), (0, 12), (13, 20), (13, 9), (1, 2), (25, 7), (25, 18), (20, 2), (7, 7), (12, 4), (12, 19), (11, 5), (11, 12), (21, 7), (13, 0), (18, 21), (13, 8), (2, 22), (12, 20), (4, 9), (25, 22), (23, 6), (21, 1), (23, 9), (15, 17), (0, 4), (5, 2), (18, 19), (13, 15), (4, 5), (18, 5), (18, 23), (11, 7), (14, 0), (22, 22), (5, 24), (16, 15), (17, 3), (12, 8), (10, 17), (21, 5), (9, 21), (6, 6), (21, 20), (17, 10), (0, 16), (8, 21), (4, 6), (12, 1), (9, 22), (0, 18), (3, 18), (21, 14), (21, 13), (14, 11), (10, 8), (4, 22), (2, 17), (12, 23), (23, 10), (7, 16), (21, 10), (9, 1), (7, 11), (14, 12), (18, 24), (2, 23), (20, 22), (9, 17), (16, 23), (25, 0), (19, 14), (14, 6), (12, 21), (16, 14), (14, 20), (22, 18), (21, 0), (2, 19), (8, 20), (19, 20), (16, 21), (9, 13), (4, 1), (2, 11), (10, 18), (10, 15), (14, 23), (11, 10), (16, 0), (3, 19), (15, 20), (25, 20), (10, 1), (17, 18), (10, 12), (18, 8), (16, 2), (21, 9), (4, 20), (3, 21), (18, 1), (13, 19), (23, 22), (10, 0), (25, 16), (7, 21), (1, 12), (21, 2), (19, 17), (18, 4), (6, 15), (15, 15), (7, 14), (0, 17), (2, 9), (1, 0), (8, 1), (17, 6), (13, 12), (10, 16), (13, 17), (10, 11), (18, 11), (13, 4), (8, 11), (17, 4), (1, 8), (7, 6), (23, 18), (13, 23), (22, 11), (6, 22), (6, 5), (15, 7), (0, 15), (14, 8), (10, 14), (25, 1), (8, 14), (9, 3), (24, 23), (6, 23), (25, 2), (14, 2), (21, 18), (17, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "885150", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), 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), (13, 3), (13, 7), (16, 5), (17, 19), (16, 10), (17, 9), (19, 12), (19, 23), (23, 12), (1, 5), (1, 11), (18, 3), (20, 25), (11, 20), (15, 14), (22, 4), (23, 0), (0, 8), (9, 3), (12, 15), (2, 22), (5, 3), (3, 14), (7, 17), (17, 12), (3, 3), (12, 1), (17, 18), (16, 2), (5, 1), (14, 12), (4, 19), (10, 7), (11, 24), (23, 5), (13, 17), (11, 18), (18, 5), (23, 13), (10, 4), (23, 11), (7, 15), (8, 3), (18, 7), (19, 14), (16, 22), (10, 14), (1, 20), (1, 13), (11, 10), (7, 23), (13, 4), (12, 8), (5, 20), (18, 24), (8, 16), (22, 23), (11, 3), (9, 5), (3, 13), (1, 12), (11, 5), (12, 25), (14, 6), (4, 16), (11, 23), (21, 24), (11, 19), (18, 10), (14, 18), (18, 11), (4, 1), (21, 4), (20, 1), (21, 25), (3, 10), (19, 4), (17, 7), (6, 3), (8, 10), (10, 21), (10, 16), (22, 5), (2, 4), (7, 21), (3, 24), (6, 0), (23, 20), (13, 8), (8, 5), (20, 7), (1, 16), (16, 17), (3, 7), (4, 12), (22, 8), (7, 3), (14, 0), (9, 21), (7, 1), (10, 3), (4, 17), (3, 6), (8, 12), (5, 7), (8, 8), (17, 17), (12, 18), (0, 3), (15, 3), (14, 3), (9, 0), (15, 5), (7, 10), (20, 23), (3, 9), (12, 11), (0, 19), (22, 24), (2, 15), (23, 6), (23, 4), (19, 8), (8, 2), (14, 1), (0, 18), (21, 7), (23, 15), (8, 17), (21, 17), (6, 16), (9, 2), (19, 1), (18, 13), (6, 24), (18, 17), (17, 14), (5, 12), (1, 3), (22, 13), (19, 21), (16, 15), (7, 7), (22, 0), (12, 9), (17, 1), (7, 19), (14, 5), (5, 16), (1, 25), (15, 20), (20, 18), (4, 13), (19, 6), (18, 8), (1, 7), (15, 4), (15, 6), (4, 23), (6, 5), (18, 20), (16, 1), (10, 2), (22, 6), (16, 21), (7, 9), (0, 2), (14, 9), (3, 8), (1, 6), (20, 24), (20, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721935", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 20), (3, 17), (4, 15), (15, 6), (16, 0), (19, 4), (5, 15), (12, 12), (15, 15), (17, 19), (24, 11), (16, 14), (9, 0), (2, 12), (19, 6), (6, 14), (8, 1), (16, 8), (22, 9), (22, 15), (13, 12), (4, 8), (0, 3), (18, 8), (9, 3), (17, 16), (14, 18), (4, 12), (19, 13), (13, 9), (13, 16), (9, 7), (23, 17), (2, 3), (5, 9), (1, 3), (9, 13), (25, 10), (11, 0), (1, 6), (25, 16), (18, 20), (17, 1), (1, 14), (24, 19), (20, 0), (9, 12), (24, 15), (9, 8), (3, 15), (16, 16), (3, 16), (16, 6), (23, 8), (24, 7), (24, 9), (1, 9), (6, 9), (6, 11), (20, 5), (16, 19), (22, 20), (25, 4), (24, 2), (14, 12), (10, 17), (25, 0), (24, 14), (13, 19), (12, 18), (18, 5), (9, 6), (20, 17), (18, 19), (11, 2), (10, 19), (6, 18), (10, 5), (1, 12), (1, 1), (11, 9), (1, 2), (17, 2), (22, 4), (14, 14), (25, 6), (10, 10), (11, 6), (22, 14), (5, 2), (23, 4), (22, 3), (23, 1), (5, 17), (6, 3), (0, 16), (20, 18), (22, 5), (10, 11), (17, 7), (19, 16), (16, 3), (9, 20), (20, 3), (12, 0), (7, 12), (21, 17), (7, 4), (9, 11), (11, 17), (7, 17), (24, 6), (21, 7), (8, 7), (25, 18), (21, 0), (4, 1), (23, 12), (2, 4), (14, 7), (22, 10), (17, 5), (15, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901020", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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, 5), (16, 2), (4, 12), (18, 11), (1, 19), (12, 12), (4, 7), (3, 10), (13, 17), (1, 6), (1, 21), (9, 9), (7, 8), (8, 14), (20, 15), (10, 24), (15, 9), (13, 19), (10, 4), (3, 23), (18, 8), (3, 4), (17, 4), (9, 22), (17, 9), (4, 19), (13, 9), (8, 24), (12, 9), (14, 12), (4, 11), (11, 15), (0, 5), (20, 1), (12, 23), (6, 8), (1, 5), (10, 7), (2, 2), (0, 14), (9, 1), (16, 20), (10, 8), (8, 12), (18, 23), (15, 23), (5, 22), (5, 14), (9, 15), (2, 24), (1, 9), (12, 20), (13, 12), (6, 2), (9, 25), (17, 21), (12, 8), (18, 16), (11, 1), (3, 19), (6, 14), (11, 12), (18, 21), (1, 13), (16, 22), (16, 1), (0, 2), (20, 21), (5, 0), (1, 20), (16, 11), (16, 14), (14, 18), (11, 19), (3, 20), (9, 2), (18, 3), (15, 3), (5, 23), (20, 16), (18, 20), (12, 2), (4, 10), (6, 0), (5, 21), (8, 0), (19, 2), (4, 22), (6, 16), (10, 14), (17, 10), (11, 3), (4, 21), (11, 20), (12, 6), (15, 12), (16, 15), (8, 18), (9, 13), (18, 12), (8, 5), (2, 6), (9, 4), (19, 22), (1, 12), (14, 17), (19, 12), (10, 15), (4, 20), (6, 19), (2, 16), (8, 22), (5, 1), (18, 13), (10, 3), (10, 2), (7, 24), (12, 7), (8, 13), (12, 14), (17, 22), (9, 17), (0, 24), (2, 20), (16, 10), (1, 14), (0, 4), (11, 7), (13, 10), (11, 0), (19, 3), (16, 5), (15, 19), (18, 6), (10, 1), (14, 21), (18, 10), (12, 11), (14, 10), (2, 12), (8, 19), (8, 1), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743130", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (11, 15), (10, 18), (8, 22), (13, 0), (4, 5), (13, 9), (5, 0), (15, 24), (2, 24), (2, 11), (10, 3), (3, 0), (9, 21), (17, 20), (13, 23), (15, 15), (19, 6), (15, 21), (14, 13), (7, 13), (1, 19), (11, 19), (15, 7), (17, 24), (9, 12), (14, 7), (14, 20), (18, 2), (16, 0), (8, 7), (3, 22), (8, 12), (18, 16), (0, 1), (8, 8), (7, 16), (18, 8), (17, 18), (9, 7), (11, 22), (13, 14), (18, 15), (10, 1), (12, 15), (16, 14), (14, 12), (11, 20), (2, 12), (2, 1), (6, 12), (7, 17), (10, 7), (15, 2), (13, 19), (14, 18), (18, 20), (19, 18), (13, 7), (9, 19), (9, 3), (10, 16), (15, 20), (18, 12), (7, 21), (9, 23), (17, 14), (2, 0), (3, 6), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751440", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 20), (22, 19), (16, 13), (7, 19), (4, 20), (8, 18), (21, 5), (2, 6), (4, 13), (21, 7), (6, 14), (13, 17), (1, 18), (22, 18), (18, 4), (18, 1), (7, 4), (20, 12), (8, 3), (4, 3), (20, 6), (12, 19), (19, 4), (14, 12), (23, 9), (17, 20), (19, 3), (15, 13), (13, 19), (4, 0), (15, 11), (11, 3), (1, 9), (1, 14), (9, 12), (12, 14), (14, 19), (3, 12), (2, 5), (11, 7), (11, 10), (6, 8), (1, 0), (17, 11), (4, 7), (0, 4), (22, 5), (15, 2), (13, 15), (9, 8), (12, 17), (13, 3), (17, 6), (8, 14), (10, 10), (24, 8), (23, 18), (10, 3), (14, 20), (4, 19), (2, 3), (22, 12), (11, 14), (23, 20), (13, 11), (15, 14), (18, 16), (5, 3), (15, 5), (6, 9), (6, 13), (24, 4), (8, 5), (19, 11), (6, 10), (24, 6), (10, 17), (0, 7), (9, 1), (17, 17), (20, 8), (6, 16), (5, 19), (18, 11), (22, 1), (3, 13), (17, 2), (10, 9), (0, 17), (11, 9), (5, 12), (8, 2), (13, 16), (24, 0), (7, 0), (7, 13), (13, 10), (21, 19), (17, 19), (18, 3), (3, 9), (15, 18), (16, 12), (7, 7), (11, 15), (5, 1), (14, 17), (21, 20), (12, 8), (20, 13), (3, 11), (22, 4), (22, 17), (22, 10), (3, 3), (17, 10), (15, 6), (14, 16), (2, 12), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984100", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 19), (11, 18), (1, 20), (14, 18), (4, 12), (23, 20), (22, 23), (6, 11), (3, 27), (4, 27), (4, 23), (9, 8), (12, 9), (20, 27), (14, 24), (25, 13), (11, 6), (22, 8), (0, 7), (7, 25), (10, 13), (15, 2), (8, 3), (16, 7), (3, 26), (7, 18), (24, 7), (5, 22), (8, 2), (15, 24), (19, 11), (8, 24), (24, 20), (9, 21), (15, 16), (2, 13), (9, 11), (20, 21), (18, 0), (18, 2), (6, 6), (16, 5), (16, 20), (6, 22), (15, 7), (16, 0), (10, 5), (1, 21), (0, 23), (11, 15), (10, 9), (0, 15), (13, 23), (12, 25), (18, 22), (22, 21), (25, 12), (17, 19), (13, 10), (3, 4), (1, 9), (1, 19), (14, 9), (10, 24), (25, 1), (25, 2), (19, 14), (22, 2), (3, 22), (11, 13), (7, 27), (0, 22), (6, 25), (3, 6), (4, 8), (15, 8), (5, 20), (24, 21), (18, 1), (17, 8), (23, 18), (18, 7), (2, 19), (21, 3), (15, 18), (15, 1), (14, 6), (6, 0), (11, 22), (23, 10), (18, 15), (14, 22), (1, 23), (13, 0), (11, 4), (12, 12), (12, 11), (11, 20), (3, 15), (7, 19), (20, 4), (20, 23), (0, 10), (19, 16), (19, 22), (11, 1), (10, 18), (9, 27), (22, 19), (10, 8), (1, 18), (11, 27), (9, 18), (1, 0), (24, 17), (13, 11), (17, 15), (21, 10), (8, 20), (9, 15), (20, 19), (19, 9), (8, 25), (13, 7), (19, 6), (10, 7), (25, 26), (3, 0), (1, 14), (2, 27), (22, 20), (22, 9), (14, 7), (16, 6), (13, 26), (13, 12), (24, 24), (9, 13), (22, 1), (4, 26), (18, 24), (19, 7), (22, 10), (17, 21), (18, 26), (9, 3), (9, 1), (1, 17), (9, 24), (9, 23), (4, 7), (25, 5), (18, 8), (24, 25), (4, 15), (1, 24), (4, 0), (21, 11), (6, 9), (16, 2), (9, 20), (15, 10), (0, 17), (11, 5), (10, 16), (19, 15), (24, 18), (14, 11), (20, 22), (8, 23), (16, 9), (7, 13), (12, 17), (5, 23), (3, 19), (25, 17), (20, 12), (9, 0), (20, 6), (18, 21), (5, 11), (15, 9), (15, 19), (20, 7), (6, 1), (12, 22), (18, 12), (4, 20), (3, 11), (14, 25), (19, 27), (3, 16), (24, 15), (5, 25), (7, 21), (7, 5), (6, 20), (5, 27), (1, 25), (16, 23), (21, 20), (2, 1), (8, 19), (0, 18), (4, 19), (7, 16), (9, 9), (1, 1), (21, 2), (4, 17), (2, 26), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943110", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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), (23, 18), (19, 13), (21, 5), (6, 23), (11, 4), (8, 1), (22, 15), (0, 5), (15, 20), (12, 8), (14, 2), (5, 6), (19, 6), (12, 5), (7, 8), (22, 23), (0, 6), (22, 0), (7, 9), (11, 17), (9, 3), (6, 10), (7, 20), (13, 11), (20, 7), (11, 16), (2, 9), (10, 3), (1, 12), (6, 17), (20, 9), (15, 7), (5, 24), (1, 18), (9, 10), (22, 12), (10, 18), (10, 9), (5, 21), (18, 6), (20, 8), (23, 3), (18, 18), (19, 24), (9, 11), (13, 9), (20, 4), (14, 6), (10, 23), (8, 22), (19, 8), (13, 16), (4, 10), (13, 21), (2, 5), (17, 21), (23, 1), (16, 5), (17, 16), (6, 15), (22, 8), (9, 6), (16, 22), (16, 14), (23, 5), (18, 5), (8, 24), (12, 9), (23, 0), (9, 8), (18, 4), (15, 1), (3, 19), (16, 3), (22, 11), (8, 7), (18, 12), (11, 1), (19, 21), (10, 19), (7, 3), (20, 20), (16, 24), (0, 1), (18, 8), (0, 17), (13, 23), (12, 0), (8, 3), (17, 19), (7, 15), (16, 20), (10, 16), (5, 15), (19, 5), (11, 8), (15, 14), (20, 19), (4, 22), (12, 22), (9, 13), (10, 13), (6, 21), (0, 2), (21, 14), (11, 12), (0, 20), (12, 2), (13, 5), (1, 23), (11, 22), (17, 13), (14, 14), (17, 12), (16, 21), (2, 11), (12, 23), (1, 1), (9, 7), (7, 18), (1, 10), (14, 21), (8, 21), (22, 9), (7, 17), (11, 11), (23, 7), (22, 4), (6, 16), (6, 20), (3, 16), (1, 6), (7, 16), (13, 17), (11, 24), (15, 24), (23, 2), (14, 4), (5, 12), (19, 3), (20, 10), (8, 6), (7, 12), (14, 0), (7, 14), (2, 18), (3, 17), (23, 9), (16, 17), (4, 19), (17, 1), (19, 10), (2, 16), (3, 13), (22, 3), (18, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470580", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 18), (8, 20), (6, 5), (20, 18), (25, 16), (19, 13), (13, 12), (18, 10), (8, 17), (6, 10), (1, 6), (16, 4), (14, 5), (22, 3), (18, 7), (9, 20), (14, 12), (11, 4), (3, 7), (4, 3), (20, 17), (24, 7), (5, 1), (0, 9), (12, 11), (20, 2), (19, 9), (4, 17), (16, 3), (4, 18), (23, 7), (19, 11), (3, 13), (16, 13), (5, 15), (10, 5), (25, 18), (3, 12), (12, 9), (21, 5), (0, 8), (0, 12), (20, 1), (6, 0), (19, 7), (7, 8), (8, 13), (18, 18), (8, 10), (4, 15), (17, 6), (16, 20), (5, 3), (10, 2), (22, 12), (1, 17), (23, 10), (18, 6), (12, 10), (15, 9), (22, 5), (5, 17), (14, 1), (6, 17), (18, 5), (10, 16), (16, 15), (24, 0), (25, 8), (14, 20), (9, 10), (0, 4), (24, 20), (19, 4), (2, 0), (24, 10), (18, 0), (22, 14), (7, 7), (25, 3), (7, 14), (2, 3), (2, 14), (15, 16), (11, 0), (10, 17), (9, 9), (22, 6), (3, 20), (5, 16), (21, 18), (17, 11), (9, 8), (13, 15), (16, 0), (15, 6), (1, 2), (9, 2), (20, 7), (19, 3), (13, 17), (20, 20), (11, 11), (15, 0), (22, 15), (6, 6), (13, 18), (12, 6), (14, 16), (5, 18), (7, 17), (21, 17), (3, 18), (9, 19), (7, 15), (17, 20), (23, 17), (2, 11), (16, 1), (4, 10), (0, 19), (11, 18), (16, 12), (18, 4), (20, 10), (12, 14), (5, 2), (24, 8), (15, 20), (3, 6), (15, 10), (18, 2), (25, 15), (6, 16), (8, 15), (19, 20), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78096", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 21), (18, 6), (3, 21), (21, 13), (24, 1), (22, 7), (3, 1), (19, 24), (10, 3), (12, 6), (22, 20), (4, 15), (21, 5), (18, 1), (24, 5), (22, 17), (23, 14), (0, 17), (1, 19), (21, 8), (21, 14), (19, 11), (20, 7), (12, 5), (2, 13), (8, 6), (24, 19), (13, 22), (6, 10), (24, 6), (23, 13), (8, 12), (12, 7), (13, 9), (19, 8), (7, 7), (24, 8), (0, 15), (24, 9), (8, 23), (19, 3), (22, 24), (5, 5), (21, 19), (4, 19), (5, 4), (23, 11), (16, 14), (6, 9), (11, 18), (8, 16), (13, 8), (6, 2), (18, 5), (12, 20), (10, 12), (2, 15), (0, 10), (22, 13), (22, 19), (3, 13), (12, 14), (1, 16), (24, 16), (22, 23), (5, 17), (15, 10), (20, 15), (15, 19), (23, 24), (6, 20), (13, 19), (3, 14), (14, 23), (2, 14), (16, 5), (8, 22), (9, 14), (14, 13), (8, 20), (13, 15), (5, 2), (22, 11), (0, 9), (3, 3), (16, 10), (18, 4), (7, 8), (22, 18), (9, 3), (19, 22), (23, 3), (9, 2), (1, 9), (23, 1), (17, 19), (4, 7), (8, 0), (11, 9), (9, 23), (9, 5), (13, 14), (7, 20), (1, 7), (18, 22), (12, 19), (10, 6), (3, 16), (6, 7), (24, 20), (7, 3), (5, 6), (6, 4), (14, 3), (22, 15), (17, 5), (21, 6), (6, 21), (16, 16), (21, 23), (16, 13), (2, 11), (6, 3), (23, 16), (13, 5), (2, 12), (22, 8), (16, 15), (20, 0), (15, 3), (13, 3), (14, 24), (3, 6), (19, 14), (10, 20), (10, 19), (20, 21), (18, 18), (5, 8), (17, 20), (4, 11), (11, 15), (10, 17), (8, 5), (7, 0), (4, 24), (7, 5), (11, 10), (1, 20), (14, 7), (5, 9), (8, 9), (14, 22), (22, 12), (4, 3), (16, 19), (6, 17), (1, 10), (24, 10), (16, 3), (18, 23), (23, 23), (19, 16), (20, 10), (9, 17), (18, 10), (2, 0), (7, 2), (20, 11), (15, 14), (22, 5), (9, 18), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672064", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (5, 12), (14, 16), (5, 7), (2, 11), (7, 19), (10, 19), (20, 24), (6, 17), (17, 8), (12, 8), (4, 23), (1, 14), (19, 3), (1, 22), (16, 5), (12, 11), (6, 16), (3, 8), (3, 3), (12, 23), (6, 22), (10, 24), (17, 17), (11, 18), (12, 22), (18, 16), (5, 21), (17, 12), (5, 2), (20, 13), (13, 19), (18, 18), (19, 0), (17, 23), (18, 7), (6, 8), (0, 23), (8, 4), (19, 20), (14, 18), (6, 19), (7, 5), (6, 4), (20, 19), (5, 25), (9, 7), (0, 15), (17, 18), (12, 1), (3, 17), (17, 20), (13, 25), (2, 7), (6, 10), (1, 4), (20, 9), (9, 2), (0, 13), (16, 6), (12, 7), (16, 14), (19, 14), (10, 18), (9, 5), (11, 5), (19, 6), (16, 25), (16, 24), (14, 23), (14, 4), (9, 16), (0, 3), (6, 2), (16, 11), (9, 4), (9, 0), (18, 25), (0, 12), (0, 24), (14, 9), (7, 17), (16, 1), (9, 14), (8, 18), (6, 20), (20, 14), (7, 7), (15, 5), (5, 1), (1, 9), (16, 17), (13, 22), (10, 0), (20, 16), (18, 24), (5, 3), (16, 16), (6, 23), (10, 15), (3, 15), (5, 0), (20, 2), (15, 18), (7, 23), (13, 0), (0, 19), (12, 0), (15, 1), (8, 1), (15, 11), (0, 10), (18, 23), (18, 21), (18, 17), (4, 7), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726816", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (23, 10), (27, 2), (13, 0), (25, 14), (4, 7), (8, 12), (17, 4), (24, 5), (16, 10), (27, 9), (0, 8), (21, 19), (13, 6), (7, 1), (17, 1), (18, 5), (11, 14), (12, 5), (24, 0), (25, 7), (24, 14), (27, 5), (3, 2), (15, 17), (3, 15), (0, 15), (24, 15), (15, 16), (16, 0), (27, 11), (13, 19), (27, 17), (13, 16), (9, 5), (16, 17), (16, 1), (6, 8), (19, 14), (7, 16), (7, 11), (10, 15), (3, 14), (10, 6), (5, 18), (20, 7), (27, 3), (23, 14), (1, 17), (22, 17), (2, 2), (25, 16), (13, 12), (11, 3), (11, 9), (3, 7), (13, 13), (14, 19), (19, 13), (5, 10), (15, 15), (3, 9), (6, 7), (2, 6), (22, 13), (27, 13), (22, 9), (8, 4), (7, 8), (18, 7), (12, 16), (21, 1), (11, 16), (6, 2), (12, 10), (26, 5), (20, 15), (25, 1), (27, 1), (8, 6), (3, 4), (21, 7), (15, 4), (24, 13), (7, 10), (10, 4), (9, 15), (2, 8), (4, 17), (20, 11), (9, 14), (16, 2), (24, 2), (5, 9), (7, 9), (0, 13), (25, 10), (18, 13), (26, 17), (1, 5), (8, 9), (17, 15), (10, 13), (9, 1), (26, 15), (13, 11), (19, 12), (17, 16), (25, 13), (11, 15), (14, 0), (0, 16), (18, 3), (27, 8), (12, 2), (11, 18), (6, 16), (17, 12), (21, 3), (15, 13), (24, 1), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248022", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), 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), (21, 19), (11, 3), (13, 12), (10, 0), (24, 22), (14, 3), (13, 0), (11, 7), (15, 16), (25, 12), (5, 13), (5, 10), (0, 15), (17, 5), (15, 21), (24, 8), (2, 8), (0, 26), (22, 10), (2, 12), (14, 1), (3, 3), (18, 11), (20, 16), (17, 17), (3, 23), (16, 22), (12, 5), (17, 12), (2, 4), (10, 20), (4, 8), (11, 16), (1, 21), (2, 9), (19, 8), (15, 18), (10, 10), (12, 21), (16, 4), (14, 6), (25, 2), (19, 23), (0, 9), (18, 20), (8, 7), (13, 26), (13, 10), (24, 10), (5, 20), (11, 21), (5, 16), (18, 17), (24, 13), (20, 2), (6, 7), (14, 10), (7, 16), (7, 20), (1, 16), (11, 25), (19, 14), (20, 23), (3, 1), (4, 6), (3, 21), (9, 12), (23, 19), (12, 22), (5, 15), (20, 7), (8, 13), (6, 1), (2, 1), (3, 17), (14, 0), (5, 4), (8, 3), (18, 21), (15, 7), (19, 9), (14, 12), (14, 16), (10, 4), (21, 10), (25, 15), (18, 7), (17, 11), (8, 24), (2, 25), (13, 3), (0, 12), (25, 0), (0, 8), (9, 26), (4, 23), (16, 26), (6, 15), (7, 26), (16, 1), (14, 17), (24, 12), (20, 4), (18, 13), (15, 24), (0, 4), (20, 6), (18, 19), (4, 22), (23, 5), (9, 3), (17, 6), (19, 6), (9, 1), (23, 14), (6, 8), (15, 15), (17, 14), (16, 19), (5, 6), (5, 25), (19, 19), (4, 16), (0, 1), (4, 17), (8, 11), (20, 25), (11, 17), (24, 15), (11, 26), (11, 13), (25, 10), (13, 7), (3, 16), (15, 20), (1, 22), (3, 18), (4, 9), (8, 4), (22, 0), (8, 15), (14, 26), (15, 0), (24, 7), (7, 4), (2, 13), (11, 20), (25, 25), (19, 0), (3, 19), (15, 23), (3, 13), (24, 19), (12, 16), (8, 6), (25, 22), (25, 11), (8, 9), (24, 5), (14, 9), (25, 21), (0, 17), (22, 16), (9, 15), (23, 6), (8, 22), (22, 19), (17, 15), (13, 13), (6, 14), (9, 8), (8, 1), (2, 15), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "737056", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 21), (3, 9), (16, 0), (19, 9), (21, 11), (10, 16), (8, 10), (9, 21), (6, 13), (10, 9), (11, 0), (13, 7), (18, 16), (2, 3), (11, 16), (19, 14), (16, 11), (12, 9), (6, 19), (16, 26), (22, 2), (7, 8), (13, 19), (18, 13), (6, 4), (6, 23), (7, 4), (21, 2), (23, 19), (15, 14), (16, 6), (11, 10), (19, 16), (12, 1), (4, 8), (4, 17), (6, 3), (4, 20), (22, 4), (13, 24), (2, 2), (20, 9), (12, 21), (8, 18), (12, 16), (10, 7), (12, 15), (21, 9), (20, 13), (5, 8), (18, 7), (21, 18), (11, 4), (21, 21), (18, 6), (11, 23), (3, 4), (24, 8), (0, 16), (22, 12), (23, 15), (20, 18), (3, 2), (9, 5), (7, 9), (9, 9), (9, 1), (11, 20), (8, 17), (11, 18), (6, 2), (20, 14), (15, 11), (5, 4), (20, 26), (2, 6), (24, 12), (23, 2), (2, 26), (4, 19), (24, 0), (3, 18), (11, 8), (14, 20), (18, 19), (20, 7), (21, 6), (14, 22), (5, 17), (18, 20), (0, 26), (17, 7), (6, 21), (0, 14), (14, 21), (12, 25), (20, 15), (17, 6), (5, 6), (9, 24), (11, 25), (9, 13), (1, 18), (23, 9), (11, 11), (14, 12), (23, 4), (12, 5), (8, 3), (18, 22), (20, 23), (6, 9), (18, 24), (4, 9), (18, 2), (9, 17), (0, 9), (19, 0), (3, 10), (4, 21), (18, 18), (16, 16), (24, 15), (21, 12), (9, 25), (0, 6), (21, 20), (4, 24), (9, 15), (13, 4), (10, 17), (12, 24), (5, 1), (18, 23), (6, 11), (24, 17), (21, 1), (22, 25), (16, 13), (7, 12), (24, 19), (3, 17), (3, 6), (13, 9), (19, 13), (5, 22), (6, 25), (13, 15), (13, 10), (16, 7), (24, 3), (17, 15), (3, 14), (8, 11), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432093", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 26), (19, 16), (4, 22), (9, 11), (20, 15), (9, 12), (22, 17), (4, 5), (21, 25), (7, 16), (6, 10), (5, 11), (12, 23), (5, 14), (13, 23), (10, 22), (18, 20), (11, 7), (16, 1), (8, 19), (8, 24), (19, 1), (9, 4), (12, 26), (3, 9), (21, 9), (5, 26), (16, 23), (9, 26), (17, 15), (14, 11), (10, 10), (9, 1), (9, 0), (5, 25), (22, 23), (12, 10), (9, 18), (14, 19), (13, 6), (3, 17), (22, 14), (15, 17), (9, 5), (10, 7), (15, 15), (18, 1), (13, 22), (19, 25), (1, 14), (2, 13), (15, 11), (21, 8), (9, 23), (19, 18), (0, 17), (11, 19), (21, 10), (3, 26), (22, 20), (0, 3), (9, 13), (17, 13), (3, 1), (12, 18), (7, 24), (16, 20), (15, 27), (9, 14), (18, 28), (13, 5), (0, 20), (13, 28), (2, 11), (22, 9), (5, 21), (7, 12), (22, 27), (10, 14), (11, 24), (9, 20), (15, 7), (20, 23), (11, 28), (20, 6), (7, 21), (3, 6), (18, 22), (1, 3), (9, 6), (5, 9), (7, 4), (13, 27), (19, 2), (0, 13), (7, 14), (2, 23), (20, 18), (21, 23), (0, 27), (20, 2), (10, 28), (8, 8), (4, 19), (5, 15), (20, 17), (1, 22), (2, 6), (7, 28), (14, 28), (19, 3), (11, 15), (7, 10), (22, 11), (20, 8), (13, 2), (11, 6), (4, 7), (9, 28), (4, 24), (11, 22), (5, 4), (4, 8), (13, 11), (10, 13), (17, 20), (1, 13), (1, 17), (17, 5), (8, 23), (19, 5), (3, 5), (21, 3), (14, 21), (11, 5), (21, 6), (2, 7), (7, 23), (6, 25), (11, 0), (6, 1), (8, 22), (16, 15), (20, 0), (15, 24), (10, 21), (12, 12), (0, 24), (18, 23), (12, 24), (8, 12), (14, 15), (0, 12), (20, 12), (16, 9), (22, 25), (14, 12), (16, 28), (3, 20), (9, 16), (7, 20), (18, 26), (8, 26), (21, 24), (1, 24), (5, 20), (7, 7), (22, 21), (6, 17), (21, 16), (17, 3), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510348", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (1, 8), (13, 20), (11, 5), (7, 17), (21, 15), (14, 19), (13, 6), (1, 13), (11, 11), (21, 13), (6, 10), (22, 20), (8, 8), (9, 2), (12, 14), (17, 7), (16, 24), (11, 16), (10, 22), (5, 16), (2, 21), (2, 14), (4, 1), (12, 16), (4, 12), (6, 25), (14, 20), (11, 7), (18, 22), (4, 3), (7, 21), (22, 3), (3, 2), (7, 24), (17, 23), (16, 21), (13, 24), (13, 9), (18, 3), (16, 3), (12, 5), (15, 4), (16, 9), (13, 12), (7, 23), (16, 4), (7, 18), (6, 13), (19, 19), (20, 20), (10, 20), (13, 4), (20, 7), (21, 1), (18, 5), (19, 10), (2, 12), (22, 24), (4, 8), (9, 15), (15, 12), (2, 16), (20, 14), (5, 9), (12, 0), (20, 23), (0, 14), (21, 5), (20, 16), (11, 25), (14, 16), (15, 21), (23, 5), (5, 18), (5, 20), (15, 16), (7, 11), (16, 22), (7, 6), (17, 10), (9, 19), (15, 19), (0, 20), (21, 19), (12, 24), (10, 15), (3, 6), (6, 0), (23, 7), (15, 2), (12, 18), (8, 4), (16, 23), (8, 22), (4, 14), (15, 6), (0, 12), (17, 6), (10, 5), (5, 12), (19, 23), (9, 8), (3, 10), (9, 6), (11, 17), (12, 19), (1, 14), (11, 23), (6, 17), (23, 19), (19, 17), (15, 18), (1, 18), (6, 11), (13, 25), (6, 20), (1, 20), (11, 14), (7, 15), (14, 7), (3, 20), (17, 21), (13, 19), (14, 3), (5, 2), (3, 24), (3, 11), (5, 7), (7, 0), (19, 13), (17, 15), (7, 8), (7, 19), (17, 3), (13, 5), (19, 4), (3, 17), (12, 17), (21, 17), (7, 4), (0, 21), (0, 15), (6, 18), (2, 5), (1, 7), (11, 0), (6, 2), (9, 25), (22, 0), (21, 23), (16, 0), (6, 5), (16, 12), (18, 24), (20, 8), (9, 24), (0, 6), (7, 16), (17, 4), (5, 8), (18, 11), (23, 8), (15, 24), (21, 3), (8, 24), (19, 0), (18, 19), (10, 9), (14, 8), (19, 15), (12, 25), (14, 2), (8, 5), (2, 6), (19, 14), (15, 5), (6, 4), (13, 21), (20, 15), (13, 1), (18, 18), (2, 22), (18, 12), (9, 12), (23, 16), (10, 6), (11, 8), (1, 0), (20, 19), (11, 4), (3, 3), (22, 6), (3, 19), (5, 24), (15, 1), (13, 2), (10, 24), (9, 18), (14, 17), (0, 5), (17, 12), (1, 24), (10, 7), (13, 15), (6, 12), (4, 10), (2, 17), (6, 19), (22, 4), (8, 18), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779400", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (16, 0), (14, 0), (22, 26), (6, 12), (22, 8), (11, 8), (1, 1), (13, 8), (5, 18), (9, 19), (10, 1), (15, 4), (9, 6), (13, 10), (2, 3), (16, 16), (3, 17), (11, 15), (2, 18), (19, 26), (3, 7), (16, 11), (0, 12), (23, 6), (11, 21), (9, 5), (12, 10), (8, 5), (10, 17), (6, 17), (8, 4), (23, 15), (5, 13), (18, 2), (20, 6), (20, 27), (11, 5), (5, 19), (10, 25), (21, 9), (5, 25), (2, 9), (1, 11), (7, 7), (21, 15), (10, 23), (9, 24), (22, 3), (20, 7), (11, 6), (0, 18), (13, 21), (4, 15), (22, 14), (14, 10), (6, 4), (14, 16), (5, 26), (20, 22), (5, 1), (11, 2), (2, 26), (0, 1), (23, 21), (8, 15), (23, 24), (21, 1), (19, 19), (15, 12), (6, 22), (22, 20), (22, 6), (18, 5), (3, 14), (10, 15), (22, 18), (1, 16), (22, 9), (18, 16), (10, 3), (20, 12), (4, 9), (7, 20), (23, 11), (11, 20), (0, 23), (7, 2), (11, 11), (8, 7), (12, 9), (21, 0), (8, 3), (13, 25), (19, 6), (14, 4), (14, 22), (2, 15), (20, 2), (15, 24), (1, 18), (0, 15), (8, 24), (12, 13), (12, 4), (13, 0), (19, 24), (18, 21), (18, 9), (20, 8), (0, 27), (6, 7), (22, 16), (13, 3), (22, 0), (16, 1), (19, 11), (21, 17), (11, 3), (10, 12), (2, 6), (2, 24), (20, 10), (18, 11), (10, 24), (0, 11), (19, 14), (3, 12), (13, 1), (13, 4), (5, 2), (3, 2), (17, 6), (18, 24), (3, 5), (7, 4), (4, 17), (12, 12), (8, 9), (4, 8), (3, 9), (1, 19), (19, 22), (3, 26), (8, 6), (0, 26), (8, 2), (9, 21), (0, 22), (13, 13), (16, 15), (12, 5), (13, 17), (3, 18), (11, 16), (18, 10), (17, 3), (21, 18), (22, 12), (1, 10), (0, 5), (6, 26), (10, 4), (23, 4), (16, 14), (12, 18), (7, 3), (23, 0), (14, 21), (17, 17), (13, 11), (17, 19), (16, 23), (23, 18), (9, 16), (8, 16), (23, 7), (3, 3), (20, 25), (19, 4), (6, 3), (17, 2), (1, 21), (3, 20), (22, 13), (23, 8), (15, 1), (12, 7), (9, 7), (20, 4), (21, 19), (16, 27), (15, 14), (22, 1), (13, 2), (13, 27), (13, 16), (21, 13), (10, 21), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "421200", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), 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), (20, 19), (14, 14), (16, 17), (18, 10), (7, 17), (18, 11), (18, 16), (0, 7), (13, 14), (0, 12), (4, 3), (16, 11), (11, 9), (14, 17), (9, 13), (16, 6), (2, 12), (15, 14), (2, 4), (6, 21), (12, 14), (17, 4), (1, 23), (13, 18), (13, 21), (19, 7), (4, 11), (5, 13), (9, 22), (3, 22), (5, 23), (5, 3), (6, 7), (2, 3), (0, 16), (11, 19), (7, 19), (16, 5), (14, 18), (19, 0), (2, 22), (6, 10), (18, 7), (16, 14), (10, 18), (4, 21), (14, 20), (5, 17), (15, 12), (17, 19), (17, 22), (19, 6), (16, 3), (2, 13), (12, 6), (1, 3), (9, 2), (4, 15), (8, 0), (1, 16), (16, 16), (17, 20), (13, 11), (17, 16), (1, 9), (2, 15), (20, 20), (8, 13), (7, 0), (2, 5), (2, 20), (10, 15), (15, 1), (18, 23), (15, 18), (17, 9), (0, 4), (11, 3), (16, 15), (12, 23), (5, 19), (5, 12), (8, 12), (3, 5), (0, 10), (15, 17), (13, 17), (13, 20), (19, 14), (10, 2), (14, 4), (8, 22), (8, 16), (1, 6), (9, 1), (6, 20), (15, 3), (8, 9), (6, 8), (12, 0), (3, 4), (4, 9), (8, 1), (17, 12), (1, 11), (18, 3), (0, 9), (5, 6), (3, 17), (16, 8), (15, 23), (8, 8), (8, 19), (9, 23), (4, 18), (9, 17), (14, 22), (11, 20), (19, 10), (20, 2), (7, 2), (12, 20), (6, 5), (9, 5), (0, 5), (20, 9), (17, 0), (5, 9), (6, 15), (14, 10), (19, 11), (2, 14), (1, 4), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256410", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), 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, 0), (21, 23), (7, 18), (9, 17), (13, 17), (10, 15), (9, 6), (17, 3), (14, 21), (8, 5), (15, 22), (18, 9), (18, 1), (5, 20), (6, 0), (21, 10), (14, 4), (10, 24), (8, 17), (20, 1), (1, 17), (10, 16), (21, 12), (11, 21), (19, 17), (17, 8), (8, 6), (21, 16), (2, 14), (12, 17), (5, 15), (3, 23), (12, 20), (7, 6), (13, 6), (15, 6), (16, 20), (7, 2), (11, 8), (9, 23), (1, 19), (12, 6), (4, 14), (3, 15), (7, 8), (12, 11), (14, 22), (22, 4), (16, 10), (18, 18), (3, 22), (2, 20), (22, 2), (19, 4), (14, 14), (18, 7), (6, 4), (16, 18), (16, 4), (3, 14), (22, 7), (1, 16), (20, 15), (16, 9), (2, 18), (6, 5), (8, 22), (16, 2), (1, 14), (11, 7), (13, 10), (12, 0), (9, 24), (1, 13), (7, 24), (18, 5), (17, 23), (4, 17), (18, 24), (5, 16), (13, 12), (12, 9), (5, 13), (10, 13), (0, 22), (0, 4), (4, 24), (11, 11), (13, 23), (15, 10), (3, 10), (3, 16), (13, 0), (6, 2), (12, 21), (11, 6), (7, 0), (20, 9), (6, 17), (18, 2), (18, 11), (9, 10), (8, 8), (1, 11), (5, 9), (9, 9), (14, 13), (9, 5), (20, 23), (13, 9), (22, 9), (4, 3), (11, 22), (2, 7), (4, 19), (9, 8), (0, 16), (15, 8), (10, 11), (11, 23), (22, 14), (22, 5), (5, 24), (7, 23), (4, 2), (12, 13), (8, 23), (10, 2), (15, 23), (5, 17), (9, 22), (9, 20), (0, 2), (12, 10), (0, 15), (16, 12), (9, 19), (14, 7), (22, 23), (20, 11), (6, 18), (6, 21), (2, 11), (12, 4), (3, 12), (6, 9), (15, 4), (9, 18), (12, 15), (8, 1), (10, 18), (20, 10), (2, 22), (22, 20), (17, 6), (11, 20), (9, 7), (4, 6), (19, 6), (16, 3), (18, 12), (10, 10), (6, 15), (14, 17), (0, 8), (0, 7), (20, 2), (0, 5), (21, 13), (5, 18), (1, 7), (17, 13), (17, 2), (19, 15), (2, 16), (14, 2), (2, 15), (13, 18), (11, 10), (1, 3), (3, 13), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "812448", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 10), (24, 2), (8, 20), (23, 13), (16, 22), (22, 24), (3, 11), (15, 20), (20, 17), (11, 22), (24, 24), (6, 28), (21, 17), (18, 23), (3, 23), (11, 24), (17, 17), (10, 1), (10, 23), (18, 9), (16, 19), (13, 25), (5, 7), (9, 18), (0, 15), (10, 6), (17, 23), (7, 11), (18, 5), (1, 25), (19, 0), (15, 15), (28, 13), (3, 28), (6, 5), (25, 7), (3, 15), (4, 8), (11, 3), (17, 25), (8, 15), (18, 16), (12, 14), (9, 16), (7, 2), (9, 27), (17, 16), (4, 10), (26, 7), (6, 27), (12, 22), (6, 11), (4, 26), (27, 22), (10, 11), (6, 16), (3, 18), (11, 8), (24, 23), (11, 17), (22, 25), (3, 5), (12, 0), (13, 7), (26, 20), (3, 6), (4, 5), (22, 19), (13, 14), (10, 18), (21, 18), (24, 20), (27, 1), (21, 24), (23, 17), (21, 3), (17, 11), (8, 1), (24, 10), (17, 1), (27, 27), (6, 1), (18, 22), (1, 22), (25, 6), (8, 27), (15, 4), (2, 8), (25, 2), (26, 17), (21, 20), (19, 19), (22, 12), (20, 16), (25, 16), (26, 22), (20, 9), (27, 26), (4, 12), (16, 8), (27, 23), (1, 20), (10, 10), (27, 19), (19, 4), (28, 12), (1, 18), (11, 11), (16, 0), (12, 16), (19, 13), (22, 17), (23, 18), (26, 2), (11, 26), (19, 27), (11, 7), (28, 22), (13, 16), (25, 15), (11, 18), (20, 15), (4, 28), (15, 21), (18, 10), (2, 6), (13, 28), (15, 26), (24, 25), (6, 25), (26, 9), (13, 19), (5, 15), (27, 16), (10, 5), (13, 26), (17, 7), (22, 0), (16, 18), (17, 6), (21, 25), (16, 11), (3, 25), (14, 28), (8, 0), (9, 9), (11, 20), (9, 26), (23, 23), (6, 6), (28, 24), (7, 16), (13, 3), (0, 5), (5, 21), (20, 7), (10, 14), (11, 6), (13, 27), (8, 8), (23, 10), (3, 0), (8, 26), (10, 17), (0, 19), (2, 5), (22, 3), (17, 28), (24, 0), (7, 6), (0, 11), (28, 0), (14, 25), (24, 7), (7, 19), (26, 26), (22, 22), (12, 9), (0, 4), (9, 2), (5, 14), (8, 28), (4, 23), (23, 1), (2, 10), (25, 9), (22, 1), (6, 26), (23, 19), (9, 11), (15, 11), (26, 23), (15, 10), (4, 20), (13, 17), (9, 4), (10, 12), (19, 7), (9, 1), (22, 23), (23, 15), (28, 17), (5, 13), (16, 5), (15, 7), (19, 25), (11, 12), (17, 15), (16, 6), (8, 9), (20, 10), (16, 20), (16, 12), (14, 18), (27, 5), (24, 18), (22, 9), (14, 12), (24, 27), (21, 22), (2, 25), (7, 12), (25, 25), (17, 10), (8, 17), (26, 14), (4, 0), (18, 26), (21, 26), (11, 28), (20, 27), (28, 11), (9, 10), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350616", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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, 12), (3, 17), (24, 7), (18, 9), (5, 22), (19, 24), (19, 22), (4, 8), (10, 10), (10, 20), (22, 10), (15, 13), (27, 14), (25, 23), (1, 5), (5, 2), (24, 13), (9, 24), (22, 8), (7, 4), (15, 12), (4, 13), (10, 26), (9, 25), (10, 22), (22, 11), (4, 16), (11, 2), (6, 14), (16, 24), (13, 1), (15, 21), (11, 15), (24, 16), (12, 18), (2, 20), (21, 15), (17, 15), (10, 7), (25, 22), (10, 14), (24, 2), (26, 18), (16, 16), (19, 21), (16, 2), (9, 19), (5, 8), (18, 4), (17, 23), (27, 5), (16, 7), (26, 11), (6, 10), (6, 0), (16, 9), (13, 26), (20, 20), (23, 15), (6, 3), (26, 20), (22, 6), (18, 8), (15, 2), (4, 9), (18, 1), (16, 23), (23, 3), (20, 21), (15, 3), (1, 22), (26, 4), (13, 5), (26, 25), (20, 5), (19, 2), (21, 14), (20, 26), (8, 6), (6, 26), (10, 9), (7, 10), (5, 16), (23, 18), (7, 14), (16, 11), (8, 5), (1, 4), (5, 26), (17, 7), (21, 18), (16, 4), (5, 15), (8, 3), (14, 9), (15, 8), (4, 14), (7, 20), (22, 16), (23, 0), (8, 2), (22, 1), (17, 16), (18, 3), (26, 10), (23, 16), (24, 17), (25, 9), (5, 1), (5, 6), (17, 17), (26, 16), (14, 12), (20, 0), (4, 24), (14, 15), (2, 25), (8, 10), (3, 20), (15, 6), (9, 22), (14, 20), (25, 10), (17, 9), (14, 0), (8, 24), (25, 4), (12, 25), (11, 21), (16, 3), (8, 21), (0, 10), (10, 21), (12, 22), (1, 14), (16, 17), (2, 15), (4, 6), (2, 16), (23, 25), (4, 20), (16, 18), (1, 1), (8, 7), (9, 26), (11, 22), (18, 11), (17, 8), (14, 5), (27, 16), (18, 19), (23, 7), (11, 12), (11, 26), (15, 24), (0, 15), (26, 26), (5, 25), (19, 17), (25, 14), (18, 18), (14, 2), (7, 7), (12, 10), (0, 3), (26, 3), (4, 26), (25, 6), (24, 21), (6, 7), (13, 11), (27, 3), (3, 15), (12, 0), (3, 24), (16, 14), (24, 10), (25, 12), (4, 15), (8, 1), (23, 26), (25, 3), (21, 21), (1, 23), (14, 18), (17, 4), (18, 0), (23, 11), (26, 2), (15, 9), (2, 10), (13, 2), (15, 10), (2, 8), (0, 9), (19, 3), (25, 5), (16, 10), (12, 11), (0, 26), (21, 20), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886320", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 20), (20, 6), (17, 5), (2, 1), (15, 5), (18, 13), (16, 4), (6, 21), (11, 19), (13, 7), (17, 15), (23, 8), (1, 10), (14, 2), (23, 10), (21, 11), (11, 21), (22, 7), (12, 18), (20, 16), (2, 9), (8, 3), (1, 13), (14, 17), (17, 12), (23, 13), (0, 13), (22, 13), (20, 11), (6, 10), (16, 0), (9, 10), (22, 16), (3, 9), (23, 16), (10, 8), (10, 9), (7, 15), (1, 9), (14, 5), (3, 15), (4, 8), (0, 5), (4, 9), (23, 9), (0, 19), (0, 12), (23, 20), (6, 19), (12, 15), (13, 1), (6, 8), (2, 0), (2, 3), (21, 16), (22, 8), (20, 4), (2, 22), (19, 3), (5, 17), (22, 4), (18, 5), (9, 14), (2, 18), (20, 14), (9, 7), (5, 11), (16, 16), (6, 16), (23, 17), (7, 14), (20, 22), (14, 0), (3, 17), (21, 5), (14, 1), (4, 2), (10, 10), (3, 0), (22, 15), (12, 4), (2, 16), (16, 13), (3, 22), (18, 22), (2, 13), (17, 1), (4, 16), (14, 12), (21, 4), (10, 14), (19, 10), (15, 15), (20, 12), (20, 19), (5, 1), (14, 20), (13, 20), (10, 2), (23, 12), (11, 2), (7, 16), (16, 1), (17, 2), (8, 11), (5, 7), (11, 11), (9, 5), (2, 6), (7, 11), (18, 11), (20, 5), (1, 12), (12, 21), (14, 8), (20, 7), (22, 10), (21, 19), (8, 1), (2, 12), (8, 12), (5, 15), (15, 21), (2, 20), (5, 21), (2, 10), (10, 17), (18, 12), (0, 1), (14, 21), (8, 17), (18, 15), (18, 6), (16, 7), (16, 3), (9, 19), (15, 4), (12, 13), (11, 22), (19, 16), (19, 11), (10, 12), (6, 17), (5, 16), (0, 10), (5, 19), (7, 2), (9, 11), (0, 17), (18, 19), (10, 15), (14, 15), (15, 0), (19, 22), (10, 3), (11, 5), (21, 18), (8, 16), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "629850", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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, 16), (13, 13), (10, 26), (7, 0), (4, 4), (9, 14), (4, 7), (10, 4), (10, 2), (3, 4), (9, 6), (17, 2), (3, 19), (13, 12), (1, 17), (7, 9), (0, 23), (16, 15), (11, 1), (1, 26), (18, 13), (3, 11), (17, 24), (15, 13), (7, 13), (9, 5), (20, 25), (0, 5), (20, 1), (6, 4), (6, 20), (11, 5), (1, 22), (18, 20), (5, 14), (3, 21), (21, 23), (17, 25), (13, 3), (1, 2), (1, 6), (12, 1), (16, 11), (15, 16), (7, 25), (6, 23), (6, 6), (7, 6), (1, 5), (4, 11), (8, 9), (15, 26), (4, 24), (3, 5), (8, 0), (13, 17), (13, 9), (16, 22), (0, 8), (5, 8), (0, 24), (11, 7), (10, 23), (3, 2), (21, 0), (13, 4), (4, 3), (14, 26), (5, 4), (12, 21), (1, 10), (21, 1), (1, 14), (17, 22), (0, 15), (20, 14), (18, 1), (7, 5), (13, 11), (17, 8), (14, 11), (3, 9), (8, 17), (7, 10), (20, 22), (19, 8), (14, 22), (11, 19), (14, 12), (7, 1), (7, 2), (13, 23), (19, 2), (21, 18), (15, 23), (14, 17), (20, 19), (12, 2), (7, 8), (14, 14), (20, 20), (2, 4), (9, 10), (14, 16), (16, 26), (0, 7), (8, 13), (8, 19), (8, 4), (4, 9), (20, 8), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383600", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 0), (3, 14), (27, 8), (19, 16), (16, 13), (5, 16), (2, 5), (20, 7), (25, 11), (14, 15), (6, 12), (9, 6), (21, 9), (23, 9), (27, 20), (7, 6), (24, 12), (10, 3), (14, 21), (12, 14), (24, 19), (15, 6), (20, 15), (8, 1), (12, 16), (24, 14), (1, 19), (17, 18), (27, 18), (7, 7), (4, 21), (12, 17), (15, 5), (25, 13), (20, 1), (15, 4), (26, 1), (7, 17), (17, 21), (9, 0), (9, 20), (13, 17), (14, 9), (19, 11), (17, 3), (25, 4), (23, 15), (8, 3), (9, 15), (8, 21), (0, 15), (17, 5), (11, 7), (26, 5), (24, 7), (16, 11), (10, 1), (26, 14), (24, 4), (9, 17), (3, 6), (3, 10), (7, 21), (27, 6), (17, 17), (12, 8), (1, 22), (9, 8), (2, 3), (21, 11), (19, 22), (21, 6), (22, 13), (16, 15), (19, 9), (23, 18), (12, 6), (21, 8), (11, 15), (13, 0), (7, 5), (25, 19), (7, 16), (18, 5), (17, 8), (25, 15), (26, 4), (1, 17), (16, 18), (26, 9), (0, 3), (11, 12), (10, 9), (19, 3), (8, 12), (11, 1), (13, 12), (9, 14), (20, 12), (16, 19), (3, 1), (3, 21), (2, 14), (21, 19), (1, 8), (20, 8), (25, 17), (8, 8), (22, 22), (6, 21), (14, 22), (15, 14), (4, 16), (4, 10), (10, 11), (18, 1), (4, 4), (16, 22), (3, 12), (22, 17), (11, 19), (16, 14), (21, 10), (17, 7), (7, 22), (21, 7), (14, 1), (8, 17), (22, 10), (23, 12), (8, 18), (14, 17), (18, 8), (8, 16), (6, 18), (5, 19), (4, 8), (15, 18), (26, 18), (11, 16), (19, 14), (11, 18), (25, 7), (0, 5), (2, 17), (6, 8), (19, 1), (5, 17), (15, 11), (5, 0), (4, 6), (14, 4), (7, 20), (20, 10), (27, 15), (16, 16), (21, 0), (24, 11), (18, 0), (0, 18), (8, 9), (5, 4), (24, 5), (17, 19), (25, 9), (21, 20), (15, 10), (15, 15), (13, 2), (6, 7), (15, 0), (11, 6), (8, 7), (7, 9), (13, 14), (17, 11), (9, 11), (9, 1), (5, 9), (6, 13), (26, 7), (1, 9), (10, 2), (14, 10), (16, 8), (10, 13), (24, 18), (26, 2), (22, 1), (25, 8), (13, 22), (0, 14), (18, 16), (27, 21), (20, 18), (0, 2), (10, 10), (20, 5), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451440", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), 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), (14, 26), (0, 9), (17, 20), (20, 26), (2, 13), (19, 10), (3, 26), (9, 24), (11, 0), (21, 17), (10, 5), (20, 15), (19, 14), (0, 10), (9, 10), (3, 24), (22, 0), (9, 1), (7, 20), (16, 10), (1, 16), (19, 1), (0, 25), (17, 16), (18, 3), (5, 3), (3, 27), (3, 3), (1, 24), (8, 26), (14, 27), (10, 9), (18, 8), (3, 18), (11, 27), (19, 11), (11, 5), (15, 10), (17, 10), (9, 17), (7, 5), (6, 10), (5, 28), (12, 21), (15, 18), (16, 14), (21, 23), (9, 0), (0, 24), (5, 24), (1, 27), (20, 17), (0, 13), (15, 16), (1, 11), (3, 11), (2, 19), (4, 15), (0, 12), (8, 6), (22, 18), (19, 7), (6, 13), (20, 20), (4, 5), (22, 8), (1, 19), (10, 17), (21, 15), (17, 25), (14, 18), (13, 27), (13, 0), (18, 18), (15, 11), (6, 3), (9, 28), (16, 9), (3, 0), (18, 22), (18, 12), (22, 3), (21, 21), (5, 12), (0, 8), (0, 3), (5, 2), (9, 23), (0, 21), (15, 8), (15, 24), (14, 13), (11, 28), (19, 3), (1, 26), (7, 16), (20, 6), (6, 6), (7, 17), (16, 21), (2, 9), (17, 6), (22, 9), (4, 10), (2, 14), (21, 25), (14, 5), (6, 9), (14, 20), (6, 11), (9, 12), (22, 20), (7, 2), (12, 7), (0, 22), (7, 11), (13, 2), (11, 24), (5, 26), (20, 21), (11, 22), (22, 1), (7, 4), (15, 2), (9, 22), (8, 7), (22, 23), (15, 12), (2, 10), (16, 23), (18, 27), (21, 14), (19, 17), (8, 10), (20, 23), (8, 12), (13, 3), (13, 25), (20, 24), (14, 21), (0, 17), (15, 21), (14, 6), (18, 5), (2, 5), (1, 20), (5, 1), (16, 5), (12, 28), (12, 15), (15, 14), (14, 19), (12, 12), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945012", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 21), (14, 18), (12, 18), (17, 7), (14, 15), (18, 19), (3, 11), (15, 20), (2, 1), (13, 8), (9, 5), (13, 6), (1, 25), (16, 1), (0, 25), (12, 11), (5, 1), (20, 11), (7, 25), (17, 5), (10, 7), (17, 4), (3, 0), (13, 10), (10, 12), (1, 12), (6, 7), (18, 12), (23, 11), (16, 3), (23, 15), (21, 4), (5, 12), (13, 20), (0, 19), (14, 22), (14, 24), (17, 12), (23, 18), (22, 14), (23, 20), (14, 7), (2, 25), (13, 9), (14, 2), (17, 10), (16, 22), (6, 14), (11, 10), (1, 4), (16, 17), (16, 18), (21, 5), (2, 14), (5, 15), (18, 16), (4, 13), (16, 6), (12, 20), (17, 20), (20, 6), (23, 21), (20, 25), (10, 23), (0, 12), (3, 3), (1, 11), (15, 3), (12, 10), (17, 23), (19, 11), (11, 6), (3, 15), (12, 4), (4, 12), (9, 12), (18, 2), (20, 21), (7, 7), (0, 16), (8, 14), (7, 24), (3, 1), (2, 12), (4, 19), (15, 12), (16, 8), (6, 18), (22, 2), (8, 6), (1, 8), (2, 19), (4, 8), (19, 1), (5, 7), (15, 2), (9, 23), (16, 12), (5, 14), (14, 19), (7, 6), (9, 10), (5, 3), (7, 4), (9, 4), (2, 13), (4, 20), (13, 5), (21, 15), (7, 20), (14, 13), (10, 2), (7, 16), (10, 9), (21, 24), (22, 20), (9, 16), (16, 20), (13, 25), (19, 14), (20, 9), (14, 25), (15, 15), (7, 0), (5, 22), (7, 17), (22, 3), (9, 14), (4, 16), (3, 7), (7, 22), (10, 16), (21, 10), (5, 10), (21, 17), (2, 10), (3, 5), (19, 6), (18, 5), (10, 13), (8, 3), (9, 0), (13, 16), (20, 20), (14, 10), (7, 14), (19, 3), (9, 15), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133407", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (22, 11), (22, 27), (16, 3), (23, 27), (21, 21), (22, 2), (7, 14), (17, 17), (17, 24), (0, 26), (5, 19), (1, 27), (10, 26), (1, 24), (8, 10), (8, 2), (23, 18), (3, 3), (11, 24), (0, 24), (3, 13), (2, 4), (21, 8), (17, 19), (14, 26), (23, 7), (11, 13), (16, 13), (8, 9), (9, 17), (9, 10), (8, 22), (24, 13), (19, 6), (8, 16), (16, 14), (3, 14), (0, 9), (12, 18), (18, 17), (6, 3), (23, 23), (11, 19), (17, 21), (19, 26), (13, 18), (25, 9), (20, 11), (1, 8), (23, 25), (25, 0), (24, 15), (18, 19), (24, 14), (25, 7), (5, 5), (9, 13), (0, 13), (21, 19), (4, 4), (13, 8), (22, 22), (19, 8), (1, 19), (26, 2), (21, 7), (5, 3), (2, 22), (7, 25), (16, 24), (15, 17), (2, 21), (4, 0), (11, 17), (18, 14), (12, 22), (12, 9), (0, 11), (21, 26), (2, 18), (1, 4), (3, 22), (1, 14), (6, 10), (15, 4), (13, 13), (12, 24), (15, 16), (23, 20), (26, 22), (13, 4), (12, 11), (5, 24), (9, 1), (6, 23), (14, 15), (26, 6), (10, 17), (6, 12), (11, 16), (20, 3), (22, 19), (7, 19), (13, 26), (21, 2), (23, 15), (24, 6), (25, 20), (1, 18), (20, 22), (5, 17), (18, 7), (24, 19), (10, 9), (2, 2), (0, 21), (16, 15), (24, 23), (14, 1), (17, 10), (4, 25), (6, 8), (1, 11), (20, 19), (3, 8), (10, 3), (4, 7), (18, 4), (5, 10), (5, 20), (17, 15), (14, 27), (14, 24), (21, 0), (19, 1), (12, 26), (3, 12), (24, 22), (9, 2), (19, 25), (2, 5), (0, 1), (17, 3), (21, 15), (13, 1), (0, 12), (6, 9), (12, 1), (23, 4), (5, 23), (18, 22), (3, 9), (14, 25), (9, 5), (7, 1), (0, 14), (20, 23), (17, 18), (17, 16), (1, 25), (25, 27), (12, 13), (7, 12), (20, 10), (1, 23), (16, 7), (16, 5), (14, 16), (15, 23), (0, 23), (6, 15), (2, 19), (23, 9), (11, 0), (13, 25), (11, 22), (9, 8), (10, 12), (16, 27), (15, 21), (6, 19), (13, 14), (6, 26), (11, 20), (16, 2), (18, 10), (12, 8), (12, 14), (13, 12), (22, 18), (23, 22), (5, 25), (22, 10), (18, 13), (0, 3), (25, 4), (16, 26), (2, 23), (14, 19), (26, 8), (15, 13), (21, 22), (18, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567312", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (12, 18), (2, 6), (18, 3), (13, 11), (18, 11), (10, 5), (7, 15), (4, 23), (18, 21), (25, 20), (21, 16), (3, 16), (21, 23), (11, 22), (2, 10), (25, 11), (20, 18), (12, 19), (17, 4), (18, 17), (16, 24), (17, 0), (23, 11), (10, 14), (15, 2), (24, 16), (22, 13), (10, 13), (13, 6), (14, 11), (6, 6), (19, 18), (2, 19), (14, 19), (24, 5), (16, 10), (12, 3), (17, 17), (23, 12), (9, 23), (24, 13), (15, 10), (4, 4), (3, 12), (17, 15), (9, 12), (20, 22), (11, 0), (13, 9), (4, 7), (6, 18), (9, 19), (7, 24), (19, 20), (1, 1), (25, 19), (0, 1), (17, 7), (6, 4), (9, 22), (23, 14), (5, 8), (13, 12), (16, 23), (22, 0), (14, 2), (10, 3), (22, 23), (22, 12), (8, 5), (7, 19), (16, 1), (7, 3), (3, 19), (21, 24), (23, 18), (9, 5), (23, 21), (20, 19), (0, 15), (3, 9), (3, 13), (0, 8), (19, 17), (24, 4), (14, 6), (15, 22), (19, 5), (21, 12), (0, 20), (17, 12), (14, 1), (22, 11), (11, 24), (4, 5), (12, 14), (24, 6), (2, 11), (12, 13), (8, 8), (20, 20), (18, 14), (12, 22), (22, 15), (11, 1), (11, 15), (21, 5), (11, 2), (8, 24), (25, 6), (0, 23), (10, 17), (15, 20), (23, 22), (12, 20), (25, 12), (0, 21), (18, 20), (24, 23), (7, 4), (2, 14), (13, 3), (19, 15), (17, 23), (25, 8), (20, 2), (15, 11), (19, 2), (1, 4), (0, 22), (8, 10), (1, 22), (19, 4), (14, 10), (15, 1), (13, 2), (5, 20), (17, 2), (7, 21), (0, 3), (4, 9), (3, 7), (7, 22), (11, 11), (12, 1), (3, 24), (16, 20), (12, 24), (23, 1), (1, 18), (7, 8), (17, 13), (17, 8), (23, 20), (4, 21), (1, 6), (20, 6), (9, 20), (22, 2), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370288", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), 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), (4, 3), (11, 4), (1, 11), (17, 17), (19, 11), (14, 11), (7, 11), (12, 12), (22, 18), (18, 8), (19, 22), (23, 12), (21, 10), (15, 19), (22, 15), (22, 5), (18, 9), (15, 21), (25, 3), (23, 3), (4, 14), (12, 21), (14, 18), (1, 25), (6, 11), (19, 17), (0, 19), (9, 25), (7, 24), (15, 22), (14, 7), (21, 20), (25, 24), (14, 21), (5, 16), (20, 10), (12, 3), (19, 16), (10, 24), (25, 2), (14, 9), (19, 1), (0, 1), (18, 10), (9, 22), (6, 1), (1, 20), (24, 8), (17, 10), (11, 25), (7, 4), (20, 14), (23, 10), (9, 2), (22, 22), (12, 25), (18, 3), (14, 25), (8, 17), (17, 0), (6, 3), (14, 15), (25, 22), (21, 12), (9, 7), (11, 17), (20, 20), (17, 21), (10, 23), (5, 3), (6, 14), (1, 17), (13, 16), (23, 24), (22, 25), (8, 1), (16, 7), (12, 18), (12, 14), (1, 15), (8, 14), (13, 14), (25, 18), (18, 16), (2, 7), (5, 1), (21, 23), (25, 13), (4, 22), (14, 0), (10, 8), (16, 23), (12, 10), (24, 6), (21, 13), (12, 16), (9, 4), (19, 13), (20, 4), (13, 8), (21, 1), (3, 22), (11, 16), (7, 3), (24, 19), (18, 13), (22, 17), (5, 18), (0, 7), (4, 24), (17, 19), (20, 6), (1, 3), (11, 22), (19, 25), (12, 4), (23, 6), (7, 13), (20, 13), (15, 6), (23, 0), (5, 0), (7, 19), (25, 0), (0, 24), (10, 13), (20, 5), (15, 2), (13, 11), (15, 9), (16, 8), (14, 20), (18, 12), (0, 8), (3, 21), (18, 4), (0, 17), (7, 15), (3, 9), (23, 16), (5, 23), (10, 6), (9, 0), (18, 25), (11, 5), (25, 19), (0, 9), (8, 16), (1, 1), (13, 24), (15, 18), (15, 0), (20, 23), (7, 20), (4, 23), (2, 13), (15, 20), (16, 10), (17, 9), (20, 16), (8, 0), (10, 15), (7, 7), (13, 3), (24, 4), (8, 19), (22, 23), (7, 1), (3, 1), (23, 9), (22, 20), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "639896", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 8), (9, 6), (0, 11), (20, 2), (0, 9), (20, 0), (15, 5), (19, 6), (15, 20), (14, 1), (14, 18), (19, 10), (18, 12), (19, 17), (8, 6), (19, 12), (23, 10), (14, 9), (16, 0), (4, 16), (1, 1), (17, 5), (24, 7), (6, 1), (3, 18), (4, 18), (9, 2), (22, 0), (13, 6), (15, 4), (12, 15), (12, 12), (10, 16), (0, 19), (11, 10), (3, 9), (10, 13), (2, 14), (24, 14), (22, 7), (9, 11), (23, 2), (12, 7), (3, 5), (17, 17), (13, 9), (22, 15), (12, 10), (19, 2), (14, 2), (0, 20), (23, 9), (18, 11), (1, 9), (23, 0), (21, 19), (21, 8), (0, 1), (21, 1), (4, 17), (17, 16), (18, 19), (20, 14), (15, 11), (2, 20), (12, 19), (15, 15), (19, 16), (7, 9), (10, 1), (9, 19), (5, 2), (6, 2), (0, 15), (23, 14), (13, 16), (15, 19), (20, 18), (13, 18), (18, 4), (20, 8), (24, 8), (1, 17), (18, 8), (23, 7), (22, 10), (16, 12), (5, 16), (6, 7), (5, 1), (2, 8), (12, 17), (10, 12), (22, 17), (9, 1), (14, 4), (18, 20), (12, 13), (4, 4), (15, 6), (13, 2), (18, 0), (7, 16), (19, 5), (21, 16), (23, 19), (22, 9), (6, 14), (6, 12), (6, 9), (9, 4), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556086", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 15), (22, 18), (12, 17), (22, 17), (1, 6), (4, 0), (1, 5), (12, 26), (23, 20), (9, 26), (8, 19), (18, 26), (3, 10), (20, 10), (6, 0), (21, 0), (3, 12), (7, 5), (1, 2), (16, 10), (3, 24), (8, 21), (6, 14), (14, 23), (25, 5), (19, 13), (11, 15), (14, 2), (5, 16), (21, 4), (22, 19), (21, 24), (22, 3), (21, 26), (19, 2), (1, 14), (14, 25), (18, 11), (15, 18), (16, 4), (19, 11), (12, 7), (6, 12), (24, 11), (18, 14), (18, 16), (16, 20), (19, 23), (9, 22), (8, 7), (18, 0), (15, 11), (0, 6), (13, 19), (1, 25), (19, 15), (3, 5), (10, 4), (9, 2), (0, 18), (24, 2), (13, 14), (5, 2), (0, 21), (12, 0), (19, 20), (8, 26), (24, 7), (25, 25), (10, 27), (13, 24), (23, 0), (18, 25), (18, 15), (12, 12), (17, 7), (12, 15), (19, 25), (8, 3), (13, 23), (13, 10), (6, 10), (2, 26), (13, 12), (4, 3), (21, 16), (20, 25), (10, 10), (23, 1), (14, 18), (9, 28), (0, 12), (17, 27), (23, 25), (24, 20), (13, 4), (19, 5), (23, 2), (2, 24), (6, 27), (16, 24), (3, 7), (6, 9), (18, 3), (0, 20), (11, 17), (16, 25), (0, 22), (15, 24), (0, 14), (1, 22), (2, 15), (1, 4), (19, 28), (2, 0), (0, 5), (11, 8), (3, 3), (18, 8), (3, 15), (7, 8), (13, 3), (16, 27), (12, 18), (2, 14), (23, 19), (25, 21), (19, 12), (5, 27), (17, 3), (20, 12), (19, 3), (24, 0), (15, 12), (13, 21), (12, 20), (21, 12), (11, 10), (11, 1), (3, 11), (13, 2), (24, 15), (12, 1), (25, 12), (22, 16), (6, 6), (16, 26), (25, 23), (6, 15), (7, 1), (14, 12), (17, 8), (5, 0), (11, 11), (9, 16), (18, 21), (17, 16), (6, 23), (5, 6), (7, 22), (15, 17), (17, 23), (4, 2), (3, 6), (4, 28), (8, 4), (4, 25), (3, 0), (21, 1), (18, 27), (5, 1), (7, 11), (6, 3), (7, 0), (7, 23), (8, 15), (25, 17), (9, 19), (14, 4), (20, 14), (5, 23), (11, 25), (9, 9), (4, 20), (12, 13), (18, 1), (24, 3), (24, 8), (5, 17), (7, 2), (5, 22), (5, 19), (20, 1), (2, 13), (15, 9), (4, 23), (20, 4), (6, 19), (15, 21), (23, 9), (19, 27), (7, 6), (9, 3), (9, 23), (16, 14), (12, 27), (23, 13), (6, 25), (21, 7), (2, 27), (10, 6), (20, 24), (20, 5), (19, 4), (8, 8), (13, 25), (25, 19), (23, 8), (11, 4), (8, 20), (14, 11), (8, 6), (13, 0), (24, 24), (19, 7), (4, 18), (15, 0), (17, 2), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436590", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 26), (8, 23), (13, 23), (5, 19), (19, 11), (14, 24), (11, 6), (10, 8), (22, 23), (19, 3), (19, 12), (13, 18), (9, 17), (5, 0), (20, 25), (5, 26), (5, 21), (17, 15), (18, 23), (10, 16), (13, 10), (16, 7), (3, 14), (16, 15), (16, 1), (19, 0), (0, 1), (5, 11), (6, 5), (8, 24), (19, 4), (4, 24), (4, 4), (12, 19), (16, 19), (10, 11), (19, 13), (2, 21), (3, 5), (18, 14), (5, 28), (15, 27), (18, 19), (8, 5), (21, 22), (8, 17), (22, 25), (7, 7), (0, 6), (9, 12), (13, 12), (5, 8), (12, 5), (16, 23), (7, 18), (1, 22), (2, 28), (1, 24), (18, 0), (9, 14), (9, 16), (8, 0), (4, 10), (10, 25), (19, 7), (15, 21), (3, 3), (4, 20), (14, 27), (9, 26), (8, 9), (1, 17), (9, 5), (22, 0), (10, 0), (0, 9), (9, 24), (13, 15), (6, 2), (13, 16), (20, 27), (8, 1), (11, 1), (5, 10), (11, 14), (13, 3), (3, 0), (19, 22), (8, 14), (17, 13), (12, 6), (11, 21), (5, 16), (15, 23), (22, 21), (20, 21), (16, 9), (17, 1), (15, 6), (22, 1), (4, 5), (20, 5), (3, 22), (16, 26), (0, 26), (4, 12), (0, 25), (1, 5), (18, 1), (5, 12), (4, 25), (22, 8), (1, 3), (20, 13), (12, 9), (19, 16), (19, 26), (17, 2), (17, 25), (23, 10), (23, 21), (7, 16), (14, 18), (9, 2), (11, 13), (12, 11), (23, 2), (16, 5), (3, 25), (3, 1), (23, 27), (7, 23), (8, 4), (19, 27), (11, 10), (18, 12), (15, 17), (14, 0), (18, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197910", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 13), (10, 10), (14, 17), (3, 20), (0, 4), (6, 6), (16, 13), (7, 14), (17, 6), (13, 11), (14, 6), (14, 16), (19, 17), (1, 7), (4, 10), (16, 9), (7, 9), (7, 22), (2, 11), (9, 15), (14, 1), (22, 12), (16, 19), (18, 4), (12, 9), (10, 23), (20, 20), (19, 16), (17, 8), (16, 0), (12, 4), (17, 19), (21, 16), (8, 14), (1, 8), (3, 23), (6, 5), (21, 4), (21, 18), (1, 3), (17, 3), (14, 5), (11, 17), (20, 16), (12, 8), (2, 8), (9, 6), (15, 19), (2, 14), (7, 6), (21, 17), (17, 14), (12, 14), (0, 8), (3, 4), (4, 14), (9, 20), (20, 5), (3, 15), (16, 21), (8, 15), (5, 23), (0, 5), (5, 10), (16, 2), (0, 18), (16, 12), (6, 1), (19, 19), (13, 0), (18, 1), (5, 8), (11, 8), (4, 15), (1, 5), (12, 7), (11, 20), (11, 6), (21, 6), (5, 21), (15, 15), (17, 2), (4, 2), (3, 19), (10, 11), (20, 7), (17, 13), (12, 11), (9, 16), (14, 19), (18, 8), (21, 19), (22, 5), (11, 9), (6, 12), (18, 15), (6, 13), (18, 23), (18, 6), (11, 14), (10, 18), (2, 22), (20, 4), (19, 0), (7, 3), (3, 14), (21, 5), (17, 15), (6, 21), (4, 0), (15, 24), (22, 18), (8, 11), (21, 12), (12, 6), (1, 17), (18, 22), (12, 13), (13, 16), (12, 20), (13, 4), (13, 3), (1, 24), (13, 15), (18, 10), (16, 17), (12, 21), (6, 23), (19, 23), (19, 10), (3, 13), (16, 24), (6, 3), (19, 20), (20, 10), (20, 22), (2, 3), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936684", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (23, 3), (0, 3), (0, 24), (25, 19), (13, 16), (19, 14), (19, 3), (13, 12), (14, 1), (25, 8), (17, 9), (21, 16), (21, 0), (22, 7), (25, 1), (23, 21), (19, 18), (24, 15), (5, 7), (8, 2), (24, 14), (15, 3), (12, 11), (5, 16), (19, 15), (20, 12), (17, 20), (14, 13), (4, 14), (17, 6), (10, 7), (7, 11), (9, 3), (21, 19), (12, 21), (21, 18), (25, 6), (1, 10), (1, 3), (22, 17), (7, 3), (18, 1), (1, 9), (0, 9), (16, 22), (3, 0), (19, 8), (17, 16), (1, 12), (13, 23), (13, 13), (20, 16), (24, 2), (11, 11), (11, 0), (20, 3), (6, 18), (20, 17), (21, 22), (20, 6), (8, 15), (5, 10), (7, 7), (6, 19), (19, 0), (5, 2), (8, 17), (10, 14), (9, 1), (11, 1), (0, 16), (19, 9), (5, 14), (23, 13), (15, 8), (16, 16), (20, 19), (17, 21), (6, 12), (2, 15), (14, 4), (4, 8), (3, 16), (7, 9), (15, 15), (9, 14), (17, 1), (21, 4), (17, 13), (3, 23), (16, 15), (1, 18), (12, 2), (9, 0), (20, 24), (10, 11), (1, 4), (13, 0), (14, 22), (4, 4), (21, 17), (9, 20), (22, 9), (3, 14), (3, 19), (22, 10), (7, 21), (6, 16), (14, 20), (11, 16), (8, 20), (11, 15), (14, 18), (20, 9), (22, 4), (14, 6), (21, 10), (7, 13), (24, 17), (19, 10), (4, 6), (13, 3), (1, 7), (5, 0), (23, 11), (10, 13), (18, 23), (6, 20), (23, 4), (2, 11), (2, 21), (0, 6), (0, 20), (12, 8), (6, 9), (3, 10), (6, 10), (4, 23), (24, 22), (19, 20), (14, 16), (15, 7), (5, 12), (3, 3), (5, 24), (14, 21), (2, 5), (24, 13), (22, 12), (22, 23), (17, 7), (12, 15), (13, 18), (23, 19), (6, 13), (25, 18), (23, 2), (8, 21), (11, 2), (9, 13), (11, 5), (25, 2), (8, 24), (4, 12), (13, 10), (15, 12), (13, 19), (24, 23), (23, 1), (7, 5), (9, 21), (21, 6), (7, 20), (10, 4), (1, 23), (11, 19), (8, 7), (2, 19), (10, 21), (10, 23), (11, 10), (16, 12), (8, 19), (20, 22), (15, 10), (15, 21), (24, 16), (19, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "709632", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), 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), (23, 5), (0, 9), (13, 10), (12, 15), (18, 20), (3, 1), (10, 14), (14, 17), (16, 8), (3, 18), (1, 20), (11, 21), (14, 3), (4, 17), (19, 23), (15, 12), (22, 5), (18, 6), (8, 12), (14, 21), (21, 4), (3, 15), (16, 4), (19, 9), (5, 1), (10, 10), (19, 2), (16, 6), (7, 15), (24, 9), (7, 0), (22, 1), (13, 4), (16, 15), (13, 14), (7, 9), (5, 17), (0, 4), (8, 21), (15, 4), (2, 18), (22, 19), (24, 13), (11, 16), (14, 1), (12, 1), (16, 19), (8, 18), (1, 7), (18, 5), (5, 3), (24, 8), (8, 0), (17, 7), (8, 20), (16, 14), (6, 12), (4, 22), (22, 18), (22, 0), (1, 6), (16, 23), (12, 2), (11, 25), (6, 11), (6, 6), (12, 4), (18, 23), (18, 21), (12, 13), (16, 11), (8, 5), (4, 14), (17, 10), (19, 11), (12, 3), (10, 24), (15, 24), (6, 23), (2, 0), (9, 24), (19, 18), (6, 19), (15, 2), (21, 5), (7, 2), (0, 21), (14, 2), (9, 16), (1, 4), (13, 6), (5, 13), (22, 13), (3, 11), (8, 1), (19, 13), (12, 7), (15, 15), (22, 8), (22, 10), (22, 3), (23, 24), (15, 14), (10, 15), (11, 20), (13, 9), (18, 15), (8, 2), (0, 11), (20, 4), (20, 18), (2, 9), (13, 15), (14, 8), (20, 9), (22, 9), (15, 3), (18, 19), (20, 20), (0, 25), (22, 11), (14, 0), (2, 17), (0, 22), (5, 16), (15, 20), (24, 23), (21, 21), (7, 11), (15, 22), (0, 7), (9, 8), (22, 24), (12, 11), (5, 8), (16, 5), (0, 8), (16, 24), (1, 8), (5, 11), (4, 8), (0, 13), (2, 11), (3, 16), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "921564", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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), (18, 16), (16, 1), (16, 5), (19, 8), (12, 12), (2, 4), (12, 11), (20, 2), (11, 6), (1, 10), (4, 11), (10, 19), (17, 18), (9, 20), (14, 13), (12, 20), (1, 19), (14, 17), (4, 2), (14, 4), (4, 10), (0, 15), (2, 2), (18, 3), (21, 16), (3, 2), (4, 1), (20, 18), (14, 0), (20, 6), (2, 17), (13, 16), (20, 20), (9, 19), (18, 13), (0, 14), (20, 7), (20, 15), (2, 1), (5, 3), (16, 16), (12, 10), (8, 20), (11, 13), (5, 11), (3, 8), (10, 1), (15, 18), (15, 8), (7, 15), (14, 16), (6, 13), (13, 9), (8, 13), (10, 16), (11, 10), (17, 4), (8, 2), (19, 13), (19, 18), (13, 5), (3, 5), (1, 6), (17, 9), (5, 7), (1, 18), (8, 8), (20, 11), (5, 8), (9, 4), (0, 12), (10, 10), (17, 20), (9, 6), (19, 20), (11, 20), (3, 10), (16, 13), (10, 7), (12, 8), (8, 10), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954373", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), 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), (24, 7), (24, 14), (24, 20), (26, 15), (2, 2), (8, 0), (14, 7), (17, 19), (3, 0), (23, 2), (2, 17), (20, 7), (27, 18), (8, 19), (2, 5), (18, 14), (22, 2), (25, 20), (14, 2), (8, 18), (2, 14), (8, 17), (5, 11), (27, 6), (2, 16), (23, 9), (7, 15), (20, 1), (9, 17), (1, 19), (18, 13), (20, 3), (9, 11), (14, 12), (13, 15), (27, 4), (7, 11), (23, 3), (6, 11), (18, 11), (23, 17), (21, 10), (0, 17), (23, 5), (6, 10), (13, 11), (20, 10), (16, 9), (6, 4), (26, 16), (22, 15), (5, 17), (14, 9), (3, 18), (10, 17), (17, 17), (15, 14), (26, 20), (6, 12), (0, 4), (8, 2), (27, 17), (26, 7), (0, 7), (3, 13), (11, 3), (23, 0), (17, 9), (7, 12), (25, 2), (21, 11), (0, 16), (9, 4), (23, 16), (2, 12), (24, 6), (10, 10), (22, 14), (24, 18), (15, 13), (25, 1), (27, 1), (22, 3), (3, 2), (23, 15), (3, 5), (7, 20), (24, 15), (12, 3), (11, 19), (6, 19), (16, 13), (0, 8), (3, 11), (11, 2), (1, 4), (3, 16), (21, 3), (17, 14), (0, 2), (8, 6), (26, 2), (26, 11), (19, 10), (18, 15), (14, 3), (14, 6), (24, 4), (22, 18), (26, 5), (19, 19), (10, 20), (7, 17), (8, 12), (24, 16), (20, 17), (22, 12), (26, 3), (11, 0), (24, 8), (23, 20), (12, 13), (12, 5), (22, 4), (22, 17), (15, 16), (13, 19), (26, 1), (11, 8), (19, 9), (25, 10), (27, 10), (0, 15), (19, 1), (21, 20), (26, 4), (10, 6), (0, 3), (27, 16), (16, 18), (21, 13), (10, 18), (19, 17), (27, 5), (17, 6), (14, 19), (11, 7), (11, 10), (3, 8), (9, 20), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912897", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 22), (5, 16), (14, 10), (16, 12), (12, 14), (15, 15), (22, 11), (1, 19), (17, 4), (7, 8), (2, 7), (5, 5), (4, 4), (15, 9), (26, 13), (12, 22), (11, 0), (14, 1), (9, 0), (22, 1), (4, 7), (6, 16), (26, 2), (22, 5), (10, 10), (14, 15), (13, 0), (15, 19), (23, 13), (4, 3), (23, 17), (17, 19), (17, 16), (9, 18), (16, 18), (18, 9), (23, 18), (22, 15), (25, 9), (9, 6), (8, 21), (25, 3), (4, 6), (15, 14), (20, 6), (18, 17), (0, 9), (19, 6), (18, 22), (0, 21), (6, 14), (24, 9), (23, 1), (14, 12), (17, 15), (3, 15), (6, 4), (22, 2), (17, 20), (1, 15), (24, 4), (3, 4), (22, 20), (24, 8), (5, 19), (21, 11), (3, 18), (5, 15), (20, 4), (21, 2), (16, 22), (10, 4), (10, 20), (8, 14), (11, 11), (17, 6), (10, 14), (18, 18), (10, 9), (23, 0), (14, 18), (18, 21), (10, 2), (19, 19), (2, 19), (25, 10), (4, 17), (22, 0), (12, 15), (10, 0), (8, 2), (12, 2), (20, 13), (11, 8), (1, 10), (21, 12), (15, 20), (9, 19), (4, 18), (5, 0), (2, 2), (14, 20), (5, 10), (0, 13), (6, 20), (16, 1), (21, 18), (16, 5), (9, 4), (2, 20), (10, 7), (2, 3), (7, 1), (1, 9), (7, 6), (12, 5), (7, 16), (17, 7), (2, 16), (14, 16), (2, 18), (25, 13), (10, 16), (19, 22), (20, 21), (1, 12), (2, 10), (6, 5), (3, 2), (0, 15), (13, 11), (25, 6), (23, 11), (26, 17), (3, 5), (0, 12), (16, 10), (18, 20), (11, 9), (22, 3), (7, 14), (19, 1), (14, 8), (14, 21), (13, 22), (4, 22), (19, 20), (2, 8), (13, 14), (1, 3), (16, 6), (25, 1), (15, 18), (13, 6), (8, 3), (17, 14), (15, 4), (20, 7), (20, 19), (26, 3), (13, 8), (20, 3), (21, 17), (7, 9), (11, 4), (5, 21), (12, 13), (20, 1), (26, 12), (4, 14), (14, 0), (24, 19), (20, 11), (18, 5), (19, 7), (3, 22), (17, 22), (3, 10), (6, 6), (3, 13), (13, 17), (2, 15), (5, 1), (23, 14), (16, 3), (13, 13), (23, 22), (22, 10), (8, 20), (21, 20), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919920", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 7), (8, 22), (5, 14), (21, 14), (22, 23), (10, 24), (5, 4), (22, 15), (22, 6), (25, 19), (5, 12), (27, 8), (13, 3), (20, 14), (14, 17), (3, 14), (19, 0), (14, 3), (21, 0), (11, 11), (25, 6), (27, 9), (14, 21), (24, 12), (2, 0), (19, 10), (25, 8), (3, 23), (0, 4), (11, 9), (15, 1), (4, 24), (10, 20), (2, 13), (18, 13), (16, 15), (16, 14), (21, 9), (7, 18), (23, 7), (15, 5), (19, 12), (24, 14), (5, 3), (3, 20), (17, 3), (4, 21), (6, 16), (22, 5), (13, 1), (9, 6), (17, 17), (7, 11), (11, 8), (26, 14), (25, 24), (24, 3), (28, 21), (25, 18), (16, 20), (27, 24), (17, 15), (16, 12), (8, 12), (11, 0), (3, 3), (3, 4), (17, 14), (26, 8), (8, 1), (15, 15), (21, 1), (27, 4), (16, 3), (15, 10), (25, 25), (9, 20), (21, 17), (13, 13), (13, 23), (23, 2), (1, 3), (21, 13), (24, 24), (16, 10), (1, 1), (28, 23), (17, 24), (14, 1), (3, 5), (22, 14), (22, 13), (1, 23), (8, 14), (22, 18), (19, 13), (18, 23), (9, 7), (5, 9), (26, 18), (20, 21), (26, 10), (16, 9), (3, 15), (11, 23), (6, 9), (1, 12), (1, 17), (28, 3), (8, 20), (1, 24), (22, 1), (2, 1), (26, 17), (16, 7), (27, 20), (13, 4), (14, 8), (13, 2), (19, 6), (10, 0), (16, 25), (24, 16), (21, 20), (20, 17), (23, 1), (13, 10), (10, 11), (6, 11), (27, 13), (11, 4), (18, 8), (12, 2), (12, 13), (27, 2), (20, 12), (14, 14), (28, 8), (4, 17), (19, 24), (24, 6), (14, 23), (27, 12), (10, 3), (27, 3), (7, 4), (28, 19), (10, 17), (0, 6), (26, 21), (14, 12), (13, 18), (28, 10), (17, 16), (21, 7), (12, 19), (24, 5), (21, 10), (15, 14), (7, 16), (11, 24), (0, 22), (26, 11), (12, 16), (19, 3), (8, 16), (8, 23), (0, 20), (9, 11), (12, 6), (7, 23), (25, 9), (1, 14), (25, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "646059", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), 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), (13, 10), (5, 8), (13, 14), (22, 5), (17, 13), (18, 10), (27, 8), (17, 7), (4, 7), (1, 11), (6, 12), (10, 15), (6, 3), (17, 15), (1, 9), (11, 17), (27, 23), (15, 22), (4, 3), (14, 12), (23, 5), (19, 15), (17, 3), (2, 1), (16, 1), (16, 12), (25, 19), (3, 18), (22, 18), (1, 10), (24, 3), (8, 17), (19, 21), (0, 20), (9, 14), (11, 24), (5, 13), (23, 9), (15, 3), (21, 10), (11, 3), (13, 3), (13, 8), (1, 7), (0, 2), (17, 0), (8, 3), (16, 20), (8, 9), (12, 12), (26, 12), (6, 17), (13, 7), (6, 5), (13, 9), (0, 6), (14, 21), (21, 11), (4, 8), (9, 10), (6, 23), (17, 21), (21, 15), (17, 22), (26, 9), (3, 16), (23, 23), (25, 3), (17, 2), (0, 19), (7, 14), (24, 1), (15, 19), (17, 16), (20, 25), (20, 13), (28, 0), (10, 3), (12, 20), (20, 23), (22, 20), (27, 11), (3, 25), (1, 18), (8, 15), (26, 23), (3, 12), (9, 25), (21, 13), (28, 10), (28, 12), (5, 18), (27, 25), (13, 20), (22, 17), (11, 1), (4, 17), (26, 7), (16, 16), (10, 14), (17, 1), (23, 24), (20, 4), (16, 19), (0, 18), (3, 10), (7, 5), (15, 9), (28, 16), (1, 13), (5, 25), (5, 6), (5, 1), (16, 24), (10, 16), (19, 5), (28, 1), (19, 25), (24, 2), (7, 17), (15, 5), (11, 23), (8, 10), (27, 17), (4, 6), (28, 19), (22, 1), (11, 10), (18, 9), (20, 22), (12, 22), (25, 8), (6, 16), (11, 7), (27, 0), (18, 20), (13, 11), (2, 13), (4, 14), (16, 7), (21, 22), (3, 14), (15, 4), (5, 5), (24, 10), (11, 25), (2, 0), (1, 25), (17, 8), (21, 6), (11, 2), (2, 21), (7, 3), (18, 22), (25, 7), (23, 16), (15, 16), (16, 15), (27, 3), (7, 7), (13, 5), (24, 18), (28, 18), (2, 4), (4, 21), (7, 15), (19, 0), (26, 13), (15, 11), (23, 3), (16, 5), (15, 12), (21, 3), (0, 8), (11, 0), (1, 24), (13, 22), (19, 3), (27, 16), (8, 14), (11, 9), (13, 25), (5, 11), (25, 21), (23, 19), (11, 8), (7, 18), (5, 15), (1, 21), (0, 10), (2, 3), (17, 5), (19, 23), (9, 20), (22, 4), (18, 13), (3, 17), (0, 12), (15, 8), (24, 22), (2, 17), (14, 10), (20, 12), (26, 21), (18, 8), (18, 23), (12, 4), (0, 15), (10, 22), (18, 0), (17, 17), (16, 11), (0, 22), (21, 24), (6, 24), (26, 0), (16, 22), (6, 7), (14, 20), (21, 9), (2, 2), (15, 25), (2, 16), (21, 2), (27, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544320", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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), (15, 10), (13, 20), (21, 1), (3, 11), (14, 12), (21, 20), (2, 6), (3, 5), (20, 24), (16, 8), (16, 9), (12, 3), (12, 13), (4, 2), (16, 4), (15, 23), (1, 12), (19, 5), (0, 17), (18, 15), (19, 24), (10, 8), (11, 2), (1, 20), (10, 19), (16, 15), (14, 20), (5, 2), (9, 12), (12, 18), (20, 22), (11, 19), (13, 24), (20, 3), (11, 0), (12, 4), (15, 19), (1, 26), (7, 22), (5, 10), (0, 19), (10, 24), (7, 1), (9, 18), (0, 24), (5, 20), (14, 0), (2, 9), (11, 14), (12, 8), (9, 6), (9, 3), (18, 24), (21, 0), (11, 24), (2, 12), (21, 19), (21, 16), (13, 2), (2, 1), (4, 3), (2, 16), (7, 5), (9, 19), (21, 4), (2, 24), (17, 17), (14, 6), (4, 7), (0, 1), (16, 0), (18, 12), (16, 11), (13, 8), (18, 10), (4, 11), (21, 10), (9, 5), (21, 21), (15, 7), (6, 8), (19, 3), (18, 3), (14, 17), (9, 2), (19, 20), (16, 18), (12, 12), (6, 14), (7, 8), (14, 9), (2, 10), (12, 5), (11, 4), (19, 6), (19, 10), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588990", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), 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, 8), (11, 19), (12, 17), (17, 19), (20, 5), (6, 12), (5, 8), (3, 9), (9, 13), (17, 5), (11, 3), (11, 5), (16, 20), (24, 4), (23, 0), (1, 15), (5, 17), (0, 13), (16, 2), (19, 2), (18, 10), (21, 10), (13, 13), (7, 2), (23, 6), (17, 18), (9, 3), (24, 9), (3, 11), (7, 12), (10, 7), (18, 0), (10, 11), (22, 0), (0, 17), (8, 2), (22, 8), (15, 2), (9, 20), (7, 10), (19, 15), (1, 3), (19, 12), (16, 10), (13, 17), (0, 20), (16, 3), (13, 8), (3, 17), (18, 17), (14, 9), (14, 3), (14, 2), (12, 4), (5, 19), (10, 20), (21, 13), (19, 18), (6, 2), (11, 20), (8, 17), (9, 10), (11, 10), (17, 13), (8, 9), (15, 8), (13, 11), (13, 3), (7, 15), (6, 3), (0, 1), (9, 18), (0, 3), (7, 5), (14, 1), (20, 19), (18, 2), (9, 16), (7, 9), (22, 1), (5, 18), (2, 10), (14, 12), (0, 21), (15, 16), (5, 14), (7, 21), (19, 9), (2, 5), (1, 5), (13, 7), (21, 15), (3, 10), (12, 7), (0, 11), (2, 16), (15, 6), (12, 18), (3, 16), (0, 5), (11, 17), (5, 9), (10, 1), (14, 21), (15, 9), (5, 6), (0, 4), (5, 10), (19, 17), (17, 6), (17, 0), (5, 4), (22, 9), (10, 0), (22, 3), (16, 5), (20, 2), (11, 18), (9, 0), (20, 12), (15, 12), (16, 19), (20, 6), (15, 10), (11, 15), (23, 10), (17, 1), (23, 17), (4, 21), (15, 0), (19, 7), (13, 0), (5, 16), (21, 7), (9, 8), (17, 9), (24, 2), (8, 7), (15, 13), (0, 16), (1, 21), (18, 15), (22, 21), (14, 6), (1, 13), (9, 14), (15, 21), (24, 0), (8, 18), (18, 11), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "442976", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), 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), (2, 13), (13, 4), (10, 23), (3, 13), (10, 6), (16, 15), (9, 6), (19, 14), (9, 9), (7, 20), (11, 16), (18, 7), (8, 11), (19, 17), (14, 1), (2, 9), (12, 23), (6, 12), (15, 15), (15, 7), (19, 12), (5, 6), (14, 22), (4, 18), (5, 2), (5, 10), (3, 0), (16, 4), (19, 16), (7, 6), (19, 19), (2, 22), (10, 4), (16, 16), (9, 18), (1, 18), (12, 21), (8, 2), (0, 17), (15, 21), (16, 8), (14, 19), (15, 2), (17, 11), (12, 13), (13, 20), (11, 11), (19, 3), (9, 21), (4, 8), (15, 0), (4, 10), (11, 6), (6, 20), (17, 7), (10, 5), (15, 17), (16, 3), (19, 9), (15, 16), (18, 5), (15, 9), (4, 15), (14, 10), (3, 5), (1, 15), (4, 12), (4, 11), (15, 10), (18, 2), (18, 14), (5, 12), (5, 4), (19, 7), (12, 18), (7, 15), (19, 11), (12, 2), (7, 9), (1, 9), (17, 6), (11, 10), (6, 10), (13, 8), (12, 0), (10, 11), (11, 20), (15, 5), (10, 8), (9, 16), (7, 17), (18, 21), (14, 7), (2, 2), (18, 23), (17, 1), (2, 6), (16, 18), (14, 15), (5, 23), (12, 7), (17, 12), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "621048", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), 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), (11, 1), (20, 10), (9, 16), (18, 12), (5, 21), (14, 18), (1, 17), (5, 23), (12, 1), (17, 14), (8, 11), (20, 11), (8, 10), (21, 6), (11, 14), (11, 22), (2, 10), (19, 12), (15, 5), (9, 0), (22, 1), (20, 12), (11, 8), (13, 2), (19, 10), (8, 21), (21, 15), (0, 3), (21, 8), (13, 10), (16, 11), (21, 2), (12, 23), (9, 21), (19, 19), (18, 1), (11, 21), (6, 20), (2, 12), (14, 7), (22, 0), (12, 13), (13, 13), (8, 22), (0, 20), (6, 10), (15, 13), (11, 12), (20, 8), (22, 9), (9, 8), (10, 9), (13, 14), (9, 15), (9, 19), (10, 14), (3, 5), (17, 12), (1, 13), (4, 7), (7, 3), (2, 18), (6, 19), (9, 6), (0, 17), (22, 10), (3, 23), (13, 15), (17, 2), (17, 6), (7, 7), (4, 8), (14, 3), (10, 20), (5, 8), (9, 2), (9, 17), (19, 16), (8, 4), (6, 3), (19, 22), (2, 21), (0, 16), (14, 12), (19, 21), (8, 17), (5, 11), (2, 22), (19, 18), (12, 4), (2, 14), (21, 5), (18, 16), (14, 8), (14, 10), (16, 10), (20, 15), (8, 9), (11, 18), (6, 23), (19, 23), (8, 15), (2, 13), (0, 7), (3, 2), (13, 16), (21, 3), (2, 7), (14, 13), (3, 6), (10, 15), (21, 13), (8, 2), (13, 17), (20, 16), (13, 4), (9, 10), (16, 22), (21, 11), (18, 9), (5, 15), (4, 22), (13, 1), (2, 20), (19, 0), (0, 8), (15, 1), (2, 5), (1, 0), (7, 13), (3, 15), (5, 3), (19, 15), (7, 0), (22, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969804", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), 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), (18, 14), (5, 8), (26, 8), (12, 19), (6, 8), (4, 15), (8, 16), (14, 12), (4, 12), (10, 3), (15, 5), (0, 14), (19, 3), (9, 17), (14, 19), (16, 2), (14, 3), (25, 9), (20, 8), (17, 3), (3, 10), (0, 6), (15, 3), (11, 7), (13, 9), (12, 18), (7, 10), (28, 9), (21, 16), (21, 11), (22, 4), (20, 17), (3, 1), (15, 1), (2, 3), (18, 11), (16, 19), (11, 2), (13, 3), (7, 13), (3, 19), (17, 9), (15, 9), (6, 9), (26, 5), (13, 5), (26, 2), (7, 7), (1, 19), (24, 17), (23, 4), (3, 15), (27, 11), (5, 5), (25, 7), (17, 19), (12, 1), (8, 10), (14, 16), (1, 18), (18, 1), (13, 19), (28, 2), (20, 19), (3, 8), (15, 13), (22, 19), (2, 1), (12, 11), (4, 6), (17, 16), (15, 16), (24, 15), (7, 4), (2, 8), (6, 18), (18, 5), (27, 6), (3, 9), (26, 14), (13, 2), (3, 3), (13, 11), (3, 13), (9, 16), (20, 15), (8, 0), (13, 10), (7, 0), (25, 12), (27, 13), (1, 13), (18, 9), (20, 9), (23, 15), (11, 6), (21, 15), (2, 6), (18, 4), (6, 16), (1, 14), (11, 13), (15, 0), (16, 16), (28, 10), (4, 16), (21, 17), (20, 1), (17, 10), (11, 11), (4, 11), (25, 0), (12, 5), (13, 12), (2, 5), (28, 16), (17, 15), (19, 19), (0, 1), (14, 17), (3, 12), (20, 4), (19, 9), (4, 1), (11, 12), (12, 3), (24, 11), (10, 9), (1, 17), (26, 18), (23, 9), (3, 0), (19, 14), (10, 6), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212242", "dataset": "MATH"}
{"messages": [{"content": "In a 29x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 22), 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), (17, 10), (3, 15), (7, 10), (13, 17), (25, 14), (4, 10), (6, 9), (10, 3), (6, 15), (16, 17), (27, 19), (15, 1), (16, 21), (6, 1), (11, 16), (14, 7), (7, 6), (23, 10), (28, 16), (12, 19), (11, 12), (2, 12), (8, 18), (12, 11), (5, 6), (14, 2), (10, 15), (3, 0), (4, 2), (5, 20), (3, 22), (7, 13), (13, 9), (9, 14), (17, 21), (17, 18), (9, 16), (21, 10), (25, 0), (18, 11), (2, 19), (27, 3), (26, 14), (1, 5), (19, 18), (5, 11), (10, 20), (6, 6), (20, 13), (2, 16), (28, 15), (14, 6), (23, 19), (25, 13), (10, 21), (11, 6), (1, 3), (6, 3), (20, 18), (14, 21), (27, 21), (6, 17), (25, 9), (8, 0), (18, 19), (15, 11), (11, 9), (12, 4), (1, 1), (2, 6), (11, 1), (19, 19), (24, 11), (3, 6), (16, 10), (13, 22), (7, 17), (13, 16), (6, 12), (24, 21), (4, 21), (23, 21), (18, 21), (16, 3), (25, 7), (12, 20), (24, 22), (13, 4), (26, 13), (26, 9), (21, 12), (28, 0), (16, 4), (4, 1), (4, 14), (7, 5), (11, 10), (14, 19), (14, 9), (6, 22), (5, 18), (2, 1), (17, 20), (27, 2), (26, 1), (8, 14), (25, 20), (6, 21), (17, 3), (25, 2), (10, 11), (20, 19), (3, 9), (22, 16), (20, 0), (21, 0), (3, 14), (23, 14), (21, 2), (17, 5), (11, 18), (20, 14), (0, 18), (1, 19), (16, 14), (26, 19), (27, 0), (3, 19), (21, 19), (8, 16), (8, 12), (2, 8), (7, 18), (23, 2), (1, 2), (4, 22), (7, 4), (2, 18), (17, 2), (10, 19), (13, 8), (0, 8), (6, 2), (26, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "995370", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 17), (6, 2), (18, 10), (14, 2), (23, 22), (7, 22), (9, 2), (15, 9), (17, 16), (0, 25), (19, 4), (8, 1), (11, 7), (1, 10), (11, 26), (12, 23), (7, 1), (4, 25), (15, 11), (4, 7), (3, 16), (11, 4), (12, 1), (12, 11), (13, 13), (1, 4), (14, 12), (15, 20), (5, 28), (5, 10), (9, 4), (19, 13), (22, 26), (13, 2), (12, 14), (15, 19), (11, 28), (3, 3), (8, 26), (21, 27), (4, 13), (4, 0), (17, 28), (0, 5), (11, 14), (11, 1), (19, 21), (6, 6), (23, 6), (7, 4), (6, 3), (6, 0), (20, 10), (16, 9), (20, 5), (9, 12), (20, 27), (20, 18), (8, 23), (8, 2), (1, 12), (0, 18), (2, 5), (1, 3), (23, 7), (23, 16), (13, 22), (10, 27), (18, 11), (6, 15), (13, 3), (19, 11), (9, 19), (11, 16), (15, 24), (21, 14), (20, 23), (15, 21), (19, 16), (10, 25), (19, 1), (7, 9), (15, 6), (9, 3), (16, 1), (3, 4), (21, 26), (23, 19), (21, 8), (23, 18), (12, 5), (11, 10), (12, 10), (1, 22), (12, 9), (23, 14), (1, 21), (13, 16), (17, 12), (7, 23), (6, 24), (2, 7), (17, 10), (16, 12), (9, 24), (23, 3), (6, 20), (5, 17), (0, 16), (8, 22), (22, 4), (1, 8), (0, 27), (10, 26), (5, 9), (10, 14), (19, 2), (15, 12), (20, 15), (11, 27), (1, 25), (4, 20), (3, 28), (10, 10), (22, 24), (17, 5), (6, 19), (4, 19), (21, 25), (7, 15), (12, 15), (21, 4), (15, 2), (12, 8), (13, 1), (15, 4), (14, 26), (6, 16), (18, 18), (18, 13), (12, 22), (17, 25), (10, 13), (0, 7), (17, 26), (2, 21), (5, 11), (21, 19), (16, 23), (8, 3), (14, 25), (18, 27), (9, 13), (21, 24), (8, 21), (23, 1), (5, 7), (3, 2), (17, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730692", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (11, 21), (12, 10), (9, 15), (10, 18), (2, 21), (1, 21), (9, 14), (18, 1), (14, 4), (2, 11), (2, 10), (16, 1), (16, 6), (1, 5), (19, 15), (1, 20), (12, 14), (17, 0), (6, 17), (15, 15), (15, 7), (19, 5), (10, 17), (14, 22), (11, 0), (15, 0), (15, 13), (12, 16), (19, 13), (13, 14), (16, 16), (11, 20), (7, 6), (11, 15), (9, 9), (5, 13), (10, 5), (4, 19), (14, 8), (11, 6), (6, 4), (10, 3), (11, 14), (18, 17), (15, 18), (10, 11), (8, 14), (12, 2), (19, 8), (12, 6), (10, 19), (7, 11), (1, 0), (18, 10), (10, 4), (17, 5), (0, 14), (7, 9), (3, 17), (4, 4), (8, 8), (15, 4), (16, 5), (12, 1), (3, 11), (5, 8), (10, 16), (14, 16), (13, 11), (11, 16), (7, 8), (19, 16), (15, 2), (19, 6), (14, 5), (18, 8), (17, 10), (2, 18), (19, 10), (11, 17), (1, 3), (16, 11), (2, 6), (17, 14), (3, 4), (10, 13), (1, 8), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474690", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), 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), (17, 3), (12, 13), (9, 23), (11, 10), (3, 12), (15, 1), (12, 6), (9, 24), (11, 18), (10, 20), (8, 22), (17, 17), (18, 19), (18, 5), (0, 10), (11, 12), (15, 13), (16, 9), (2, 10), (21, 17), (18, 15), (13, 11), (20, 3), (14, 7), (10, 8), (10, 7), (1, 15), (6, 20), (20, 7), (6, 10), (18, 0), (10, 15), (13, 5), (20, 2), (22, 21), (1, 21), (7, 18), (6, 7), (13, 20), (2, 16), (8, 6), (8, 10), (13, 19), (12, 23), (3, 23), (6, 12), (0, 23), (2, 0), (20, 0), (21, 2), (14, 20), (19, 6), (4, 15), (19, 20), (11, 13), (10, 14), (7, 10), (12, 1), (18, 24), (7, 22), (17, 21), (9, 1), (17, 7), (0, 21), (12, 14), (12, 20), (12, 15), (5, 18), (22, 14), (10, 11), (11, 1), (3, 13), (12, 17), (19, 9), (3, 20), (11, 23), (8, 4), (19, 1), (2, 8), (9, 0), (18, 3), (9, 16), (12, 22), (6, 14), (16, 14), (13, 10), (9, 7), (4, 6), (20, 21), (4, 4), (21, 1), (2, 24), (20, 5), (12, 2), (17, 18), (8, 7), (0, 18), (9, 18), (22, 23), (4, 24), (14, 22), (21, 21), (0, 15), (4, 9), (22, 0), (14, 16), (9, 17), (21, 7), (2, 18), (21, 10), (14, 15), (19, 23), (11, 7), (4, 0), (19, 3), (10, 23), (16, 3), (22, 4), (8, 19), (3, 15), (9, 21), (3, 14), (4, 19), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "673920", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (3, 11), (4, 20), (10, 20), (16, 4), (22, 16), (4, 0), (1, 9), (12, 8), (23, 11), (20, 10), (12, 6), (6, 12), (11, 3), (0, 12), (1, 8), (11, 5), (12, 4), (9, 3), (14, 3), (22, 13), (14, 20), (13, 20), (19, 0), (20, 3), (14, 17), (10, 18), (5, 20), (24, 11), (6, 3), (9, 6), (9, 18), (16, 14), (0, 7), (16, 2), (14, 14), (17, 0), (12, 17), (18, 17), (15, 6), (23, 6), (1, 11), (13, 12), (14, 12), (12, 14), (14, 0), (7, 10), (8, 12), (9, 4), (11, 6), (9, 13), (10, 16), (2, 6), (18, 18), (10, 4), (3, 19), (11, 9), (2, 12), (17, 11), (16, 17), (21, 4), (11, 19), (15, 10), (0, 19), (0, 1), (18, 16), (21, 5), (11, 17), (15, 14), (3, 1), (21, 7), (20, 13), (5, 15), (8, 3), (6, 13), (0, 8), (22, 14), (5, 3), (16, 11), (12, 3), (3, 7), (15, 13), (19, 14), (18, 7), (8, 8), (18, 13), (3, 9), (1, 7), (9, 11), (11, 0), (12, 15), (16, 10), (2, 20), (4, 16), (14, 1), (5, 12), (22, 20), (13, 13), (24, 19), (13, 10), (22, 0), (1, 12), (19, 8), (5, 1), (14, 4), (21, 2), (21, 8), (5, 19), (9, 9), (5, 6), (13, 1), (2, 9), (5, 2), (17, 14), (3, 12), (17, 6), (24, 14), (7, 0), (18, 2), (12, 11), (24, 16), (3, 0), (24, 12), (19, 7), (22, 18), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "801444", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 8), (7, 12), (5, 14), (5, 11), (0, 12), (27, 22), (21, 23), (6, 10), (24, 12), (25, 16), (9, 7), (26, 3), (2, 3), (13, 18), (22, 19), (17, 25), (13, 15), (7, 9), (27, 6), (13, 0), (27, 13), (16, 1), (1, 17), (15, 10), (22, 1), (18, 16), (0, 24), (15, 14), (21, 17), (1, 8), (13, 14), (10, 25), (18, 5), (0, 14), (21, 19), (3, 24), (22, 13), (10, 21), (26, 11), (20, 7), (16, 13), (19, 21), (16, 8), (3, 12), (11, 7), (13, 17), (20, 0), (7, 0), (17, 19), (0, 18), (3, 5), (4, 0), (25, 15), (21, 1), (22, 2), (10, 6), (3, 23), (20, 24), (14, 20), (2, 16), (9, 2), (10, 7), (0, 21), (27, 14), (6, 6), (22, 3), (23, 16), (1, 9), (16, 5), (12, 7), (26, 22), (5, 16), (12, 17), (19, 16), (16, 12), (11, 3), (12, 15), (10, 12), (10, 13), (14, 21), (4, 25), (25, 6), (10, 10), (10, 14), (23, 9), (22, 5), (20, 18), (0, 7), (22, 8), (22, 12), (22, 16), (12, 13), (20, 21), (4, 10), (20, 16), (26, 6), (14, 14), (12, 3), (27, 8), (19, 1), (14, 24), (18, 11), (8, 11), (4, 23), (21, 18), (10, 8), (22, 25), (23, 19), (23, 7), (10, 15), (24, 0), (23, 5), (4, 16), (17, 3), (14, 9), (18, 4), (13, 1), (22, 10), (16, 14), (7, 17), (27, 24), (24, 14), (22, 18), (16, 0), (20, 17), (12, 19), (0, 5), (1, 21), (4, 3), (18, 24), (22, 17), (21, 5), (26, 1), (10, 11), (14, 11), (25, 25), (4, 12), (3, 19), (14, 25), (11, 1), (25, 11), (8, 18), (16, 22), (21, 8), (21, 12), (10, 1), (22, 11), (25, 19), (5, 21), (10, 3), (17, 5), (8, 3), (20, 8), (11, 14), (19, 24), (9, 12), (6, 24), (12, 25), (9, 13), (20, 12), (0, 9), (17, 22), (19, 10), (2, 17), (23, 17), (20, 15), (14, 3), (2, 20), (8, 1), (17, 24), (24, 25), (25, 12), (11, 12), (1, 20), (1, 12), (20, 9), (8, 16), (5, 9), (16, 25), (5, 7), (24, 22), (15, 21), (24, 16), (19, 15), (11, 24), (9, 17), (7, 2), (4, 8), (4, 1), (4, 15), (15, 25), (15, 2), (8, 15), (22, 7), (0, 19), (25, 17), (16, 3), (2, 25), (25, 3), (1, 22), (12, 22), (5, 18), (17, 18), (5, 25), (15, 23), (25, 5), (19, 11), (7, 25), (9, 10), (26, 7), (18, 20), (9, 14), (17, 20), (18, 0), (23, 15), (13, 19), (2, 6), (21, 2), (2, 23), (20, 3), (6, 12), (6, 13), (11, 0), (17, 7), (11, 15), (26, 17), (0, 20), (9, 11), (6, 4), (1, 0), (6, 15), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "698544", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 18), (25, 12), (11, 20), (26, 9), (17, 19), (21, 8), (5, 5), (16, 9), (18, 12), (3, 18), (24, 21), (23, 3), (14, 13), (10, 11), (22, 4), (8, 11), (24, 15), (7, 9), (0, 13), (23, 11), (4, 17), (8, 22), (22, 21), (0, 9), (7, 19), (16, 3), (5, 15), (5, 3), (13, 23), (11, 17), (17, 12), (9, 8), (20, 4), (21, 7), (19, 18), (9, 16), (0, 2), (21, 14), (7, 8), (11, 11), (7, 10), (9, 11), (2, 13), (18, 4), (14, 19), (5, 19), (3, 0), (16, 10), (26, 0), (9, 22), (3, 9), (1, 18), (25, 22), (14, 20), (26, 18), (21, 1), (20, 12), (7, 1), (15, 8), (7, 20), (1, 1), (18, 15), (5, 1), (20, 3), (26, 10), (25, 13), (3, 17), (25, 16), (2, 4), (19, 16), (3, 7), (0, 7), (16, 2), (14, 22), (7, 21), (6, 12), (16, 17), (1, 14), (0, 4), (18, 0), (15, 3), (4, 13), (6, 0), (16, 19), (26, 16), (6, 3), (9, 17), (17, 8), (21, 18), (17, 20), (2, 8), (24, 9), (26, 1), (2, 19), (25, 21), (6, 11), (22, 13), (26, 22), (21, 5), (11, 14), (15, 1), (2, 16), (23, 16), (16, 14), (15, 13), (24, 2), (22, 3), (23, 2), (11, 0), (24, 5), (8, 7), (14, 9), (23, 6), (18, 16), (17, 11), (9, 3), (6, 2), (8, 2), (17, 13), (26, 12), (8, 4), (23, 17), (5, 9), (19, 0), (25, 0), (11, 5), (15, 23), (16, 0), (10, 16), (7, 22), (21, 16), (2, 15), (18, 2), (12, 11), (5, 16), (18, 5), (11, 16), (4, 20), (3, 3), (7, 4), (20, 19), (22, 2), (16, 18), (6, 15), (21, 19), (6, 4), (23, 9), (22, 0), (16, 13), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813210", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), 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), (10, 19), (8, 7), (16, 20), (5, 0), (16, 12), (15, 3), (1, 16), (16, 10), (18, 20), (10, 5), (5, 1), (4, 4), (13, 15), (12, 20), (0, 5), (7, 2), (14, 16), (0, 19), (8, 10), (13, 17), (10, 18), (6, 8), (3, 13), (11, 12), (6, 3), (2, 7), (17, 17), (0, 7), (0, 11), (10, 10), (12, 15), (10, 12), (8, 0), (13, 13), (11, 7), (19, 7), (18, 9), (11, 1), (2, 10), (0, 18), (18, 19), (6, 15), (1, 12), (16, 14), (18, 8), (20, 6), (12, 13), (5, 20), (11, 3), (18, 4), (2, 20), (20, 0), (11, 13), (12, 14), (12, 16), (17, 0), (11, 14), (15, 2), (17, 12), (3, 14), (16, 13), (13, 3), (1, 20), (20, 19), (14, 6), (9, 20), (10, 17), (11, 17), (11, 19), (11, 18), (14, 0), (1, 18), (11, 0), (1, 6), (12, 5), (0, 9), (9, 10), (17, 7), (16, 18), (17, 8), (18, 10), (16, 16), (7, 0), (18, 7), (13, 11), (2, 6), (1, 19), (0, 8), (8, 14), (19, 10), (14, 12), (9, 19), (8, 19), (0, 14), (2, 1), (13, 19), (20, 9), (15, 9), (0, 3), (1, 17), (1, 14), (11, 20), (6, 20), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970416", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 19), (5, 0), (11, 12), (2, 11), (15, 16), (10, 5), (18, 7), (17, 7), (11, 5), (9, 3), (12, 1), (10, 19), (13, 4), (18, 14), (16, 11), (3, 3), (4, 4), (6, 3), (10, 17), (7, 11), (5, 5), (1, 4), (16, 12), (20, 8), (6, 21), (12, 6), (17, 0), (0, 18), (14, 0), (9, 14), (7, 9), (19, 14), (9, 7), (11, 2), (1, 17), (9, 8), (10, 18), (15, 21), (0, 16), (1, 13), (8, 7), (15, 6), (9, 4), (17, 11), (14, 7), (2, 19), (14, 11), (13, 15), (8, 12), (20, 11), (5, 8), (19, 21), (1, 9), (12, 21), (9, 10), (2, 20), (14, 14), (20, 15), (3, 18), (6, 9), (1, 20), (14, 17), (9, 17), (15, 11), (0, 6), (6, 11), (13, 9), (15, 1), (5, 1), (5, 20), (14, 18), (16, 3), (3, 13), (18, 6), (1, 7), (2, 2), (20, 1), (2, 6), (7, 12), (2, 10), (1, 16), (1, 15), (18, 17), (3, 14), (8, 18), (18, 3), (4, 7), (3, 9), (12, 10), (9, 5), (9, 2), (7, 7), (5, 4), (10, 3), (15, 17), (4, 0), (6, 17), (14, 6), (5, 2), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949266", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 9), (4, 18), (19, 19), (10, 8), (8, 16), (16, 9), (11, 26), (16, 11), (19, 2), (9, 23), (5, 11), (16, 22), (20, 23), (12, 3), (14, 23), (15, 11), (19, 10), (7, 10), (8, 22), (8, 8), (15, 26), (16, 26), (18, 22), (0, 13), (3, 15), (7, 4), (5, 26), (0, 27), (21, 21), (2, 23), (22, 20), (16, 2), (7, 19), (4, 14), (14, 8), (14, 24), (19, 3), (8, 6), (6, 22), (2, 25), (11, 3), (20, 19), (7, 21), (21, 0), (5, 21), (1, 10), (1, 6), (20, 5), (7, 6), (1, 21), (16, 20), (8, 0), (0, 17), (0, 3), (16, 14), (19, 25), (7, 26), (8, 27), (0, 12), (9, 8), (0, 6), (6, 25), (6, 16), (1, 2), (17, 23), (16, 5), (4, 12), (14, 6), (20, 18), (1, 11), (15, 23), (12, 17), (10, 16), (19, 15), (6, 4), (1, 22), (22, 16), (9, 27), (20, 16), (9, 1), (9, 14), (16, 19), (22, 23), (12, 16), (9, 18), (20, 25), (7, 17), (17, 12), (5, 0), (11, 17), (12, 1), (21, 23), (7, 22), (3, 21), (0, 24), (4, 6), (22, 3), (10, 4), (3, 13), (19, 26), (4, 10), (17, 17), (2, 12), (12, 7), (10, 26), (6, 20), (9, 2), (8, 19), (1, 8), (12, 15), (12, 0), (2, 4), (20, 21), (16, 8), (6, 11), (15, 4), (5, 6), (19, 1), (16, 10), (13, 4), (4, 5), (3, 14), (0, 7), (17, 0), (4, 7), (21, 24), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217764", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), 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), (20, 7), (25, 7), (26, 6), (21, 17), (10, 27), (17, 25), (0, 7), (20, 9), (2, 26), (11, 15), (18, 12), (26, 11), (8, 6), (20, 19), (6, 0), (7, 14), (25, 19), (18, 11), (0, 16), (10, 17), (10, 12), (5, 20), (22, 2), (2, 5), (21, 27), (21, 28), (2, 1), (20, 26), (10, 24), (25, 11), (20, 23), (27, 17), (18, 4), (5, 11), (15, 17), (16, 15), (16, 24), (25, 2), (7, 20), (21, 23), (5, 16), (19, 13), (21, 2), (10, 0), (9, 6), (28, 18), (15, 0), (15, 25), (21, 14), (19, 3), (7, 21), (6, 22), (1, 2), (23, 8), (18, 16), (16, 26), (28, 20), (8, 20), (27, 26), (1, 24), (25, 3), (2, 10), (19, 4), (28, 17), (25, 17), (24, 19), (22, 19), (13, 1), (20, 3), (18, 17), (10, 6), (7, 28), (4, 28), (8, 3), (0, 22), (13, 4), (15, 6), (22, 21), (9, 11), (13, 14), (8, 13), (6, 15), (5, 19), (16, 5), (27, 3), (28, 14), (8, 5), (14, 13), (23, 19), (13, 25), (17, 16), (15, 13), (3, 6), (16, 27), (3, 10), (6, 9), (7, 11), (20, 4), (3, 9), (18, 5), (9, 7), (2, 15), (17, 27), (12, 0), (0, 23), (22, 0), (12, 10), (3, 18), (20, 10), (17, 23), (0, 26), (26, 10), (24, 15), (16, 19), (28, 15), (9, 14), (26, 16), (13, 24), (15, 12), (3, 25), (18, 21), (24, 13), (6, 5), (3, 3), (27, 20), (12, 25), (25, 20), (10, 22), (25, 9), (0, 21), (14, 23), (1, 23), (23, 27), (6, 2), (8, 2), (21, 20), (11, 22), (3, 16), (10, 8), (9, 12), (22, 9), (24, 12), (12, 17), (13, 23), (3, 21), (26, 19), (11, 24), (27, 9), (27, 8), (12, 3), (10, 28), (14, 10), (3, 17), (4, 21), (12, 13), (7, 18), (15, 7), (26, 25), (24, 5), (1, 28), (8, 24), (9, 0), (26, 4), (26, 8), (3, 12), (18, 24), (17, 24), (20, 11), (17, 22), (24, 24), (11, 16), (22, 12), (11, 27), (21, 8), (28, 24), (8, 28), (9, 1), (19, 8), (14, 11), (0, 6), (10, 3), (3, 24), (4, 9), (26, 26), (14, 18), (15, 15), (26, 1), (2, 16), (15, 3), (24, 25), (7, 23), (6, 8), (21, 3), (18, 6), (17, 4), (11, 14), (7, 16), (24, 28), (5, 27), (13, 19), (5, 6), (19, 25), (4, 16), (12, 16), (25, 26), (26, 7), (27, 0), (12, 26), (14, 26), (6, 28), (11, 25), (28, 7), (9, 23), (9, 28), (7, 9), (6, 12), (25, 10), (0, 24), (27, 23), (5, 0), (7, 25), (9, 2), (21, 7), (5, 7), (11, 20), (5, 23), (13, 22), (7, 26), (27, 22), (18, 13), (5, 2), (8, 27), (8, 8), (16, 23), (7, 22), (23, 2), (9, 21), (9, 16), (5, 4), (7, 10), (9, 18), (14, 7), (25, 8), (25, 1), (0, 13), (16, 25), (22, 10), (14, 21), (23, 13), (4, 23), (0, 4), (12, 21), (12, 8), (20, 5), (27, 24), (23, 4), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479808", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), 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), (3, 13), (13, 3), (16, 17), (4, 20), (1, 3), (15, 9), (12, 1), (15, 11), (11, 17), (5, 27), (20, 27), (4, 17), (0, 1), (2, 15), (2, 24), (14, 10), (6, 17), (7, 4), (11, 10), (4, 26), (8, 8), (11, 14), (17, 0), (2, 23), (12, 7), (22, 3), (0, 16), (15, 20), (19, 23), (3, 0), (4, 1), (19, 7), (21, 12), (23, 21), (19, 17), (6, 27), (18, 2), (5, 11), (10, 18), (22, 18), (2, 16), (21, 10), (11, 15), (23, 7), (20, 1), (23, 20), (16, 11), (14, 8), (3, 16), (7, 13), (8, 16), (12, 13), (7, 8), (8, 4), (24, 9), (3, 3), (8, 5), (7, 24), (15, 5), (24, 19), (4, 9), (17, 17), (1, 18), (23, 9), (6, 16), (14, 24), (2, 11), (24, 0), (4, 3), (5, 4), (8, 15), (13, 27), (11, 1), (17, 20), (22, 2), (12, 8), (0, 5), (18, 27), (9, 23), (12, 27), (5, 15), (11, 22), (15, 2), (9, 5), (19, 16), (10, 13), (21, 7), (5, 10), (0, 21), (20, 12), (9, 25), (22, 19), (9, 0), (12, 4), (13, 9), (6, 12), (17, 26), (10, 22), (24, 8), (24, 11), (24, 22), (18, 10), (13, 23), (24, 17), (5, 16), (19, 8), (21, 0), (14, 22), (3, 20), (0, 24), (8, 19), (14, 18), (4, 5), (11, 18), (12, 25), (20, 3), (12, 23), (4, 4), (12, 16), (20, 18), (14, 23), (17, 10), (6, 2), (13, 15), (14, 20), (11, 5), (21, 21), (10, 7), (3, 23), (18, 22), (8, 26), (19, 10), (11, 24), (3, 15), (8, 27), (3, 19), (17, 13), (24, 16), (0, 10), (8, 11), (16, 27), (24, 13), (23, 3), (13, 22), (19, 15), (23, 4), (24, 3), (10, 24), (3, 25), (2, 18), (2, 5), (10, 4), (11, 11), (4, 25), (21, 4), (15, 0), (7, 21), (13, 11), (0, 11), (7, 18), (1, 24), (18, 12), (1, 12), (22, 25), (23, 8), (14, 13), (22, 12), (21, 25), (24, 21), (4, 10), (12, 12), (2, 26), (24, 12), (20, 9), (19, 26), (24, 4), (23, 13), (16, 13), (2, 20), (7, 20), (20, 14), (8, 17), (16, 0), (13, 6), (24, 10), (14, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135324", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 14), (1, 11), (6, 15), (3, 10), (0, 5), (2, 18), (10, 13), (1, 3), (19, 0), (17, 16), (15, 4), (6, 11), (11, 0), (7, 10), (13, 8), (14, 20), (7, 14), (11, 13), (2, 11), (14, 16), (7, 9), (9, 5), (5, 10), (11, 1), (14, 21), (16, 1), (18, 2), (11, 9), (4, 9), (5, 20), (3, 18), (13, 2), (15, 16), (0, 12), (9, 10), (11, 8), (8, 6), (10, 17), (12, 19), (17, 12), (4, 6), (0, 4), (10, 21), (3, 21), (10, 18), (4, 4), (16, 5), (17, 21), (10, 5), (13, 7), (6, 6), (1, 13), (13, 19), (19, 2), (16, 0), (4, 2), (9, 17), (19, 17), (7, 6), (12, 17), (12, 20), (15, 10), (15, 17), (1, 18), (14, 6), (5, 17), (3, 14), (6, 21), (16, 11), (9, 4), (17, 20), (4, 12), (3, 9), (5, 4), (2, 0), (1, 20), (5, 1), (15, 8), (4, 21), (3, 6), (3, 20), (13, 17), (5, 7), (14, 1), (3, 12), (18, 8), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575760", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 21), (8, 25), (16, 12), (7, 24), (2, 26), (3, 23), (3, 15), (0, 24), (17, 25), (6, 14), (4, 20), (17, 21), (8, 19), (18, 1), (7, 19), (17, 16), (2, 24), (13, 10), (12, 2), (19, 17), (16, 0), (2, 2), (0, 10), (9, 6), (6, 20), (5, 1), (5, 15), (12, 21), (5, 18), (3, 12), (8, 20), (1, 2), (18, 26), (5, 7), (13, 14), (10, 17), (9, 17), (12, 3), (17, 23), (15, 19), (9, 24), (7, 16), (9, 12), (18, 3), (14, 13), (4, 4), (11, 13), (17, 26), (8, 0), (16, 18), (3, 1), (13, 17), (16, 23), (20, 5), (16, 4), (12, 14), (6, 3), (6, 23), (1, 25), (12, 0), (8, 2), (13, 9), (11, 3), (6, 10), (18, 19), (14, 24), (17, 9), (11, 24), (20, 23), (1, 17), (8, 7), (15, 21), (12, 25), (14, 12), (3, 16), (10, 19), (20, 16), (20, 24), (18, 24), (16, 10), (8, 9), (14, 8), (17, 4), (19, 4), (13, 11), (2, 23), (15, 12), (19, 9), (18, 5), (13, 26), (15, 18), (6, 18), (14, 23), (7, 1), (13, 24), (3, 4), (14, 9), (20, 21), (19, 13), (4, 22), (0, 13), (7, 18), (7, 6), (11, 20), (5, 19), (3, 6), (7, 5), (9, 26), (9, 25), (0, 2), (12, 12), (13, 13), (13, 3), (10, 20), (20, 2), (3, 5), (10, 26), (1, 20), (6, 24), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351540", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 6), (9, 5), (21, 12), (18, 17), (16, 7), (15, 5), (16, 18), (23, 3), (15, 9), (9, 18), (9, 16), (21, 17), (27, 4), (20, 5), (24, 17), (4, 13), (3, 5), (22, 9), (18, 13), (25, 6), (1, 3), (12, 16), (8, 12), (26, 19), (4, 7), (27, 3), (20, 11), (11, 17), (19, 3), (23, 12), (13, 10), (6, 19), (17, 12), (0, 17), (19, 10), (0, 11), (14, 9), (7, 20), (5, 6), (26, 5), (10, 3), (16, 12), (6, 6), (15, 1), (21, 14), (2, 0), (15, 19), (4, 18), (6, 14), (11, 10), (4, 20), (3, 19), (19, 5), (8, 16), (5, 0), (25, 19), (10, 17), (20, 17), (20, 16), (14, 20), (14, 2), (22, 3), (3, 6), (3, 13), (9, 8), (2, 19), (23, 9), (26, 13), (4, 2), (20, 14), (11, 1), (27, 13), (11, 19), (26, 11), (9, 4), (18, 0), (22, 18), (12, 8), (13, 18), (3, 10), (2, 15), (17, 10), (22, 8), (10, 14), (7, 19), (19, 9), (19, 15), (11, 16), (12, 13), (24, 16), (19, 14), (23, 5), (6, 1), (23, 13), (2, 17), (2, 11), (5, 10), (0, 18), (15, 0), (1, 0), (13, 16), (5, 11), (27, 19), (23, 0), (17, 15), (27, 5), (3, 1), (25, 17), (1, 20), (2, 3), (11, 6), (12, 3), (0, 13), (13, 12), (15, 8), (5, 14), (21, 10), (3, 0), (17, 8), (1, 15), (0, 20), (20, 3), (19, 11), (14, 0), (11, 13), (6, 5), (10, 11), (2, 2), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "681408", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 5), (0, 1), (17, 7), (4, 0), (6, 5), (1, 4), (13, 20), (3, 3), (5, 3), (12, 9), (2, 2), (0, 6), (13, 19), (15, 12), (6, 6), (19, 8), (14, 18), (18, 2), (3, 21), (14, 7), (13, 4), (15, 20), (9, 22), (18, 12), (4, 1), (13, 1), (14, 8), (17, 0), (3, 5), (13, 10), (13, 0), (3, 17), (7, 8), (19, 0), (15, 6), (0, 19), (9, 9), (11, 11), (5, 20), (0, 11), (3, 16), (14, 5), (19, 11), (4, 10), (16, 4), (6, 21), (1, 14), (19, 14), (4, 5), (4, 21), (16, 7), (14, 15), (14, 22), (8, 14), (6, 8), (12, 15), (18, 17), (12, 4), (8, 6), (14, 2), (4, 4), (4, 22), (13, 15), (0, 23), (13, 11), (0, 21), (7, 1), (2, 11), (4, 11), (0, 16), (3, 18), (5, 4), (6, 15), (6, 20), (16, 17), (18, 19), (1, 12), (8, 16), (17, 5), (18, 14), (17, 19), (11, 22), (7, 10), (19, 10), (5, 9), (7, 13), (8, 7), (1, 22), (7, 4), (0, 7), (11, 4), (15, 23), (16, 3), (13, 16), (19, 20), (8, 19), (9, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933220", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 14), (26, 6), (10, 4), (25, 11), (25, 0), (14, 4), (27, 3), (18, 5), (11, 0), (22, 19), (6, 18), (22, 5), (9, 11), (12, 10), (24, 3), (11, 7), (25, 2), (24, 0), (0, 11), (17, 15), (24, 16), (25, 9), (10, 1), (8, 18), (6, 0), (26, 8), (3, 11), (16, 16), (27, 2), (7, 6), (7, 7), (7, 17), (19, 11), (8, 9), (25, 19), (1, 13), (2, 9), (16, 5), (2, 16), (7, 15), (12, 5), (18, 3), (14, 12), (8, 11), (16, 6), (20, 17), (1, 5), (22, 7), (22, 10), (27, 18), (12, 8), (1, 10), (23, 10), (15, 5), (15, 9), (18, 9), (4, 8), (21, 4), (5, 2), (15, 11), (21, 15), (24, 15), (1, 18), (0, 5), (19, 14), (13, 13), (4, 10), (1, 6), (25, 13), (14, 18), (19, 12), (20, 9), (27, 6), (10, 17), (20, 6), (24, 11), (20, 0), (3, 4), (17, 8), (8, 10), (11, 1), (20, 15), (22, 6), (22, 4), (15, 12), (22, 11), (18, 0), (18, 18), (23, 8), (3, 7), (4, 0), (19, 19), (2, 5), (20, 3), (2, 4), (8, 3), (12, 3), (1, 3), (20, 11), (4, 17), (8, 7), (18, 6), (10, 9), (21, 16), (20, 4), (7, 1), (6, 13), (23, 3), (6, 5), (5, 1), (21, 17), (5, 14), (5, 17), (13, 10), (4, 15), (4, 4), (24, 14), (0, 4), (14, 7), (6, 17), (21, 18), (8, 16), (16, 17), (7, 5), (12, 13), (2, 14), (23, 15), (9, 16), (3, 19), (6, 9), (5, 18), (0, 7), (21, 12), (14, 3), (4, 13), (17, 2), (26, 17), (12, 11), (3, 12), (23, 4), (23, 12), (2, 17), (16, 4), (1, 11), (23, 13), (10, 0), (2, 8), (18, 16), (5, 19), (9, 15), (11, 2), (12, 7), (26, 1), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685440", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 4), (11, 1), (21, 17), (13, 19), (6, 21), (19, 18), (9, 11), (17, 21), (1, 21), (15, 18), (22, 1), (13, 20), (10, 5), (26, 18), (18, 0), (19, 10), (4, 14), (21, 14), (20, 0), (7, 9), (18, 15), (2, 9), (3, 0), (13, 13), (24, 15), (28, 6), (21, 1), (17, 3), (13, 10), (5, 1), (4, 7), (26, 21), (9, 18), (4, 9), (19, 14), (21, 8), (11, 10), (5, 6), (16, 1), (13, 15), (3, 2), (11, 2), (12, 14), (17, 0), (10, 6), (21, 19), (18, 1), (17, 14), (6, 14), (6, 16), (5, 2), (19, 7), (27, 6), (8, 15), (25, 21), (13, 9), (23, 7), (18, 21), (21, 20), (15, 13), (15, 9), (4, 11), (28, 9), (15, 17), (8, 4), (22, 0), (10, 16), (14, 2), (14, 18), (18, 12), (3, 15), (8, 2), (11, 4), (23, 1), (23, 11), (14, 14), (8, 12), (27, 18), (6, 17), (24, 9), (27, 8), (12, 13), (4, 15), (20, 18), (16, 18), (13, 11), (6, 19), (20, 15), (26, 6), (13, 21), (1, 5), (21, 6), (18, 9), (7, 16), (12, 18), (25, 17), (9, 2), (26, 5), (2, 16), (17, 20), (14, 13), (4, 2), (14, 1), (9, 10), (16, 19), (2, 3), (19, 3), (28, 2), (17, 6), (23, 16), (11, 18), (22, 18), (28, 14), (21, 2), (12, 9), (11, 0), (22, 2), (2, 2), (2, 1), (4, 16), (4, 17), (22, 10), (28, 15), (7, 11), (11, 11), (22, 20), (28, 4), (23, 13), (28, 12), (25, 11), (26, 3), (5, 7), (13, 6), (25, 7), (23, 8), (10, 4), (20, 8), (6, 7), (16, 7), (1, 2), (10, 9), (14, 15), (26, 9), (20, 16), (10, 13), (12, 1), (0, 7), (9, 5), (2, 17), (18, 18), (2, 6), (5, 12), (15, 8), (27, 12), (2, 20), (1, 11), (27, 5), (14, 6), (25, 3), (4, 1), (12, 2), (9, 3), (23, 5), (13, 4), (0, 6), (18, 16), (13, 12), (8, 11), (9, 0), (8, 16), (14, 19), (17, 4), (20, 11), (23, 2), (1, 19), (25, 4), (10, 0), (21, 5), (3, 10), (4, 6), (8, 10), (6, 0), (25, 2), (21, 10), (0, 15), (19, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "765060", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (2, 9), (3, 12), (19, 4), (3, 17), (10, 16), (17, 0), (9, 17), (8, 16), (1, 9), (16, 10), (6, 18), (17, 19), (15, 10), (17, 12), (17, 3), (18, 12), (16, 12), (8, 20), (1, 1), (1, 4), (14, 6), (14, 16), (11, 19), (2, 19), (6, 15), (3, 4), (13, 20), (6, 12), (4, 14), (15, 11), (4, 5), (1, 12), (13, 19), (10, 10), (6, 6), (2, 6), (5, 19), (16, 13), (7, 8), (5, 15), (0, 12), (18, 19), (9, 1), (14, 20), (7, 11), (4, 17), (13, 7), (15, 20), (5, 6), (7, 4), (8, 0), (11, 18), (4, 10), (3, 10), (4, 7), (10, 2), (19, 0), (2, 14), (5, 13), (16, 7), (0, 10), (17, 4), (5, 5), (19, 12), (10, 3), (17, 9), (16, 5), (2, 16), (12, 6), (10, 7), (8, 12), (12, 14), (2, 12), (9, 18), (12, 13), (9, 11), (18, 14), (7, 13), (5, 4), (18, 13), (0, 3), (14, 0), (10, 5), (13, 1), (8, 11), (18, 17), (13, 18), (12, 11), (17, 1), (19, 9), (8, 14), (18, 0), (1, 14), (6, 4), (16, 20), (9, 12), (18, 4), (2, 11), (12, 5), (14, 9), (5, 2), (18, 15), (14, 5), (6, 11), (9, 13), (7, 5), (10, 11), (0, 9), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981489", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (13, 18), (13, 7), (10, 0), (11, 16), (17, 5), (22, 2), (15, 8), (2, 0), (17, 18), (20, 4), (7, 1), (19, 1), (14, 15), (21, 5), (24, 22), (20, 3), (6, 0), (7, 9), (8, 11), (4, 6), (13, 11), (6, 2), (12, 7), (17, 16), (8, 0), (7, 22), (11, 11), (19, 20), (16, 15), (9, 24), (22, 3), (0, 9), (5, 3), (21, 24), (0, 4), (5, 22), (5, 5), (9, 2), (14, 20), (8, 16), (13, 4), (7, 13), (4, 2), (5, 16), (6, 18), (19, 3), (12, 2), (7, 10), (24, 4), (11, 6), (17, 9), (18, 20), (23, 4), (18, 18), (22, 24), (22, 18), (18, 23), (14, 0), (12, 22), (8, 12), (18, 6), (5, 4), (12, 0), (7, 23), (18, 3), (0, 24), (21, 12), (4, 24), (13, 24), (21, 10), (20, 18), (19, 18), (22, 1), (14, 18), (25, 8), (20, 20), (8, 18), (19, 14), (14, 1), (19, 7), (10, 14), (3, 0), (11, 4), (3, 5), (1, 2), (12, 17), (15, 6), (23, 5), (4, 12), (7, 19), (1, 16), (24, 21), (20, 17), (15, 13), (12, 9), (22, 4), (2, 17), (12, 24), (18, 16), (25, 20), (11, 21), (11, 2), (12, 15), (15, 15), (2, 24), (18, 14), (5, 6), (23, 11), (6, 5), (20, 23), (8, 2), (9, 8), (20, 5), (6, 22), (22, 15), (14, 9), (21, 1), (23, 16), (8, 1), (16, 20), (4, 4), (25, 0), (22, 23), (10, 4), (9, 9), (21, 7), (14, 19), (10, 24), (21, 13), (20, 7), (17, 17), (18, 8), (13, 9), (1, 12), (18, 21), (10, 3), (22, 0), (20, 10), (0, 10), (24, 19), (14, 2), (4, 21), (4, 5), (20, 2), (2, 14), (4, 13), (18, 10), (5, 23), (12, 16), (13, 0), (23, 20), (14, 7), (3, 19), (19, 23), (6, 24), (22, 10), (2, 16), (18, 1), (25, 16), (12, 12), (21, 11), (15, 22), (18, 13), (21, 21), (21, 0), (17, 15), (6, 14), (8, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804726", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), 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, 11), (12, 5), (12, 20), (6, 9), (2, 8), (9, 13), (21, 11), (2, 13), (21, 4), (20, 9), (4, 1), (13, 13), (2, 17), (20, 10), (0, 12), (0, 19), (17, 3), (17, 9), (8, 6), (2, 20), (19, 19), (7, 17), (16, 17), (0, 16), (6, 6), (18, 16), (14, 2), (0, 10), (4, 0), (11, 19), (20, 15), (1, 9), (8, 3), (15, 20), (7, 13), (16, 5), (14, 6), (13, 3), (1, 18), (19, 0), (7, 2), (2, 7), (3, 12), (5, 5), (4, 15), (19, 14), (1, 8), (2, 5), (14, 17), (13, 7), (18, 6), (12, 3), (6, 10), (17, 14), (0, 1), (13, 18), (5, 19), (1, 4), (12, 18), (11, 1), (19, 16), (8, 20), (7, 0), (14, 20), (2, 19), (3, 11), (11, 11), (8, 10), (17, 15), (0, 11), (1, 3), (16, 8), (9, 9), (14, 15), (1, 2), (6, 4), (19, 8), (16, 7), (13, 6), (11, 13), (12, 9), (15, 10), (0, 4), (12, 19), (15, 7), (1, 20), (20, 12), (9, 18), (6, 15), (17, 11), (0, 14), (10, 10), (2, 15), (17, 2), (18, 15), (4, 7), (11, 6), (12, 1), (16, 0), (13, 14), (18, 11), (20, 5), (6, 7), (17, 1), (16, 20), (14, 18), (12, 16), (5, 3), (14, 9), (19, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "817022", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 19), (10, 4), (12, 15), (19, 15), (9, 5), (15, 6), (5, 5), (19, 3), (4, 14), (21, 3), (9, 18), (21, 12), (2, 12), (19, 20), (16, 18), (3, 9), (17, 0), (23, 16), (23, 4), (14, 8), (21, 7), (5, 9), (17, 7), (12, 12), (21, 10), (3, 0), (9, 1), (12, 18), (21, 0), (3, 15), (19, 11), (5, 10), (18, 21), (23, 13), (2, 6), (22, 15), (6, 5), (22, 7), (21, 4), (4, 6), (1, 6), (0, 9), (1, 21), (11, 12), (18, 5), (3, 10), (14, 19), (5, 8), (12, 17), (1, 8), (12, 6), (23, 9), (21, 8), (7, 19), (5, 18), (22, 20), (6, 7), (18, 11), (1, 1), (0, 11), (14, 6), (16, 19), (1, 18), (5, 19), (19, 18), (23, 14), (13, 17), (10, 20), (20, 17), (18, 15), (22, 11), (8, 16), (6, 9), (0, 14), (14, 15), (2, 13), (18, 6), (6, 13), (8, 19), (13, 9), (8, 8), (11, 7), (1, 14), (5, 4), (23, 17), (15, 2), (21, 1), (6, 18), (12, 16), (4, 18), (16, 3), (16, 2), (22, 19), (17, 12), (7, 7), (12, 10), (18, 17), (14, 4), (9, 10), (17, 3), (14, 18), (19, 12), (11, 6), (16, 7), (9, 21), (10, 0), (13, 3), (19, 16), (18, 4), (16, 8), (8, 7), (12, 0), (21, 21), (15, 3), (8, 14), (13, 16), (16, 1), (4, 16), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "773442", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (4, 16), (21, 3), (13, 19), (7, 18), (12, 8), (22, 6), (10, 10), (3, 7), (7, 2), (23, 4), (7, 13), (9, 4), (23, 14), (15, 9), (9, 9), (22, 17), (13, 7), (9, 16), (0, 15), (4, 2), (21, 15), (21, 5), (21, 9), (7, 9), (2, 1), (14, 14), (18, 3), (22, 9), (3, 16), (10, 19), (3, 18), (20, 14), (20, 2), (20, 13), (13, 1), (13, 10), (6, 15), (11, 17), (8, 2), (4, 19), (7, 6), (10, 3), (10, 4), (21, 14), (17, 2), (20, 18), (2, 10), (14, 7), (11, 16), (9, 7), (20, 8), (15, 13), (0, 16), (19, 12), (12, 11), (2, 7), (1, 18), (16, 0), (16, 8), (6, 2), (19, 2), (23, 15), (7, 0), (23, 5), (2, 0), (21, 12), (20, 9), (1, 17), (14, 2), (3, 3), (1, 11), (14, 17), (22, 2), (7, 15), (23, 1), (13, 5), (19, 10), (17, 9), (14, 11), (11, 13), (13, 18), (19, 1), (16, 9), (21, 19), (14, 13), (0, 10), (9, 2), (8, 5), (14, 15), (4, 12), (20, 10), (17, 6), (22, 12), (12, 17), (14, 0), (16, 4), (19, 16), (10, 14), (19, 8), (8, 3), (2, 16), (9, 14), (22, 15), (17, 12), (18, 12), (11, 4), (2, 2), (18, 19), (11, 14), (6, 19), (15, 8), (14, 6), (15, 2), (4, 14), (6, 12), (20, 12), (1, 7), (8, 19), (23, 13), (19, 19), (21, 6), (1, 5), (17, 1), (8, 6), (9, 18), (2, 18), (21, 2), (7, 5), (23, 3), (4, 9), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "438768", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 19), (24, 1), (4, 8), (8, 16), (23, 1), (9, 19), (7, 9), (6, 0), (4, 17), (7, 11), (22, 1), (0, 8), (2, 5), (21, 16), (4, 9), (13, 2), (5, 3), (9, 5), (21, 5), (9, 0), (10, 21), (11, 20), (8, 6), (17, 4), (9, 2), (11, 3), (1, 6), (4, 12), (0, 6), (19, 17), (24, 10), (0, 2), (23, 6), (12, 11), (23, 17), (14, 21), (18, 13), (13, 4), (9, 20), (20, 2), (24, 12), (8, 13), (13, 12), (19, 4), (9, 14), (19, 2), (15, 1), (4, 4), (6, 1), (19, 0), (14, 10), (13, 0), (0, 15), (7, 4), (22, 8), (18, 8), (18, 14), (6, 20), (5, 5), (8, 20), (2, 0), (2, 15), (24, 9), (2, 8), (6, 15), (17, 16), (1, 17), (6, 9), (5, 20), (2, 2), (18, 19), (12, 9), (3, 8), (14, 3), (3, 14), (23, 13), (18, 10), (3, 15), (20, 19), (0, 9), (15, 0), (13, 11), (6, 12), (2, 18), (23, 7), (17, 5), (23, 12), (8, 3), (21, 14), (10, 16), (0, 3), (16, 17), (16, 21), (7, 1), (1, 12), (16, 8), (8, 15), (13, 1), (4, 16), (10, 6), (5, 17), (5, 19), (11, 17), (15, 15), (16, 4), (2, 4), (11, 4), (24, 8), (17, 21), (18, 20), (9, 12), (14, 5), (11, 14), (24, 2), (4, 1), (18, 18), (11, 6), (15, 10), (12, 8), (12, 15), (8, 14), (22, 16), (8, 1), (17, 9), (24, 0), (7, 12), (21, 19), (19, 12), (1, 0), (9, 17), (15, 5), (3, 10), (16, 7), (9, 11), (17, 7), (7, 20), (1, 21), (16, 1), (20, 4), (22, 9), (2, 21), (24, 20), (5, 1), (6, 17), (12, 2), (15, 4), (2, 10), (20, 1), (7, 6), (23, 3), (0, 18), (10, 17), (15, 9), (18, 5), (23, 0), (11, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158400", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), 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), (2, 16), (20, 15), (19, 21), (21, 8), (10, 9), (17, 18), (1, 9), (6, 4), (18, 16), (20, 16), (21, 10), (11, 14), (16, 21), (23, 13), (0, 6), (13, 14), (16, 18), (1, 14), (19, 0), (12, 20), (1, 3), (3, 9), (15, 18), (4, 8), (0, 15), (6, 3), (18, 10), (13, 11), (13, 20), (13, 7), (4, 18), (19, 19), (9, 2), (5, 17), (20, 5), (16, 11), (13, 10), (8, 14), (21, 20), (17, 16), (5, 4), (2, 10), (11, 4), (10, 18), (11, 12), (12, 7), (5, 15), (10, 1), (14, 13), (12, 15), (11, 11), (21, 21), (14, 5), (16, 19), (18, 13), (0, 3), (5, 16), (5, 7), (20, 18), (17, 12), (4, 6), (8, 12), (14, 14), (2, 4), (16, 4), (22, 4), (18, 11), (1, 12), (6, 5), (20, 3), (22, 0), (0, 13), (22, 6), (20, 8), (21, 16), (8, 6), (22, 20), (21, 4), (15, 10), (15, 8), (21, 14), (11, 17), (20, 6), (14, 3), (19, 1), (17, 13), (6, 18), (5, 12), (9, 11), (1, 13), (21, 2), (11, 0), (4, 19), (9, 14), (8, 11), (9, 6), (4, 15), (14, 8), (17, 11), (11, 16), (0, 20), (0, 18), (4, 12), (7, 9), (23, 4), (1, 10), (6, 20), (20, 21), (23, 18), (22, 12), (6, 2), (19, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "817323", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 3), (13, 20), (23, 24), (16, 2), (20, 19), (12, 9), (9, 18), (6, 16), (17, 22), (4, 18), (15, 8), (24, 18), (18, 20), (4, 16), (0, 18), (15, 25), (10, 11), (9, 14), (22, 22), (10, 12), (18, 8), (5, 10), (7, 14), (18, 15), (4, 1), (22, 19), (23, 25), (24, 26), (8, 8), (18, 4), (7, 21), (16, 6), (15, 13), (8, 22), (18, 23), (23, 18), (15, 11), (10, 7), (2, 10), (0, 16), (0, 25), (24, 11), (2, 11), (23, 15), (25, 21), (11, 23), (16, 25), (24, 15), (10, 1), (2, 16), (21, 19), (23, 22), (25, 14), (10, 10), (7, 23), (19, 20), (3, 4), (0, 19), (17, 11), (17, 23), (11, 22), (12, 12), (6, 24), (10, 15), (6, 11), (11, 24), (18, 9), (9, 15), (14, 21), (17, 26), (10, 2), (19, 10), (11, 16), (26, 20), (15, 16), (5, 6), (10, 0), (0, 6), (19, 6), (2, 2), (7, 15), (2, 20), (10, 6), (7, 25), (15, 24), (16, 1), (15, 0), (12, 26), (22, 9), (19, 19), (4, 7), (9, 1), (13, 17), (4, 20), (3, 8), (5, 19), (24, 22), (15, 26), (23, 14), (8, 6), (25, 10), (2, 19), (14, 13), (22, 24), (26, 1), (23, 17), (13, 5), (22, 16), (21, 5), (17, 5), (12, 10), (16, 4), (10, 24), (2, 0), (21, 24), (19, 5), (4, 9), (16, 13), (8, 5), (25, 13), (20, 3), (26, 19), (3, 19), (7, 16), (9, 6), (17, 12), (2, 5), (10, 19), (24, 5), (9, 8), (23, 5), (23, 10), (15, 15), (8, 10), (0, 13), (24, 25), (6, 17), (3, 20), (1, 25), (0, 11), (21, 2), (14, 19), (7, 6), (8, 18), (16, 8), (13, 14), (26, 14), (25, 26), (7, 3), (21, 14), (20, 17), (17, 2), (5, 17), (3, 9), (18, 25), (14, 4), (22, 0), (10, 13), (25, 5), (6, 20), (9, 12), (4, 14), (14, 5), (24, 8), (16, 3), (8, 20), (25, 20), (24, 0), (2, 22), (5, 11), (22, 25), (11, 12), (21, 17), (13, 6), (26, 6), (26, 24), (17, 10), (11, 11), (26, 21), (20, 4), (16, 16), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77760", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), 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, 6), (21, 10), (7, 8), (7, 7), (26, 9), (6, 1), (11, 8), (26, 13), (5, 20), (22, 10), (8, 20), (10, 11), (3, 1), (20, 8), (6, 0), (9, 5), (21, 16), (6, 5), (4, 13), (19, 0), (25, 1), (4, 19), (7, 3), (13, 12), (6, 13), (17, 1), (18, 6), (8, 15), (11, 17), (20, 5), (25, 15), (25, 12), (18, 20), (13, 1), (12, 18), (1, 10), (22, 8), (15, 18), (19, 5), (24, 20), (13, 9), (14, 15), (6, 2), (11, 12), (10, 12), (2, 2), (9, 16), (12, 15), (8, 1), (18, 8), (27, 6), (20, 10), (10, 3), (24, 17), (3, 15), (23, 2), (15, 15), (22, 6), (1, 0), (5, 15), (21, 4), (10, 5), (3, 19), (24, 12), (17, 14), (16, 13), (21, 8), (14, 2), (15, 6), (6, 15), (12, 1), (4, 6), (10, 10), (11, 14), (11, 7), (13, 19), (11, 3), (12, 7), (25, 6), (5, 11), (26, 15), (16, 5), (20, 9), (5, 10), (9, 15), (6, 3), (24, 11), (18, 10), (7, 11), (6, 7), (4, 14), (24, 9), (21, 2), (16, 1), (7, 20), (25, 7), (17, 8), (2, 3), (6, 10), (9, 14), (8, 8), (13, 6), (22, 16), (12, 10), (14, 13), (20, 3), (3, 16), (9, 10), (9, 13), (8, 19), (17, 7), (3, 6), (18, 1), (22, 0), (21, 20), (15, 0), (13, 10), (18, 7), (11, 4), (7, 10), (27, 2), (10, 18), (11, 13), (11, 2), (20, 0), (7, 4), (12, 16), (17, 13), (22, 14), (16, 17), (6, 12), (8, 12), (12, 4), (13, 15), (18, 12), (1, 13), (11, 5), (17, 4), (16, 20), (26, 10), (3, 7), (0, 10), (2, 5), (18, 9), (23, 11), (27, 1), (4, 1), (2, 15), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779960", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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), (14, 8), (19, 2), (12, 0), (4, 0), (9, 0), (17, 7), (18, 18), (8, 26), (25, 12), (15, 26), (0, 22), (11, 25), (17, 6), (12, 14), (11, 0), (1, 12), (23, 1), (21, 0), (1, 7), (16, 19), (8, 13), (14, 15), (26, 7), (3, 24), (17, 1), (1, 17), (27, 14), (25, 7), (5, 24), (5, 4), (13, 15), (14, 2), (23, 9), (21, 19), (4, 16), (7, 21), (2, 24), (23, 15), (11, 22), (25, 21), (14, 22), (26, 19), (2, 4), (26, 0), (1, 26), (5, 25), (24, 23), (18, 21), (7, 19), (11, 15), (3, 3), (14, 9), (6, 6), (12, 12), (6, 19), (2, 15), (18, 16), (6, 15), (0, 6), (10, 24), (17, 19), (1, 9), (16, 12), (4, 26), (16, 16), (11, 18), (9, 18), (10, 1), (8, 20), (6, 2), (5, 3), (19, 11), (5, 15), (6, 12), (3, 19), (22, 19), (6, 4), (26, 9), (12, 2), (18, 7), (24, 12), (1, 11), (6, 24), (7, 10), (13, 0), (0, 20), (22, 22), (19, 19), (26, 22), (17, 3), (25, 24), (14, 0), (18, 11), (21, 11), (1, 13), (24, 11), (4, 19), (6, 1), (14, 13), (18, 25), (9, 25), (9, 20), (20, 10), (15, 10), (11, 3), (2, 7), (17, 0), (24, 17), (13, 2), (21, 20), (9, 11), (13, 11), (19, 10), (10, 16), (20, 11), (15, 24), (9, 5), (12, 16), (21, 13), (21, 7), (14, 6), (10, 19), (25, 11), (3, 7), (19, 4), (16, 14), (9, 8), (3, 12), (22, 18), (2, 22), (25, 8), (20, 7), (27, 11), (26, 20), (18, 20), (27, 8), (17, 13), (9, 17), (5, 2), (20, 25), (7, 13), (11, 23), (21, 24), (16, 11), (11, 17), (3, 5), (5, 26), (21, 5), (0, 25), (10, 13), (6, 13), (7, 25), (18, 8), (6, 18), (5, 10), (7, 18), (13, 21), (21, 26), (11, 16), (4, 10), (4, 9), (13, 17), (26, 17), (6, 10), (21, 10), (17, 18), (4, 20), (24, 4), (16, 4), (14, 12), (27, 16), (13, 18), (26, 11), (23, 17), (8, 25), (25, 16), (1, 6), (8, 10), (12, 26), (8, 17), (26, 10), (1, 8), (13, 14), (10, 7), (12, 10), (27, 3), (24, 1), (8, 3), (24, 10), (7, 2), (24, 7), (22, 26), (0, 1), (9, 15), (3, 10), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35280", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 17), (4, 18), (1, 3), (7, 15), (12, 9), (18, 1), (8, 14), (19, 8), (14, 8), (12, 21), (17, 3), (10, 22), (16, 22), (15, 7), (16, 12), (18, 2), (12, 5), (13, 1), (15, 20), (1, 4), (2, 1), (8, 5), (5, 18), (12, 4), (8, 16), (14, 21), (6, 0), (17, 7), (14, 7), (16, 11), (10, 21), (0, 12), (5, 11), (2, 7), (19, 10), (3, 10), (6, 15), (14, 14), (7, 8), (8, 11), (12, 1), (0, 22), (2, 21), (5, 5), (4, 16), (15, 0), (4, 1), (15, 8), (13, 19), (12, 14), (14, 15), (2, 5), (10, 5), (6, 14), (19, 12), (11, 13), (5, 12), (2, 18), (18, 0), (20, 4), (17, 15), (3, 16), (7, 19), (14, 9), (3, 19), (5, 0), (6, 12), (9, 5), (2, 17), (12, 7), (19, 22), (19, 2), (9, 12), (20, 1), (15, 4), (17, 4), (16, 13), (9, 4), (15, 14), (1, 7), (17, 22), (5, 17), (11, 16), (18, 13), (2, 9), (14, 22), (18, 5), (10, 18), (3, 14), (18, 19), (7, 17), (5, 1), (6, 20), (11, 21), (11, 15), (8, 20), (13, 6), (5, 9), (11, 12), (19, 9), (16, 18), (20, 18), (4, 17), (10, 9), (9, 9), (5, 19), (0, 20), (1, 12), (3, 4), (6, 7), (11, 7), (17, 14), (19, 16), (6, 21), (11, 0), (10, 12), (20, 10), (12, 8), (17, 1), (9, 18), (20, 2), (18, 11), (10, 7), (10, 19), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171315", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 10), (21, 16), (15, 2), (12, 3), (11, 11), (6, 15), (14, 20), (3, 0), (9, 14), (2, 19), (3, 20), (9, 2), (9, 13), (18, 13), (12, 17), (9, 16), (19, 20), (5, 16), (3, 4), (17, 20), (6, 18), (18, 2), (12, 9), (21, 5), (18, 0), (2, 4), (12, 19), (11, 18), (20, 4), (3, 16), (1, 13), (6, 8), (5, 7), (19, 6), (19, 19), (20, 13), (12, 16), (14, 7), (7, 13), (17, 17), (14, 13), (18, 16), (18, 20), (3, 19), (7, 2), (10, 14), (13, 11), (3, 9), (0, 9), (19, 15), (9, 12), (14, 18), (5, 0), (8, 15), (6, 12), (19, 7), (6, 9), (6, 5), (17, 14), (18, 17), (0, 20), (6, 4), (5, 6), (1, 10), (17, 16), (7, 18), (9, 5), (3, 10), (6, 19), (2, 18), (16, 19), (1, 2), (20, 3), (4, 5), (0, 1), (21, 0), (13, 1), (0, 19), (8, 3), (15, 19), (4, 3), (6, 11), (5, 14), (2, 7), (8, 6), (4, 20), (13, 7), (7, 16), (12, 11), (11, 13), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330208", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (0, 3), (11, 7), (14, 16), (2, 4), (1, 18), (4, 8), (1, 12), (8, 21), (6, 1), (18, 9), (13, 5), (13, 0), (5, 22), (14, 11), (19, 21), (9, 14), (4, 13), (15, 18), (7, 17), (5, 5), (3, 9), (18, 8), (10, 8), (17, 13), (5, 13), (0, 8), (12, 8), (18, 7), (8, 7), (19, 1), (16, 12), (2, 7), (10, 11), (1, 15), (0, 14), (2, 18), (8, 5), (1, 1), (12, 15), (15, 2), (9, 22), (13, 1), (14, 3), (17, 8), (17, 7), (10, 5), (1, 9), (9, 10), (7, 7), (3, 1), (12, 2), (19, 13), (19, 19), (2, 2), (8, 10), (6, 12), (16, 6), (11, 4), (18, 16), (10, 0), (3, 5), (0, 2), (6, 14), (11, 8), (13, 20), (9, 9), (4, 19), (4, 5), (19, 8), (11, 13), (17, 11), (2, 11), (15, 13), (3, 2), (4, 10), (10, 15), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572328", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), 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), (16, 13), (18, 27), (11, 18), (2, 13), (5, 26), (17, 0), (7, 9), (17, 5), (16, 19), (2, 17), (5, 9), (21, 16), (15, 14), (10, 2), (20, 1), (10, 6), (14, 17), (21, 24), (12, 25), (1, 11), (21, 1), (5, 22), (14, 21), (16, 21), (2, 28), (19, 20), (3, 11), (11, 4), (4, 6), (20, 14), (16, 15), (11, 24), (1, 10), (10, 17), (4, 8), (1, 13), (0, 12), (16, 24), (6, 13), (3, 16), (5, 21), (21, 23), (4, 7), (10, 16), (19, 1), (14, 26), (4, 3), (14, 19), (10, 28), (21, 9), (1, 25), (9, 18), (19, 5), (12, 10), (20, 10), (14, 6), (21, 13), (6, 7), (20, 6), (20, 8), (21, 15), (14, 23), (11, 27), (14, 2), (15, 15), (19, 13), (17, 16), (1, 1), (10, 3), (15, 20), (20, 26), (18, 1), (11, 2), (12, 22), (14, 15), (3, 27), (20, 0), (9, 5), (21, 25), (7, 15), (3, 17), (0, 3), (7, 24), (16, 17), (11, 8), (8, 12), (0, 28), (21, 20), (12, 18), (9, 28), (19, 18), (19, 10), (4, 0), (2, 12), (7, 3), (16, 9), (11, 25), (16, 7), (7, 10), (18, 23), (8, 10), (4, 1), (16, 14), (19, 25), (8, 16), (15, 24), (7, 27), (3, 4), (9, 3), (10, 9), (11, 9), (6, 11), (1, 19), (11, 23), (13, 2), (17, 28), (20, 7), (0, 8), (7, 17), (0, 1), (6, 26), (17, 11), (6, 24), (8, 22), (15, 21), (21, 22), (9, 9), (9, 16), (20, 17), (8, 11), (2, 11), (10, 25), (19, 12), (13, 4), (2, 27), (3, 19), (13, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84357", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 9), (13, 9), (18, 16), (19, 21), (9, 22), (24, 2), (21, 13), (16, 15), (18, 14), (12, 1), (23, 17), (16, 2), (5, 11), (13, 4), (19, 1), (7, 23), (11, 24), (20, 21), (18, 18), (18, 5), (12, 10), (15, 4), (15, 15), (10, 23), (3, 20), (10, 14), (20, 11), (4, 7), (0, 1), (22, 25), (11, 4), (20, 0), (11, 12), (1, 11), (14, 3), (20, 22), (8, 26), (4, 8), (3, 7), (11, 5), (6, 16), (13, 3), (17, 2), (8, 3), (9, 23), (7, 20), (19, 14), (22, 9), (24, 8), (1, 13), (10, 16), (1, 5), (20, 20), (3, 18), (13, 11), (24, 4), (0, 21), (7, 16), (4, 18), (7, 5), (8, 23), (10, 12), (1, 7), (22, 21), (8, 7), (9, 24), (12, 3), (21, 11), (11, 20), (6, 14), (22, 5), (14, 6), (7, 0), (0, 6), (16, 21), (3, 15), (20, 2), (20, 12), (4, 20), (17, 18), (3, 19), (22, 15), (0, 22), (6, 15), (22, 11), (24, 13), (10, 2), (12, 16), (10, 11), (4, 12), (3, 8), (7, 26), (5, 14), (24, 6), (7, 18), (10, 7), (2, 4), (17, 21), (13, 23), (10, 24), (24, 22), (19, 6), (11, 26), (6, 3), (6, 20), (11, 16), (20, 16), (6, 21), (14, 25), (2, 8), (16, 8), (3, 3), (14, 26), (2, 6), (0, 24), (16, 11), (8, 8), (9, 13), (0, 8), (19, 9), (23, 21), (16, 4), (21, 8), (7, 15), (1, 20), (14, 11), (2, 22), (3, 10), (17, 17), (7, 12), (11, 21), (1, 10), (24, 23), (12, 11), (2, 0), (13, 21), (5, 10), (1, 17), (21, 16), (19, 18), (8, 15), (12, 9), (11, 25), (5, 26), (11, 22), (23, 14), (13, 6), (5, 17), (18, 26), (13, 7), (22, 4), (3, 17), (19, 7), (7, 7), (23, 25), (4, 14), (18, 2), (2, 23), (12, 13), (2, 7), (4, 24), (18, 4), (5, 6), (17, 19), (20, 3), (5, 13), (24, 3), (1, 22), (12, 6), (19, 12), (8, 22), (8, 11), (8, 0), (11, 13), (13, 18), (11, 11), (20, 23), (2, 3), (0, 13), (8, 1), (2, 17), (18, 1), (15, 14), (8, 5), (22, 3), (16, 5), (18, 19), (22, 18), (12, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484926", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), 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), (6, 20), (15, 9), (11, 2), (20, 14), (3, 21), (7, 0), (13, 7), (7, 15), (15, 5), (7, 21), (16, 11), (22, 17), (2, 3), (1, 16), (0, 17), (6, 17), (5, 4), (15, 7), (12, 12), (1, 2), (11, 12), (21, 11), (14, 11), (5, 2), (21, 0), (2, 1), (7, 3), (21, 10), (8, 2), (9, 5), (18, 17), (16, 9), (11, 8), (17, 14), (0, 20), (6, 4), (5, 20), (4, 18), (8, 17), (1, 8), (22, 7), (16, 21), (14, 7), (12, 0), (9, 0), (17, 3), (12, 8), (4, 13), (17, 8), (6, 6), (0, 13), (10, 8), (14, 5), (10, 11), (11, 18), (15, 20), (0, 9), (15, 19), (9, 12), (13, 1), (16, 8), (9, 1), (18, 20), (9, 19), (20, 3), (20, 20), (11, 16), (2, 11), (3, 4), (14, 13), (1, 7), (14, 20), (20, 4), (16, 10), (8, 21), (2, 4), (21, 20), (4, 14), (17, 0), (21, 18), (14, 2), (21, 9), (5, 13), (5, 14), (1, 19), (22, 12), (17, 6), (14, 21), (3, 0), (14, 14), (4, 0), (17, 21), (20, 19), (20, 17), (9, 3), (13, 14), (4, 19), (21, 4), (1, 6), (4, 16), (6, 14), (21, 16), (13, 6), (10, 10), (2, 21), (17, 11), (9, 16), (12, 4), (3, 6), (19, 6), (22, 13), (1, 17), (9, 6), (7, 20), (3, 16), (10, 4), (19, 4), (10, 15), (8, 4), (21, 8), (1, 13), (18, 16), (21, 3), (13, 9), (18, 12), (14, 15), (19, 18), (6, 12), (14, 10), (6, 9), (2, 16), (2, 12), (19, 3), (15, 3), (1, 21), (18, 5), (16, 4), (10, 21), (13, 11), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "714114", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 25), (20, 0), (1, 22), (4, 13), (10, 7), (6, 23), (18, 11), (4, 9), (20, 7), (13, 9), (19, 23), (11, 28), (20, 23), (1, 12), (24, 8), (24, 14), (0, 25), (16, 9), (11, 5), (3, 12), (5, 15), (21, 12), (17, 7), (14, 4), (4, 7), (8, 12), (7, 11), (16, 22), (3, 14), (1, 28), (19, 19), (0, 3), (18, 9), (21, 20), (22, 3), (24, 24), (15, 25), (3, 26), (3, 6), (19, 24), (0, 11), (7, 21), (18, 5), (20, 2), (20, 15), (16, 25), (11, 16), (3, 0), (10, 8), (19, 12), (24, 26), (20, 1), (12, 9), (19, 2), (13, 22), (4, 4), (21, 21), (24, 4), (22, 8), (13, 23), (24, 16), (16, 4), (1, 15), (5, 20), (18, 0), (6, 19), (22, 17), (23, 4), (8, 13), (9, 6), (2, 20), (5, 10), (7, 12), (21, 15), (23, 16), (18, 7), (13, 12), (6, 4), (14, 25), (5, 19), (13, 20), (9, 22), (14, 1), (24, 10), (8, 14), (19, 11), (13, 19), (0, 22), (15, 8), (17, 24), (0, 23), (6, 13), (6, 6), (8, 8), (3, 9), (24, 1), (8, 17), (0, 13), (22, 19), (5, 21), (22, 22), (16, 10), (17, 10), (19, 0), (10, 1), (24, 19), (7, 13), (11, 20), (11, 22), (2, 3), (4, 18), (4, 26), (10, 9), (21, 8), (3, 3), (15, 28), (1, 19), (5, 17), (4, 25), (18, 24), (9, 26), (21, 13), (7, 26), (2, 4), (7, 15), (9, 18), (5, 23), (4, 6), (19, 3), (11, 6), (21, 7), (15, 18), (14, 18), (6, 2), (14, 28), (13, 27), (5, 6), (15, 21), (14, 20), (2, 28), (6, 11), (10, 15), (10, 5), (16, 1), (12, 1), (19, 18), (16, 28), (7, 18), (1, 3), (13, 14), (13, 21), (0, 10), (0, 5), (18, 26), (2, 19), (16, 3), (3, 7), (13, 15), (7, 7), (19, 21), (9, 15), (8, 6), (12, 17), (5, 12), (4, 15), (19, 7), (11, 2), (21, 9), (20, 26), (21, 23), (22, 6), (19, 14), (6, 22), (16, 16), (18, 8), (13, 2), (3, 15), (18, 3), (17, 23), (14, 3), (11, 15), (9, 7), (17, 2), (6, 7), (15, 27), (0, 24), (5, 2), (5, 13), (15, 23), (15, 6), (2, 1), (3, 24), (6, 17), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536976", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), 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), (16, 8), (17, 12), (11, 8), (13, 4), (26, 5), (10, 3), (19, 11), (12, 4), (22, 6), (12, 18), (21, 1), (15, 5), (19, 5), (25, 4), (17, 6), (2, 6), (16, 14), (11, 3), (16, 16), (22, 7), (7, 6), (20, 4), (2, 20), (4, 0), (14, 10), (9, 22), (4, 20), (8, 13), (1, 12), (16, 13), (21, 3), (9, 12), (8, 11), (27, 19), (6, 10), (24, 14), (13, 1), (3, 21), (2, 22), (6, 18), (7, 0), (24, 0), (8, 4), (3, 11), (2, 4), (21, 19), (27, 8), (27, 9), (1, 8), (7, 10), (12, 6), (8, 20), (5, 4), (4, 9), (2, 12), (9, 4), (12, 9), (4, 18), (14, 0), (26, 16), (10, 5), (16, 6), (25, 21), (10, 4), (19, 22), (23, 12), (5, 20), (5, 9), (13, 21), (26, 8), (20, 3), (25, 22), (4, 8), (20, 9), (14, 15), (20, 0), (1, 4), (27, 21), (5, 8), (19, 18), (12, 20), (20, 5), (10, 14), (23, 14), (20, 7), (5, 22), (15, 11), (18, 21), (12, 14), (11, 0), (12, 5), (3, 18), (20, 10), (11, 16), (4, 10), (10, 6), (18, 9), (17, 14), (19, 3), (3, 7), (22, 13), (15, 15), (24, 17), (7, 15), (24, 6), (0, 2), (6, 11), (13, 0), (22, 9), (21, 16), (11, 12), (21, 17), (18, 6), (0, 5), (27, 3), (1, 3), (7, 16), (15, 3), (19, 19), (25, 6), (10, 15), (23, 0), (16, 11), (3, 9), (25, 5), (22, 0), (19, 7), (25, 2), (10, 2), (18, 10), (17, 18), (8, 8), (16, 0), (3, 3), (22, 8), (3, 10), (16, 3), (14, 6), (26, 19), (8, 5), (11, 14), (3, 12), (1, 15), (1, 11), (4, 14), (13, 11), (20, 13), (19, 8), (20, 6), (27, 20), (24, 15), (15, 4), (17, 17), (3, 17), (9, 2), (26, 4), (3, 16), (1, 7), (24, 4), (24, 3), (13, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610487", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), 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), (16, 17), (23, 9), (19, 13), (18, 13), (10, 6), (26, 1), (0, 19), (27, 3), (22, 10), (7, 8), (16, 25), (22, 0), (23, 14), (0, 25), (0, 22), (11, 7), (20, 6), (7, 24), (6, 13), (7, 0), (11, 21), (20, 0), (3, 23), (7, 19), (12, 4), (18, 20), (20, 18), (0, 18), (11, 15), (22, 15), (25, 12), (12, 14), (25, 25), (27, 7), (21, 13), (6, 23), (13, 10), (13, 0), (14, 1), (18, 18), (6, 19), (22, 3), (18, 5), (23, 18), (2, 13), (7, 12), (8, 12), (8, 15), (6, 7), (14, 20), (12, 20), (21, 8), (1, 10), (0, 16), (2, 23), (1, 2), (16, 18), (25, 7), (14, 12), (21, 24), (18, 2), (6, 8), (15, 17), (12, 16), (14, 21), (4, 19), (18, 15), (24, 8), (15, 21), (23, 24), (0, 8), (9, 8), (5, 1), (17, 4), (9, 10), (8, 20), (26, 6), (3, 1), (20, 13), (20, 3), (2, 10), (1, 1), (15, 3), (5, 3), (7, 17), (10, 16), (15, 6), (21, 21), (3, 12), (6, 10), (0, 9), (2, 19), (15, 22), (5, 12), (26, 14), (5, 8), (16, 19), (12, 5), (26, 9), (21, 1), (2, 24), (2, 14), (16, 16), (23, 11), (15, 16), (12, 24), (21, 5), (5, 11), (27, 24), (9, 18), (17, 14), (10, 21), (7, 18), (22, 5), (5, 6), (14, 13), (10, 7), (26, 2), (12, 21), (4, 21), (24, 1), (8, 19), (9, 17), (19, 3), (17, 3), (5, 18), (13, 16), (25, 2), (9, 1), (5, 19), (1, 17), (14, 11), (12, 9), (3, 2), (7, 25), (19, 24), (24, 19), (3, 17), (8, 21), (6, 18), (18, 21), (23, 19), (25, 11), (18, 7), (24, 12), (4, 1), (20, 12), (2, 1), (27, 20), (14, 15), (8, 23), (19, 25), (19, 6), (22, 13), (9, 22), (15, 2), (12, 19), (11, 19), (9, 24), (18, 11), (14, 2), (12, 15), (0, 15), (20, 24), (6, 3), (27, 13), (16, 4), (1, 11), (24, 20), (6, 9), (0, 2), (16, 5), (3, 9), (11, 11), (5, 16), (17, 17), (9, 13), (5, 17), (6, 5), (13, 11), (1, 8), (14, 7), (7, 21), (11, 12), (11, 17), (11, 10), (22, 24), (0, 17), (5, 22), (26, 10), (13, 20), (12, 17), (4, 20), (0, 24), (25, 18), (11, 23), (19, 11), (10, 8), (7, 23), (20, 23), (27, 11), (15, 1), (20, 15), (13, 18), (27, 22), (22, 16), (25, 20), (19, 23), (1, 18), (26, 20), (13, 14), (3, 3), (15, 7), (8, 1), (5, 24), (12, 25), (25, 23), (4, 12), (12, 10), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "815360", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), 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), (4, 19), (17, 16), (16, 9), (7, 7), (1, 13), (4, 4), (11, 20), (2, 0), (17, 11), (18, 24), (10, 4), (14, 22), (5, 3), (9, 6), (2, 18), (8, 26), (20, 17), (17, 18), (15, 11), (5, 26), (4, 12), (16, 22), (9, 10), (11, 3), (6, 19), (1, 17), (17, 8), (11, 6), (6, 10), (3, 20), (19, 19), (6, 6), (16, 10), (6, 16), (20, 20), (15, 1), (8, 14), (7, 5), (2, 19), (8, 1), (5, 18), (15, 24), (18, 13), (14, 14), (11, 2), (18, 10), (14, 26), (6, 7), (20, 23), (2, 10), (17, 19), (11, 26), (11, 12), (17, 13), (2, 24), (1, 2), (7, 19), (13, 3), (9, 22), (14, 21), (2, 8), (18, 19), (20, 21), (9, 5), (4, 6), (17, 22), (19, 10), (4, 1), (13, 0), (15, 7), (8, 6), (1, 10), (2, 25), (2, 23), (6, 26), (10, 11), (12, 12), (9, 4), (5, 9), (13, 26), (4, 26), (6, 25), (0, 16), (19, 3), (0, 9), (9, 0), (11, 19), (18, 4), (19, 16), (12, 22), (4, 23), (10, 23), (2, 1), (5, 13), (10, 14), (10, 5), (7, 18), (18, 5), (6, 11), (8, 7), (2, 11), (8, 17), (5, 4), (20, 11), (7, 10), (6, 8), (11, 16), (5, 5), (14, 3), (3, 12), (10, 20), (3, 4), (10, 24), (3, 16), (15, 10), (6, 23), (11, 18), (11, 13), (19, 14), (17, 2), (6, 17), (18, 8), (3, 19), (5, 23), (2, 16), (4, 20), (20, 10), (4, 21), (15, 26), (20, 12), (11, 9), (3, 1), (13, 5), (19, 7), (17, 26), (8, 21), (6, 14), (18, 18), (4, 10), (5, 8), (3, 21), (0, 20), (19, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367188", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (13, 4), (3, 15), (25, 1), (19, 9), (26, 2), (24, 13), (11, 17), (15, 6), (26, 4), (13, 0), (15, 8), (26, 1), (12, 6), (19, 20), (14, 2), (24, 20), (5, 16), (25, 17), (0, 1), (17, 10), (7, 4), (4, 17), (23, 9), (1, 9), (11, 11), (5, 17), (25, 13), (24, 0), (0, 4), (6, 16), (11, 1), (17, 18), (26, 17), (12, 20), (11, 5), (1, 10), (16, 15), (11, 8), (18, 7), (15, 9), (18, 15), (6, 2), (14, 3), (7, 5), (22, 14), (19, 6), (5, 6), (2, 6), (20, 16), (19, 16), (15, 2), (15, 12), (2, 5), (0, 15), (16, 3), (16, 2), (17, 13), (23, 17), (23, 13), (9, 14), (22, 12), (4, 18), (23, 14), (7, 0), (2, 9), (14, 20), (10, 1), (18, 16), (10, 19), (22, 17), (10, 5), (14, 19), (11, 6), (3, 17), (17, 6), (21, 5), (24, 4), (21, 12), (12, 4), (0, 5), (9, 12), (18, 1), (9, 11), (14, 13), (15, 17), (26, 12), (12, 15), (9, 20), (1, 20), (7, 8), (1, 11), (10, 10), (12, 1), (6, 0), (17, 14), (18, 17), (17, 2), (1, 2), (9, 17), (0, 18), (21, 4), (18, 2), (6, 18), (17, 9), (20, 11), (23, 20), (16, 10), (8, 3), (22, 16), (10, 14), (19, 11), (25, 14), (12, 19), (9, 6), (4, 12), (26, 18), (10, 2), (8, 15), (0, 7), (24, 1), (10, 6), (18, 18), (7, 3), (5, 10), (8, 12), (25, 4), (14, 10), (8, 8), (2, 13), (14, 17), (15, 5), (14, 8), (16, 8), (26, 16), (8, 13), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807392", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 10), (25, 19), (6, 21), (17, 20), (9, 9), (14, 11), (9, 7), (26, 4), (20, 25), (0, 3), (26, 11), (15, 21), (3, 25), (10, 22), (9, 8), (11, 25), (25, 24), (17, 1), (1, 11), (19, 25), (27, 2), (8, 3), (7, 12), (11, 24), (0, 6), (10, 10), (28, 17), (6, 23), (1, 8), (2, 3), (11, 12), (13, 16), (10, 2), (17, 12), (28, 13), (17, 11), (1, 16), (24, 11), (24, 8), (7, 7), (5, 10), (17, 24), (2, 20), (25, 11), (15, 7), (0, 21), (23, 11), (12, 4), (0, 11), (3, 3), (7, 18), (26, 10), (28, 2), (9, 24), (19, 0), (10, 25), (16, 5), (1, 20), (23, 25), (18, 2), (7, 24), (17, 19), (15, 10), (17, 5), (8, 1), (25, 10), (2, 19), (5, 8), (26, 3), (21, 17), (10, 11), (22, 13), (3, 9), (28, 6), (3, 13), (9, 15), (16, 20), (15, 4), (18, 26), (0, 4), (3, 19), (24, 0), (28, 1), (7, 2), (28, 24), (22, 12), (23, 2), (18, 6), (14, 23), (1, 17), (1, 0), (1, 9), (10, 24), (11, 15), (25, 17), (4, 21), (21, 20), (24, 10), (15, 20), (26, 0), (21, 12), (0, 23), (7, 13), (20, 19), (17, 7), (0, 18), (23, 24), (16, 12), (11, 6), (13, 4), (4, 2), (18, 3), (0, 5), (7, 9), (24, 4), (12, 22), (12, 17), (4, 9), (16, 1), (2, 2), (20, 11), (26, 16), (7, 15), (23, 0), (2, 26), (22, 25), (3, 7), (27, 11), (22, 26), (25, 9), (18, 12), (13, 2), (12, 25), (15, 18), (14, 21), (16, 21), (4, 15), (13, 11), (5, 5), (27, 5), (23, 19), (18, 18), (10, 14), (16, 14), (26, 1), (5, 18), (6, 4), (28, 4), (1, 15), (7, 23), (19, 24), (16, 8), (18, 22), (27, 26), (27, 12), (5, 26), (13, 24), (2, 15), (16, 25), (8, 26), (22, 19), (10, 8), (24, 16), (21, 15), (14, 14), (5, 22), (0, 15), (3, 17), (23, 7), (10, 20), (3, 18), (22, 6), (6, 10), (19, 14), (4, 7), (0, 7), (18, 1), (15, 15), (7, 4), (20, 6), (20, 8), (14, 5), (5, 19), (17, 17), (11, 16), (22, 11), (24, 19), (24, 2), (9, 11), (10, 18), (22, 21), (14, 24), (22, 22), (26, 20), (8, 11), (7, 6), (4, 3), (15, 14), (15, 24), (13, 17), (2, 1), (24, 15), (28, 8), (5, 20), (18, 11), (6, 13), (5, 2), (19, 16), (12, 10), (6, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719712", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 8), (23, 16), (17, 6), (16, 3), (16, 11), (13, 8), (24, 15), (17, 14), (14, 19), (6, 16), (23, 10), (2, 17), (19, 4), (9, 3), (6, 10), (15, 9), (14, 12), (13, 19), (20, 18), (9, 10), (11, 15), (3, 6), (11, 8), (0, 10), (21, 6), (20, 7), (17, 11), (9, 17), (20, 19), (11, 1), (7, 7), (7, 0), (3, 16), (14, 14), (16, 14), (16, 2), (22, 9), (11, 2), (0, 15), (0, 3), (18, 12), (9, 9), (21, 14), (5, 14), (5, 16), (24, 16), (18, 10), (17, 17), (4, 8), (11, 7), (0, 12), (10, 3), (1, 3), (1, 7), (17, 18), (22, 7), (11, 16), (0, 7), (2, 19), (6, 13), (19, 14), (19, 9), (14, 7), (6, 8), (21, 2), (4, 0), (8, 15), (6, 12), (7, 2), (23, 1), (19, 5), (8, 4), (20, 15), (16, 13), (17, 13), (9, 5), (8, 13), (23, 5), (3, 14), (10, 9), (14, 5), (3, 4), (23, 3), (21, 3), (24, 12), (18, 18), (6, 1), (8, 10), (1, 12), (21, 7), (13, 5), (15, 6), (17, 7), (8, 7), (16, 12), (4, 3), (9, 12), (3, 7), (22, 15), (24, 2), (23, 18), (9, 19), (13, 3), (0, 18), (21, 4), (22, 3), (20, 3), (7, 16), (20, 5), (8, 12), (4, 4), (16, 1), (0, 11), (22, 0), (5, 8), (10, 4), (19, 0), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950040", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 21), (21, 16), (21, 23), (22, 2), (8, 16), (17, 14), (2, 24), (14, 7), (8, 5), (19, 14), (22, 0), (13, 14), (0, 24), (1, 24), (3, 19), (18, 22), (10, 22), (15, 17), (15, 4), (9, 11), (9, 21), (12, 14), (11, 21), (22, 16), (20, 0), (10, 6), (16, 18), (5, 20), (6, 2), (9, 12), (9, 24), (1, 19), (22, 4), (4, 5), (13, 9), (12, 16), (19, 6), (12, 8), (20, 25), (4, 17), (5, 16), (9, 19), (16, 24), (4, 24), (9, 22), (11, 19), (13, 5), (3, 23), (16, 11), (8, 23), (16, 4), (2, 22), (3, 3), (11, 7), (20, 6), (19, 9), (14, 15), (18, 20), (5, 14), (3, 6), (18, 9), (6, 20), (5, 0), (15, 6), (15, 25), (21, 21), (21, 10), (9, 6), (5, 4), (10, 23), (8, 8), (8, 9), (17, 20), (7, 5), (2, 21), (17, 10), (3, 10), (17, 11), (15, 7), (3, 20), (2, 16), (15, 1), (0, 4), (14, 3), (18, 15), (5, 18), (16, 23), (20, 2), (0, 22), (9, 10), (13, 20), (12, 11), (13, 23), (9, 9), (11, 9), (9, 15), (7, 12), (10, 11), (10, 3), (6, 1), (2, 4), (2, 18), (0, 21), (13, 15), (16, 20), (11, 11), (13, 24), (4, 16), (9, 25), (14, 9), (22, 12), (0, 20), (4, 7), (19, 3), (11, 10), (3, 12), (12, 21), (18, 5), (20, 21), (15, 8), (4, 25), (3, 2), (13, 8), (8, 19), (1, 11), (17, 21), (18, 25), (0, 17), (21, 25), (2, 5), (2, 15), (13, 22), (14, 21), (17, 12), (1, 0), (15, 22), (8, 21), (10, 10), (20, 1), (16, 1), (12, 19), (20, 16), (16, 3), (17, 13), (3, 14), (22, 10), (6, 5), (3, 8), (10, 9), (18, 21), (14, 11), (4, 21), (4, 0), (13, 16), (15, 24), (11, 15), (5, 23), (21, 8), (8, 12), (21, 4), (19, 21), (11, 0), (19, 15), (19, 16), (12, 12), (19, 10), (13, 0), (20, 5), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956628", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (21, 14), (12, 19), (24, 8), (5, 18), (14, 18), (11, 4), (22, 24), (12, 15), (9, 2), (24, 17), (9, 11), (25, 10), (0, 24), (7, 3), (20, 8), (24, 21), (18, 24), (13, 22), (24, 9), (16, 23), (25, 2), (16, 13), (0, 15), (22, 7), (15, 2), (14, 8), (11, 13), (13, 20), (24, 2), (7, 2), (13, 4), (4, 13), (4, 3), (8, 10), (22, 21), (3, 16), (10, 5), (8, 4), (1, 16), (18, 21), (12, 20), (20, 24), (12, 17), (23, 6), (23, 17), (21, 21), (0, 5), (15, 5), (8, 11), (6, 9), (22, 15), (4, 7), (3, 6), (4, 24), (23, 8), (12, 21), (25, 1), (21, 17), (24, 5), (5, 14), (7, 5), (17, 16), (24, 1), (18, 22), (13, 7), (7, 16), (17, 3), (7, 22), (17, 2), (20, 16), (24, 20), (11, 17), (6, 20), (3, 14), (11, 7), (15, 11), (24, 18), (1, 24), (24, 11), (6, 11), (10, 20), (9, 23), (15, 24), (13, 18), (12, 22), (15, 19), (15, 4), (5, 24), (22, 14), (10, 24), (5, 5), (8, 0), (13, 10), (20, 5), (0, 3), (6, 7), (17, 17), (16, 9), (15, 3), (25, 16), (7, 15), (19, 23), (9, 21), (11, 10), (13, 23), (16, 6), (12, 2), (4, 15), (7, 4), (23, 11), (10, 15), (18, 6), (19, 4), (10, 17), (23, 22), (20, 10), (9, 19), (13, 9), (22, 23), (14, 23), (2, 4), (16, 11), (12, 6), (0, 4), (9, 24), (9, 16), (7, 21), (13, 13), (10, 8), (11, 21), (25, 13), (17, 21), (18, 18), (22, 19), (17, 5), (15, 18), (23, 21), (16, 15), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898390", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (20, 14), (15, 12), (8, 14), (4, 9), (13, 7), (5, 0), (3, 0), (20, 1), (5, 9), (15, 17), (7, 5), (11, 13), (8, 10), (20, 4), (12, 1), (21, 15), (13, 13), (18, 8), (18, 12), (22, 15), (2, 15), (9, 2), (15, 3), (2, 4), (14, 12), (17, 11), (9, 18), (18, 13), (9, 9), (0, 13), (6, 5), (10, 3), (2, 14), (10, 19), (14, 8), (12, 6), (6, 14), (10, 13), (11, 15), (9, 1), (6, 11), (14, 2), (2, 2), (21, 5), (9, 0), (0, 14), (16, 18), (18, 4), (12, 20), (13, 4), (5, 6), (11, 2), (1, 4), (0, 11), (9, 3), (22, 16), (16, 20), (20, 8), (15, 7), (7, 14), (21, 2), (15, 19), (9, 13), (16, 1), (12, 3), (15, 6), (19, 19), (18, 17), (9, 4), (18, 6), (4, 0), (19, 8), (9, 11), (22, 6), (22, 2), (22, 1), (7, 0), (22, 19), (13, 5), (15, 8), (11, 14), (11, 3), (12, 16), (1, 10), (6, 1), (15, 10), (0, 9), (0, 17), (8, 1), (10, 1), (8, 12), (11, 19), (18, 0), (8, 16), (10, 4), (7, 13), (2, 19), (21, 12), (0, 16), (1, 15), (5, 5), (4, 8), (11, 10), (4, 2), (2, 0), (9, 17), (5, 4), (9, 15), (2, 3), (8, 7), (7, 1), (22, 11), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610200", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 20), (16, 0), (3, 11), (6, 22), (22, 10), (21, 7), (7, 4), (9, 4), (12, 16), (14, 14), (18, 17), (9, 14), (25, 5), (0, 22), (15, 15), (6, 6), (14, 5), (22, 12), (0, 18), (10, 15), (15, 2), (10, 20), (17, 22), (0, 2), (0, 14), (22, 14), (12, 15), (18, 10), (24, 14), (27, 2), (14, 21), (17, 5), (7, 2), (0, 4), (7, 13), (15, 9), (3, 21), (25, 16), (10, 14), (17, 2), (8, 1), (12, 21), (25, 15), (0, 12), (9, 7), (11, 5), (20, 12), (19, 22), (16, 18), (19, 14), (9, 8), (26, 9), (26, 11), (18, 2), (2, 20), (5, 16), (22, 4), (1, 2), (8, 15), (15, 16), (19, 18), (21, 20), (5, 15), (8, 16), (24, 10), (12, 17), (2, 11), (14, 1), (15, 1), (26, 16), (0, 3), (21, 11), (14, 15), (8, 18), (1, 10), (21, 1), (3, 16), (13, 0), (8, 21), (18, 6), (15, 11), (23, 12), (9, 15), (4, 11), (13, 17), (20, 18), (5, 9), (16, 8), (20, 7), (7, 1), (11, 17), (21, 10), (4, 2), (16, 13), (13, 9), (21, 0), (13, 15), (0, 10), (15, 8), (2, 18), (27, 9), (0, 1), (25, 2), (24, 7), (26, 20), (2, 12), (1, 18), (2, 7), (1, 7), (9, 21), (0, 21), (11, 8), (11, 4), (12, 4), (14, 9), (4, 10), (27, 16), (25, 3), (7, 14), (23, 9), (14, 3), (2, 14), (16, 10), (24, 4), (12, 9), (27, 15), (13, 16), (5, 5), (3, 8), (19, 15), (7, 12), (21, 19), (3, 1), (6, 8), (25, 21), (3, 19), (22, 8), (16, 3), (19, 0), (17, 16), (17, 11), (24, 22), (8, 0), (2, 10), (23, 10), (1, 19), (8, 9), (13, 18), (23, 20), (6, 11), (13, 3), (17, 1), (0, 11), (9, 13), (20, 10), (3, 0), (24, 0), (26, 17), (21, 15), (11, 7), (5, 14), (13, 13), (3, 4), (17, 4), (5, 17), (23, 5), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255744", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 23), (16, 17), (11, 20), (1, 19), (8, 5), (2, 25), (11, 1), (0, 15), (13, 15), (14, 9), (22, 4), (16, 20), (3, 1), (0, 24), (5, 12), (18, 24), (12, 21), (20, 4), (20, 17), (18, 25), (7, 24), (2, 22), (14, 8), (8, 8), (8, 9), (13, 11), (21, 16), (18, 4), (17, 5), (16, 18), (21, 17), (20, 10), (0, 9), (17, 22), (20, 16), (9, 4), (5, 24), (17, 8), (9, 5), (12, 5), (14, 0), (21, 20), (16, 7), (3, 5), (21, 14), (9, 14), (20, 15), (4, 21), (4, 20), (21, 10), (18, 19), (16, 24), (3, 18), (21, 25), (22, 2), (15, 5), (6, 5), (4, 23), (19, 5), (11, 17), (5, 9), (22, 19), (4, 2), (1, 15), (2, 13), (9, 19), (9, 2), (20, 12), (12, 19), (0, 10), (11, 3), (17, 23), (19, 12), (9, 17), (21, 6), (15, 19), (19, 2), (15, 20), (15, 8), (11, 15), (5, 5), (12, 24), (8, 13), (22, 14), (20, 7), (19, 9), (17, 3), (3, 22), (3, 14), (2, 21), (13, 16), (17, 20), (2, 6), (11, 8), (18, 21), (3, 15), (22, 23), (1, 2), (10, 13), (13, 13), (10, 2), (12, 23), (18, 22), (3, 8), (20, 19), (5, 21), (18, 0), (16, 21), (17, 2), (16, 13), (10, 22), (6, 25), (4, 8), (5, 18), (3, 12), (18, 8), (10, 17), (1, 5), (13, 1), (22, 11), (16, 12), (8, 23), (9, 24), (12, 2), (9, 15), (2, 4), (2, 10), (17, 9), (0, 1), (14, 20), (2, 15), (5, 11), (5, 3), (6, 11), (17, 18), (10, 16), (7, 1), (5, 23), (10, 20), (8, 16), (8, 17), (17, 15), (12, 3), (9, 0), (6, 21), (22, 12), (17, 11), (8, 1), (3, 7), (22, 8), (6, 4), (6, 17), (14, 2), (11, 7), (7, 10), (9, 25), (15, 12), (19, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513726", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (18, 18), (24, 16), (15, 14), (5, 8), (13, 8), (23, 13), (26, 12), (10, 1), (14, 13), (7, 11), (26, 9), (18, 14), (21, 3), (24, 18), (11, 5), (3, 10), (22, 17), (6, 14), (23, 20), (12, 15), (22, 15), (4, 2), (9, 17), (21, 19), (0, 9), (9, 19), (19, 8), (19, 1), (15, 7), (6, 18), (0, 16), (21, 8), (17, 10), (8, 13), (18, 19), (4, 17), (1, 20), (1, 18), (18, 16), (11, 9), (21, 7), (25, 19), (8, 11), (17, 9), (20, 14), (9, 12), (15, 12), (14, 11), (15, 4), (20, 0), (1, 16), (17, 0), (13, 19), (20, 1), (15, 17), (6, 13), (18, 4), (14, 10), (10, 9), (2, 13), (5, 15), (13, 9), (1, 1), (23, 10), (21, 4), (13, 10), (0, 12), (23, 5), (22, 2), (8, 6), (12, 12), (18, 3), (2, 8), (6, 1), (24, 5), (24, 12), (18, 10), (10, 11), (4, 13), (12, 7), (19, 17), (14, 18), (12, 17), (2, 14), (18, 0), (21, 18), (19, 20), (5, 9), (2, 7), (6, 0), (18, 12), (12, 2), (4, 6), (4, 14), (23, 2), (13, 16), (25, 11), (14, 20), (23, 9), (6, 15), (15, 11), (12, 16), (2, 10), (23, 14), (5, 16), (23, 1), (1, 2), (7, 6), (16, 0), (3, 16), (2, 6), (17, 15), (25, 0), (17, 11), (11, 0), (22, 20), (24, 1), (24, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752993", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), 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), (21, 3), (20, 15), (17, 8), (13, 13), (12, 10), (6, 5), (2, 18), (21, 0), (10, 2), (8, 27), (0, 15), (7, 5), (24, 9), (0, 27), (18, 16), (5, 7), (17, 25), (22, 27), (14, 2), (18, 4), (14, 3), (11, 20), (20, 16), (23, 14), (2, 7), (24, 20), (4, 18), (13, 22), (4, 1), (11, 2), (20, 6), (22, 25), (9, 22), (19, 8), (8, 25), (4, 20), (14, 1), (24, 26), (7, 9), (17, 14), (15, 14), (20, 27), (15, 1), (20, 24), (14, 17), (10, 8), (12, 4), (24, 4), (6, 20), (6, 11), (2, 9), (24, 22), (15, 23), (8, 11), (17, 22), (9, 19), (20, 14), (4, 11), (8, 16), (3, 18), (24, 18), (7, 18), (7, 4), (22, 15), (1, 5), (22, 17), (21, 18), (8, 19), (14, 26), (4, 9), (2, 13), (24, 15), (24, 2), (17, 9), (10, 13), (9, 25), (8, 21), (22, 8), (13, 18), (22, 19), (22, 21), (6, 13), (14, 10), (13, 24), (8, 4), (2, 16), (16, 27), (16, 1), (5, 11), (23, 24), (15, 26), (12, 11), (1, 27), (15, 21), (19, 9), (11, 4), (5, 16), (16, 10), (21, 5), (17, 16), (4, 12), (23, 1), (9, 7), (24, 8), (11, 7), (22, 22), (16, 25), (19, 0), (8, 20), (23, 0), (12, 17), (19, 17), (24, 17), (9, 11), (19, 25), (16, 18), (19, 22), (7, 11), (13, 11), (2, 6), (8, 8), (9, 18), (14, 6), (3, 24), (9, 15), (1, 23), (12, 12), (7, 3), (19, 24), (23, 19), (1, 22), (2, 22), (21, 8), (18, 0), (20, 1), (5, 17), (23, 9), (21, 14), (16, 19), (20, 0), (4, 6), (24, 1), (15, 18), (12, 21), (16, 0), (15, 22), (19, 19), (4, 3), (23, 15), (19, 6), (8, 3), (21, 12), (16, 13), (5, 0), (17, 19), (11, 8), (9, 6), (7, 20), (16, 5), (8, 9), (12, 2), (16, 17), (23, 23), (15, 12), (0, 10), (1, 20), (16, 16), (21, 2), (24, 21), (19, 27), (4, 16), (11, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870448", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 24), (9, 1), (22, 3), (22, 2), (9, 23), (12, 26), (12, 17), (3, 18), (5, 10), (12, 1), (3, 25), (16, 12), (4, 11), (17, 0), (20, 19), (10, 2), (12, 15), (8, 6), (17, 1), (8, 24), (12, 12), (8, 21), (3, 12), (21, 26), (10, 19), (10, 21), (12, 23), (13, 11), (22, 13), (20, 21), (10, 17), (4, 12), (16, 24), (14, 12), (6, 6), (2, 3), (17, 22), (10, 14), (17, 11), (6, 9), (6, 14), (4, 24), (3, 2), (22, 11), (7, 0), (19, 21), (8, 13), (5, 5), (9, 15), (17, 18), (1, 12), (11, 14), (6, 15), (7, 21), (15, 1), (20, 25), (22, 5), (6, 10), (5, 6), (19, 8), (4, 0), (9, 5), (9, 22), (21, 24), (1, 18), (8, 5), (0, 22), (22, 0), (18, 15), (17, 20), (7, 2), (4, 25), (13, 12), (22, 21), (0, 21), (11, 15), (6, 5), (1, 8), (22, 7), (22, 19), (14, 20), (9, 24), (10, 26), (18, 23), (17, 5), (2, 20), (6, 3), (1, 21), (19, 3), (4, 9), (14, 18), (15, 25), (17, 13), (1, 19), (5, 2), (15, 14), (5, 4), (19, 20), (14, 23), (17, 14), (22, 17), (17, 21), (18, 24), (13, 6), (11, 18), (14, 13), (2, 17), (21, 19), (7, 7), (19, 7), (22, 16), (5, 13), (16, 2), (18, 10), (21, 15), (12, 22), (7, 15), (4, 4), (6, 11), (22, 8), (12, 13), (4, 18), (0, 6), (1, 15), (18, 14), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643836", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (14, 15), (13, 1), (18, 17), (3, 0), (17, 17), (3, 14), (11, 19), (17, 20), (6, 5), (19, 18), (17, 1), (1, 4), (18, 4), (4, 16), (1, 19), (13, 13), (4, 5), (1, 2), (3, 9), (16, 16), (3, 10), (10, 4), (6, 10), (10, 7), (4, 15), (15, 7), (18, 2), (11, 21), (5, 2), (13, 0), (16, 18), (8, 7), (18, 14), (13, 18), (7, 15), (4, 7), (16, 11), (17, 18), (18, 9), (15, 19), (19, 14), (4, 18), (14, 6), (14, 8), (9, 20), (7, 12), (18, 10), (19, 16), (15, 21), (15, 20), (2, 13), (19, 20), (17, 19), (4, 12), (8, 11), (5, 16), (15, 12), (18, 16), (8, 6), (5, 22), (2, 19), (14, 18), (11, 10), (1, 16), (4, 14), (14, 11), (2, 9), (18, 6), (17, 21), (5, 19), (16, 17), (12, 16), (12, 21), (3, 17), (18, 13), (16, 2), (16, 5), (8, 17), (14, 5), (14, 13), (13, 16), (0, 21), (11, 9), (13, 19), (7, 22), (10, 13), (2, 21), (0, 3), (14, 7), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "796734", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 15), (12, 2), (28, 15), (12, 12), (7, 2), (20, 8), (21, 7), (10, 9), (1, 12), (16, 12), (15, 11), (27, 14), (25, 21), (26, 7), (4, 10), (9, 12), (18, 17), (6, 5), (28, 7), (22, 8), (20, 17), (26, 18), (12, 21), (7, 15), (4, 9), (18, 3), (22, 6), (20, 6), (15, 18), (25, 4), (6, 16), (13, 2), (26, 4), (17, 8), (14, 1), (26, 8), (17, 5), (22, 1), (15, 9), (10, 3), (1, 4), (17, 21), (7, 19), (24, 3), (13, 11), (20, 16), (12, 20), (24, 17), (14, 20), (17, 12), (20, 3), (16, 8), (25, 12), (20, 2), (28, 10), (22, 9), (0, 18), (15, 16), (15, 19), (2, 14), (25, 18), (1, 19), (6, 13), (0, 16), (24, 2), (9, 6), (10, 19), (7, 0), (19, 9), (2, 7), (16, 1), (5, 14), (0, 15), (17, 16), (18, 16), (5, 0), (8, 17), (13, 0), (11, 7), (10, 11), (3, 6), (26, 6), (3, 7), (2, 21), (23, 18), (12, 1), (11, 20), (28, 12), (28, 9), (1, 14), (23, 1), (3, 10), (18, 8), (24, 7), (22, 17), (26, 2), (1, 1), (14, 21), (22, 10), (14, 9), (16, 21), (27, 4), (15, 5), (26, 20), (28, 2), (7, 21), (14, 5), (15, 7), (8, 7), (8, 16), (9, 5), (11, 17), (8, 3), (15, 8), (0, 9), (8, 5), (8, 11), (15, 12), (11, 14), (5, 10), (16, 6), (19, 19), (21, 20), (6, 21), (19, 16), (10, 18), (28, 16), (19, 2), (7, 9), (22, 13), (2, 11), (23, 9), (26, 17), (24, 21), (21, 13), (24, 12), (1, 11), (7, 12), (0, 2), (11, 12), (14, 12), (0, 21), (27, 10), (19, 13), (26, 5), (18, 13), (3, 11), (20, 9), (25, 6), (19, 21), (26, 19), (11, 4), (28, 5), (16, 3), (17, 17), (18, 7), (4, 8), (18, 14), (10, 13), (10, 1), (25, 3), (20, 7), (5, 11), (11, 8), (27, 19), (17, 19), (17, 9), (10, 21), (16, 15), (17, 11), (2, 17), (23, 2), (21, 19), (13, 6), (28, 11), (25, 5), (13, 18), (13, 12), (8, 21), (18, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2592", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 3), (3, 12), (9, 1), (13, 26), (7, 20), (1, 1), (20, 11), (12, 2), (14, 18), (2, 19), (21, 25), (20, 25), (20, 8), (18, 1), (3, 25), (20, 20), (8, 4), (2, 2), (12, 27), (3, 27), (7, 14), (15, 0), (15, 26), (16, 10), (15, 7), (19, 12), (18, 23), (4, 17), (19, 22), (14, 9), (16, 13), (12, 17), (1, 18), (16, 6), (13, 27), (7, 10), (13, 1), (16, 23), (9, 3), (23, 10), (15, 5), (24, 10), (5, 8), (17, 16), (4, 9), (16, 7), (16, 3), (18, 3), (3, 7), (6, 10), (14, 16), (15, 16), (9, 18), (6, 4), (10, 26), (7, 0), (0, 14), (17, 19), (8, 26), (20, 24), (22, 3), (2, 4), (16, 11), (18, 26), (23, 0), (5, 6), (4, 4), (23, 27), (12, 18), (10, 0), (3, 0), (10, 2), (11, 2), (18, 14), (20, 26), (21, 26), (13, 3), (17, 4), (3, 23), (4, 24), (7, 16), (17, 20), (17, 17), (2, 6), (15, 17), (21, 27), (24, 24), (20, 22), (0, 23), (6, 15), (11, 15), (5, 20), (3, 3), (8, 27), (20, 15), (14, 10), (2, 0), (7, 19), (6, 27), (21, 4), (18, 21), (0, 24), (6, 12), (17, 7), (9, 20), (15, 12), (23, 6), (15, 24), (21, 10), (15, 4), (3, 6), (20, 19), (20, 1), (12, 26), (22, 5), (24, 13), (18, 16), (23, 13), (20, 21), (8, 25), (22, 28), (7, 22), (9, 26), (23, 17), (24, 0), (19, 11), (24, 19), (17, 9), (21, 13), (1, 24), (22, 17), (9, 10), (7, 2), (12, 23), (3, 1), (14, 7), (19, 4), (22, 12), (4, 15), (18, 11), (22, 11), (1, 12), (4, 8), (1, 28), (1, 5), (14, 1), (19, 13), (2, 18), (11, 10), (5, 7), (23, 11), (19, 26), (22, 22), (24, 6), (10, 10), (1, 16), (10, 3), (17, 5), (15, 11), (23, 9), (8, 5), (19, 28), (17, 21), (8, 20), (5, 3), (22, 26), (8, 18), (16, 14), (1, 10), (22, 19), (8, 17), (4, 1), (24, 20), (17, 12), (23, 7), (14, 14), (12, 11), (22, 23), (14, 12), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182868", "dataset": "MATH"}
{"messages": [{"content": "In a 29x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 22), 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), (6, 11), (11, 15), (10, 5), (21, 21), (26, 17), (23, 1), (9, 10), (28, 4), (8, 8), (4, 10), (27, 15), (8, 9), (1, 21), (6, 8), (21, 4), (11, 18), (9, 3), (16, 0), (3, 10), (7, 19), (20, 20), (11, 7), (2, 1), (21, 6), (2, 5), (17, 9), (7, 8), (3, 14), (19, 8), (1, 16), (8, 22), (25, 11), (0, 20), (25, 22), (10, 3), (9, 6), (17, 3), (7, 9), (5, 18), (22, 1), (7, 7), (6, 22), (4, 5), (13, 20), (25, 8), (4, 12), (18, 12), (5, 22), (4, 15), (20, 0), (7, 0), (3, 15), (12, 6), (21, 15), (22, 5), (23, 3), (22, 12), (2, 14), (25, 9), (4, 16), (26, 16), (3, 8), (5, 0), (23, 13), (15, 0), (15, 10), (3, 2), (19, 7), (23, 21), (28, 5), (8, 4), (12, 0), (11, 2), (9, 15), (27, 7), (26, 2), (13, 11), (5, 9), (4, 13), (2, 21), (10, 2), (3, 1), (10, 12), (14, 18), (20, 15), (0, 6), (21, 14), (6, 12), (27, 8), (20, 21), (11, 11), (19, 0), (14, 5), (18, 7), (0, 9), (15, 1), (3, 21), (4, 2), (24, 12), (19, 12), (8, 19), (0, 17), (18, 22), (5, 7), (28, 2), (9, 9), (14, 8), (15, 21), (16, 5), (22, 21), (5, 3), (11, 9), (23, 10), (11, 17), (25, 16), (4, 11), (14, 2), (8, 0), (8, 7), (23, 5), (6, 2), (25, 18), (14, 12), (17, 11), (13, 18), (1, 7), (21, 7), (0, 5), (11, 22), (7, 20), (6, 5), (20, 6), (9, 11), (26, 15), (1, 22), (27, 9), (11, 0), (3, 9), (8, 13), (13, 0), (12, 21), (17, 16), (21, 10), (16, 16), (17, 12), (6, 4), (0, 1), (13, 2), (5, 4), (6, 13), (22, 11), (19, 16), (26, 18), (8, 14), (13, 8), (17, 2), (18, 16), (7, 10), (25, 12), (21, 18), (9, 20), (21, 9), (28, 11), (25, 15), (9, 2), (10, 7), (1, 18), (19, 21), (22, 20), (26, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "837820", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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, 17), (6, 20), (18, 9), (2, 5), (13, 22), (10, 4), (3, 19), (4, 8), (2, 2), (16, 16), (1, 5), (21, 7), (14, 13), (12, 23), (13, 21), (13, 15), (21, 25), (6, 25), (2, 3), (21, 11), (2, 13), (13, 23), (4, 22), (0, 1), (16, 15), (16, 6), (3, 7), (2, 15), (13, 6), (5, 10), (5, 25), (13, 2), (14, 23), (13, 20), (4, 17), (12, 20), (6, 3), (1, 19), (13, 24), (12, 12), (6, 5), (3, 22), (7, 8), (7, 11), (16, 4), (14, 18), (19, 3), (4, 18), (16, 12), (5, 16), (10, 20), (9, 20), (6, 1), (5, 11), (19, 7), (4, 0), (9, 16), (10, 25), (2, 12), (1, 21), (11, 20), (19, 13), (5, 15), (13, 10), (21, 16), (0, 21), (0, 7), (8, 18), (21, 15), (2, 4), (12, 22), (21, 14), (9, 14), (7, 7), (12, 10), (10, 0), (8, 11), (1, 7), (15, 23), (13, 18), (1, 6), (17, 6), (13, 26), (8, 0), (6, 8), (19, 15), (9, 10), (6, 10), (16, 14), (3, 24), (11, 5), (3, 20), (7, 21), (8, 15), (21, 24), (0, 22), (4, 14), (15, 22), (15, 18), (9, 3), (12, 16), (2, 20), (0, 10), (20, 15), (12, 0), (3, 18), (14, 19), (18, 13), (18, 20), (11, 21), (3, 10), (11, 12), (12, 25), (15, 15), (6, 13), (4, 26), (20, 23), (12, 7), (20, 16), (6, 18), (18, 17), (20, 13), (6, 7), (18, 16), (0, 5), (15, 8), (21, 22), (17, 2), (19, 16), (11, 2), (14, 5), (9, 11), (8, 14), (13, 11), (7, 16), (12, 8), (16, 7), (12, 3), (5, 17), (21, 23), (0, 13), (0, 8), (8, 22), (21, 2), (16, 2), (9, 21), (14, 24), (7, 17), (18, 11), (12, 1), (18, 1), (4, 11), (16, 8), (2, 21), (18, 21), (5, 18), (10, 9), (0, 23), (15, 21), (0, 14), (2, 7), (4, 7), (16, 13), (14, 26), (13, 0), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895200", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), 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, 3), (18, 1), (18, 4), (10, 4), (13, 23), (0, 19), (22, 9), (18, 8), (17, 24), (21, 5), (23, 13), (20, 5), (10, 9), (15, 24), (8, 2), (14, 3), (1, 0), (1, 2), (11, 26), (2, 18), (0, 4), (10, 14), (6, 19), (6, 9), (19, 15), (16, 12), (2, 4), (7, 2), (11, 25), (1, 4), (8, 7), (6, 16), (14, 5), (0, 12), (4, 9), (16, 18), (17, 26), (14, 19), (16, 21), (14, 8), (1, 22), (10, 1), (21, 11), (17, 2), (19, 19), (15, 13), (19, 12), (23, 21), (5, 21), (12, 18), (22, 23), (20, 10), (0, 3), (14, 10), (7, 25), (22, 3), (12, 19), (9, 21), (12, 23), (4, 3), (15, 9), (20, 7), (19, 9), (23, 2), (19, 13), (9, 25), (8, 5), (20, 13), (4, 5), (8, 6), (4, 24), (8, 14), (21, 8), (14, 18), (20, 17), (2, 24), (13, 20), (1, 9), (10, 17), (2, 22), (8, 21), (13, 18), (5, 2), (22, 12), (17, 16), (12, 1), (8, 9), (17, 3), (3, 16), (0, 25), (16, 4), (1, 7), (3, 20), (15, 11), (11, 17), (4, 12), (17, 14), (13, 19), (9, 8), (22, 25), (19, 2), (16, 10), (2, 0), (12, 12), (8, 15), (13, 3), (9, 22), (15, 6), (2, 14), (15, 26), (9, 14), (11, 13), (1, 6), (5, 17), (0, 16), (5, 18), (3, 0), (20, 21), (18, 0), (22, 17), (16, 14), (8, 0), (17, 6), (10, 10), (21, 13), (12, 2), (15, 16), (14, 0), (6, 18), (11, 24), (17, 9), (18, 22), (16, 2), (11, 12), (6, 13), (21, 21), (13, 12), (0, 18), (18, 24), (18, 25), (4, 23), (17, 19), (20, 1), (16, 16), (17, 21), (22, 11), (3, 13), (7, 1), (11, 2), (19, 26), (13, 1), (18, 9), (13, 5), (1, 12), (7, 6), (21, 19), (16, 26), (12, 8), (11, 23), (9, 15), (17, 4), (14, 7), (7, 0), (2, 26), (10, 21), (3, 21), (9, 23), (2, 17), (11, 22), (12, 16), (12, 0), (8, 18), (14, 9), (4, 7), (16, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836334", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), 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), (18, 19), (18, 5), (14, 1), (14, 18), (0, 6), (17, 4), (2, 17), (17, 21), (11, 9), (9, 4), (3, 10), (20, 8), (22, 18), (16, 13), (8, 15), (14, 3), (1, 0), (5, 1), (25, 12), (10, 9), (18, 6), (22, 2), (21, 11), (17, 5), (16, 17), (11, 10), (9, 20), (8, 17), (8, 2), (3, 12), (1, 20), (3, 20), (13, 19), (19, 16), (7, 9), (25, 11), (1, 12), (22, 20), (24, 21), (19, 2), (10, 13), (1, 13), (13, 7), (12, 7), (8, 21), (8, 10), (5, 9), (1, 18), (15, 6), (22, 11), (5, 6), (3, 17), (7, 7), (1, 11), (19, 7), (7, 2), (21, 9), (21, 0), (8, 20), (8, 7), (4, 0), (13, 1), (9, 0), (21, 6), (22, 12), (2, 20), (23, 6), (15, 1), (18, 17), (18, 2), (21, 1), (15, 17), (12, 20), (5, 16), (3, 13), (0, 14), (22, 15), (24, 0), (16, 8), (8, 18), (18, 14), (20, 21), (6, 19), (23, 5), (1, 3), (6, 12), (3, 16), (18, 7), (23, 18), (17, 6), (6, 14), (5, 11), (1, 6), (9, 6), (9, 17), (22, 10), (6, 0), (9, 2), (25, 10), (3, 14), (1, 1), (19, 18), (8, 5), (19, 13), (16, 5), (13, 18), (21, 10), (1, 10), (19, 10), (17, 9), (22, 5), (24, 7), (15, 20), (18, 12), (11, 19), (25, 16), (14, 16), (22, 9), (17, 20), (10, 11), (10, 3), (19, 20), (9, 9), (2, 16), (17, 16), (10, 2), (14, 11), (1, 4), (11, 12), (6, 17), (25, 2), (20, 3), (13, 2), (6, 20), (10, 21), (0, 9), (19, 6), (12, 21), (22, 6), (11, 4), (23, 19), (7, 17), (4, 10), (7, 1), (9, 12), (18, 11), (8, 0), (18, 4), (18, 13), (23, 0), (10, 18), (2, 1), (19, 5), (7, 15), (7, 3), (4, 18), (13, 6), (12, 1), (8, 12), (8, 11), (24, 12), (16, 1), (11, 5), (2, 11), (23, 9), (8, 9), (20, 0), (3, 21), (5, 4), (10, 10), (22, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374544", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 14), (7, 19), (1, 19), (19, 1), (4, 18), (3, 21), (12, 9), (3, 8), (17, 17), (5, 18), (14, 0), (15, 14), (7, 18), (17, 6), (6, 7), (15, 5), (1, 3), (3, 3), (9, 11), (3, 2), (14, 12), (1, 6), (14, 20), (13, 10), (1, 15), (14, 2), (6, 15), (8, 6), (16, 3), (5, 8), (13, 4), (0, 17), (9, 15), (16, 1), (12, 13), (4, 5), (7, 15), (3, 6), (3, 10), (9, 21), (9, 8), (18, 18), (6, 14), (17, 4), (16, 4), (6, 17), (11, 11), (9, 6), (13, 21), (3, 15), (16, 16), (4, 8), (0, 3), (13, 2), (1, 12), (12, 3), (5, 20), (6, 18), (7, 7), (14, 21), (16, 18), (2, 16), (8, 2), (12, 18), (11, 8), (5, 6), (2, 14), (12, 6), (16, 12), (10, 4), (17, 16), (14, 8), (17, 21), (14, 11), (15, 3), (9, 4), (7, 11), (3, 1), (12, 17), (11, 19), (0, 19), (4, 15), (17, 11), (11, 21), (6, 12), (16, 6), (15, 17), (5, 3), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800946", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), 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), (14, 3), (9, 25), (23, 9), (12, 23), (24, 4), (8, 17), (9, 24), (16, 3), (16, 24), (23, 22), (18, 14), (4, 14), (2, 11), (22, 19), (2, 17), (4, 6), (9, 9), (5, 10), (15, 12), (2, 0), (21, 23), (14, 1), (4, 22), (8, 19), (9, 15), (16, 17), (19, 2), (5, 25), (14, 22), (9, 10), (13, 21), (23, 10), (6, 0), (10, 5), (16, 12), (14, 13), (4, 5), (23, 14), (24, 11), (1, 9), (4, 11), (4, 9), (7, 18), (17, 19), (21, 5), (0, 2), (7, 0), (15, 23), (7, 6), (0, 17), (4, 18), (19, 0), (21, 9), (17, 20), (14, 20), (13, 0), (10, 11), (21, 14), (5, 4), (17, 9), (15, 22), (13, 22), (22, 25), (12, 21), (12, 9), (22, 14), (10, 9), (24, 19), (4, 19), (13, 13), (14, 8), (1, 20), (16, 9), (3, 10), (3, 13), (19, 14), (6, 25), (17, 5), (5, 19), (24, 9), (11, 22), (18, 5), (16, 8), (24, 15), (22, 1), (16, 18), (7, 11), (5, 24), (21, 16), (18, 15), (9, 16), (15, 21), (4, 4), (1, 21), (7, 13), (2, 4), (20, 6), (6, 15), (16, 10), (22, 5), (22, 8), (15, 10), (22, 20), (14, 17), (3, 9), (24, 6), (11, 7), (8, 3), (23, 4), (5, 23), (9, 2), (5, 21), (16, 22), (10, 18), (18, 9), (11, 17), (20, 0), (12, 0), (4, 13), (24, 22), (0, 15), (20, 10), (12, 5), (6, 1), (24, 3), (6, 14), (20, 5), (5, 0), (3, 8), (9, 1), (21, 0), (5, 17), (3, 24), (12, 6), (16, 19), (13, 3), (15, 17), (7, 9), (9, 20), (11, 8), (19, 17), (16, 6), (21, 17), (19, 16), (2, 3), (7, 2), (22, 15), (10, 13), (23, 2), (20, 19), (0, 4), (21, 1), (8, 21), (7, 20), (22, 23), (23, 15), (11, 14), (11, 6), (17, 6), (15, 14), (0, 21), (23, 5), (4, 17), (21, 3), (17, 0), (16, 15), (6, 7), (2, 5), (8, 5), (10, 4), (21, 13), (0, 24), (4, 3), (18, 13), (2, 13), (5, 13), (10, 10), (11, 9), (1, 16), (14, 6), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404160", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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), (22, 24), (16, 12), (19, 21), (0, 7), (23, 8), (5, 12), (5, 21), (15, 17), (15, 7), (9, 21), (3, 9), (15, 23), (14, 15), (28, 7), (26, 16), (1, 2), (7, 13), (13, 19), (8, 12), (25, 11), (18, 4), (1, 0), (26, 10), (28, 15), (9, 1), (18, 10), (4, 24), (11, 15), (21, 10), (1, 15), (4, 15), (24, 16), (22, 14), (28, 24), (20, 20), (8, 19), (27, 3), (23, 16), (17, 1), (19, 16), (20, 10), (20, 6), (26, 14), (10, 5), (14, 4), (14, 11), (14, 2), (13, 9), (9, 6), (12, 23), (23, 0), (4, 0), (15, 3), (19, 26), (9, 26), (5, 18), (4, 13), (6, 16), (11, 13), (28, 2), (12, 19), (8, 7), (13, 2), (26, 24), (1, 14), (21, 8), (20, 22), (25, 24), (23, 2), (14, 5), (8, 11), (25, 26), (21, 21), (13, 20), (22, 8), (6, 19), (15, 11), (1, 24), (5, 4), (10, 23), (25, 2), (0, 6), (16, 9), (6, 17), (15, 12), (27, 19), (27, 13), (15, 15), (0, 11), (5, 14), (13, 12), (13, 3), (15, 26), (25, 13), (27, 24), (23, 6), (17, 6), (2, 5), (13, 26), (22, 12), (17, 12), (11, 6), (19, 20), (4, 1), (12, 21), (6, 2), (11, 24), (17, 9), (9, 8), (15, 18), (4, 25), (3, 18), (27, 10), (16, 5), (20, 25), (19, 3), (13, 8), (27, 6), (8, 1), (10, 4), (3, 0), (7, 9), (15, 0), (16, 18), (12, 4), (25, 17), (5, 3), (23, 1), (18, 12), (12, 1), (3, 12), (11, 0), (4, 20), (4, 10), (2, 15), (27, 11), (26, 26), (9, 15), (12, 24), (18, 25), (21, 6), (25, 3), (3, 2), (24, 6), (0, 19), (10, 26), (22, 18), (0, 22), (27, 1), (20, 0), (14, 13), (4, 18), (21, 26), (11, 3), (26, 1), (24, 11), (17, 22), (20, 15), (8, 0), (12, 15), (17, 24), (7, 18), (24, 18), (19, 15), (9, 22), (14, 21), (8, 10), (9, 14), (17, 21), (22, 9), (26, 18), (13, 6), (24, 12), (25, 1), (12, 14), (5, 15), (5, 1), (15, 20), (26, 3), (10, 9), (23, 24), (15, 14), (11, 2), (25, 4), (10, 3), (27, 2), (20, 12), (5, 13), (24, 15), (28, 0), (21, 14), (4, 23), (10, 25), (27, 12), (6, 0), (25, 16), (6, 25), (1, 13), (1, 9), (12, 26), (28, 20), (12, 3), (21, 3), (15, 1), (27, 15), (28, 21), (25, 22), (20, 17), (17, 8), (14, 24), (15, 10), (17, 26), (10, 8), (19, 7), (28, 9), (13, 10), (14, 10), (16, 20), (23, 26), (2, 2), (4, 2), (18, 19), (18, 3), (3, 1), (7, 7), (7, 20), (11, 20), (22, 23), (3, 5), (8, 17), (14, 14), (19, 12), (14, 26), (23, 12), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149612", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 15), (10, 14), (19, 16), (6, 5), (1, 2), (9, 21), (20, 19), (9, 1), (7, 16), (9, 20), (0, 7), (12, 14), (1, 17), (17, 19), (17, 1), (13, 11), (20, 7), (9, 6), (17, 6), (20, 10), (12, 16), (13, 19), (1, 7), (7, 9), (9, 5), (17, 2), (10, 21), (11, 15), (17, 12), (14, 4), (9, 19), (2, 20), (19, 10), (1, 0), (12, 11), (0, 3), (8, 17), (3, 11), (12, 21), (17, 14), (5, 19), (14, 11), (3, 4), (7, 1), (11, 22), (17, 15), (12, 5), (6, 21), (4, 13), (13, 1), (16, 22), (20, 6), (0, 8), (13, 18), (17, 7), (12, 1), (18, 17), (16, 19), (9, 8), (14, 19), (10, 3), (3, 15), (4, 16), (1, 23), (12, 20), (2, 22), (18, 9), (15, 7), (15, 6), (7, 23), (0, 15), (20, 11), (14, 1), (5, 3), (11, 10), (13, 9), (11, 7), (10, 16), (16, 21), (20, 12), (15, 23), (18, 19), (1, 21), (14, 18), (11, 6), (17, 20), (6, 22), (8, 21), (1, 12), (4, 17), (7, 6), (8, 13), (2, 18), (20, 1), (0, 18), (19, 15), (20, 22), (3, 0), (5, 9), (0, 12), (4, 19), (16, 20), (9, 15), (15, 19), (10, 2), (20, 4), (19, 9), (9, 18), (5, 20), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882057", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 23), (0, 11), (10, 25), (9, 17), (10, 5), (3, 4), (2, 16), (16, 0), (19, 22), (3, 1), (2, 14), (1, 25), (1, 23), (3, 11), (12, 17), (0, 23), (4, 7), (16, 3), (17, 18), (7, 2), (13, 21), (6, 3), (11, 22), (5, 10), (17, 10), (2, 13), (7, 22), (14, 23), (17, 0), (19, 12), (12, 14), (17, 23), (3, 13), (14, 12), (17, 8), (1, 22), (6, 2), (18, 18), (9, 6), (3, 19), (9, 4), (17, 25), (12, 20), (9, 12), (15, 2), (14, 0), (3, 17), (18, 0), (11, 13), (6, 4), (11, 8), (2, 3), (10, 11), (18, 21), (5, 9), (14, 25), (15, 15), (11, 20), (3, 5), (17, 14), (7, 14), (1, 1), (2, 7), (6, 20), (14, 6), (7, 0), (16, 20), (13, 7), (8, 24), (18, 10), (18, 12), (19, 3), (8, 18), (11, 15), (15, 18), (16, 14), (1, 10), (7, 18), (12, 2), (9, 23), (2, 12), (4, 19), (7, 16), (15, 25), (16, 19), (11, 0), (12, 10), (3, 23), (8, 20), (18, 22), (6, 21), (2, 18), (19, 23), (6, 23), (10, 2), (18, 16), (9, 15), (0, 6), (6, 13), (16, 16), (5, 14), (14, 18), (8, 17), (4, 11), (15, 12), (5, 20), (19, 6), (14, 14), (8, 10), (2, 25), (9, 13), (10, 13), (15, 17), (2, 19), (12, 25), (13, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922208", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (8, 2), (14, 9), (21, 5), (18, 2), (23, 26), (1, 18), (6, 3), (3, 5), (6, 2), (4, 6), (25, 0), (9, 4), (8, 17), (17, 1), (23, 18), (19, 6), (3, 28), (25, 23), (9, 27), (19, 20), (4, 22), (25, 11), (5, 3), (16, 18), (6, 11), (12, 17), (2, 0), (15, 4), (2, 16), (6, 27), (8, 26), (12, 16), (5, 8), (0, 1), (22, 11), (24, 9), (15, 21), (9, 2), (16, 21), (16, 14), (14, 20), (14, 19), (12, 25), (19, 16), (23, 16), (3, 10), (15, 9), (4, 20), (3, 27), (21, 7), (20, 10), (23, 25), (15, 15), (24, 11), (23, 1), (20, 6), (7, 19), (6, 12), (11, 7), (4, 21), (11, 17), (18, 21), (16, 9), (20, 12), (22, 3), (15, 2), (7, 15), (1, 21), (14, 28), (7, 1), (22, 24), (16, 12), (23, 14), (1, 5), (10, 0), (17, 4), (20, 14), (10, 12), (21, 11), (22, 9), (12, 24), (18, 24), (23, 8), (1, 14), (17, 3), (11, 3), (16, 7), (4, 9), (0, 9), (10, 19), (1, 12), (22, 25), (5, 12), (21, 20), (19, 7), (10, 6), (2, 21), (1, 23), (13, 18), (18, 20), (8, 1), (1, 28), (18, 8), (23, 4), (16, 26), (1, 16), (14, 3), (5, 1), (2, 1), (7, 27), (15, 28), (2, 20), (5, 10), (25, 25), (9, 22), (4, 12), (13, 9), (15, 18), (17, 15), (17, 20), (12, 26), (9, 26), (22, 21), (22, 7), (12, 4), (7, 12), (23, 5), (21, 24), (25, 2), (14, 22), (21, 3), (14, 23), (0, 4), (9, 21), (2, 10), (4, 28), (5, 23), (3, 13), (15, 26), (21, 18), (10, 23), (24, 13), (24, 18), (16, 13), (22, 6), (25, 10), (2, 25), (2, 26), (7, 18), (19, 22), (13, 17), (13, 16), (10, 22), (3, 12), (11, 1), (23, 0), (11, 8), (6, 19), (13, 25), (18, 12), (24, 28), (13, 7), (2, 11), (18, 7), (14, 7), (10, 14), (8, 6), (10, 15), (8, 9), (9, 24), (23, 12), (19, 17), (16, 17), (5, 6), (9, 1), (16, 4), (8, 0), (24, 16), (4, 19), (21, 25), (11, 14), (22, 17), (8, 24), (23, 22), (14, 24), (11, 4), (11, 6), (7, 17), (1, 6), (5, 26), (18, 25), (9, 23), (12, 8), (9, 10), (11, 2), (12, 2), (14, 15), (10, 8), (13, 10), (20, 13), (15, 16), (5, 25), (23, 9), (20, 25), (24, 19), (21, 10), (25, 22), (25, 4), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800212", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), 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), (16, 5), (16, 4), (4, 7), (20, 14), (20, 5), (14, 16), (18, 16), (15, 17), (8, 9), (3, 3), (13, 15), (1, 5), (7, 4), (18, 5), (10, 9), (4, 0), (21, 5), (22, 2), (11, 5), (10, 0), (0, 17), (21, 2), (8, 5), (9, 0), (3, 0), (11, 12), (4, 8), (12, 9), (18, 11), (15, 11), (4, 1), (10, 3), (20, 17), (7, 19), (15, 19), (18, 0), (20, 3), (15, 14), (9, 13), (1, 10), (13, 2), (20, 6), (4, 16), (1, 0), (6, 19), (11, 7), (13, 0), (10, 19), (5, 4), (2, 13), (8, 8), (11, 4), (11, 16), (10, 13), (9, 16), (8, 13), (22, 8), (10, 12), (20, 9), (11, 18), (16, 7), (0, 13), (15, 5), (22, 12), (19, 10), (6, 0), (17, 17), (8, 2), (9, 4), (9, 7), (12, 0), (9, 17), (4, 10), (21, 7), (20, 7), (22, 7), (12, 4), (14, 0), (0, 4), (6, 16), (18, 18), (0, 16), (10, 16), (14, 11), (3, 5), (21, 11), (0, 2), (13, 8), (15, 18), (7, 6), (17, 10), (6, 18), (11, 19), (2, 11), (15, 4), (22, 5), (9, 8), (22, 15), (13, 10), (6, 13), (16, 19), (12, 15), (18, 13), (22, 14), (12, 18), (1, 8), (10, 8), (16, 18), (17, 3), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739520", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 23), (11, 5), (16, 11), (9, 25), (18, 19), (13, 19), (3, 9), (10, 13), (17, 3), (16, 3), (11, 27), (16, 10), (20, 5), (16, 5), (4, 7), (2, 22), (8, 0), (0, 15), (20, 3), (11, 4), (1, 18), (18, 25), (8, 2), (18, 0), (0, 6), (9, 21), (7, 15), (6, 15), (20, 21), (16, 12), (9, 22), (17, 19), (13, 2), (11, 20), (6, 9), (17, 5), (6, 8), (20, 0), (12, 15), (10, 0), (1, 23), (7, 25), (19, 11), (1, 27), (17, 20), (1, 13), (2, 6), (6, 24), (18, 11), (14, 3), (14, 12), (3, 27), (15, 11), (4, 27), (2, 18), (7, 7), (18, 24), (9, 23), (20, 25), (8, 18), (10, 16), (3, 14), (15, 6), (9, 4), (5, 14), (15, 9), (9, 3), (19, 15), (9, 1), (9, 5), (12, 22), (4, 22), (18, 1), (1, 17), (8, 15), (4, 24), (8, 13), (3, 12), (9, 18), (0, 10), (8, 7), (6, 14), (17, 11), (17, 10), (8, 21), (4, 15), (13, 17), (12, 0), (5, 9), (17, 23), (14, 0), (16, 26), (0, 27), (0, 26), (8, 20), (12, 9), (20, 1), (19, 0), (3, 2), (3, 6), (7, 14), (18, 3), (16, 17), (14, 16), (3, 21), (11, 22), (15, 16), (10, 3), (1, 4), (6, 11), (14, 21), (1, 16), (7, 18), (11, 10), (0, 17), (8, 16), (3, 4), (20, 8), (12, 21), (9, 7), (7, 13), (1, 7), (17, 25), (13, 23), (16, 20), (6, 20), (13, 27), (18, 9), (11, 8), (16, 19), (13, 10), (0, 8), (18, 26), (18, 5), (15, 23), (14, 1), (14, 19), (16, 21), (7, 3), (6, 12), (13, 25), (10, 1), (16, 24), (15, 4), (2, 5), (14, 8), (4, 5), (2, 25), (13, 18), (14, 6), (10, 21), (15, 19), (17, 15), (10, 5), (6, 13), (18, 13), (8, 4), (16, 25), (7, 22), (8, 8), (14, 20), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260338", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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, 6), (10, 5), (13, 13), (10, 21), (7, 17), (4, 18), (2, 3), (15, 18), (3, 12), (5, 11), (5, 19), (17, 0), (2, 5), (4, 10), (16, 19), (19, 3), (5, 8), (8, 2), (19, 12), (5, 0), (18, 14), (6, 17), (15, 12), (12, 4), (4, 8), (4, 6), (18, 11), (2, 21), (17, 13), (19, 0), (3, 17), (13, 22), (17, 8), (14, 3), (6, 1), (6, 4), (6, 6), (18, 2), (10, 10), (2, 1), (0, 19), (10, 8), (19, 9), (5, 10), (1, 12), (0, 10), (19, 1), (6, 13), (17, 5), (12, 16), (10, 2), (11, 2), (18, 10), (6, 3), (18, 4), (4, 12), (6, 5), (3, 22), (5, 15), (12, 21), (16, 14), (3, 5), (5, 13), (12, 20), (11, 13), (11, 1), (14, 14), (8, 22), (1, 0), (15, 6), (2, 11), (2, 9), (11, 18), (18, 5), (5, 18), (1, 5), (7, 11), (6, 0), (1, 1), (16, 16), (3, 16), (9, 8), (6, 18), (9, 12), (17, 21), (8, 19), (11, 14), (2, 12), (15, 9), (17, 1), (14, 13), (7, 4), (12, 15), (11, 16), (15, 5), (5, 22), (0, 13), (12, 7), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876793", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), 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), (7, 3), (7, 11), (11, 20), (15, 23), (18, 21), (6, 3), (0, 7), (14, 28), (9, 17), (18, 17), (10, 12), (0, 11), (19, 5), (1, 13), (4, 28), (12, 25), (15, 20), (12, 2), (14, 12), (14, 11), (5, 8), (2, 26), (15, 18), (19, 19), (9, 27), (12, 15), (10, 5), (3, 1), (8, 21), (13, 26), (14, 16), (6, 7), (18, 5), (4, 1), (8, 19), (5, 4), (5, 10), (10, 24), (6, 16), (1, 0), (1, 23), (19, 3), (12, 20), (11, 10), (5, 15), (1, 10), (13, 8), (15, 9), (12, 17), (3, 11), (10, 26), (9, 24), (0, 26), (1, 24), (12, 14), (19, 11), (1, 20), (0, 17), (18, 4), (11, 7), (15, 22), (16, 3), (2, 9), (17, 22), (9, 18), (11, 8), (8, 25), (8, 17), (15, 2), (1, 8), (4, 0), (10, 13), (6, 14), (3, 5), (17, 10), (3, 17), (15, 0), (0, 20), (12, 18), (2, 4), (12, 19), (17, 6), (9, 14), (2, 17), (9, 4), (5, 0), (14, 3), (4, 11), (2, 8), (18, 15), (2, 5), (14, 14), (10, 20), (6, 1), (19, 0), (3, 28), (14, 21), (2, 23), (14, 2), (8, 0), (1, 2), (19, 9), (14, 17), (5, 26), (3, 7), (13, 20), (13, 9), (6, 4), (2, 3), (19, 6), (13, 2), (16, 25), (11, 15), (14, 15), (13, 4), (11, 5), (13, 3), (7, 15), (13, 6), (0, 13), (10, 1), (0, 14), (16, 2), (17, 23), (17, 17), (7, 22), (3, 23), (2, 20), (15, 26), (17, 19), (2, 0), (12, 16), (1, 15), (16, 6), (0, 21), (18, 13), (17, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953744", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), 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, 19), (8, 18), (17, 23), (19, 1), (22, 20), (17, 22), (8, 6), (15, 24), (6, 10), (20, 22), (22, 14), (16, 9), (14, 2), (5, 16), (7, 19), (23, 5), (11, 20), (11, 13), (6, 16), (17, 9), (16, 7), (6, 17), (21, 17), (22, 12), (13, 22), (0, 12), (18, 8), (4, 4), (7, 14), (17, 4), (18, 3), (5, 10), (1, 0), (7, 1), (24, 18), (0, 4), (17, 17), (2, 11), (7, 6), (12, 1), (20, 1), (21, 3), (12, 14), (8, 8), (8, 0), (12, 17), (2, 20), (21, 9), (9, 22), (16, 24), (7, 17), (14, 23), (21, 22), (10, 11), (9, 17), (2, 15), (12, 20), (22, 6), (0, 9), (2, 5), (20, 3), (4, 14), (20, 9), (3, 12), (20, 16), (4, 12), (16, 21), (2, 17), (15, 9), (5, 14), (3, 19), (20, 24), (2, 1), (5, 20), (17, 2), (3, 21), (5, 5), (7, 23), (11, 10), (14, 4), (21, 1), (7, 15), (24, 4), (16, 17), (4, 23), (10, 3), (4, 16), (20, 6), (0, 19), (13, 14), (20, 21), (2, 13), (15, 2), (11, 12), (23, 10), (4, 2), (17, 18), (13, 19), (2, 0), (8, 20), (24, 20), (1, 12), (11, 9), (7, 24), (23, 16), (9, 23), (18, 23), (9, 9), (23, 15), (1, 5), (22, 10), (11, 15), (16, 18), (17, 14), (23, 22), (7, 9), (8, 22), (23, 19), (3, 2), (14, 14), (19, 14), (12, 11), (14, 11), (22, 23), (20, 0), (22, 22), (6, 2), (5, 22), (5, 6), (1, 18), (21, 24), (10, 7), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366546", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), 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), (1, 12), (25, 16), (24, 13), (21, 3), (7, 7), (8, 2), (14, 8), (21, 21), (15, 6), (10, 6), (2, 19), (1, 8), (7, 19), (27, 9), (2, 14), (25, 12), (25, 15), (3, 18), (20, 3), (27, 2), (19, 4), (5, 9), (18, 6), (15, 2), (24, 19), (4, 22), (18, 22), (18, 2), (9, 4), (19, 5), (3, 3), (21, 14), (22, 6), (3, 17), (3, 16), (21, 10), (22, 10), (7, 5), (10, 15), (20, 14), (21, 15), (11, 17), (15, 10), (17, 21), (26, 19), (14, 2), (22, 15), (4, 21), (16, 13), (10, 8), (4, 20), (17, 11), (23, 16), (7, 12), (26, 12), (12, 0), (1, 16), (15, 1), (19, 13), (6, 17), (16, 1), (24, 9), (27, 5), (16, 19), (0, 20), (10, 1), (6, 19), (13, 22), (16, 22), (4, 3), (25, 6), (11, 1), (10, 20), (15, 17), (2, 5), (16, 11), (24, 14), (25, 0), (23, 20), (12, 13), (21, 12), (2, 15), (14, 14), (17, 14), (19, 6), (20, 9), (13, 7), (24, 23), (19, 10), (3, 4), (17, 0), (7, 16), (13, 13), (12, 19), (12, 5), (20, 0), (21, 9), (6, 1), (6, 5), (3, 11), (10, 13), (11, 3), (25, 2), (17, 16), (14, 0), (16, 21), (12, 15), (18, 11), (23, 21), (18, 15), (20, 12), (22, 11), (17, 1), (19, 20), (27, 1), (22, 4), (15, 15), (9, 13), (18, 19), (12, 20), (18, 10), (17, 10), (26, 18), (14, 7), (25, 21), (0, 17), (10, 18), (14, 10), (27, 4), (15, 7), (6, 6), (14, 17), (27, 0), (2, 1), (4, 18), (26, 17), (12, 11), (15, 8), (7, 20), (5, 5), (1, 18), (27, 13), (20, 5), (0, 22), (7, 6), (8, 4), (12, 3), (1, 23), (16, 18), (14, 20), (17, 23), (20, 11), (23, 23), (16, 5), (1, 0), (27, 20), (24, 5), (2, 8), (18, 23), (10, 10), (21, 7), (22, 19), (16, 4), (7, 22), (24, 22), (5, 14), (5, 13), (23, 17), (10, 23), (24, 6), (10, 3), (24, 1), (3, 12), (9, 1), (21, 1), (19, 2), (2, 10), (8, 16), (23, 14), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912120", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), 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), (13, 4), (19, 3), (20, 17), (0, 7), (8, 15), (3, 5), (9, 14), (15, 5), (9, 17), (9, 3), (0, 20), (20, 13), (11, 6), (8, 4), (17, 21), (13, 2), (21, 17), (9, 10), (16, 15), (19, 9), (4, 21), (7, 6), (1, 15), (3, 20), (4, 1), (21, 15), (18, 5), (22, 8), (2, 13), (3, 13), (0, 3), (5, 21), (16, 7), (11, 21), (8, 17), (15, 13), (11, 15), (13, 7), (11, 8), (15, 17), (12, 3), (4, 2), (7, 1), (14, 8), (14, 7), (8, 1), (10, 3), (3, 1), (2, 5), (17, 16), (13, 12), (11, 9), (12, 0), (18, 1), (3, 6), (3, 8), (11, 12), (20, 7), (1, 19), (6, 19), (4, 0), (0, 4), (6, 2), (14, 19), (15, 4), (1, 5), (10, 15), (16, 4), (22, 13), (18, 4), (2, 3), (17, 13), (21, 0), (12, 21), (9, 6), (14, 10), (9, 7), (1, 9), (12, 10), (7, 18), (16, 18), (1, 16), (6, 7), (5, 3), (9, 2), (15, 1), (19, 17), (10, 2), (7, 21), (22, 3), (19, 12), (19, 4), (10, 17), (8, 0), (5, 5), (16, 1), (7, 3), (18, 17), (5, 17), (2, 10), (14, 12), (11, 1), (0, 2), (14, 9), (14, 0), (16, 14), (12, 16), (13, 0), (13, 16), (21, 3), (15, 7), (20, 14), (18, 20), (3, 0), (8, 10), (6, 3), (9, 19), (6, 12), (6, 4), (6, 6), (12, 11), (4, 18), (1, 10), (2, 4), (21, 20), (5, 10), (20, 2), (11, 7), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390240", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), 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), (7, 7), (17, 18), (10, 2), (12, 9), (14, 13), (9, 11), (12, 5), (14, 4), (3, 9), (10, 8), (4, 12), (10, 1), (0, 21), (14, 21), (19, 12), (8, 14), (7, 5), (2, 3), (17, 10), (16, 22), (14, 18), (10, 11), (6, 17), (0, 12), (7, 13), (13, 25), (12, 25), (8, 10), (13, 10), (19, 23), (10, 24), (11, 23), (18, 10), (16, 7), (11, 9), (17, 20), (12, 7), (13, 5), (8, 19), (8, 22), (3, 25), (6, 5), (19, 16), (12, 6), (16, 9), (14, 22), (7, 22), (19, 18), (15, 19), (17, 1), (4, 3), (3, 2), (19, 5), (5, 14), (1, 8), (11, 6), (13, 24), (12, 13), (7, 8), (9, 18), (5, 13), (2, 21), (18, 15), (19, 15), (14, 7), (5, 25), (5, 6), (18, 23), (3, 17), (8, 7), (8, 6), (19, 11), (18, 17), (13, 6), (8, 13), (6, 6), (17, 22), (19, 4), (12, 24), (9, 0), (7, 9), (5, 18), (2, 18), (16, 11), (18, 25), (4, 23), (2, 16), (19, 1), (18, 0), (13, 17), (2, 4), (3, 16), (2, 23), (5, 0), (13, 18), (9, 23), (17, 21), (17, 16), (13, 4), (5, 19), (15, 14), (1, 12), (11, 1), (12, 2), (7, 20), (18, 20), (7, 14), (19, 8), (16, 16), (5, 1), (11, 14), (9, 17), (7, 11), (18, 14), (14, 14), (4, 21), (10, 9), (14, 3), (14, 17), (2, 2), (0, 15), (1, 6), (3, 14), (11, 21), (4, 10), (17, 8), (13, 23), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267621", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), 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), (22, 13), (6, 9), (25, 4), (14, 19), (10, 18), (14, 7), (22, 0), (20, 16), (13, 12), (15, 15), (5, 0), (17, 11), (9, 19), (25, 10), (17, 2), (15, 6), (7, 22), (11, 8), (25, 7), (18, 0), (22, 4), (24, 0), (1, 6), (13, 23), (24, 15), (14, 12), (4, 0), (25, 6), (26, 6), (15, 16), (10, 4), (14, 20), (10, 22), (24, 16), (14, 8), (21, 21), (26, 2), (11, 22), (4, 12), (15, 4), (1, 18), (9, 12), (20, 19), (25, 23), (17, 18), (2, 22), (20, 6), (22, 21), (6, 7), (1, 20), (7, 8), (16, 23), (1, 23), (20, 1), (8, 13), (7, 14), (0, 23), (2, 5), (21, 0), (4, 22), (17, 13), (6, 4), (13, 17), (19, 21), (2, 12), (10, 3), (0, 11), (0, 15), (3, 2), (16, 15), (9, 2), (26, 16), (26, 1), (25, 21), (2, 15), (25, 8), (25, 11), (13, 2), (17, 16), (2, 10), (23, 5), (4, 2), (8, 20), (19, 13), (6, 20), (22, 1), (20, 13), (12, 12), (9, 23), (9, 10), (16, 1), (15, 13), (23, 16), (10, 12), (17, 14), (23, 8), (20, 3), (12, 8), (1, 11), (5, 4), (11, 3), (8, 9), (1, 12), (7, 11), (23, 11), (1, 22), (14, 9), (6, 1), (15, 12), (4, 20), (12, 3), (8, 22), (13, 3), (18, 23), (5, 9), (24, 23), (11, 16), (21, 20), (0, 21), (16, 16), (16, 11), (22, 2), (22, 12), (18, 14), (11, 12), (19, 7), (2, 8), (6, 15), (26, 18), (19, 23), (14, 23), (25, 14), (21, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701452", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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), (18, 20), (21, 0), (5, 15), (8, 14), (14, 1), (5, 25), (4, 13), (1, 8), (12, 10), (3, 12), (3, 11), (6, 1), (12, 19), (3, 0), (10, 24), (7, 20), (8, 21), (9, 21), (1, 7), (4, 8), (6, 22), (17, 12), (5, 6), (15, 13), (17, 0), (18, 8), (2, 23), (4, 1), (4, 12), (0, 12), (14, 5), (7, 21), (8, 6), (7, 22), (13, 6), (16, 22), (7, 6), (3, 24), (7, 8), (20, 2), (8, 16), (5, 0), (20, 7), (21, 17), (14, 4), (13, 2), (0, 7), (0, 16), (2, 16), (18, 23), (14, 21), (16, 20), (15, 18), (9, 11), (19, 1), (14, 15), (0, 24), (17, 20), (4, 19), (3, 4), (13, 18), (1, 13), (16, 7), (18, 14), (11, 14), (17, 23), (13, 1), (13, 12), (3, 19), (11, 24), (16, 2), (5, 14), (20, 16), (17, 7), (13, 22), (14, 7), (2, 5), (19, 7), (12, 11), (18, 0), (11, 15), (9, 19), (16, 8), (20, 19), (19, 18), (17, 3), (8, 2), (6, 17), (4, 16), (13, 3), (12, 3), (16, 5), (12, 22), (3, 20), (10, 22), (11, 23), (19, 12), (11, 0), (18, 2), (7, 24), (5, 19), (6, 11), (12, 26), (8, 5), (9, 8), (11, 21), (2, 0), (6, 18), (13, 19), (19, 24), (1, 25), (16, 23), (11, 19), (10, 23), (9, 16), (8, 13), (6, 9), (20, 5), (0, 9), (0, 2), (8, 24), (0, 26), (8, 12), (4, 2), (13, 25), (11, 7), (1, 23), (14, 6), (2, 13), (19, 20), (6, 0), (14, 24), (20, 25), (4, 18), (17, 1), (6, 12), (19, 2), (21, 4), (13, 15), (11, 6), (1, 6), (19, 25), (15, 24), (0, 20), (2, 18), (20, 24), (15, 15), (18, 12), (11, 22), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349632", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 17), (12, 0), (20, 19), (22, 27), (14, 10), (1, 9), (12, 23), (2, 21), (17, 1), (24, 19), (10, 21), (5, 12), (23, 19), (7, 4), (2, 14), (0, 25), (1, 11), (9, 1), (7, 22), (1, 0), (19, 8), (13, 23), (19, 26), (12, 10), (5, 22), (6, 5), (24, 18), (3, 24), (2, 1), (10, 9), (21, 0), (6, 14), (10, 15), (21, 25), (4, 7), (8, 2), (21, 28), (16, 16), (16, 4), (19, 0), (9, 19), (2, 5), (21, 7), (21, 11), (2, 28), (5, 17), (25, 13), (24, 26), (7, 25), (9, 5), (4, 22), (19, 13), (4, 26), (21, 6), (1, 26), (20, 12), (12, 12), (0, 17), (9, 26), (9, 10), (3, 13), (9, 22), (16, 19), (1, 27), (6, 4), (15, 0), (12, 14), (2, 15), (22, 3), (21, 5), (16, 0), (14, 12), (13, 24), (7, 16), (9, 16), (1, 5), (1, 14), (5, 9), (18, 14), (15, 27), (8, 7), (3, 28), (5, 11), (19, 12), (5, 15), (1, 19), (4, 6), (6, 28), (13, 20), (7, 12), (21, 4), (13, 4), (6, 21), (16, 1), (17, 27), (22, 23), (13, 7), (9, 12), (22, 7), (12, 7), (6, 15), (11, 8), (18, 8), (10, 16), (22, 28), (8, 11), (20, 0), (2, 26), (7, 9), (10, 5), (9, 18), (16, 14), (22, 8), (19, 28), (8, 10), (17, 14), (18, 24), (12, 17), (6, 9), (9, 6), (6, 3), (18, 13), (13, 2), (10, 4), (12, 2), (24, 3), (11, 9), (6, 20), (11, 6), (13, 25), (23, 0), (1, 10), (3, 22), (22, 2), (13, 17), (17, 9), (22, 10), (8, 13), (15, 11), (20, 17), (23, 10), (8, 21), (4, 23), (22, 17), (10, 14), (16, 13), (9, 21), (10, 8), (4, 27), (7, 13), (7, 15), (11, 23), (1, 2), (16, 9), (9, 8), (5, 16), (25, 19), (18, 20), (6, 16), (13, 26), (3, 15), (0, 22), (23, 20), (23, 15), (9, 27), (17, 18), (7, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "773875", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 26), (8, 3), (5, 8), (6, 6), (10, 2), (15, 3), (13, 25), (21, 16), (9, 4), (4, 9), (17, 20), (13, 12), (6, 23), (3, 26), (12, 16), (16, 17), (8, 26), (9, 17), (1, 24), (18, 6), (13, 4), (17, 26), (5, 12), (17, 23), (16, 10), (20, 17), (13, 20), (9, 19), (11, 26), (1, 25), (21, 2), (15, 12), (1, 12), (14, 14), (22, 6), (20, 5), (5, 25), (22, 15), (9, 13), (7, 2), (7, 22), (3, 18), (2, 25), (18, 5), (14, 5), (22, 4), (5, 14), (13, 19), (2, 8), (16, 5), (14, 9), (0, 18), (2, 6), (15, 5), (16, 9), (17, 4), (7, 3), (6, 1), (17, 0), (19, 22), (3, 20), (17, 7), (18, 16), (14, 0), (6, 11), (17, 13), (0, 4), (3, 10), (2, 26), (4, 19), (20, 6), (16, 18), (14, 23), (11, 3), (20, 13), (19, 9), (12, 4), (5, 23), (14, 21), (18, 21), (17, 22), (7, 8), (22, 13), (15, 18), (0, 2), (6, 24), (16, 13), (7, 21), (6, 16), (7, 7), (6, 5), (18, 17), (15, 2), (18, 15), (8, 9), (19, 5), (1, 16), (12, 25), (11, 15), (11, 16), (7, 0), (9, 8), (7, 6), (11, 22), (3, 2), (5, 15), (12, 27), (7, 18), (12, 7), (4, 6), (22, 11), (1, 23), (10, 0), (14, 13), (5, 1), (2, 12), (4, 1), (5, 20), (14, 6), (20, 9), (22, 17), (6, 21), (2, 2), (16, 25), (9, 25), (7, 5), (5, 7), (17, 3), (20, 20), (14, 19), (10, 21), (21, 26), (19, 11), (18, 13), (7, 15), (9, 11), (12, 0), (13, 7), (19, 20), (5, 27), (21, 20), (3, 27), (3, 25), (2, 15), (3, 0), (21, 25), (20, 14), (19, 15), (22, 14), (5, 4), (16, 20), (12, 23), (21, 18), (16, 14), (2, 17), (0, 12), (4, 2), (10, 12), (0, 11), (19, 0), (19, 18), (21, 19), (8, 10), (4, 23), (2, 7), (14, 12), (1, 19), (3, 3), (13, 11), (22, 5), (19, 1), (4, 17), (14, 11), (2, 1), (10, 8), (20, 7), (1, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759720", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 9), (16, 9), (24, 22), (11, 19), (9, 8), (5, 21), (21, 18), (21, 14), (10, 11), (3, 22), (16, 22), (17, 18), (20, 2), (6, 15), (10, 14), (0, 5), (2, 17), (2, 10), (17, 9), (10, 15), (12, 22), (25, 1), (9, 15), (11, 12), (19, 9), (23, 5), (13, 23), (5, 6), (9, 10), (1, 3), (10, 1), (24, 3), (5, 26), (19, 7), (22, 3), (10, 13), (11, 13), (11, 10), (10, 16), (0, 20), (18, 15), (15, 4), (17, 8), (5, 12), (24, 17), (0, 25), (4, 23), (23, 10), (14, 11), (7, 6), (21, 25), (1, 10), (12, 18), (24, 0), (18, 26), (18, 1), (17, 24), (16, 16), (16, 7), (3, 19), (11, 14), (24, 20), (14, 21), (20, 9), (16, 12), (11, 8), (3, 25), (12, 16), (22, 17), (13, 21), (11, 0), (8, 10), (18, 19), (10, 26), (23, 9), (22, 12), (16, 4), (20, 14), (5, 17), (3, 24), (6, 18), (3, 4), (19, 26), (7, 23), (8, 9), (15, 9), (15, 19), (13, 12), (20, 18), (23, 13), (10, 21), (8, 24), (22, 14), (11, 18), (4, 0), (25, 8), (3, 0), (0, 17), (12, 3), (18, 24), (15, 20), (13, 5), (23, 21), (11, 24), (8, 6), (14, 23), (9, 25), (21, 12), (9, 19), (12, 9), (1, 11), (25, 7), (23, 16), (16, 13), (1, 12), (1, 13), (14, 10), (1, 25), (6, 25), (20, 1), (22, 10), (13, 17), (16, 10), (6, 7), (8, 13), (7, 9), (3, 14), (18, 3), (6, 26), (21, 11), (22, 9), (1, 21), (18, 9), (16, 24), (20, 7), (8, 8), (22, 11), (21, 16), (13, 8), (15, 26), (12, 19), (17, 1), (17, 22), (21, 5), (14, 20), (1, 16), (24, 26), (6, 0), (24, 7), (13, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900032", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 5), (18, 9), (25, 20), (18, 8), (20, 8), (23, 7), (15, 22), (25, 0), (14, 12), (0, 8), (12, 13), (2, 0), (0, 2), (14, 15), (13, 2), (22, 19), (5, 13), (16, 4), (21, 19), (9, 20), (1, 17), (3, 0), (12, 17), (19, 14), (22, 12), (12, 14), (1, 19), (17, 15), (6, 11), (10, 10), (1, 8), (19, 7), (14, 7), (14, 5), (17, 14), (8, 4), (4, 6), (22, 2), (2, 23), (3, 2), (19, 8), (11, 16), (18, 15), (6, 0), (7, 18), (16, 13), (11, 18), (7, 1), (4, 8), (20, 7), (16, 7), (21, 8), (25, 18), (18, 13), (2, 22), (12, 20), (3, 3), (0, 10), (9, 8), (5, 14), (20, 13), (3, 22), (21, 9), (10, 5), (20, 22), (1, 7), (17, 6), (9, 7), (12, 11), (24, 20), (2, 16), (4, 17), (12, 19), (19, 5), (13, 8), (23, 10), (11, 20), (9, 19), (17, 0), (14, 3), (24, 18), (25, 4), (8, 12), (22, 18), (18, 11), (17, 12), (16, 3), (5, 8), (7, 21), (6, 7), (10, 8), (7, 13), (3, 13), (6, 5), (6, 10), (4, 22), (4, 0), (13, 19), (10, 20), (0, 17), (18, 22), (2, 2), (24, 2), (13, 22), (11, 13), (15, 21), (4, 23), (0, 20), (9, 14), (5, 21), (6, 8), (1, 2), (25, 6), (14, 0), (25, 14), (17, 13), (16, 21), (14, 18), (15, 9), (25, 9), (2, 14), (13, 15), (6, 6), (1, 23), (14, 16), (24, 22), (20, 18), (5, 6), (8, 7), (18, 14), (4, 18), (7, 7), (15, 19), (17, 17), (24, 9), (3, 19), (22, 22), (5, 15), (21, 11), (25, 22), (20, 16), (8, 20), (6, 14), (2, 5), (18, 5), (6, 21), (10, 2), (3, 9), (20, 11), (5, 1), (13, 5), (9, 21), (8, 17), (16, 17), (12, 23), (8, 22), (6, 23), (0, 7), (15, 3), (8, 13), (20, 12), (4, 20), (2, 7), (3, 4), (19, 9), (18, 2), (19, 22), (22, 1), (7, 4), (5, 16), (12, 5), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "762396", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 9), (20, 3), (0, 11), (3, 13), (10, 3), (2, 11), (24, 10), (0, 3), (19, 20), (16, 2), (11, 1), (6, 7), (13, 0), (17, 11), (10, 2), (2, 7), (12, 11), (17, 18), (14, 5), (25, 5), (22, 9), (14, 15), (4, 13), (22, 8), (9, 14), (17, 13), (8, 8), (22, 14), (24, 13), (6, 14), (6, 0), (0, 15), (4, 5), (18, 5), (16, 19), (21, 12), (24, 7), (3, 4), (3, 3), (20, 12), (4, 17), (19, 3), (3, 2), (3, 5), (22, 6), (9, 1), (5, 18), (17, 1), (15, 9), (0, 9), (4, 15), (0, 13), (25, 19), (22, 18), (4, 11), (21, 18), (7, 4), (11, 16), (23, 14), (22, 1), (14, 16), (13, 12), (4, 7), (7, 0), (10, 14), (16, 18), (7, 15), (10, 18), (13, 10), (22, 19), (1, 14), (3, 11), (25, 7), (8, 17), (5, 4), (24, 0), (23, 6), (2, 20), (3, 19), (2, 16), (17, 9), (24, 12), (14, 13), (21, 20), (19, 19), (11, 9), (11, 18), (4, 8), (11, 14), (7, 17), (4, 14), (8, 9), (3, 10), (16, 3), (4, 18), (11, 6), (24, 18), (9, 3), (2, 1), (1, 19), (19, 11), (1, 15), (22, 15), (14, 4), (12, 3), (18, 4), (5, 14), (15, 6), (7, 14), (6, 16), (16, 6), (11, 0), (8, 4), (17, 16), (25, 16), (6, 2), (24, 16), (2, 6), (15, 20), (25, 13), (1, 2), (14, 18), (1, 1), (6, 20), (24, 3), (21, 16), (12, 9), (20, 14), (24, 14), (6, 8), (21, 9), (21, 3), (13, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606662", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (8, 8), (23, 6), (23, 1), (23, 16), (11, 17), (1, 3), (3, 2), (16, 22), (21, 12), (20, 12), (8, 16), (7, 24), (10, 13), (1, 0), (0, 7), (4, 10), (7, 27), (2, 5), (6, 9), (17, 5), (1, 9), (22, 24), (4, 17), (22, 17), (15, 25), (22, 25), (9, 2), (5, 25), (18, 10), (19, 6), (20, 9), (6, 21), (6, 4), (7, 7), (1, 16), (15, 28), (7, 6), (11, 5), (21, 4), (18, 27), (19, 4), (8, 7), (18, 0), (19, 1), (12, 5), (8, 5), (12, 24), (12, 28), (19, 2), (0, 20), (10, 5), (18, 24), (4, 20), (8, 9), (11, 18), (21, 18), (14, 22), (15, 1), (20, 13), (5, 22), (18, 16), (0, 3), (22, 23), (1, 20), (6, 28), (12, 12), (9, 24), (15, 23), (15, 10), (5, 24), (9, 3), (23, 3), (20, 3), (17, 2), (1, 19), (7, 4), (9, 0), (20, 20), (4, 7), (6, 11), (22, 15), (17, 25), (19, 24), (17, 7), (19, 0), (4, 15), (6, 10), (2, 26), (4, 1), (13, 27), (20, 11), (20, 25), (17, 27), (1, 10), (9, 23), (6, 17), (3, 21), (6, 12), (12, 11), (8, 3), (4, 8), (8, 12), (6, 20), (0, 24), (19, 23), (17, 21), (15, 27), (13, 5), (10, 8), (1, 17), (20, 6), (15, 24), (13, 20), (5, 0), (2, 17), (11, 22), (2, 21), (19, 10), (11, 7), (21, 11), (11, 19), (12, 9), (5, 2), (12, 19), (13, 18), (23, 11), (18, 8), (13, 2), (15, 18), (7, 20), (10, 4), (8, 21), (17, 18), (6, 22), (2, 6), (18, 20), (11, 20), (17, 24), (13, 25), (0, 27), (22, 7), (20, 8), (2, 11), (13, 15), (19, 8), (2, 24), (1, 21), (21, 9), (21, 22), (13, 1), (16, 12), (15, 15), (8, 6), (8, 19), (9, 8), (3, 7), (20, 19), (18, 25), (2, 28), (5, 28), (21, 20), (4, 6), (3, 8), (6, 15), (22, 28), (10, 10), (15, 2), (4, 18), (22, 0), (21, 10), (19, 13), (10, 0), (16, 27), (9, 12), (16, 18), (14, 2), (5, 9), (8, 20), (16, 4), (14, 8), (22, 9), (6, 25), (16, 3), (12, 18), (18, 17), (8, 24), (11, 2), (16, 10), (17, 0), (11, 9), (23, 13), (19, 3), (2, 10), (0, 11), (0, 19), (2, 15), (2, 13), (22, 6), (7, 16), (22, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926316", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), 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), (17, 15), (13, 2), (10, 9), (5, 9), (3, 18), (15, 19), (17, 21), (4, 0), (6, 23), (6, 5), (6, 19), (17, 24), (18, 24), (23, 21), (10, 7), (0, 18), (2, 22), (8, 1), (12, 12), (12, 22), (18, 6), (21, 1), (21, 6), (18, 3), (21, 16), (0, 20), (5, 16), (14, 6), (9, 17), (9, 21), (9, 24), (6, 25), (18, 20), (16, 8), (12, 7), (20, 25), (3, 23), (12, 6), (10, 4), (13, 22), (11, 25), (12, 8), (20, 10), (9, 22), (13, 12), (13, 1), (7, 13), (20, 15), (10, 2), (18, 11), (14, 25), (19, 6), (20, 3), (20, 17), (20, 23), (1, 5), (3, 26), (5, 11), (6, 26), (18, 7), (2, 24), (13, 6), (15, 4), (6, 6), (2, 13), (18, 16), (9, 14), (7, 3), (4, 2), (7, 18), (5, 12), (14, 12), (5, 1), (6, 20), (15, 20), (16, 11), (10, 25), (1, 24), (5, 15), (17, 11), (4, 11), (7, 23), (6, 0), (12, 21), (8, 6), (16, 6), (9, 16), (11, 17), (16, 19), (23, 23), (23, 17), (7, 15), (4, 15), (17, 13), (24, 13), (0, 10), (23, 22), (7, 19), (15, 16), (3, 21), (21, 7), (23, 9), (19, 2), (16, 12), (13, 15), (14, 16), (0, 25), (1, 19), (9, 25), (13, 9), (16, 20), (17, 16), (11, 24), (21, 13), (14, 19), (14, 9), (23, 24), (16, 16), (16, 21), (18, 10), (0, 13), (13, 0), (1, 18), (12, 25), (0, 8), (3, 11), (8, 21), (15, 6), (4, 20), (10, 23), (18, 14), (8, 4), (11, 7), (2, 8), (21, 10), (9, 18), (10, 15), (23, 7), (18, 9), (8, 8), (22, 1), (20, 11), (0, 14), (5, 10), (14, 13), (8, 18), (23, 13), (16, 1), (12, 0), (5, 17), (14, 7), (9, 2), (4, 19), (23, 0), (10, 22), (3, 17), (21, 21), (14, 21), (5, 14), (22, 2), (12, 3), (22, 6), (22, 4), (17, 20), (13, 23), (19, 15), (0, 7), (3, 13), (7, 16), (24, 0), (6, 2), (4, 18), (22, 15), (1, 23), (3, 6), (8, 20), (16, 18), (6, 15), (17, 22), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3135", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 14), (22, 12), (12, 9), (13, 2), (20, 12), (20, 8), (0, 25), (5, 21), (5, 18), (14, 15), (13, 1), (3, 10), (10, 5), (21, 21), (20, 17), (8, 11), (8, 9), (19, 22), (6, 1), (20, 19), (10, 8), (19, 0), (18, 7), (3, 23), (13, 10), (18, 20), (19, 20), (18, 3), (4, 7), (11, 8), (7, 9), (20, 21), (18, 13), (14, 25), (18, 16), (16, 2), (22, 11), (19, 7), (15, 1), (10, 11), (11, 13), (3, 12), (9, 10), (13, 25), (7, 8), (16, 16), (17, 24), (2, 23), (2, 22), (21, 5), (12, 1), (9, 15), (16, 15), (20, 5), (5, 2), (14, 2), (3, 7), (6, 11), (18, 22), (20, 2), (4, 19), (5, 14), (13, 13), (19, 5), (2, 6), (17, 18), (0, 2), (1, 6), (16, 20), (14, 4), (11, 9), (8, 8), (22, 10), (14, 8), (0, 11), (14, 6), (15, 2), (18, 14), (2, 14), (4, 5), (1, 18), (3, 15), (3, 5), (19, 17), (16, 3), (11, 22), (6, 17), (6, 15), (19, 25), (10, 6), (4, 14), (15, 17), (5, 13), (18, 23), (22, 6), (12, 14), (16, 19), (3, 17), (6, 16), (2, 2), (4, 23), (16, 22), (17, 16), (7, 25), (21, 1), (2, 1), (18, 0), (17, 11), (8, 5), (17, 21), (16, 11), (12, 6), (22, 16), (4, 2), (6, 12), (14, 16), (7, 20), (13, 4), (13, 20), (22, 7), (8, 14), (6, 14), (10, 0), (21, 6), (2, 16), (8, 23), (22, 8), (21, 9), (9, 5), (20, 9), (8, 22), (16, 8), (1, 2), (11, 7), (0, 12), (7, 21), (6, 7), (3, 1), (9, 25), (15, 18), (3, 13), (15, 11), (20, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632132", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 11), (5, 21), (13, 14), (13, 22), (20, 2), (28, 10), (7, 12), (24, 2), (7, 0), (4, 7), (6, 18), (11, 0), (15, 16), (28, 13), (18, 18), (17, 16), (0, 19), (14, 6), (21, 24), (18, 13), (10, 3), (9, 5), (8, 16), (4, 10), (11, 1), (11, 24), (7, 20), (3, 2), (13, 21), (23, 21), (4, 1), (13, 25), (0, 23), (2, 12), (27, 22), (15, 12), (16, 12), (23, 19), (25, 16), (21, 9), (12, 12), (19, 1), (2, 11), (14, 11), (11, 22), (5, 2), (23, 25), (11, 11), (9, 10), (7, 15), (6, 17), (5, 24), (13, 17), (18, 2), (28, 1), (19, 7), (7, 18), (18, 4), (27, 18), (10, 5), (11, 3), (28, 0), (17, 15), (26, 7), (1, 16), (20, 0), (13, 13), (6, 4), (6, 20), (18, 14), (1, 24), (10, 0), (0, 4), (6, 23), (27, 23), (16, 11), (20, 7), (26, 9), (15, 10), (9, 9), (9, 16), (16, 13), (3, 4), (15, 9), (28, 18), (5, 20), (20, 13), (11, 12), (5, 12), (19, 14), (19, 5), (5, 18), (5, 6), (24, 22), (11, 13), (15, 0), (11, 6), (4, 11), (24, 10), (27, 17), (20, 18), (6, 6), (2, 15), (0, 25), (21, 14), (14, 25), (7, 7), (14, 8), (8, 5), (19, 16), (11, 21), (22, 21), (14, 9), (19, 10), (25, 10), (11, 4), (12, 13), (16, 14), (25, 24), (26, 4), (26, 25), (9, 14), (4, 23), (6, 15), (26, 6), (23, 4), (8, 24), (11, 23), (12, 15), (14, 22), (4, 16), (5, 1), (4, 13), (0, 17), (24, 0), (9, 8), (18, 19), (21, 5), (27, 7), (12, 0), (7, 14), (28, 14), (15, 20), (4, 8), (20, 17), (12, 25), (26, 21), (5, 22), (15, 21), (17, 3), (8, 17), (15, 22), (14, 13), (7, 1), (21, 2), (8, 3), (23, 10), (13, 6), (24, 16), (17, 2), (23, 23), (20, 23), (20, 15), (13, 8), (17, 25), (5, 8), (23, 15), (7, 4), (7, 22), (22, 3), (9, 11), (1, 25), (2, 14), (15, 3), (20, 16), (18, 23), (16, 5), (28, 7), (17, 24), (28, 5), (11, 17), (4, 15), (20, 22), (19, 21), (12, 2), (18, 6), (6, 13), (20, 12), (23, 18), (21, 22), (12, 8), (2, 2), (5, 14), (27, 4), (23, 6), (20, 25), (26, 17), (23, 24), (16, 19), (3, 14), (16, 23), (20, 5), (14, 16), (10, 22), (10, 1), (24, 8), (18, 25), (27, 13), (17, 17), (1, 7), (3, 0), (1, 18), (16, 6), (14, 12), (28, 2), (23, 12), (15, 18), (19, 24), (25, 17), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870912", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 8), (3, 9), (20, 11), (13, 13), (12, 19), (7, 15), (24, 22), (8, 12), (19, 6), (27, 17), (28, 20), (26, 13), (6, 17), (3, 3), (24, 21), (24, 2), (23, 18), (9, 16), (7, 25), (12, 14), (19, 13), (6, 1), (11, 14), (28, 10), (5, 22), (21, 25), (24, 16), (11, 5), (8, 25), (7, 5), (27, 25), (21, 10), (6, 4), (17, 24), (22, 24), (17, 15), (28, 3), (12, 1), (26, 15), (15, 3), (16, 3), (11, 7), (11, 11), (13, 17), (3, 12), (13, 4), (9, 11), (11, 18), (2, 21), (17, 22), (0, 17), (6, 19), (2, 12), (0, 6), (3, 21), (11, 0), (13, 10), (4, 8), (23, 15), (4, 22), (16, 14), (7, 6), (28, 14), (17, 12), (16, 15), (24, 25), (26, 2), (17, 10), (15, 14), (16, 9), (9, 6), (27, 11), (20, 14), (11, 19), (2, 3), (18, 4), (8, 13), (22, 18), (20, 8), (6, 3), (20, 7), (10, 20), (22, 22), (26, 3), (0, 25), (5, 14), (26, 22), (16, 25), (28, 9), (21, 0), (18, 20), (6, 21), (26, 25), (10, 2), (3, 7), (21, 3), (1, 25), (2, 11), (2, 22), (26, 4), (5, 5), (14, 0), (8, 9), (26, 19), (25, 25), (22, 25), (27, 14), (25, 4), (9, 19), (14, 17), (14, 21), (4, 12), (7, 23), (20, 20), (1, 11), (5, 7), (22, 1), (8, 1), (17, 9), (13, 9), (18, 11), (27, 8), (0, 12), (23, 4), (21, 6), (1, 5), (19, 5), (23, 14), (1, 3), (13, 6), (14, 18), (28, 1), (16, 5), (19, 21), (16, 7), (20, 10), (10, 3), (22, 0), (9, 10), (17, 11), (21, 5), (25, 0), (19, 15), (9, 15), (8, 2), (8, 23), (25, 1), (10, 7), (5, 9), (5, 20), (6, 22), (20, 3), (0, 16), (20, 15), (2, 1), (17, 23), (5, 12), (3, 13), (20, 17), (6, 23), (17, 21), (12, 15), (15, 23), (21, 19), (22, 6), (24, 18), (24, 13), (2, 5), (4, 14), (18, 13), (28, 16), (22, 17), (4, 3), (20, 13), (11, 25), (21, 22), (11, 4), (0, 10), (25, 10), (6, 6), (2, 23), (16, 12), (26, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "745624", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 23), (12, 8), (19, 22), (22, 20), (9, 18), (20, 7), (21, 8), (19, 23), (2, 6), (4, 21), (14, 6), (10, 17), (9, 16), (8, 19), (7, 6), (24, 5), (0, 18), (21, 17), (24, 19), (20, 25), (4, 24), (5, 11), (23, 9), (27, 9), (10, 14), (24, 22), (28, 19), (6, 17), (16, 16), (24, 4), (16, 1), (20, 4), (3, 6), (0, 21), (13, 23), (15, 18), (19, 25), (14, 23), (1, 22), (23, 13), (11, 18), (5, 2), (24, 0), (13, 11), (17, 6), (10, 22), (7, 13), (9, 24), (10, 4), (23, 5), (12, 1), (5, 22), (8, 20), (8, 10), (6, 21), (9, 6), (2, 2), (24, 25), (19, 14), (2, 18), (18, 5), (13, 9), (25, 3), (5, 4), (23, 24), (26, 14), (27, 10), (23, 10), (17, 16), (22, 5), (19, 20), (21, 11), (4, 10), (25, 4), (6, 18), (15, 22), (26, 21), (18, 19), (14, 18), (15, 17), (23, 25), (7, 15), (9, 21), (5, 21), (9, 20), (0, 5), (28, 13), (15, 1), (2, 20), (9, 25), (21, 24), (3, 0), (16, 17), (25, 21), (8, 0), (14, 15), (5, 25), (17, 18), (20, 15), (4, 1), (18, 3), (28, 10), (14, 25), (0, 15), (4, 18), (9, 17), (5, 5), (18, 20), (7, 2), (3, 23), (27, 16), (22, 17), (6, 25), (12, 11), (5, 18), (6, 24), (12, 15), (27, 3), (16, 13), (20, 13), (6, 4), (25, 17), (8, 6), (25, 2), (18, 21), (10, 20), (8, 8), (8, 23), (26, 15), (11, 22), (2, 7), (2, 5), (16, 15), (3, 20), (10, 0), (6, 20), (15, 14), (14, 17), (16, 4), (8, 2), (7, 10), (28, 0), (18, 8), (26, 4), (15, 13), (24, 10), (6, 1), (20, 12), (11, 24), (15, 25), (26, 11), (13, 14), (21, 5), (20, 14), (16, 20), (5, 3), (3, 5), (7, 19), (21, 9), (4, 7), (28, 3), (18, 11), (1, 10), (26, 0), (17, 22), (27, 4), (14, 5), (16, 2), (10, 12), (14, 22), (8, 22), (22, 24), (27, 24), (22, 3), (28, 15), (20, 0), (28, 24), (5, 7), (10, 19), (11, 9), (3, 14), (27, 21), (4, 4), (18, 16), (15, 10), (12, 9), (13, 16), (1, 20), (24, 11), (13, 13), (18, 22), (13, 18), (21, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "989400", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (15, 24), (1, 8), (9, 11), (22, 2), (21, 23), (14, 1), (17, 9), (19, 10), (22, 6), (7, 26), (1, 4), (22, 25), (8, 15), (8, 6), (6, 25), (15, 23), (8, 17), (13, 12), (23, 12), (22, 23), (20, 23), (5, 9), (19, 6), (13, 19), (12, 27), (6, 22), (15, 12), (21, 10), (20, 25), (0, 25), (23, 20), (4, 13), (0, 8), (23, 17), (5, 1), (1, 18), (2, 15), (9, 2), (0, 22), (20, 10), (23, 8), (1, 10), (9, 9), (17, 25), (1, 26), (21, 18), (8, 28), (19, 13), (7, 5), (15, 9), (14, 6), (0, 21), (5, 22), (16, 17), (11, 3), (7, 20), (9, 4), (12, 2), (23, 0), (10, 8), (15, 5), (16, 18), (8, 27), (13, 0), (16, 26), (22, 21), (19, 3), (18, 2), (5, 13), (0, 6), (18, 7), (7, 9), (7, 3), (15, 0), (18, 23), (0, 5), (10, 18), (3, 28), (17, 1), (5, 17), (0, 18), (2, 4), (6, 9), (22, 0), (2, 23), (2, 13), (0, 17), (23, 18), (22, 19), (15, 16), (17, 12), (0, 11), (1, 12), (11, 13), (12, 3), (0, 24), (12, 26), (7, 10), (11, 14), (20, 8), (22, 5), (14, 17), (20, 26), (0, 9), (0, 4), (6, 10), (1, 25), (16, 27), (23, 13), (8, 2), (18, 25), (9, 21), (1, 13), (6, 19), (11, 23), (19, 9), (7, 13), (7, 16), (16, 22), (8, 4), (3, 24), (22, 20), (11, 22), (20, 17), (16, 24), (23, 10), (16, 10), (22, 12), (21, 11), (18, 26), (19, 23), (2, 0), (21, 8), (18, 8), (20, 7), (17, 22), (19, 26), (1, 3), (19, 0), (10, 27), (13, 16), (5, 14), (10, 22), (4, 12), (11, 8), (14, 0), (0, 2), (1, 2), (10, 7), (23, 23), (3, 10), (12, 1), (10, 17), (19, 24), (1, 0), (21, 9), (8, 3), (17, 6), (23, 24), (0, 13), (23, 16), (14, 14), (5, 2), (12, 18), (15, 4), (4, 0), (7, 0), (15, 19), (3, 9), (16, 21), (19, 5), (7, 4), (16, 13), (18, 17), (20, 20), (15, 27), (20, 3), (16, 12), (14, 11), (18, 1), (4, 20), (21, 17), (6, 18), (2, 28), (23, 1), (20, 19), (21, 7), (13, 26), (11, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505626", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 13), (0, 7), (25, 9), (10, 12), (26, 8), (1, 13), (20, 20), (22, 19), (11, 23), (19, 10), (8, 5), (24, 18), (0, 1), (9, 25), (5, 9), (26, 26), (9, 23), (1, 3), (0, 22), (19, 25), (21, 22), (7, 17), (13, 0), (4, 7), (24, 10), (22, 26), (22, 6), (11, 5), (8, 13), (8, 20), (2, 3), (1, 18), (18, 16), (22, 9), (1, 4), (18, 18), (17, 4), (7, 19), (24, 3), (9, 5), (4, 5), (2, 12), (12, 26), (4, 11), (10, 2), (9, 12), (23, 12), (21, 0), (20, 9), (14, 3), (16, 2), (1, 5), (17, 26), (4, 12), (25, 5), (23, 1), (8, 7), (5, 17), (24, 2), (11, 20), (5, 3), (23, 4), (19, 9), (26, 23), (17, 5), (20, 16), (4, 23), (11, 4), (6, 17), (9, 4), (21, 25), (16, 24), (19, 14), (27, 11), (3, 13), (24, 17), (15, 17), (26, 4), (20, 5), (18, 6), (18, 13), (11, 6), (8, 8), (9, 26), (19, 20), (13, 13), (21, 14), (5, 2), (4, 19), (7, 23), (21, 19), (5, 15), (23, 7), (15, 11), (14, 14), (10, 9), (21, 23), (10, 5), (22, 2), (22, 21), (17, 22), (13, 4), (9, 17), (6, 21), (25, 10), (20, 25), (23, 26), (10, 8), (17, 3), (27, 23), (27, 8), (11, 24), (0, 10), (24, 0), (24, 6), (13, 21), (18, 11), (20, 3), (25, 19), (21, 20), (25, 12), (23, 6), (20, 18), (9, 24), (1, 21), (13, 17), (11, 18), (27, 16), (15, 2), (14, 17), (17, 12), (13, 26), (8, 19), (24, 16), (17, 13), (21, 12), (19, 4), (25, 21), (14, 21), (23, 9), (4, 1), (27, 1), (9, 0), (10, 24), (6, 11), (20, 13), (0, 24), (19, 26), (11, 7), (16, 6), (5, 22), (11, 15), (3, 16), (17, 0), (12, 22), (21, 17), (22, 25), (25, 17), (25, 23), (19, 23), (24, 9), (18, 2), (10, 10), (4, 13), (4, 15), (21, 6), (15, 26), (14, 4), (4, 24), (6, 5), (24, 5), (27, 18), (20, 11), (7, 25), (3, 17), (11, 16), (14, 9), (14, 5), (26, 25), (14, 25), (16, 11), (16, 7), (9, 1), (13, 3), (5, 6), (3, 19), (8, 23), (0, 23), (15, 14), (23, 22), (6, 10), (6, 0), (3, 11), (20, 17), (16, 25), (8, 25), (19, 15), (26, 9), (0, 12), (16, 13), (10, 11), (18, 1), (18, 15), (12, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "442718", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), 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), (14, 15), (20, 9), (9, 6), (9, 21), (7, 6), (7, 9), (5, 22), (16, 23), (14, 10), (14, 21), (11, 21), (24, 0), (18, 10), (14, 8), (11, 17), (1, 12), (3, 0), (12, 21), (0, 6), (17, 14), (12, 23), (4, 8), (25, 7), (13, 1), (2, 10), (2, 3), (2, 17), (9, 7), (15, 10), (17, 7), (15, 21), (12, 7), (11, 4), (15, 17), (7, 14), (17, 17), (11, 13), (15, 22), (9, 14), (19, 22), (16, 0), (2, 18), (9, 19), (19, 18), (10, 10), (17, 23), (20, 15), (23, 1), (0, 16), (13, 4), (12, 14), (11, 5), (5, 12), (21, 17), (24, 21), (17, 3), (24, 22), (10, 19), (20, 19), (18, 8), (19, 19), (16, 19), (23, 14), (6, 18), (10, 8), (10, 22), (16, 21), (18, 15), (2, 7), (18, 11), (8, 12), (7, 18), (4, 12), (5, 23), (6, 19), (24, 19), (4, 9), (22, 22), (18, 22), (19, 16), (4, 4), (7, 20), (17, 8), (4, 13), (4, 2), (25, 16), (20, 1), (23, 23), (23, 21), (4, 7), (12, 5), (8, 15), (11, 2), (8, 23), (15, 7), (5, 20), (18, 1), (0, 4), (8, 6), (10, 21), (21, 14), (14, 23), (21, 13), (8, 5), (23, 2), (8, 14), (20, 11), (3, 18), (2, 16), (19, 6), (2, 0), (1, 3), (17, 15), (9, 0), (21, 6), (6, 0), (2, 4), (5, 19), (13, 11), (5, 4), (13, 2), (18, 17), (14, 0), (20, 22), (25, 13), (14, 22), (21, 12), (7, 5), (10, 7), (11, 10), (18, 14), (8, 17), (7, 21), (0, 3), (20, 3), (14, 19), (12, 9), (24, 4), (11, 12), (16, 8), (16, 13), (22, 0), (1, 14), (12, 12), (20, 20), (15, 19), (7, 16), (10, 11), (21, 16), (17, 22), (13, 8), (22, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730954", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (22, 23), (5, 20), (0, 24), (1, 23), (10, 18), (14, 12), (3, 7), (4, 18), (8, 17), (15, 13), (20, 14), (7, 16), (20, 7), (4, 12), (17, 5), (23, 10), (0, 6), (15, 3), (21, 15), (18, 22), (22, 22), (8, 4), (4, 23), (6, 17), (12, 6), (22, 9), (20, 3), (16, 27), (11, 13), (11, 19), (23, 5), (4, 22), (13, 1), (16, 11), (0, 13), (5, 5), (22, 21), (20, 0), (15, 15), (15, 23), (15, 5), (13, 24), (10, 5), (18, 9), (6, 19), (9, 25), (17, 17), (23, 8), (20, 2), (8, 25), (14, 14), (7, 9), (21, 13), (12, 26), (7, 13), (5, 2), (10, 21), (13, 10), (18, 1), (12, 19), (18, 21), (12, 4), (23, 13), (13, 21), (7, 4), (7, 6), (22, 20), (19, 20), (6, 24), (10, 25), (11, 9), (23, 12), (14, 18), (15, 22), (0, 27), (13, 8), (19, 14), (10, 9), (2, 0), (3, 15), (3, 20), (0, 19), (2, 24), (4, 26), (4, 5), (20, 4), (14, 16), (6, 7), (2, 16), (7, 3), (20, 12), (21, 21), (20, 5), (5, 6), (22, 8), (18, 6), (4, 0), (10, 27), (20, 26), (18, 12), (18, 14), (5, 18), (11, 3), (21, 8), (11, 21), (17, 23), (7, 23), (1, 2), (23, 4), (23, 11), (19, 0), (21, 3), (0, 11), (3, 26), (14, 1), (21, 19), (8, 21), (5, 19), (6, 22), (6, 18), (15, 17), (17, 15), (17, 27), (14, 24), (23, 7), (7, 12), (19, 27), (13, 11), (23, 16), (1, 7), (20, 6), (10, 24), (0, 15), (20, 27), (23, 0), (23, 20), (1, 9), (1, 24), (19, 4), (19, 24), (16, 12), (17, 25), (9, 11), (21, 12), (14, 0), (14, 10), (22, 19), (16, 10), (6, 25), (18, 13), (6, 3), (11, 27), (10, 17), (11, 11), (16, 26), (15, 24), (12, 14), (18, 18), (22, 25), (4, 27), (18, 3), (12, 1), (11, 23), (13, 14), (18, 7), (19, 13), (19, 18), (23, 9), (4, 19), (16, 19), (7, 0), (23, 6), (20, 21), (6, 8), (9, 10), (21, 22), (1, 14), (5, 17), (21, 2), (22, 7), (19, 1), (10, 4), (22, 0), (10, 26), (12, 27), (4, 3), (0, 22), (0, 1), (1, 18), (17, 13), (17, 4), (11, 15), (13, 27), (12, 10), (1, 22), (20, 16), (22, 5), (12, 20), (9, 5), (12, 15), (1, 13), (13, 22), (3, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "982368", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 26), (1, 25), (4, 6), (8, 17), (1, 5), (0, 24), (9, 8), (9, 14), (14, 17), (1, 14), (5, 12), (3, 22), (0, 14), (14, 24), (11, 16), (15, 0), (4, 18), (8, 16), (1, 11), (9, 12), (3, 27), (7, 1), (10, 18), (9, 19), (2, 15), (15, 10), (13, 22), (5, 1), (2, 5), (10, 1), (6, 20), (13, 15), (12, 1), (3, 11), (12, 7), (5, 15), (11, 13), (9, 13), (8, 0), (3, 17), (15, 21), (18, 20), (0, 15), (15, 8), (8, 7), (14, 18), (17, 11), (5, 23), (2, 7), (6, 25), (5, 24), (13, 16), (19, 12), (12, 20), (3, 23), (9, 9), (11, 4), (14, 22), (6, 2), (12, 9), (4, 10), (2, 18), (19, 14), (17, 13), (3, 26), (6, 16), (17, 5), (10, 14), (9, 23), (8, 12), (1, 19), (18, 9), (14, 7), (14, 26), (11, 9), (19, 25), (7, 0), (1, 2), (6, 24), (2, 0), (8, 23), (8, 20), (2, 21), (15, 22), (16, 17), (4, 0), (2, 23), (3, 7), (1, 15), (15, 26), (9, 26), (8, 1), (6, 0), (13, 23), (8, 9), (7, 22), (4, 5), (1, 24), (17, 2), (16, 27), (3, 24), (5, 20), (10, 8), (16, 26), (4, 9), (9, 10), (13, 9), (19, 22), (4, 15), (4, 12), (18, 19), (2, 19), (7, 26), (10, 27), (14, 13), (3, 6), (10, 9), (14, 9), (7, 13), (4, 20), (11, 21), (2, 4), (8, 2), (14, 21), (16, 0), (17, 25), (5, 27), (8, 11), (15, 20), (4, 11), (17, 8), (18, 14), (14, 20), (12, 11), (11, 14), (7, 8), (15, 24), (14, 15), (1, 8), (1, 12), (18, 17), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144012", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 27), (16, 20), (12, 24), (1, 13), (11, 21), (7, 8), (2, 22), (4, 13), (16, 25), (1, 5), (10, 28), (1, 27), (15, 20), (12, 10), (9, 9), (2, 23), (18, 24), (15, 4), (17, 17), (11, 20), (3, 15), (8, 14), (17, 9), (0, 11), (3, 24), (6, 5), (0, 6), (19, 7), (1, 15), (16, 26), (10, 1), (4, 12), (4, 20), (5, 6), (13, 6), (4, 27), (12, 2), (11, 0), (18, 7), (0, 21), (9, 11), (12, 13), (1, 16), (13, 16), (16, 13), (9, 5), (16, 14), (16, 27), (12, 7), (14, 25), (12, 1), (2, 24), (13, 22), (6, 12), (7, 19), (13, 15), (17, 22), (13, 0), (19, 13), (18, 9), (17, 18), (17, 28), (11, 11), (16, 17), (5, 20), (18, 17), (10, 14), (4, 3), (10, 21), (11, 22), (5, 9), (5, 11), (15, 14), (14, 8), (19, 17), (16, 5), (0, 4), (1, 14), (2, 14), (10, 17), (17, 5), (15, 27), (1, 21), (8, 7), (12, 16), (3, 1), (15, 28), (13, 28), (7, 5), (13, 19), (2, 15), (5, 25), (5, 17), (11, 13), (12, 14), (3, 12), (8, 21), (4, 21), (10, 4), (19, 0), (16, 8), (2, 12), (0, 27), (11, 10), (8, 23), (6, 26), (4, 14), (0, 28), (1, 24), (17, 26), (11, 15), (3, 19), (12, 5), (4, 4), (5, 22), (7, 0), (11, 8), (13, 24), (6, 10), (14, 16), (2, 9), (14, 22), (4, 24), (18, 15), (14, 13), (1, 17), (2, 4), (16, 18), (1, 11), (4, 19), (16, 6), (17, 3), (9, 23), (17, 27), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8640", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 19), (11, 22), (18, 16), (2, 13), (17, 24), (11, 15), (3, 17), (16, 5), (2, 21), (12, 21), (19, 24), (9, 3), (0, 22), (17, 20), (4, 5), (16, 12), (4, 12), (13, 8), (12, 11), (22, 17), (10, 16), (12, 16), (13, 19), (0, 4), (9, 22), (4, 6), (20, 6), (16, 23), (15, 15), (19, 11), (17, 0), (10, 23), (5, 16), (8, 2), (14, 22), (11, 11), (12, 8), (19, 9), (14, 13), (16, 15), (19, 8), (4, 2), (0, 21), (17, 4), (10, 14), (7, 1), (5, 15), (6, 19), (0, 20), (17, 7), (4, 9), (10, 3), (13, 23), (2, 4), (11, 8), (14, 5), (3, 21), (4, 10), (12, 18), (16, 0), (13, 18), (10, 7), (21, 8), (0, 13), (14, 21), (7, 3), (2, 3), (18, 2), (12, 13), (10, 11), (13, 1), (10, 4), (16, 21), (8, 8), (20, 3), (1, 3), (12, 3), (20, 14), (12, 12), (3, 9), (14, 6), (18, 13), (12, 0), (5, 9), (7, 16), (8, 5), (9, 20), (15, 2), (20, 22), (15, 24), (2, 19), (20, 20), (22, 21), (15, 18), (19, 0), (22, 22), (22, 15), (5, 24), (13, 7), (3, 5), (10, 2), (8, 4), (19, 22), (5, 20), (12, 1), (14, 14), (11, 3), (2, 5), (2, 16), (7, 7), (4, 1), (16, 9), (3, 12), (0, 9), (1, 18), (9, 8), (15, 10), (14, 16), (1, 16), (18, 3), (20, 16), (9, 14), (1, 9), (13, 0), (6, 20), (1, 10), (17, 18), (16, 18), (21, 1), (18, 1), (4, 22), (0, 17), (13, 5), (20, 0), (1, 5), (15, 0), (4, 24), (14, 24), (2, 20), (13, 24), (10, 18), (13, 22), (5, 23), (22, 3), (17, 10), (11, 17), (3, 1), (15, 4), (15, 1), (16, 19), (14, 1), (3, 16), (22, 23), (12, 24), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949200", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), 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), (14, 3), (7, 23), (4, 19), (13, 19), (5, 7), (10, 21), (5, 9), (20, 4), (13, 18), (3, 3), (17, 22), (18, 25), (0, 21), (19, 11), (5, 17), (14, 16), (2, 4), (9, 5), (1, 24), (11, 17), (3, 22), (20, 1), (25, 22), (12, 0), (20, 16), (17, 21), (20, 14), (9, 8), (8, 22), (10, 1), (11, 8), (12, 24), (12, 14), (23, 8), (9, 24), (9, 15), (2, 25), (13, 21), (9, 12), (3, 10), (17, 8), (15, 24), (14, 21), (6, 16), (3, 18), (4, 16), (25, 6), (17, 12), (25, 8), (14, 23), (18, 8), (2, 20), (17, 9), (0, 8), (19, 8), (6, 11), (23, 24), (18, 6), (11, 4), (20, 17), (11, 5), (1, 3), (8, 4), (9, 2), (7, 16), (3, 0), (4, 13), (9, 23), (21, 14), (14, 19), (10, 4), (25, 10), (19, 16), (19, 21), (8, 15), (2, 11), (16, 5), (16, 2), (22, 12), (18, 17), (13, 13), (22, 23), (20, 3), (18, 13), (16, 12), (18, 24), (21, 5), (17, 1), (1, 5), (17, 4), (5, 0), (8, 5), (2, 6), (4, 9), (19, 12), (11, 18), (20, 0), (12, 12), (3, 15), (19, 4), (16, 15), (9, 20), (21, 20), (12, 9), (19, 10), (15, 8), (11, 6), (6, 1), (11, 24), (21, 6), (0, 24), (19, 17), (10, 3), (25, 16), (20, 13), (9, 10), (14, 12), (16, 16), (23, 19), (3, 4), (23, 0), (14, 17), (18, 9), (6, 25), (5, 8), (16, 9), (18, 11), (22, 16), (1, 23), (7, 8), (14, 10), (22, 9), (13, 11), (14, 6), (19, 5), (6, 20), (19, 1), (2, 22), (7, 18), (24, 25), (3, 20), (11, 25), (14, 22), (19, 13), (13, 2), (5, 6), (15, 7), (25, 0), (15, 5), (8, 11), (17, 11), (18, 21), (12, 2), (24, 17), (3, 13), (6, 8), (20, 21), (23, 4), (7, 5), (7, 19), (1, 10), (23, 7), (21, 0), (9, 18), (21, 22), (1, 15), (2, 0), (4, 10), (17, 24), (2, 2), (14, 9), (13, 20), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645120", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), 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), (12, 9), (15, 1), (11, 14), (2, 3), (18, 9), (16, 19), (1, 2), (11, 5), (12, 12), (4, 18), (22, 3), (14, 10), (21, 13), (19, 14), (21, 14), (5, 15), (7, 13), (15, 9), (16, 12), (11, 7), (12, 11), (10, 2), (18, 18), (17, 16), (12, 1), (11, 11), (9, 15), (19, 7), (7, 0), (2, 16), (6, 13), (22, 2), (8, 19), (12, 2), (21, 7), (10, 13), (21, 15), (5, 7), (3, 1), (9, 8), (13, 17), (20, 9), (18, 4), (6, 1), (12, 6), (20, 7), (15, 5), (4, 2), (1, 13), (16, 4), (22, 5), (14, 12), (9, 9), (3, 2), (21, 5), (20, 8), (16, 10), (10, 10), (13, 19), (19, 19), (6, 11), (12, 7), (6, 18), (10, 15), (7, 9), (2, 18), (13, 5), (18, 16), (22, 6), (18, 13), (5, 5), (8, 3), (14, 15), (18, 6), (21, 17), (13, 7), (15, 19), (21, 19), (7, 14), (3, 19), (8, 4), (17, 19), (1, 12), (12, 17), (2, 19), (11, 3), (14, 17), (14, 13), (20, 19), (2, 10), (21, 8), (12, 5), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533764", "dataset": "MATH"}
{"messages": [{"content": "In a 27x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (14, 15), (10, 18), (1, 17), (10, 0), (12, 16), (12, 15), (13, 13), (7, 23), (3, 22), (25, 13), (13, 22), (19, 10), (25, 8), (7, 8), (19, 17), (6, 1), (6, 10), (20, 16), (22, 4), (15, 21), (1, 24), (17, 10), (24, 7), (23, 9), (19, 16), (25, 7), (6, 22), (3, 6), (4, 6), (9, 0), (1, 18), (11, 23), (17, 3), (24, 24), (8, 19), (21, 4), (2, 5), (26, 9), (3, 7), (8, 14), (1, 6), (6, 24), (26, 12), (25, 18), (26, 7), (22, 6), (16, 13), (10, 7), (11, 13), (0, 7), (18, 18), (21, 2), (15, 0), (0, 10), (19, 2), (26, 2), (14, 17), (21, 24), (11, 14), (16, 23), (10, 4), (16, 18), (26, 15), (11, 15), (17, 24), (10, 12), (9, 18), (10, 3), (4, 17), (4, 3), (19, 7), (24, 14), (7, 18), (17, 17), (26, 23), (15, 19), (17, 8), (13, 11), (18, 8), (3, 4), (14, 24), (18, 11), (15, 18), (14, 0), (22, 0), (5, 19), (14, 8), (1, 14), (8, 1), (10, 24), (20, 6), (13, 7), (13, 14), (23, 4), (19, 11), (4, 4), (25, 21), (20, 13), (24, 22), (26, 8), (22, 8), (14, 23), (12, 18), (22, 13), (20, 3), (13, 5), (21, 14), (25, 9), (21, 6), (2, 15), (23, 14), (6, 3), (23, 11), (2, 8), (3, 21), (2, 19), (20, 15), (24, 20), (3, 0), (1, 0), (11, 21), (18, 20), (7, 4), (17, 4), (19, 3), (9, 3), (15, 24), (22, 17), (3, 9), (0, 17), (2, 16), (11, 1), (22, 24), (13, 16), (1, 16), (2, 6), (24, 18), (8, 21), (21, 5), (5, 20), (4, 9), (9, 4), (20, 24), (12, 14), (13, 4), (24, 5), (19, 5), (8, 7), (25, 0), (10, 6), (4, 7), (22, 11), (21, 12), (15, 3), (23, 13), (17, 12), (5, 21), (2, 11), (22, 19), (12, 20), (0, 24), (20, 1), (18, 22), (0, 3), (23, 8), (16, 10), (26, 11), (10, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277608", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 3), (6, 11), (6, 22), (0, 13), (16, 24), (3, 23), (15, 9), (18, 9), (23, 1), (9, 9), (1, 15), (11, 4), (15, 17), (14, 6), (22, 14), (1, 3), (6, 16), (24, 20), (8, 11), (1, 6), (23, 22), (13, 24), (4, 18), (9, 2), (2, 20), (10, 0), (16, 19), (1, 17), (19, 6), (3, 24), (11, 21), (20, 25), (3, 16), (23, 11), (6, 17), (24, 1), (5, 10), (8, 10), (21, 17), (3, 12), (14, 10), (0, 9), (3, 0), (1, 25), (9, 24), (25, 9), (19, 5), (0, 21), (17, 18), (16, 16), (20, 17), (17, 24), (25, 19), (5, 12), (5, 25), (11, 7), (16, 11), (12, 20), (18, 2), (10, 22), (5, 4), (3, 8), (3, 25), (22, 5), (4, 5), (7, 15), (1, 16), (23, 25), (9, 12), (13, 10), (4, 15), (19, 17), (25, 16), (12, 0), (7, 1), (7, 12), (23, 19), (15, 25), (18, 1), (12, 16), (7, 18), (0, 22), (23, 23), (18, 19), (22, 9), (8, 19), (11, 8), (7, 5), (22, 12), (11, 6), (1, 22), (7, 2), (13, 9), (20, 18), (10, 4), (21, 16), (5, 11), (0, 1), (6, 15), (5, 7), (24, 14), (16, 15), (6, 24), (16, 7), (10, 23), (3, 14), (15, 21), (24, 13), (16, 22), (4, 21), (22, 23), (19, 2), (23, 10), (13, 23), (18, 5), (15, 8), (25, 18), (14, 9), (10, 11), (25, 14), (7, 11), (25, 6), (18, 21), (0, 8), (9, 22), (12, 10), (4, 25), (1, 21), (21, 21), (9, 11), (22, 11), (21, 18), (21, 7), (11, 25), (22, 25), (11, 1), (23, 15), (24, 10), (2, 9), (6, 20), (2, 4), (17, 3), (2, 25), (20, 5), (15, 13), (13, 12), (12, 22), (12, 19), (24, 11), (20, 19), (23, 0), (13, 16), (10, 21), (15, 18), (17, 1), (21, 5), (4, 20), (5, 22), (25, 21), (0, 2), (20, 7), (25, 4), (17, 19), (11, 20), (22, 2), (19, 22), (7, 17), (18, 6), (13, 8), (16, 20), (17, 25), (0, 10), (13, 13), (17, 16), (6, 0), (10, 1), (2, 10), (23, 5), (3, 21), (19, 8), (1, 10), (8, 6), (23, 21), (25, 17), (12, 18), (16, 21), (1, 7), (22, 4), (4, 23), (15, 1), (19, 0), (17, 7), (15, 0), (21, 1), (7, 13), (9, 13), (1, 9), (4, 24), (3, 4), (19, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "828800", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 15), (12, 5), (2, 7), (22, 10), (5, 16), (1, 0), (16, 3), (6, 0), (16, 6), (13, 13), (4, 0), (17, 19), (9, 2), (20, 8), (6, 7), (19, 2), (4, 6), (6, 12), (15, 15), (7, 16), (7, 10), (9, 17), (22, 15), (7, 19), (12, 15), (13, 6), (3, 19), (17, 20), (1, 11), (20, 5), (5, 10), (4, 4), (21, 18), (10, 12), (12, 3), (5, 17), (8, 20), (20, 18), (12, 17), (8, 9), (9, 16), (22, 17), (12, 2), (11, 1), (12, 13), (6, 17), (9, 18), (11, 10), (11, 13), (18, 16), (10, 0), (16, 13), (6, 16), (4, 9), (18, 14), (13, 19), (9, 1), (6, 10), (1, 8), (18, 19), (0, 15), (5, 4), (3, 12), (17, 0), (21, 17), (12, 7), (6, 1), (1, 3), (5, 15), (2, 1), (11, 18), (8, 8), (21, 16), (15, 16), (19, 3), (17, 16), (18, 10), (4, 11), (18, 12), (1, 5), (21, 12), (15, 20), (15, 8), (7, 1), (1, 17), (6, 6), (5, 2), (3, 8), (3, 3), (10, 16), (14, 17), (9, 13), (8, 15), (10, 2), (2, 13), (3, 0), (8, 3), (22, 3), (0, 14), (14, 15), (8, 17), (18, 5), (3, 15), (3, 6), (22, 16), (13, 7), (5, 12), (12, 18), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744008", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), 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), (8, 19), (7, 0), (13, 9), (11, 24), (1, 8), (20, 6), (3, 6), (11, 21), (4, 17), (13, 7), (21, 14), (12, 15), (3, 4), (15, 18), (20, 2), (16, 6), (9, 24), (17, 12), (21, 21), (18, 15), (6, 6), (22, 1), (21, 25), (22, 11), (1, 10), (15, 22), (13, 0), (6, 1), (22, 21), (21, 8), (17, 18), (9, 3), (19, 23), (7, 14), (1, 4), (12, 17), (8, 9), (9, 22), (8, 8), (21, 17), (12, 22), (18, 20), (14, 0), (20, 23), (9, 13), (18, 5), (10, 25), (20, 22), (18, 4), (6, 22), (23, 16), (2, 5), (23, 17), (4, 2), (4, 22), (16, 1), (12, 4), (12, 16), (22, 12), (5, 25), (19, 0), (14, 20), (22, 16), (12, 21), (14, 16), (10, 3), (2, 12), (13, 2), (7, 18), (1, 14), (17, 14), (12, 7), (23, 7), (19, 18), (10, 19), (14, 19), (18, 12), (13, 17), (17, 9), (19, 11), (5, 24), (7, 5), (10, 6), (21, 16), (21, 23), (14, 22), (0, 1), (15, 7), (15, 25), (11, 7), (21, 6), (23, 13), (14, 9), (18, 19), (7, 23), (8, 0), (7, 13), (3, 16), (0, 19), (15, 10), (19, 4), (3, 2), (13, 13), (2, 23), (21, 4), (2, 17), (18, 14), (6, 3), (4, 0), (19, 2), (13, 19), (3, 11), (7, 4), (14, 2), (17, 22), (13, 22), (14, 8), (13, 25), (13, 12), (15, 5), (18, 17), (6, 4), (21, 19), (20, 3), (11, 6), (15, 14), (13, 24), (16, 23), (13, 1), (6, 25), (23, 19), (0, 4), (14, 14), (4, 9), (8, 23), (10, 17), (7, 8), (5, 19), (9, 8), (21, 13), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963284", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), 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), (3, 2), (6, 15), (15, 17), (19, 8), (14, 6), (10, 6), (17, 2), (1, 15), (1, 3), (3, 6), (13, 11), (15, 0), (12, 13), (11, 6), (21, 6), (7, 12), (16, 19), (21, 9), (25, 1), (9, 9), (7, 15), (2, 1), (23, 19), (5, 1), (8, 3), (2, 4), (6, 6), (6, 12), (20, 11), (6, 4), (19, 9), (15, 5), (16, 16), (18, 17), (21, 7), (10, 16), (9, 11), (7, 7), (2, 17), (22, 17), (16, 4), (0, 2), (14, 8), (11, 9), (26, 16), (8, 9), (7, 1), (24, 2), (13, 5), (26, 13), (9, 7), (22, 0), (17, 10), (12, 6), (21, 19), (13, 4), (3, 9), (8, 7), (20, 4), (23, 17), (6, 18), (1, 9), (22, 19), (0, 12), (18, 4), (18, 2), (24, 17), (6, 8), (10, 19), (24, 3), (0, 1), (1, 19), (9, 19), (4, 3), (24, 16), (4, 1), (16, 3), (15, 6), (5, 4), (3, 1), (11, 3), (3, 15), (22, 8), (10, 13), (6, 13), (17, 13), (26, 6), (11, 4), (23, 6), (1, 7), (24, 12), (15, 15), (12, 2), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565302", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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, 13), (3, 5), (14, 15), (9, 17), (18, 4), (6, 4), (15, 4), (17, 7), (12, 13), (9, 13), (6, 1), (11, 13), (6, 13), (17, 9), (8, 8), (1, 9), (9, 14), (15, 3), (15, 16), (9, 2), (21, 10), (17, 16), (17, 20), (9, 15), (13, 16), (16, 15), (15, 2), (6, 3), (7, 20), (19, 8), (3, 10), (4, 12), (13, 13), (0, 7), (14, 3), (23, 2), (13, 0), (5, 13), (20, 20), (18, 10), (21, 8), (1, 17), (17, 17), (8, 19), (21, 12), (4, 1), (10, 1), (5, 20), (5, 14), (11, 15), (12, 5), (10, 11), (20, 9), (3, 4), (7, 15), (4, 10), (6, 5), (14, 17), (16, 17), (22, 10), (17, 2), (15, 10), (23, 18), (18, 18), (21, 6), (0, 18), (4, 0), (23, 1), (23, 6), (11, 10), (5, 2), (22, 15), (16, 16), (8, 9), (14, 6), (11, 5), (2, 15), (21, 4), (10, 9), (23, 5), (8, 18), (3, 17), (19, 3), (2, 17), (2, 9), (10, 0), (6, 7), (15, 5), (22, 12), (6, 6), (10, 16), (23, 15), (8, 20), (9, 3), (20, 2), (16, 9), (8, 4), (16, 4), (1, 19), (4, 19), (18, 8), (11, 19), (20, 11), (10, 8), (3, 3), (10, 20), (11, 7), (5, 4), (9, 16), (7, 7), (0, 19), (10, 7), (6, 19), (2, 12), (0, 14), (3, 19), (22, 14), (0, 16), (18, 0), (15, 8), (16, 10), (9, 6), (9, 7), (19, 12), (0, 9), (7, 5), (16, 14), (13, 8), (6, 16), (13, 6), (12, 15), (18, 20), (6, 20), (3, 2), (8, 2), (0, 13), (16, 11), (19, 10), (9, 11), (5, 19), (20, 5), (7, 19), (17, 11), (21, 17), (21, 19), (16, 5), (22, 20), (20, 14), (3, 15), (21, 14), (18, 9), (3, 20), (19, 5), (11, 18), (9, 18), (19, 16), (4, 17), (23, 16), (5, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "611933", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 20), (22, 7), (9, 9), (18, 10), (24, 16), (20, 1), (13, 20), (23, 1), (4, 12), (16, 4), (21, 20), (17, 20), (14, 14), (12, 4), (18, 19), (4, 5), (8, 4), (7, 4), (12, 14), (9, 21), (20, 13), (6, 12), (9, 19), (0, 1), (0, 7), (0, 3), (21, 3), (21, 10), (5, 1), (8, 1), (15, 15), (16, 13), (24, 17), (2, 13), (6, 0), (1, 4), (3, 12), (19, 21), (1, 20), (11, 5), (20, 4), (10, 1), (10, 4), (10, 21), (23, 4), (8, 15), (13, 5), (22, 0), (25, 10), (4, 2), (17, 15), (8, 7), (1, 16), (0, 13), (19, 9), (13, 8), (7, 21), (19, 6), (16, 6), (2, 9), (13, 21), (19, 1), (14, 9), (7, 14), (13, 10), (20, 7), (14, 15), (12, 7), (17, 17), (21, 17), (1, 18), (6, 18), (10, 9), (11, 19), (5, 17), (3, 20), (8, 16), (21, 11), (8, 19), (8, 6), (17, 11), (14, 4), (16, 7), (12, 5), (14, 16), (15, 17), (21, 21), (12, 20), (21, 12), (16, 20), (4, 16), (1, 11), (20, 18), (7, 17), (12, 0), (22, 11), (15, 12), (0, 12), (3, 19), (23, 11), (22, 19), (2, 12), (5, 15), (19, 14), (12, 17), (24, 12), (13, 16), (14, 0), (22, 1), (18, 17), (5, 10), (6, 5), (3, 3), (14, 7), (15, 6), (7, 15), (14, 6), (10, 11), (2, 15), (11, 8), (7, 19), (6, 6), (17, 13), (25, 16), (3, 13), (13, 7), (6, 7), (23, 9), (21, 1), (14, 2), (1, 5), (13, 11), (18, 18), (9, 6), (10, 20), (7, 7), (3, 0), (15, 4), (23, 14), (22, 2), (5, 2), (14, 3), (23, 17), (9, 8), (9, 17), (3, 9), (0, 19), (18, 20), (12, 19), (11, 10), (15, 10), (9, 15), (18, 21), (2, 6), (6, 13), (25, 14), (25, 12), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "597600", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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), (26, 14), (25, 17), (17, 7), (12, 4), (3, 16), (20, 7), (3, 0), (6, 7), (1, 0), (6, 20), (22, 18), (18, 15), (17, 14), (20, 11), (13, 20), (18, 0), (25, 20), (22, 20), (15, 6), (3, 9), (8, 1), (10, 13), (15, 18), (2, 2), (25, 14), (22, 3), (15, 4), (1, 9), (20, 10), (13, 17), (2, 21), (22, 0), (18, 18), (8, 3), (22, 5), (18, 1), (25, 21), (22, 9), (9, 20), (2, 12), (1, 2), (5, 3), (24, 18), (16, 0), (22, 17), (26, 11), (9, 9), (26, 9), (3, 17), (26, 0), (9, 13), (5, 7), (3, 8), (19, 0), (22, 8), (4, 16), (2, 7), (21, 17), (9, 10), (18, 13), (16, 13), (13, 2), (23, 0), (7, 12), (21, 4), (11, 7), (8, 7), (23, 1), (4, 8), (17, 1), (2, 14), (14, 12), (6, 13), (10, 10), (3, 4), (17, 8), (1, 11), (26, 1), (15, 17), (24, 0), (5, 11), (16, 11), (23, 9), (5, 12), (25, 7), (21, 12), (7, 1), (19, 11), (15, 13), (22, 15), (24, 6), (24, 16), (17, 21), (23, 8), (10, 17), (2, 3), (18, 19), (0, 8), (23, 5), (7, 21), (0, 14), (1, 14), (12, 21), (19, 8), (6, 10), (6, 8), (26, 3), (14, 17), (5, 2), (6, 21), (6, 4), (26, 16), (17, 18), (12, 14), (8, 6), (6, 0), (7, 5), (3, 13), (13, 19), (6, 3), (19, 12), (23, 12), (13, 7), (12, 6), (23, 18), (19, 10), (16, 8), (14, 10), (11, 21), (9, 21), (3, 21), (14, 1), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602276", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 21), (8, 7), (14, 4), (7, 18), (15, 7), (13, 18), (6, 13), (5, 23), (6, 14), (11, 17), (4, 4), (0, 16), (9, 17), (10, 15), (5, 5), (16, 1), (9, 1), (4, 14), (12, 13), (9, 11), (21, 19), (6, 10), (19, 2), (14, 3), (3, 8), (11, 4), (0, 1), (8, 9), (12, 3), (18, 11), (5, 2), (13, 7), (19, 11), (16, 6), (2, 17), (1, 18), (6, 19), (3, 23), (16, 5), (21, 1), (4, 12), (15, 6), (5, 4), (13, 2), (1, 10), (13, 15), (22, 17), (17, 16), (18, 4), (20, 16), (20, 6), (22, 1), (22, 22), (8, 6), (19, 4), (17, 11), (19, 13), (17, 10), (10, 18), (7, 1), (1, 15), (17, 5), (4, 23), (4, 18), (22, 3), (11, 18), (3, 18), (0, 12), (19, 8), (10, 16), (16, 4), (16, 15), (7, 4), (17, 17), (20, 1), (11, 11), (9, 15), (13, 4), (0, 15), (12, 12), (10, 8), (2, 2), (7, 16), (8, 13), (5, 7), (3, 15), (18, 0), (21, 12), (18, 15), (21, 8), (15, 9), (20, 5), (0, 14), (14, 9), (17, 3), (6, 11), (8, 5), (18, 14), (12, 8), (19, 16), (7, 7), (7, 12), (9, 3), (9, 16), (8, 19), (15, 14), (20, 11), (20, 4), (16, 23), (11, 16), (22, 19), (17, 1), (4, 22), (20, 21), (7, 3), (2, 0), (12, 14), (10, 22), (8, 1), (10, 10), (14, 13), (12, 11), (14, 2), (22, 12), (0, 23), (6, 5), (12, 18), (21, 22), (2, 8), (2, 3), (6, 0), (16, 14), (3, 6), (10, 7), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "929454", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 6), (3, 15), (8, 24), (18, 4), (13, 20), (13, 21), (12, 17), (16, 0), (5, 11), (0, 8), (6, 10), (13, 10), (0, 2), (0, 6), (16, 10), (12, 14), (19, 21), (10, 23), (2, 8), (9, 4), (21, 13), (14, 18), (8, 0), (13, 13), (14, 9), (4, 22), (13, 2), (4, 24), (4, 5), (14, 20), (9, 12), (11, 9), (21, 17), (2, 13), (9, 2), (6, 8), (18, 21), (2, 16), (1, 16), (3, 0), (1, 24), (8, 6), (14, 13), (2, 4), (19, 20), (20, 6), (10, 16), (3, 8), (0, 21), (12, 18), (19, 3), (10, 18), (15, 19), (1, 5), (22, 5), (1, 14), (18, 14), (4, 17), (22, 22), (19, 11), (7, 23), (6, 7), (20, 15), (22, 7), (19, 17), (16, 12), (10, 8), (7, 21), (7, 7), (16, 1), (9, 10), (13, 16), (8, 5), (16, 15), (20, 10), (8, 21), (22, 17), (2, 5), (21, 7), (15, 6), (16, 11), (10, 3), (17, 6), (20, 12), (19, 18), (19, 9), (1, 0), (6, 11), (3, 6), (18, 22), (16, 21), (11, 6), (6, 23), (22, 20), (1, 12), (18, 24), (21, 5), (17, 3), (4, 21), (8, 8), (22, 11), (20, 18), (13, 19), (8, 3), (4, 20), (8, 7), (7, 10), (9, 19), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213921", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 7), (13, 12), (10, 19), (22, 8), (21, 7), (25, 14), (19, 9), (11, 15), (8, 22), (3, 3), (24, 16), (13, 0), (5, 22), (24, 21), (13, 3), (17, 18), (26, 11), (1, 9), (18, 12), (27, 3), (7, 16), (27, 13), (1, 10), (22, 20), (0, 10), (18, 6), (2, 10), (17, 20), (22, 21), (9, 22), (25, 3), (15, 14), (23, 19), (7, 23), (21, 3), (7, 20), (15, 16), (8, 8), (3, 10), (1, 12), (12, 15), (22, 6), (9, 12), (7, 19), (7, 0), (14, 18), (1, 0), (25, 15), (23, 10), (6, 11), (12, 8), (12, 18), (9, 15), (14, 17), (11, 17), (27, 10), (25, 12), (13, 20), (28, 17), (3, 19), (1, 22), (15, 20), (19, 17), (15, 7), (28, 20), (22, 13), (28, 16), (8, 23), (28, 8), (25, 21), (0, 6), (18, 8), (23, 3), (13, 22), (7, 12), (2, 3), (28, 14), (1, 17), (2, 14), (20, 2), (21, 22), (7, 22), (12, 14), (4, 13), (13, 1), (18, 9), (16, 21), (27, 5), (17, 19), (1, 13), (9, 4), (6, 22), (18, 13), (9, 5), (20, 23), (12, 10), (4, 12), (3, 22), (5, 8), (23, 1), (14, 2), (1, 15), (17, 21), (7, 3), (28, 4), (19, 12), (11, 7), (16, 20), (19, 0), (7, 9), (24, 0), (10, 20), (1, 20), (16, 19), (3, 15), (0, 3), (2, 9), (10, 7), (26, 10), (24, 20), (9, 14), (13, 8), (13, 10), (5, 18), (16, 22), (9, 11), (10, 11), (2, 6), (22, 14), (28, 21), (13, 17), (18, 11), (9, 20), (0, 2), (4, 16), (11, 1), (4, 18), (28, 15), (1, 19), (8, 2), (2, 0), (22, 22), (19, 11), (20, 4), (22, 18), (17, 10), (14, 20), (21, 20), (5, 1), (18, 16), (2, 20), (0, 14), (9, 23), (2, 23), (16, 6), (0, 5), (12, 13), (18, 2), (16, 13), (27, 11), (7, 8), (17, 8), (13, 5), (23, 2), (8, 18), (10, 15), (8, 3), (1, 7), (11, 5), (21, 17), (6, 20), (20, 7), (1, 6), (18, 14), (24, 7), (1, 8), (18, 1), (5, 13), (16, 15), (2, 15), (1, 11), (23, 4), (16, 4), (21, 16), (19, 2), (25, 7), (4, 4), (4, 22), (26, 13), (27, 0), (18, 23), (28, 12), (7, 7), (8, 16), (4, 17), (26, 22), (24, 17), (26, 4), (11, 19), (3, 2), (9, 16), (14, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "381696", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 20), (17, 4), (9, 22), (6, 1), (12, 16), (17, 5), (14, 16), (21, 2), (17, 13), (20, 3), (2, 21), (10, 16), (3, 20), (4, 16), (10, 13), (4, 19), (8, 21), (19, 11), (8, 4), (13, 17), (1, 20), (5, 19), (22, 11), (13, 25), (19, 16), (20, 16), (11, 9), (0, 25), (15, 10), (12, 7), (23, 17), (9, 17), (13, 24), (21, 19), (18, 22), (11, 4), (13, 4), (13, 0), (6, 20), (23, 2), (15, 9), (1, 3), (3, 2), (11, 6), (10, 23), (1, 17), (7, 0), (1, 9), (6, 14), (7, 12), (11, 11), (12, 24), (16, 24), (16, 10), (22, 18), (14, 3), (7, 6), (11, 24), (13, 23), (4, 23), (5, 8), (21, 17), (22, 6), (22, 21), (6, 12), (10, 21), (13, 15), (4, 1), (11, 19), (0, 11), (20, 25), (20, 14), (22, 4), (9, 13), (22, 17), (17, 15), (19, 15), (14, 19), (14, 12), (10, 8), (23, 15), (19, 20), (23, 11), (2, 4), (6, 17), (5, 25), (4, 8), (18, 13), (5, 0), (9, 23), (1, 22), (20, 12), (16, 7), (14, 18), (20, 0), (8, 11), (5, 14), (4, 15), (21, 4), (4, 11), (6, 18), (7, 10), (13, 6), (21, 15), (6, 13), (14, 23), (10, 6), (11, 20), (21, 9), (10, 0), (22, 15), (12, 6), (8, 9), (11, 12), (7, 13), (13, 16), (4, 17), (5, 9), (5, 12), (18, 10), (8, 24), (14, 5), (13, 12), (7, 24), (22, 24), (11, 25), (2, 14), (14, 2), (19, 22), (8, 22), (10, 7), (2, 20), (1, 13), (13, 18), (10, 19), (0, 22), (19, 5), (23, 0), (14, 0), (16, 20), (7, 16), (16, 13), (15, 8), (0, 23), (1, 19), (13, 7), (7, 21), (21, 18), (2, 3), (1, 18), (7, 7), (22, 9), (5, 7), (12, 19), (8, 3), (22, 12), (3, 3), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538776", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 3), (7, 19), (0, 19), (4, 25), (2, 23), (19, 22), (23, 23), (2, 15), (2, 26), (0, 21), (16, 9), (23, 12), (0, 22), (2, 14), (11, 15), (9, 3), (20, 21), (11, 14), (5, 8), (3, 3), (1, 18), (14, 20), (17, 11), (6, 17), (4, 20), (15, 2), (21, 10), (6, 10), (23, 8), (16, 15), (3, 20), (10, 20), (23, 22), (2, 20), (13, 18), (3, 25), (9, 6), (13, 25), (10, 8), (6, 11), (17, 25), (10, 1), (8, 20), (5, 10), (19, 1), (17, 19), (11, 12), (19, 16), (12, 6), (9, 14), (16, 7), (14, 14), (23, 5), (7, 20), (0, 25), (5, 14), (0, 18), (15, 15), (17, 8), (2, 22), (14, 0), (10, 10), (4, 1), (4, 5), (7, 5), (12, 26), (11, 8), (9, 17), (2, 10), (21, 6), (22, 25), (15, 17), (15, 14), (6, 19), (17, 9), (12, 12), (22, 5), (19, 17), (0, 20), (9, 2), (20, 1), (1, 5), (11, 17), (7, 24), (1, 21), (8, 15), (21, 15), (8, 10), (0, 16), (3, 4), (16, 6), (20, 15), (6, 22), (1, 22), (6, 5), (14, 8), (10, 3), (4, 22), (20, 10), (21, 11), (10, 25), (20, 11), (21, 4), (9, 11), (1, 19), (3, 24), (13, 14), (4, 17), (9, 24), (18, 7), (12, 7), (12, 3), (2, 5), (8, 24), (3, 10), (7, 4), (6, 13), (22, 19), (2, 3), (16, 21), (13, 26), (2, 6), (13, 12), (10, 17), (5, 19), (13, 13), (13, 23), (3, 17), (10, 11), (21, 17), (14, 2), (2, 4), (13, 6), (21, 13), (13, 4), (1, 17), (4, 14), (11, 4), (18, 20), (2, 7), (4, 23), (3, 18), (17, 18), (20, 18), (6, 23), (5, 4), (19, 13), (1, 14), (15, 16), (21, 8), (1, 13), (9, 20), (22, 13), (22, 22), (6, 14), (5, 12), (12, 15), (14, 15), (10, 7), (9, 5), (6, 1), (19, 2), (21, 7), (14, 10), (12, 23), (11, 13), (14, 3), (23, 16), (8, 2), (22, 18), (16, 2), (14, 25), (8, 4), (15, 7), (14, 21), (2, 2), (14, 23), (16, 19), (17, 20), (3, 26), (22, 4), (21, 23), (22, 6), (22, 1), (8, 8), (5, 15), (17, 5), (16, 1), (12, 20), (0, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238232", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (17, 18), (17, 22), (7, 17), (2, 10), (18, 14), (17, 25), (19, 13), (16, 19), (4, 7), (2, 7), (2, 24), (7, 20), (8, 21), (1, 12), (20, 24), (11, 14), (15, 12), (11, 23), (7, 1), (10, 22), (13, 9), (7, 22), (4, 18), (3, 4), (21, 19), (18, 2), (14, 13), (4, 16), (2, 1), (2, 2), (10, 3), (19, 19), (3, 23), (10, 21), (1, 15), (10, 12), (4, 20), (0, 12), (5, 6), (9, 5), (6, 2), (18, 5), (3, 13), (17, 4), (9, 22), (11, 16), (18, 20), (6, 3), (18, 8), (3, 16), (13, 1), (12, 11), (0, 24), (15, 22), (11, 17), (12, 23), (7, 19), (18, 0), (8, 22), (10, 10), (0, 2), (15, 24), (2, 8), (3, 14), (3, 10), (11, 0), (20, 18), (21, 12), (7, 15), (16, 13), (3, 21), (8, 9), (11, 2), (3, 2), (8, 8), (7, 2), (19, 1), (20, 3), (2, 0), (1, 18), (12, 6), (20, 16), (7, 0), (9, 4), (14, 16), (10, 6), (5, 9), (8, 7), (6, 17), (16, 24), (3, 3), (5, 21), (12, 21), (0, 3), (9, 10), (12, 19), (10, 24), (20, 8), (17, 3), (1, 7), (5, 15), (13, 12), (9, 8), (12, 5), (17, 15), (20, 11), (4, 0), (10, 0), (11, 11), (2, 18), (16, 20), (19, 2), (21, 9), (7, 13), (1, 16), (0, 6), (1, 10), (11, 7), (5, 18), (11, 6), (6, 18), (15, 21), (9, 15), (0, 14), (9, 2), (6, 8), (2, 11), (17, 11), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "396600", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 10), (9, 13), (24, 12), (0, 19), (9, 25), (9, 22), (11, 11), (9, 2), (6, 22), (23, 16), (11, 9), (24, 23), (26, 19), (18, 11), (0, 12), (6, 3), (5, 14), (2, 3), (11, 10), (13, 7), (8, 7), (24, 17), (13, 24), (18, 20), (18, 15), (6, 0), (6, 7), (16, 1), (17, 0), (3, 18), (0, 5), (15, 9), (27, 0), (22, 5), (11, 12), (25, 22), (14, 3), (27, 19), (16, 20), (0, 14), (16, 7), (10, 14), (14, 18), (12, 7), (23, 11), (26, 22), (2, 5), (17, 24), (5, 17), (19, 21), (3, 15), (26, 18), (15, 8), (23, 15), (7, 21), (21, 16), (19, 10), (15, 13), (11, 14), (1, 24), (9, 8), (9, 12), (21, 24), (15, 0), (12, 8), (1, 18), (5, 9), (1, 15), (19, 14), (7, 0), (18, 0), (20, 6), (13, 8), (7, 5), (26, 14), (14, 13), (14, 12), (4, 11), (21, 11), (13, 10), (15, 6), (7, 14), (10, 24), (10, 13), (10, 21), (0, 6), (4, 0), (13, 20), (5, 21), (7, 15), (21, 20), (16, 16), (18, 7), (15, 14), (20, 14), (26, 1), (22, 2), (15, 5), (22, 3), (2, 25), (24, 15), (12, 1), (25, 16), (20, 8), (3, 17), (24, 6), (6, 4), (27, 18), (27, 12), (27, 8), (0, 8), (0, 20), (1, 14), (4, 22), (15, 20), (24, 1), (14, 22), (6, 20), (24, 14), (21, 5), (27, 21), (6, 21), (23, 2), (13, 15), (24, 18), (17, 17), (9, 16), (20, 13), (6, 15), (21, 25), (20, 21), (22, 1), (12, 4), (8, 25), (3, 12), (7, 22), (13, 25), (16, 10), (14, 19), (13, 12), (3, 3), (17, 8), (14, 23), (14, 4), (25, 25), (1, 17), (1, 7), (23, 0), (20, 18), (9, 20), (3, 21), (19, 3), (10, 16), (9, 9), (27, 4), (11, 1), (21, 8), (13, 26), (7, 3), (7, 20), (21, 21), (2, 13), (5, 7), (27, 5), (19, 17), (2, 23), (20, 15), (17, 3), (20, 17), (19, 25), (5, 2), (18, 21), (19, 26), (0, 16), (2, 20), (14, 21), (1, 4), (14, 7), (6, 11), (5, 20), (21, 12), (10, 9), (4, 7), (8, 11), (27, 2), (19, 15), (4, 14), (18, 14), (12, 11), (18, 12), (27, 24), (6, 18), (2, 19), (3, 13), (23, 18), (6, 19), (5, 0), (13, 16), (23, 6), (9, 6), (17, 25), (15, 7), (11, 4), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17424", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 23), (15, 19), (20, 17), (15, 20), (24, 13), (11, 9), (4, 3), (21, 17), (14, 16), (12, 17), (0, 11), (4, 4), (11, 14), (5, 3), (1, 20), (17, 24), (6, 12), (24, 5), (2, 11), (23, 16), (7, 3), (23, 18), (6, 6), (16, 24), (1, 6), (1, 15), (1, 13), (12, 3), (1, 0), (1, 18), (7, 24), (24, 14), (2, 17), (11, 18), (22, 13), (15, 25), (6, 16), (5, 12), (3, 24), (8, 18), (16, 17), (11, 12), (13, 7), (2, 21), (18, 4), (17, 7), (16, 5), (3, 6), (4, 19), (9, 11), (1, 12), (20, 24), (12, 23), (10, 5), (8, 0), (11, 0), (23, 25), (4, 1), (13, 10), (2, 22), (6, 18), (15, 13), (2, 24), (3, 21), (10, 3), (19, 10), (9, 12), (4, 15), (17, 2), (0, 9), (3, 13), (9, 20), (22, 14), (6, 1), (9, 23), (1, 8), (9, 3), (0, 21), (7, 10), (5, 1), (15, 22), (21, 0), (13, 24), (16, 18), (1, 11), (22, 9), (17, 10), (1, 4), (3, 20), (17, 6), (5, 19), (8, 15), (19, 2), (11, 4), (17, 12), (15, 15), (12, 10), (6, 10), (19, 21), (5, 8), (19, 18), (8, 17), (18, 6), (20, 7), (10, 16), (5, 13), (16, 8), (0, 2), (7, 7), (10, 19), (9, 25), (17, 22), (17, 25), (23, 7), (3, 3), (16, 10), (9, 1), (20, 9), (24, 3), (14, 22), (6, 19), (10, 0), (1, 19), (1, 17), (3, 14), (6, 7), (1, 9), (0, 16), (24, 21), (5, 18), (7, 22), (15, 8), (9, 24), (4, 7), (3, 4), (13, 5), (19, 16), (18, 9), (1, 25), (20, 8), (6, 24), (0, 25), (18, 13), (3, 17), (16, 13), (22, 0), (7, 18), (15, 16), (15, 9), (17, 20), (4, 5), (23, 13), (7, 0), (23, 12), (24, 9), (12, 13), (21, 20), (15, 10), (19, 8), (2, 0), (10, 11), (12, 14), (1, 23), (22, 18), (3, 18), (18, 17), (16, 2), (14, 3), (22, 12), (12, 19), (3, 22), (4, 6), (1, 16), (23, 21), (7, 20), (10, 10), (19, 13), (0, 15), (2, 13), (18, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918432", "dataset": "MATH"}
{"messages": [{"content": "In a 25x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 22), 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, 2), (14, 3), (22, 16), (23, 15), (2, 3), (3, 10), (11, 6), (15, 1), (1, 10), (15, 17), (16, 0), (23, 22), (19, 12), (24, 3), (2, 15), (11, 15), (14, 5), (23, 7), (4, 9), (20, 20), (24, 6), (24, 13), (22, 1), (3, 0), (12, 10), (21, 3), (14, 21), (10, 0), (3, 5), (23, 9), (15, 16), (20, 10), (15, 13), (17, 17), (1, 14), (10, 22), (14, 10), (18, 7), (21, 22), (18, 20), (2, 13), (15, 4), (8, 21), (4, 3), (3, 21), (20, 18), (5, 0), (6, 12), (5, 21), (7, 10), (7, 11), (24, 15), (13, 4), (19, 3), (4, 5), (1, 2), (15, 20), (23, 18), (16, 15), (15, 3), (24, 0), (7, 18), (12, 9), (19, 8), (8, 20), (15, 11), (1, 18), (16, 4), (13, 21), (18, 15), (22, 0), (20, 16), (10, 17), (23, 3), (15, 19), (4, 15), (16, 21), (9, 20), (13, 3), (20, 8), (11, 9), (0, 10), (10, 4), (6, 0), (14, 8), (10, 21), (21, 11), (16, 8), (0, 13), (2, 18), (5, 2), (2, 12), (23, 16), (12, 3), (3, 15), (9, 12), (9, 15), (18, 6), (11, 14), (2, 22), (23, 21), (7, 13), (17, 16), (18, 0), (9, 3), (12, 12), (24, 1), (21, 10), (4, 8), (9, 0), (23, 5), (9, 14), (4, 18), (14, 18), (17, 13), (20, 11), (18, 4), (15, 22), (2, 4), (11, 1), (1, 13), (19, 15), (4, 4), (15, 7), (21, 14), (24, 5), (0, 1), (4, 21), (3, 14), (21, 4), (24, 11), (21, 9), (14, 20), (16, 9), (21, 5), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767800", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 7), (17, 8), (5, 12), (22, 10), (16, 17), (7, 3), (22, 14), (26, 6), (10, 14), (9, 14), (21, 1), (17, 10), (19, 4), (13, 17), (15, 11), (14, 16), (3, 6), (6, 13), (25, 20), (2, 20), (23, 14), (11, 4), (24, 21), (7, 12), (26, 1), (6, 1), (18, 16), (18, 0), (23, 3), (11, 3), (14, 14), (25, 19), (8, 13), (24, 22), (8, 12), (16, 14), (14, 13), (20, 15), (7, 4), (21, 22), (24, 2), (10, 11), (19, 14), (19, 10), (26, 0), (22, 0), (11, 14), (18, 13), (4, 12), (11, 11), (7, 0), (21, 4), (24, 10), (13, 12), (17, 17), (8, 10), (6, 2), (21, 6), (19, 20), (13, 6), (6, 0), (16, 5), (5, 18), (24, 19), (23, 7), (1, 9), (20, 6), (0, 8), (16, 2), (26, 3), (25, 21), (18, 1), (11, 18), (8, 0), (25, 22), (16, 10), (3, 18), (25, 0), (23, 18), (8, 1), (15, 6), (12, 21), (2, 12), (0, 20), (17, 16), (12, 19), (8, 11), (15, 14), (16, 4), (9, 3), (11, 2), (4, 0), (11, 15), (1, 10), (5, 13), (9, 5), (8, 3), (18, 8), (22, 4), (17, 15), (24, 1), (8, 22), (12, 12), (23, 11), (1, 22), (3, 11), (21, 2), (5, 15), (3, 16), (15, 21), (20, 10), (15, 7), (23, 4), (16, 18), (25, 14), (25, 5), (20, 9), (20, 7), (24, 11), (2, 17), (18, 4), (15, 1), (12, 20), (24, 9), (11, 7), (15, 0), (14, 20), (4, 2), (19, 18), (4, 21), (6, 20), (3, 20), (0, 22), (18, 12), (19, 0), (7, 17), (1, 8), (16, 0), (12, 16), (23, 13), (14, 9), (0, 18), (19, 16), (9, 13), (7, 20), (9, 18), (0, 13), (7, 21), (20, 13), (16, 13), (12, 4), (0, 21), (5, 14), (18, 19), (24, 17), (6, 21), (25, 1), (11, 19), (23, 12), (25, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120270", "dataset": "MATH"}
{"messages": [{"content": "In a 24x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 22), 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, 4), (21, 3), (7, 4), (0, 22), (3, 9), (11, 9), (15, 19), (17, 15), (20, 20), (16, 16), (23, 2), (16, 8), (0, 2), (21, 1), (16, 18), (16, 10), (20, 10), (6, 2), (14, 2), (4, 3), (8, 13), (3, 5), (7, 22), (18, 5), (15, 7), (20, 17), (4, 15), (0, 19), (3, 11), (20, 12), (23, 17), (10, 20), (8, 5), (0, 17), (6, 1), (2, 21), (21, 7), (17, 1), (6, 9), (12, 19), (22, 8), (7, 19), (11, 1), (16, 14), (1, 21), (1, 2), (4, 12), (5, 15), (23, 11), (8, 0), (14, 12), (13, 22), (15, 22), (16, 15), (17, 7), (1, 1), (13, 8), (10, 21), (15, 20), (20, 13), (14, 4), (12, 2), (7, 8), (0, 12), (1, 16), (5, 12), (22, 7), (17, 17), (13, 9), (9, 5), (1, 10), (16, 0), (8, 1), (9, 7), (10, 18), (17, 13), (9, 17), (4, 22), (2, 13), (11, 6), (19, 0), (1, 20), (22, 5), (16, 20), (8, 21), (14, 10), (17, 16), (1, 18), (19, 18), (8, 9), (5, 5), (18, 1), (2, 8), (2, 1), (1, 13), (6, 7), (12, 7), (1, 17), (22, 1), (6, 22), (10, 9), (11, 17), (1, 4), (19, 9), (13, 0), (16, 13), (5, 16), (13, 13), (10, 13), (9, 8), (20, 18), (9, 10), (8, 20), (7, 10), (1, 15), (17, 21), (0, 20), (21, 9), (12, 16), (4, 20), (13, 21), (21, 15), (8, 22), (2, 19), (8, 11), (18, 17), (15, 13), (18, 0), (0, 14), (17, 6), (14, 0), (4, 4), (14, 17), (0, 13), (3, 14), (10, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280608", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 6), (9, 1), (17, 12), (18, 11), (5, 11), (5, 12), (18, 20), (14, 11), (9, 12), (9, 18), (12, 9), (15, 5), (21, 11), (18, 6), (1, 19), (0, 18), (15, 8), (2, 8), (5, 1), (3, 13), (16, 11), (11, 14), (12, 5), (12, 15), (4, 11), (8, 12), (20, 17), (18, 17), (0, 11), (15, 4), (11, 17), (15, 14), (20, 2), (8, 11), (16, 13), (13, 2), (20, 10), (1, 1), (20, 5), (6, 0), (8, 10), (8, 16), (9, 5), (5, 2), (12, 1), (16, 17), (18, 16), (15, 2), (14, 19), (3, 10), (13, 16), (4, 5), (19, 9), (12, 13), (13, 1), (16, 7), (19, 14), (11, 6), (4, 1), (10, 20), (16, 15), (6, 19), (21, 18), (15, 12), (0, 9), (16, 19), (10, 7), (7, 14), (19, 3), (8, 5), (20, 13), (13, 14), (6, 12), (12, 10), (3, 5), (1, 16), (15, 20), (19, 15), (3, 16), (20, 16), (18, 4), (7, 4), (5, 17), (15, 7), (14, 3), (10, 16), (19, 18), (19, 0), (18, 13), (14, 5), (0, 20), (3, 19), (11, 7), (9, 2), (20, 15), (20, 20), (1, 17), (4, 9), (17, 17), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "802410", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), 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), (19, 5), (10, 0), (14, 11), (7, 16), (14, 24), (5, 26), (6, 6), (13, 10), (14, 16), (5, 3), (13, 7), (21, 8), (23, 14), (1, 7), (18, 24), (11, 1), (12, 16), (21, 13), (9, 4), (24, 3), (6, 11), (12, 13), (1, 11), (26, 9), (27, 15), (24, 6), (11, 24), (24, 8), (0, 18), (10, 24), (14, 19), (8, 15), (1, 2), (24, 15), (10, 9), (17, 1), (2, 19), (8, 0), (21, 7), (13, 11), (15, 25), (9, 3), (22, 26), (7, 14), (16, 13), (18, 10), (24, 25), (16, 11), (16, 16), (9, 19), (23, 13), (10, 14), (19, 7), (12, 19), (6, 12), (17, 6), (13, 8), (19, 9), (0, 21), (18, 15), (17, 10), (15, 12), (3, 4), (27, 8), (15, 10), (12, 18), (21, 21), (10, 18), (18, 5), (10, 17), (12, 1), (27, 21), (10, 13), (26, 22), (8, 7), (7, 7), (13, 14), (23, 19), (23, 15), (12, 6), (12, 5), (7, 9), (8, 13), (18, 26), (7, 11), (15, 23), (15, 26), (4, 14), (18, 16), (19, 0), (14, 18), (12, 3), (15, 24), (16, 26), (19, 25), (7, 24), (9, 15), (22, 10), (14, 5), (1, 15), (17, 19), (25, 17), (10, 22), (21, 3), (25, 8), (17, 25), (21, 10), (21, 2), (16, 2), (22, 6), (20, 12), (3, 3), (10, 1), (1, 25), (2, 9), (3, 10), (19, 3), (19, 21), (24, 5), (21, 15), (1, 5), (19, 15), (11, 5), (13, 13), (22, 22), (6, 16), (0, 12), (24, 2), (0, 11), (25, 14), (17, 14), (6, 5), (14, 13), (23, 10), (27, 18), (0, 4), (0, 15), (1, 24), (15, 7), (25, 4), (8, 11), (18, 0), (26, 15), (4, 2), (14, 4), (11, 7), (18, 25), (6, 15), (17, 17), (25, 25), (13, 3), (0, 7), (26, 0), (2, 1), (9, 16), (13, 16), (13, 19), (26, 7), (5, 0), (24, 26), (1, 8), (11, 8), (4, 15), (20, 14), (2, 24), (18, 3), (25, 3), (6, 1), (16, 19), (22, 12), (14, 17), (9, 21), (26, 25), (7, 19), (16, 9), (0, 13), (20, 10), (25, 1), (26, 26), (19, 13), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428652", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), 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), (7, 6), (7, 19), (6, 11), (0, 8), (2, 11), (15, 21), (20, 18), (11, 22), (3, 22), (5, 15), (13, 5), (1, 15), (5, 23), (17, 24), (11, 10), (7, 11), (15, 23), (0, 15), (15, 7), (16, 14), (10, 11), (12, 20), (20, 8), (18, 5), (5, 4), (9, 15), (7, 2), (10, 8), (15, 2), (2, 21), (19, 17), (14, 18), (6, 17), (10, 15), (1, 3), (11, 6), (5, 1), (10, 12), (17, 0), (14, 0), (17, 23), (15, 4), (12, 14), (2, 1), (11, 2), (0, 18), (14, 1), (9, 16), (15, 10), (14, 13), (0, 3), (12, 4), (1, 22), (10, 4), (12, 22), (14, 22), (6, 3), (18, 0), (14, 12), (1, 23), (4, 6), (2, 4), (13, 1), (4, 20), (0, 23), (4, 8), (9, 17), (2, 23), (6, 13), (10, 13), (0, 6), (14, 6), (14, 10), (14, 16), (20, 15), (8, 4), (5, 12), (8, 23), (16, 6), (13, 9), (3, 12), (15, 5), (7, 7), (8, 5), (20, 5), (19, 19), (11, 16), (7, 16), (8, 0), (4, 11), (19, 24), (10, 14), (7, 24), (19, 16), (12, 8), (1, 17), (11, 11), (16, 11), (9, 18), (13, 7), (18, 19), (5, 22), (1, 21), (5, 13), (10, 6), (20, 0), (11, 17), (15, 20), (18, 6), (3, 0), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541752", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 20), (14, 13), (5, 17), (16, 9), (12, 14), (15, 21), (13, 15), (9, 7), (2, 0), (22, 11), (10, 9), (19, 4), (17, 20), (16, 17), (7, 4), (2, 10), (2, 9), (14, 18), (1, 13), (23, 13), (0, 7), (0, 6), (6, 2), (4, 20), (13, 5), (12, 18), (15, 20), (6, 7), (13, 4), (8, 21), (14, 6), (10, 15), (1, 10), (8, 0), (15, 6), (20, 1), (25, 19), (16, 2), (10, 13), (26, 2), (18, 16), (0, 17), (11, 12), (25, 18), (11, 3), (2, 11), (7, 3), (9, 9), (23, 5), (8, 17), (24, 17), (3, 9), (3, 6), (7, 12), (20, 8), (23, 19), (5, 12), (7, 21), (22, 15), (14, 5), (10, 11), (11, 7), (26, 19), (21, 18), (6, 10), (4, 18), (18, 17), (21, 20), (23, 9), (11, 2), (5, 13), (5, 8), (10, 3), (14, 2), (15, 4), (3, 4), (22, 21), (3, 3), (21, 7), (1, 1), (25, 15), (15, 8), (24, 13), (0, 16), (5, 9), (13, 14), (12, 17), (6, 17), (12, 11), (7, 17), (7, 1), (4, 17), (9, 19), (19, 16), (1, 8), (17, 17), (13, 13), (1, 14), (12, 8), (1, 3), (14, 8), (9, 18), (17, 5), (22, 10), (19, 11), (21, 13), (10, 8), (20, 20), (17, 9), (9, 5), (22, 4), (6, 13), (6, 1), (1, 17), (25, 11), (22, 9), (20, 15), (26, 18), (19, 13), (26, 20), (16, 5), (22, 13), (15, 18), (4, 14), (9, 0), (1, 0), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994032", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 4), (5, 18), (7, 10), (8, 1), (16, 16), (18, 7), (16, 15), (24, 19), (16, 19), (27, 0), (16, 12), (7, 9), (2, 3), (3, 2), (14, 7), (18, 16), (27, 6), (10, 7), (2, 0), (7, 14), (7, 5), (22, 17), (14, 14), (11, 13), (23, 10), (19, 9), (8, 17), (7, 16), (19, 8), (4, 4), (6, 13), (7, 7), (22, 3), (23, 4), (19, 2), (23, 6), (15, 19), (10, 11), (8, 0), (20, 14), (25, 6), (3, 9), (14, 17), (12, 4), (15, 8), (7, 3), (25, 16), (23, 16), (5, 2), (10, 20), (20, 8), (8, 7), (27, 14), (16, 3), (17, 2), (0, 10), (18, 3), (1, 9), (21, 12), (22, 9), (1, 18), (19, 14), (22, 0), (0, 13), (17, 7), (27, 1), (23, 0), (15, 16), (12, 9), (24, 3), (21, 3), (21, 0), (23, 20), (3, 18), (19, 18), (9, 3), (11, 4), (0, 12), (27, 11), (15, 6), (11, 20), (9, 14), (7, 2), (11, 11), (9, 11), (17, 1), (23, 18), (4, 14), (25, 14), (2, 20), (26, 13), (4, 17), (10, 16), (8, 6), (23, 5), (25, 1), (14, 9), (25, 9), (1, 7), (14, 2), (10, 10), (2, 8), (8, 9), (8, 11), (4, 5), (12, 14), (23, 3), (22, 15), (26, 4), (13, 13), (8, 5), (12, 8), (25, 4), (3, 1), (26, 15), (22, 18), (22, 19), (20, 7), (18, 4), (16, 2), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899136", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (4, 1), (9, 2), (8, 22), (1, 12), (15, 22), (21, 1), (22, 7), (13, 4), (19, 20), (23, 0), (5, 10), (21, 16), (11, 13), (1, 7), (12, 6), (6, 5), (22, 3), (19, 27), (0, 26), (1, 9), (22, 22), (6, 21), (0, 17), (16, 24), (17, 20), (17, 25), (21, 3), (17, 10), (9, 22), (13, 8), (9, 17), (12, 25), (1, 5), (10, 6), (7, 22), (23, 8), (1, 2), (14, 12), (20, 17), (17, 12), (10, 8), (0, 23), (17, 22), (13, 25), (15, 2), (18, 15), (16, 16), (18, 14), (11, 14), (21, 26), (18, 21), (10, 5), (21, 20), (4, 21), (7, 19), (19, 12), (23, 3), (9, 21), (5, 15), (20, 25), (8, 6), (8, 8), (5, 20), (15, 15), (14, 3), (16, 21), (18, 8), (15, 24), (18, 16), (14, 17), (7, 8), (2, 0), (11, 18), (10, 21), (10, 26), (0, 15), (12, 21), (4, 15), (8, 27), (5, 14), (7, 20), (12, 1), (3, 2), (4, 13), (20, 26), (10, 16), (21, 24), (23, 6), (3, 22), (1, 11), (20, 4), (21, 6), (12, 27), (16, 6), (12, 3), (5, 26), (7, 3), (2, 26), (8, 21), (13, 24), (11, 24), (18, 2), (15, 11), (17, 3), (2, 5), (0, 16), (23, 19), (2, 4), (22, 9), (13, 12), (20, 2), (5, 4), (20, 22), (5, 0), (0, 25), (17, 24), (20, 9), (12, 13), (19, 6), (6, 12), (18, 6), (14, 7), (22, 10), (10, 17), (13, 18), (18, 5), (23, 26), (5, 12), (23, 20), (4, 7), (9, 24), (8, 20), (22, 4), (15, 16), (23, 11), (12, 10), (12, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351046", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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, 1), (17, 9), (18, 8), (4, 15), (13, 18), (21, 5), (11, 11), (5, 6), (11, 5), (4, 9), (4, 12), (1, 7), (0, 19), (26, 15), (20, 1), (5, 19), (24, 5), (5, 10), (23, 11), (22, 12), (14, 2), (13, 9), (1, 4), (19, 7), (15, 13), (25, 18), (23, 4), (7, 21), (14, 15), (6, 7), (12, 1), (10, 7), (3, 4), (2, 3), (11, 14), (10, 18), (5, 9), (8, 10), (20, 13), (23, 0), (24, 7), (16, 15), (26, 0), (15, 4), (0, 8), (3, 0), (0, 18), (19, 19), (0, 10), (17, 7), (3, 20), (19, 9), (20, 0), (26, 18), (9, 8), (18, 15), (11, 21), (1, 5), (10, 10), (22, 6), (0, 4), (18, 1), (13, 14), (5, 11), (11, 15), (6, 13), (5, 7), (21, 17), (2, 0), (3, 15), (15, 3), (5, 5), (11, 16), (12, 3), (15, 5), (1, 14), (13, 12), (3, 3), (7, 7), (17, 20), (23, 10), (2, 9), (24, 9), (16, 21), (17, 19), (24, 0), (18, 19), (2, 15), (20, 18), (10, 17), (4, 1), (16, 8), (1, 12), (7, 2), (7, 18), (15, 18), (2, 12), (22, 9), (2, 11), (0, 7), (1, 10), (1, 15), (7, 8), (13, 8), (3, 1), (24, 10), (14, 19), (1, 17), (20, 9), (1, 8), (6, 2), (25, 19), (25, 17), (6, 19), (1, 21), (26, 19), (24, 12), (7, 4), (17, 18), (19, 11), (25, 10), (0, 13), (25, 15), (3, 8), (5, 4), (17, 11), (9, 9), (1, 20), (21, 18), (25, 20), (23, 12), (18, 6), (5, 13), (19, 5), (10, 6), (15, 21), (16, 1), (8, 20), (9, 4), (8, 0), (7, 0), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64350", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 3), (17, 4), (14, 7), (19, 15), (1, 15), (13, 2), (15, 17), (14, 11), (6, 12), (1, 4), (17, 3), (23, 0), (23, 15), (8, 15), (15, 10), (15, 14), (16, 19), (21, 17), (4, 6), (15, 6), (6, 18), (14, 6), (0, 10), (1, 16), (21, 0), (9, 0), (9, 3), (18, 13), (18, 0), (1, 11), (20, 11), (3, 16), (15, 2), (11, 6), (20, 0), (3, 8), (3, 17), (12, 12), (17, 0), (0, 17), (0, 18), (12, 3), (20, 7), (11, 4), (13, 15), (21, 12), (16, 13), (6, 6), (11, 15), (22, 3), (14, 16), (6, 13), (23, 17), (11, 3), (4, 15), (3, 15), (19, 1), (21, 9), (11, 10), (22, 0), (14, 9), (4, 16), (19, 9), (9, 1), (18, 1), (9, 9), (3, 13), (11, 12), (17, 9), (2, 11), (22, 2), (1, 1), (9, 19), (2, 8), (18, 9), (18, 7), (9, 10), (7, 3), (19, 8), (8, 14), (3, 10), (21, 14), (0, 13), (18, 8), (2, 17), (18, 5), (6, 2), (21, 2), (5, 6), (3, 7), (21, 13), (22, 6), (18, 6), (3, 0), (4, 8), (19, 14), (2, 10), (21, 11), (2, 14), (13, 16), (5, 16), (1, 2), (9, 5), (7, 8), (9, 14), (12, 13), (4, 2), (7, 14), (12, 9), (21, 15), (22, 14), (4, 17), (4, 18), (19, 17), (14, 4), (7, 16), (0, 14), (21, 4), (15, 8), (14, 5), (11, 17), (23, 5), (12, 6), (16, 10), (8, 9), (19, 2), (6, 4), (17, 19), (10, 18), (2, 12), (5, 1), (11, 18), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960750", "dataset": "MATH"}
{"messages": [{"content": "In a 22x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 19), (6, 4), (10, 22), (10, 26), (12, 17), (5, 24), (0, 6), (1, 19), (2, 18), (13, 24), (10, 20), (4, 4), (9, 28), (3, 16), (11, 17), (12, 27), (7, 23), (8, 3), (21, 1), (11, 18), (16, 10), (2, 1), (2, 7), (7, 28), (0, 18), (5, 8), (9, 24), (15, 26), (20, 5), (3, 8), (5, 2), (5, 11), (15, 18), (2, 24), (13, 20), (14, 12), (1, 13), (16, 3), (10, 28), (20, 12), (8, 9), (6, 19), (6, 27), (18, 28), (10, 24), (12, 6), (3, 18), (4, 8), (3, 14), (5, 19), (14, 8), (13, 21), (10, 4), (16, 12), (15, 23), (19, 1), (16, 1), (1, 17), (7, 15), (19, 11), (13, 1), (15, 5), (13, 27), (3, 24), (9, 5), (0, 22), (5, 20), (3, 20), (19, 6), (16, 0), (16, 24), (17, 22), (14, 2), (18, 24), (6, 12), (7, 4), (11, 14), (20, 20), (2, 5), (14, 24), (5, 23), (3, 25), (12, 5), (14, 7), (6, 23), (14, 18), (5, 3), (18, 10), (19, 24), (13, 26), (13, 23), (18, 0), (4, 6), (16, 18), (8, 17), (3, 17), (17, 17), (19, 17), (0, 23), (13, 6), (3, 19), (19, 7), (4, 22), (17, 23), (20, 2), (4, 17), (13, 10), (10, 7), (0, 17), (8, 7), (1, 3), (18, 3), (9, 4), (0, 2), (2, 10), (10, 8), (3, 5), (1, 16), (8, 4), (4, 2), (0, 21), (20, 3), (21, 2), (6, 1), (19, 14), (16, 4), (4, 10), (11, 3), (7, 12), (1, 6), (5, 22), (1, 27), (20, 1), (18, 11), (13, 7), (13, 8), (2, 13), (11, 26), (19, 2), (17, 16), (18, 2), (6, 28), (11, 11), (12, 19), (11, 10), (6, 17), (2, 6), (9, 23), (18, 7), (16, 19), (3, 4), (5, 15), (6, 6), (21, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408600", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), 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), (9, 16), (6, 22), (20, 9), (17, 10), (6, 15), (19, 11), (5, 26), (11, 20), (6, 8), (21, 13), (12, 6), (5, 19), (8, 6), (17, 7), (21, 8), (4, 20), (19, 6), (21, 3), (22, 16), (4, 1), (15, 15), (8, 11), (0, 3), (18, 25), (22, 1), (8, 3), (1, 4), (12, 19), (15, 8), (10, 13), (5, 2), (22, 4), (2, 1), (0, 12), (9, 0), (7, 8), (11, 7), (20, 2), (13, 7), (11, 5), (10, 19), (14, 10), (6, 3), (21, 23), (4, 11), (12, 4), (3, 19), (14, 0), (19, 25), (22, 17), (9, 25), (6, 20), (7, 4), (15, 26), (3, 7), (17, 0), (8, 9), (17, 20), (10, 3), (6, 26), (1, 19), (5, 13), (3, 10), (1, 9), (7, 21), (9, 13), (6, 12), (1, 7), (19, 22), (3, 17), (0, 13), (3, 6), (18, 17), (3, 5), (22, 24), (10, 18), (21, 17), (2, 13), (8, 15), (12, 9), (16, 16), (3, 2), (18, 6), (6, 27), (3, 26), (7, 1), (13, 14), (5, 9), (16, 22), (16, 0), (19, 5), (22, 19), (9, 11), (20, 19), (4, 26), (4, 25), (21, 18), (21, 20), (7, 27), (7, 16), (19, 9), (22, 7), (11, 11), (3, 21), (13, 20), (18, 10), (22, 10), (5, 22), (8, 4), (6, 4), (12, 22), (13, 6), (18, 26), (4, 9), (0, 15), (9, 14), (9, 8), (16, 13), (15, 14), (20, 27), (18, 20), (18, 5), (9, 2), (13, 2), (0, 24), (11, 25), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156144", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 17), (16, 0), (23, 3), (17, 20), (18, 6), (10, 14), (0, 8), (5, 15), (17, 7), (7, 14), (9, 14), (5, 7), (17, 9), (15, 4), (4, 14), (13, 13), (11, 17), (2, 21), (16, 15), (4, 6), (4, 12), (11, 3), (18, 16), (12, 12), (17, 5), (14, 11), (18, 20), (13, 9), (6, 0), (10, 16), (11, 13), (5, 8), (2, 11), (13, 5), (11, 7), (21, 20), (19, 11), (21, 4), (17, 14), (8, 3), (8, 2), (13, 12), (7, 21), (10, 19), (10, 15), (10, 9), (14, 17), (16, 18), (16, 7), (0, 18), (13, 11), (7, 11), (9, 4), (2, 7), (13, 14), (1, 20), (5, 19), (23, 8), (22, 18), (13, 15), (24, 11), (11, 20), (11, 10), (23, 9), (7, 6), (7, 5), (2, 18), (6, 8), (22, 0), (22, 10), (4, 10), (2, 5), (23, 7), (23, 6), (2, 17), (10, 13), (4, 9), (5, 18), (19, 7), (23, 14), (15, 15), (7, 4), (16, 2), (11, 19), (8, 10), (24, 17), (14, 18), (24, 13), (15, 10), (15, 7), (1, 14), (23, 19), (22, 4), (6, 16), (20, 5), (21, 8), (1, 21), (1, 1), (8, 19), (10, 17), (23, 15), (24, 8), (3, 1), (14, 14), (9, 12), (0, 9), (8, 13), (19, 17), (22, 17), (19, 10), (20, 19), (8, 20), (3, 21), (14, 13), (16, 4), (0, 5), (22, 21), (15, 9), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "651496", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 16), (16, 21), (10, 9), (6, 5), (3, 16), (17, 3), (17, 7), (18, 3), (21, 5), (21, 19), (8, 17), (11, 23), (12, 1), (10, 10), (10, 5), (16, 10), (7, 2), (17, 24), (13, 15), (6, 9), (9, 15), (14, 13), (9, 2), (2, 25), (10, 13), (12, 7), (13, 9), (20, 20), (11, 8), (14, 2), (11, 15), (13, 1), (20, 19), (20, 7), (4, 23), (12, 19), (10, 22), (9, 4), (6, 15), (16, 6), (14, 11), (21, 2), (3, 0), (9, 5), (18, 11), (13, 2), (19, 4), (0, 14), (21, 24), (22, 1), (9, 13), (12, 12), (20, 10), (16, 19), (5, 20), (5, 17), (0, 22), (7, 5), (13, 19), (17, 11), (5, 1), (11, 21), (20, 21), (8, 1), (4, 21), (15, 15), (12, 2), (19, 0), (18, 21), (9, 10), (12, 22), (4, 3), (0, 19), (3, 18), (11, 13), (0, 25), (6, 25), (14, 7), (16, 13), (5, 21), (18, 16), (4, 14), (9, 3), (17, 14), (15, 3), (22, 3), (3, 9), (7, 9), (21, 13), (1, 9), (1, 0), (9, 23), (13, 14), (7, 18), (15, 20), (9, 0), (11, 17), (22, 15), (4, 1), (13, 3), (18, 2), (5, 19), (11, 12), (0, 6), (0, 11), (15, 8), (1, 20), (10, 8), (7, 1), (7, 22), (8, 6), (10, 12), (5, 25), (8, 22), (19, 16), (13, 21), (15, 18), (4, 24), (19, 21), (19, 1), (10, 7), (1, 24), (13, 11), (21, 0), (0, 5), (16, 8), (6, 24), (3, 10), (5, 14), (2, 19), (10, 2), (14, 0), (12, 5), (4, 2), (18, 4), (12, 0), (21, 11), (15, 19), (2, 16), (21, 23), (18, 13), (20, 22), (2, 2), (14, 17), (22, 22), (18, 18), (20, 3), (20, 15), (3, 17), (8, 0), (11, 9), (20, 9), (3, 23), (17, 13), (19, 15), (5, 18), (13, 18), (1, 10), (14, 4), (17, 12), (17, 15), (14, 5), (19, 3), (0, 15), (16, 23), (0, 2), (21, 4), (11, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1140", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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), (11, 9), (9, 4), (12, 15), (24, 16), (20, 8), (21, 18), (4, 15), (11, 13), (12, 0), (14, 2), (17, 14), (5, 3), (12, 21), (2, 11), (15, 20), (24, 11), (21, 9), (3, 21), (17, 17), (26, 2), (20, 15), (19, 17), (6, 16), (10, 3), (23, 14), (6, 18), (11, 17), (20, 10), (7, 3), (13, 14), (12, 8), (7, 10), (14, 4), (21, 11), (2, 9), (19, 7), (7, 2), (24, 7), (25, 2), (1, 13), (2, 7), (6, 6), (3, 19), (4, 21), (10, 6), (0, 12), (0, 9), (18, 9), (12, 3), (7, 15), (1, 7), (5, 20), (15, 5), (25, 3), (18, 13), (3, 13), (18, 14), (13, 19), (1, 1), (22, 13), (4, 20), (21, 20), (8, 8), (26, 12), (23, 18), (12, 4), (8, 18), (12, 1), (0, 8), (18, 0), (9, 12), (4, 14), (20, 0), (1, 0), (10, 11), (7, 12), (15, 16), (21, 19), (0, 5), (19, 8), (5, 12), (26, 13), (26, 11), (20, 3), (25, 14), (22, 9), (20, 4), (24, 8), (10, 20), (11, 18), (13, 18), (3, 16), (22, 5), (16, 4), (20, 2), (26, 14), (15, 7), (21, 17), (11, 6), (14, 18), (17, 16), (4, 13), (4, 11), (19, 15), (10, 15), (15, 17), (3, 15), (25, 21), (14, 20), (20, 20), (17, 1), (8, 9), (15, 21), (15, 6), (19, 2), (14, 1), (14, 13), (10, 2), (11, 12), (4, 0), (21, 12), (17, 5), (8, 4), (24, 15), (1, 9), (23, 17), (7, 18), (5, 16), (14, 0), (22, 4), (3, 8), (5, 4), (2, 3), (2, 8), (7, 16), (0, 21), (25, 7), (6, 7), (17, 4), (24, 5), (12, 11), (22, 11), (23, 5), (17, 9), (22, 3), (4, 12), (10, 8), (2, 0), (1, 12), (7, 21), (5, 11), (9, 5), (25, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427320", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), 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), (14, 11), (14, 1), (7, 18), (1, 18), (19, 7), (14, 9), (8, 8), (24, 3), (25, 22), (14, 24), (6, 1), (16, 19), (5, 2), (1, 17), (8, 3), (16, 18), (1, 16), (27, 16), (20, 22), (24, 23), (14, 3), (12, 16), (26, 23), (14, 4), (20, 15), (13, 20), (0, 4), (23, 11), (17, 24), (22, 16), (27, 6), (24, 24), (19, 17), (18, 13), (5, 15), (7, 0), (21, 6), (3, 1), (18, 14), (15, 20), (4, 1), (1, 1), (17, 10), (22, 4), (4, 11), (12, 9), (26, 13), (10, 13), (27, 7), (20, 13), (5, 20), (23, 24), (14, 2), (24, 4), (13, 23), (18, 0), (8, 20), (16, 12), (1, 3), (8, 10), (11, 15), (4, 4), (26, 0), (24, 22), (4, 19), (16, 15), (8, 19), (15, 23), (2, 4), (3, 11), (7, 15), (26, 14), (9, 5), (25, 4), (21, 14), (15, 2), (23, 10), (12, 18), (9, 1), (20, 11), (4, 2), (15, 8), (18, 23), (13, 8), (16, 21), (23, 20), (10, 14), (22, 8), (5, 17), (26, 9), (21, 15), (17, 18), (16, 3), (22, 24), (4, 24), (13, 6), (21, 16), (25, 9), (1, 14), (17, 5), (3, 20), (25, 15), (13, 2), (14, 6), (10, 2), (22, 12), (12, 24), (15, 17), (10, 4), (9, 14), (23, 1), (0, 23), (10, 1), (25, 12), (1, 4), (2, 13), (6, 17), (21, 1), (7, 24), (6, 9), (11, 24), (11, 0), (21, 24), (19, 15), (3, 23), (7, 11), (19, 3), (27, 13), (10, 11), (3, 15), (5, 8), (15, 21), (13, 17), (12, 10), (5, 12), (18, 15), (16, 11), (9, 17), (6, 21), (2, 24), (6, 2), (1, 21), (20, 1), (18, 22), (26, 22), (1, 19), (23, 3), (12, 22), (2, 5), (2, 1), (6, 10), (3, 22), (18, 24), (24, 12), (19, 19), (15, 16), (15, 6), (26, 19), (6, 13), (21, 20), (10, 7), (10, 12), (26, 2), (11, 1), (21, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891000", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 3), (12, 17), (0, 20), (9, 14), (10, 22), (11, 20), (12, 6), (10, 8), (8, 24), (6, 18), (20, 7), (3, 18), (18, 6), (18, 20), (19, 20), (18, 4), (20, 19), (2, 18), (9, 7), (14, 15), (15, 6), (9, 27), (0, 12), (0, 21), (21, 7), (11, 6), (9, 2), (18, 16), (3, 21), (17, 0), (12, 8), (8, 1), (14, 6), (21, 12), (11, 18), (5, 9), (1, 18), (11, 12), (2, 20), (18, 10), (18, 24), (11, 13), (5, 14), (9, 9), (4, 18), (5, 23), (10, 25), (19, 7), (17, 15), (18, 11), (20, 8), (3, 19), (20, 23), (13, 0), (7, 2), (5, 15), (10, 11), (15, 7), (3, 7), (15, 10), (1, 0), (15, 8), (15, 25), (12, 25), (14, 26), (7, 27), (4, 24), (13, 14), (17, 17), (6, 20), (6, 21), (5, 6), (2, 12), (10, 16), (4, 15), (0, 26), (4, 13), (14, 8), (19, 5), (11, 1), (14, 3), (3, 25), (8, 4), (14, 10), (12, 13), (20, 20), (10, 21), (16, 6), (4, 1), (1, 9), (7, 25), (18, 22), (11, 22), (19, 11), (11, 5), (0, 27), (20, 11), (9, 22), (14, 17), (1, 22), (4, 6), (10, 19), (7, 0), (12, 14), (13, 9), (3, 20), (10, 18), (0, 10), (4, 4), (4, 23), (14, 5), (1, 4), (7, 11), (21, 9), (15, 11), (19, 16), (15, 2), (18, 8), (0, 15), (14, 19), (0, 25), (9, 20), (21, 21), (16, 26), (0, 5), (3, 9), (1, 16), (0, 7), (10, 3), (13, 12), (21, 15), (6, 19), (13, 22), (8, 22), (18, 17), (17, 21), (11, 11), (3, 10), (10, 7), (18, 26), (15, 13), (20, 16), (14, 2), (19, 3), (4, 16), (1, 8), (10, 0), (16, 1), (17, 18), (16, 15), (20, 25), (13, 21), (16, 23), (4, 3), (12, 23), (13, 10), (12, 4), (12, 16), (4, 17), (2, 27), (15, 22), (5, 27), (7, 17), (5, 16), (2, 24), (6, 11), (21, 5), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997920", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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), (15, 7), (14, 0), (3, 26), (23, 6), (9, 21), (12, 18), (13, 10), (16, 8), (1, 1), (1, 16), (18, 4), (0, 9), (6, 15), (5, 4), (0, 23), (14, 22), (9, 12), (6, 24), (3, 18), (26, 2), (8, 8), (19, 21), (11, 22), (7, 20), (4, 19), (3, 0), (25, 5), (5, 12), (17, 0), (7, 14), (9, 26), (4, 5), (16, 13), (0, 16), (3, 9), (8, 11), (1, 5), (27, 23), (13, 17), (8, 1), (17, 2), (18, 1), (6, 12), (20, 7), (24, 1), (0, 3), (9, 25), (25, 6), (12, 7), (15, 4), (26, 7), (7, 12), (12, 22), (5, 21), (17, 5), (2, 11), (1, 25), (20, 3), (14, 24), (14, 18), (2, 22), (18, 6), (24, 9), (18, 8), (24, 5), (1, 18), (23, 12), (9, 8), (12, 24), (15, 13), (15, 3), (28, 12), (20, 18), (11, 15), (22, 24), (26, 25), (22, 19), (9, 23), (6, 18), (15, 0), (6, 19), (22, 6), (15, 15), (16, 15), (13, 0), (17, 20), (22, 26), (15, 8), (18, 19), (27, 4), (23, 10), (11, 8), (9, 7), (2, 25), (13, 25), (20, 17), (25, 13), (7, 2), (26, 11), (13, 9), (22, 21), (24, 14), (14, 16), (25, 4), (10, 21), (20, 25), (20, 8), (7, 6), (14, 2), (25, 23), (20, 26), (9, 15), (18, 26), (23, 15), (15, 9), (27, 5), (6, 16), (21, 5), (4, 25), (17, 18), (6, 6), (7, 24), (19, 1), (27, 22), (4, 1), (12, 14), (4, 20), (3, 12), (2, 14), (10, 23), (22, 13), (7, 15), (0, 12), (3, 22), (22, 18), (1, 9), (27, 24), (2, 17), (19, 11), (16, 3), (20, 14), (28, 25), (11, 19), (5, 1), (14, 10), (28, 23), (0, 2), (27, 19), (19, 17), (4, 3), (24, 19), (12, 3), (24, 8), (14, 14), (10, 16), (4, 24), (14, 1), (12, 5), (4, 10), (27, 9), (8, 5), (23, 26), (15, 25), (4, 18), (22, 0), (8, 9), (2, 16), (25, 2), (11, 24), (21, 16), (17, 7), (18, 16), (22, 2), (5, 22), (14, 3), (26, 6), (5, 3), (8, 20), (1, 2), (27, 3), (10, 20), (27, 1), (24, 24), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "815110", "dataset": "MATH"}
{"messages": [{"content": "In a 26x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 19), 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), (10, 2), (9, 5), (17, 0), (19, 6), (5, 9), (7, 19), (14, 2), (5, 4), (16, 2), (14, 16), (2, 7), (14, 9), (2, 14), (20, 7), (9, 10), (16, 5), (4, 5), (18, 13), (7, 16), (2, 5), (11, 18), (8, 17), (13, 8), (8, 10), (4, 6), (22, 5), (1, 10), (24, 9), (3, 2), (23, 16), (15, 16), (25, 18), (11, 5), (5, 2), (4, 19), (5, 6), (8, 2), (14, 1), (19, 13), (17, 6), (12, 11), (9, 17), (2, 9), (15, 15), (17, 12), (20, 13), (25, 14), (9, 16), (0, 5), (20, 9), (22, 3), (4, 11), (0, 2), (24, 15), (16, 16), (7, 7), (8, 19), (3, 18), (21, 18), (25, 7), (19, 8), (7, 13), (20, 0), (4, 3), (21, 19), (2, 11), (11, 8), (1, 3), (13, 14), (18, 11), (20, 6), (18, 15), (3, 1), (9, 15), (7, 10), (2, 10), (19, 3), (4, 4), (0, 19), (18, 12), (11, 0), (15, 10), (13, 5), (22, 1), (10, 19), (1, 11), (12, 17), (10, 5), (7, 8), (14, 14), (22, 8), (1, 8), (23, 13), (0, 10), (7, 2), (10, 10), (23, 5), (6, 11), (22, 15), (1, 15), (20, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690480", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 2), (4, 15), (16, 3), (13, 15), (19, 21), (3, 8), (17, 18), (10, 13), (11, 1), (6, 20), (10, 8), (14, 7), (11, 3), (3, 18), (6, 10), (12, 15), (0, 19), (15, 19), (20, 10), (5, 17), (16, 10), (18, 2), (16, 1), (2, 0), (14, 0), (21, 0), (13, 20), (6, 3), (12, 3), (3, 1), (10, 17), (9, 18), (13, 13), (14, 5), (17, 21), (15, 6), (18, 16), (13, 6), (18, 0), (8, 2), (14, 10), (13, 17), (1, 19), (15, 14), (12, 6), (15, 8), (5, 0), (16, 11), (1, 5), (5, 19), (10, 1), (13, 4), (20, 1), (8, 11), (5, 4), (10, 11), (17, 9), (7, 13), (16, 20), (9, 21), (16, 5), (3, 12), (4, 19), (17, 6), (9, 16), (16, 21), (2, 10), (14, 17), (6, 1), (14, 8), (20, 11), (12, 1), (4, 6), (20, 0), (18, 14), (19, 1), (7, 12), (12, 14), (6, 14), (3, 3), (8, 19), (17, 10), (11, 0), (1, 12), (6, 19), (21, 4), (21, 11), (9, 7), (18, 3), (2, 1), (10, 5), (5, 1), (11, 19), (13, 0), (13, 9), (8, 8), (8, 4), (0, 4), (19, 11), (15, 21), (13, 5), (4, 18), (4, 3), (9, 0), (12, 0), (9, 15), (1, 17), (14, 16), (18, 12), (5, 14), (5, 12), (21, 3), (11, 4), (1, 0), (8, 16), (6, 2), (17, 11), (12, 17), (17, 3), (14, 2), (18, 19), (1, 9), (3, 13), (2, 18), (3, 20), (4, 8), (6, 18), (16, 8), (5, 9), (4, 0), (11, 10), (10, 6), (12, 18), (16, 4), (7, 3), (19, 16), (20, 16), (12, 8), (16, 18), (11, 13), (8, 1), (5, 13), (19, 13), (9, 5), (17, 0), (21, 7), (2, 11), (19, 19), (18, 13), (2, 6), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278304", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 19), (1, 19), (7, 2), (18, 10), (9, 11), (10, 23), (15, 4), (12, 18), (4, 20), (12, 8), (14, 13), (8, 17), (13, 12), (19, 11), (6, 21), (3, 14), (17, 11), (20, 11), (0, 13), (20, 20), (20, 8), (18, 7), (19, 12), (6, 10), (9, 3), (18, 15), (6, 4), (2, 12), (6, 0), (4, 6), (0, 19), (8, 8), (14, 17), (6, 16), (13, 19), (16, 11), (11, 13), (17, 4), (14, 22), (16, 0), (16, 6), (11, 3), (8, 6), (10, 19), (18, 5), (18, 18), (10, 3), (0, 6), (15, 7), (0, 9), (13, 14), (11, 15), (5, 1), (15, 6), (16, 22), (8, 18), (4, 11), (6, 14), (8, 19), (10, 10), (4, 10), (11, 5), (13, 4), (2, 19), (4, 15), (5, 3), (5, 10), (4, 4), (7, 0), (1, 10), (4, 23), (17, 23), (3, 1), (15, 5), (2, 16), (8, 2), (9, 4), (10, 17), (0, 20), (8, 9), (20, 13), (14, 12), (18, 13), (0, 17), (19, 7), (2, 10), (9, 23), (8, 12), (7, 13), (0, 16), (5, 8), (1, 13), (16, 5), (1, 6), (7, 21), (0, 23), (10, 12), (18, 21), (15, 19), (1, 0), (3, 3), (6, 19), (2, 1), (4, 0), (7, 6), (11, 8), (6, 8), (19, 17), (20, 19), (2, 11), (14, 9), (1, 14), (7, 12), (3, 6), (18, 8), (0, 18), (18, 4), (0, 12), (10, 8), (11, 21), (12, 22), (4, 1), (18, 3), (12, 7), (2, 9), (5, 20), (19, 19), (18, 9), (12, 19), (1, 20), (11, 4), (7, 23), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303744", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 6), (9, 2), (17, 11), (24, 0), (2, 20), (27, 2), (8, 3), (12, 11), (14, 0), (13, 5), (19, 0), (20, 14), (1, 18), (24, 18), (10, 1), (9, 7), (6, 5), (4, 5), (0, 13), (11, 3), (22, 16), (4, 8), (14, 14), (25, 20), (22, 10), (3, 9), (8, 5), (1, 15), (5, 9), (11, 13), (17, 5), (9, 9), (17, 8), (6, 9), (18, 14), (19, 1), (2, 5), (23, 5), (7, 15), (6, 11), (11, 16), (0, 11), (10, 8), (18, 13), (14, 1), (20, 18), (14, 12), (16, 9), (19, 6), (1, 2), (7, 18), (13, 8), (3, 12), (0, 17), (19, 5), (13, 16), (16, 11), (24, 7), (1, 0), (21, 19), (13, 0), (25, 19), (3, 6), (24, 9), (2, 6), (17, 18), (20, 6), (4, 17), (0, 18), (7, 19), (15, 8), (16, 5), (15, 0), (23, 19), (20, 11), (16, 18), (9, 3), (4, 12), (27, 15), (24, 3), (8, 8), (26, 0), (5, 17), (11, 1), (8, 16), (14, 7), (11, 19), (27, 9), (19, 18), (5, 20), (14, 11), (16, 13), (0, 7), (23, 3), (2, 14), (9, 11), (2, 3), (8, 12), (12, 18), (8, 11), (13, 14), (19, 3), (0, 15), (18, 4), (13, 11), (25, 16), (26, 15), (22, 17), (20, 7), (8, 19), (7, 4), (8, 10), (13, 12), (0, 14), (27, 11), (2, 10), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51282", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), 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), (2, 0), (4, 15), (13, 15), (4, 1), (13, 19), (2, 3), (18, 4), (20, 12), (13, 21), (3, 21), (1, 20), (13, 6), (12, 17), (16, 20), (6, 9), (14, 17), (0, 15), (1, 17), (20, 9), (1, 6), (3, 16), (16, 10), (4, 4), (5, 17), (11, 1), (4, 2), (17, 21), (2, 13), (20, 11), (7, 5), (7, 9), (0, 19), (17, 4), (20, 16), (12, 15), (19, 17), (20, 17), (18, 0), (15, 9), (14, 11), (2, 9), (15, 18), (3, 17), (20, 8), (18, 13), (6, 4), (15, 6), (3, 8), (12, 9), (19, 13), (20, 20), (18, 1), (12, 4), (10, 10), (12, 13), (13, 12), (2, 10), (2, 11), (7, 7), (10, 0), (13, 5), (7, 8), (14, 19), (13, 13), (16, 5), (4, 13), (1, 1), (18, 6), (15, 4), (8, 18), (16, 4), (0, 5), (12, 21), (10, 19), (4, 11), (18, 17), (0, 4), (14, 2), (1, 16), (12, 18), (4, 5), (13, 16), (17, 19), (8, 11), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "985260", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (4, 25), (27, 21), (2, 17), (15, 14), (15, 24), (3, 22), (9, 13), (24, 19), (10, 23), (19, 5), (0, 20), (12, 6), (27, 13), (16, 2), (21, 15), (14, 14), (13, 14), (9, 20), (2, 3), (7, 5), (17, 4), (21, 27), (10, 18), (12, 19), (20, 5), (1, 20), (28, 4), (11, 0), (17, 24), (23, 7), (1, 6), (8, 6), (10, 20), (6, 18), (13, 16), (3, 0), (3, 10), (20, 9), (22, 16), (19, 16), (3, 4), (7, 4), (12, 2), (23, 11), (28, 25), (17, 3), (22, 23), (13, 5), (18, 17), (26, 13), (3, 1), (25, 19), (7, 6), (13, 26), (28, 7), (22, 21), (6, 9), (12, 10), (7, 17), (1, 17), (22, 27), (16, 3), (21, 25), (4, 24), (10, 9), (17, 22), (8, 14), (0, 8), (13, 1), (17, 8), (21, 22), (2, 5), (10, 5), (22, 13), (14, 23), (12, 26), (25, 6), (14, 25), (15, 3), (21, 7), (20, 21), (28, 6), (25, 11), (24, 14), (28, 3), (1, 23), (3, 7), (16, 4), (20, 23), (23, 21), (14, 12), (11, 20), (15, 22), (25, 27), (12, 15), (16, 22), (1, 18), (20, 19), (7, 7), (12, 24), (8, 15), (9, 19), (14, 9), (23, 5), (18, 14), (11, 11), (9, 8), (27, 12), (12, 5), (23, 0), (0, 27), (12, 7), (25, 13), (23, 1), (28, 16), (10, 19), (0, 3), (4, 6), (2, 0), (16, 8), (15, 12), (22, 1), (2, 13), (21, 12), (15, 2), (23, 22), (3, 8), (22, 25), (7, 25), (22, 12), (28, 2), (10, 16), (9, 18), (20, 16), (1, 8), (12, 13), (28, 12), (26, 21), (13, 15), (15, 6), (19, 10), (19, 6), (28, 5), (22, 11), (23, 8), (11, 22), (17, 6), (26, 7), (6, 15), (4, 12), (16, 21), (11, 1), (18, 5), (9, 14), (28, 0), (2, 12), (17, 1), (9, 12), (2, 24), (0, 2), (10, 25), (6, 20), (6, 24), (4, 22), (3, 6), (21, 14), (10, 11), (10, 10), (11, 7), (3, 5), (12, 23), (19, 4), (5, 9), (17, 13), (25, 26), (21, 2), (14, 4), (27, 27), (2, 4), (9, 7), (8, 3), (13, 6), (28, 22), (9, 10), (14, 3), (9, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354096", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 12), (13, 15), (12, 15), (22, 6), (11, 19), (11, 15), (1, 5), (7, 18), (16, 1), (9, 19), (19, 6), (5, 14), (9, 3), (5, 6), (2, 15), (11, 8), (20, 9), (17, 13), (22, 14), (0, 1), (20, 13), (8, 10), (14, 5), (15, 11), (4, 9), (20, 6), (10, 1), (21, 9), (6, 10), (1, 19), (13, 9), (19, 10), (3, 20), (20, 15), (0, 8), (18, 9), (20, 12), (14, 10), (2, 4), (8, 7), (18, 12), (8, 1), (9, 0), (19, 18), (1, 6), (15, 0), (10, 8), (4, 5), (11, 9), (14, 17), (1, 7), (16, 15), (9, 2), (12, 1), (21, 15), (6, 7), (11, 16), (20, 17), (6, 2), (5, 3), (20, 4), (20, 20), (20, 3), (12, 6), (18, 20), (19, 15), (21, 1), (14, 14), (14, 19), (10, 17), (19, 14), (16, 6), (6, 15), (12, 7), (20, 2), (2, 10), (7, 16), (22, 15), (7, 14), (12, 0), (4, 6), (9, 18), (10, 7), (0, 4), (5, 11), (10, 2), (1, 2), (6, 9), (17, 10), (5, 7), (13, 5), (0, 16), (6, 17), (3, 5), (21, 3), (0, 5), (7, 7), (5, 12), (19, 12), (21, 11), (13, 18), (5, 2), (7, 11), (4, 1), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610812", "dataset": "MATH"}
{"messages": [{"content": "In a 22x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 0), (20, 21), (6, 7), (19, 9), (16, 8), (1, 20), (5, 4), (7, 13), (20, 4), (4, 20), (13, 5), (2, 9), (13, 1), (4, 10), (14, 3), (19, 15), (0, 10), (18, 16), (7, 18), (12, 3), (13, 13), (15, 21), (13, 3), (16, 12), (2, 3), (0, 1), (0, 5), (14, 21), (3, 7), (8, 10), (19, 6), (10, 15), (6, 2), (4, 15), (1, 19), (5, 11), (0, 3), (0, 2), (11, 13), (15, 6), (15, 14), (5, 5), (16, 13), (16, 17), (11, 11), (15, 11), (14, 10), (6, 18), (20, 6), (6, 14), (1, 13), (21, 18), (21, 6), (2, 13), (18, 5), (17, 12), (17, 1), (9, 13), (5, 2), (3, 1), (0, 21), (21, 8), (5, 18), (14, 5), (8, 13), (20, 17), (1, 21), (2, 7), (10, 17), (20, 10), (15, 20), (14, 6), (12, 0), (18, 19), (20, 7), (7, 20), (18, 1), (14, 13), (9, 5), (11, 16), (12, 2), (11, 14), (7, 1), (18, 20), (21, 17), (1, 11), (9, 8), (10, 7), (17, 11), (0, 17), (2, 19), (1, 16), (6, 21), (19, 0), (15, 18), (19, 17), (13, 11), (0, 7), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928620", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 10), (12, 15), (1, 21), (4, 13), (6, 10), (3, 23), (27, 19), (17, 3), (5, 13), (13, 7), (2, 4), (3, 7), (8, 19), (9, 12), (2, 7), (9, 2), (19, 1), (5, 9), (26, 15), (4, 21), (4, 19), (2, 22), (20, 18), (20, 20), (10, 0), (3, 20), (27, 5), (10, 19), (18, 9), (20, 15), (18, 21), (18, 0), (11, 9), (22, 11), (23, 11), (2, 2), (21, 9), (5, 8), (4, 3), (22, 8), (5, 5), (12, 20), (24, 19), (6, 7), (2, 12), (18, 10), (24, 7), (11, 12), (23, 3), (5, 2), (13, 11), (7, 16), (9, 20), (3, 19), (0, 13), (12, 8), (10, 8), (25, 1), (20, 11), (9, 21), (4, 12), (12, 12), (15, 0), (24, 15), (22, 12), (4, 11), (18, 19), (26, 23), (5, 19), (9, 16), (5, 16), (27, 3), (19, 11), (12, 9), (26, 11), (10, 18), (17, 21), (21, 8), (12, 0), (18, 14), (27, 12), (11, 22), (17, 14), (26, 14), (25, 3), (13, 19), (6, 21), (6, 6), (1, 9), (7, 14), (4, 23), (16, 9), (15, 22), (8, 10), (25, 6), (2, 13), (14, 15), (22, 23), (11, 17), (20, 12), (1, 14), (4, 20), (27, 20), (22, 10), (10, 4), (25, 9), (15, 10), (12, 21), (15, 7), (16, 1), (19, 8), (25, 12), (5, 21), (13, 20), (19, 19), (2, 11), (23, 0), (0, 17), (17, 5), (0, 10), (24, 20), (20, 1), (8, 16), (21, 7), (23, 12), (10, 17), (5, 23), (1, 8), (16, 20), (22, 21), (3, 14), (13, 2), (23, 19), (6, 4), (9, 22), (7, 6), (6, 3), (2, 18), (10, 13), (10, 14), (11, 4), (24, 22), (5, 6), (24, 16), (12, 7), (18, 7), (17, 7), (26, 21), (13, 8), (17, 16), (17, 12), (3, 6), (14, 21), (16, 17), (18, 23), (8, 3), (21, 17), (4, 8), (7, 3), (17, 23), (15, 16), (25, 17), (20, 7), (24, 1), (9, 17), (12, 22), (13, 21), (22, 2), (19, 20), (12, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556080", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 23), (23, 10), (4, 14), (21, 16), (13, 21), (4, 16), (19, 24), (16, 20), (1, 19), (0, 7), (2, 13), (13, 1), (13, 23), (14, 16), (6, 19), (5, 16), (2, 21), (20, 17), (13, 17), (25, 9), (14, 15), (1, 2), (22, 20), (9, 1), (10, 12), (2, 22), (12, 15), (9, 23), (22, 25), (14, 21), (1, 25), (14, 0), (6, 17), (25, 23), (23, 1), (12, 9), (18, 16), (3, 11), (6, 14), (18, 22), (0, 25), (1, 1), (0, 3), (6, 3), (1, 24), (10, 13), (24, 9), (19, 8), (11, 23), (21, 22), (2, 4), (12, 24), (24, 0), (21, 23), (22, 4), (20, 1), (6, 20), (2, 11), (7, 18), (21, 11), (2, 1), (1, 6), (17, 8), (17, 5), (3, 14), (5, 4), (7, 9), (24, 18), (0, 17), (19, 25), (5, 11), (3, 13), (23, 23), (24, 17), (7, 7), (3, 10), (23, 6), (16, 18), (18, 2), (25, 16), (2, 18), (5, 0), (1, 22), (14, 3), (13, 4), (3, 25), (15, 19), (9, 22), (22, 22), (13, 9), (10, 8), (20, 14), (16, 0), (9, 11), (12, 5), (22, 8), (11, 25), (15, 13), (1, 3), (9, 13), (4, 4), (0, 16), (19, 20), (19, 3), (21, 12), (19, 12), (11, 14), (2, 10), (3, 8), (9, 5), (13, 3), (11, 2), (25, 12), (7, 14), (9, 19), (15, 8), (10, 19), (1, 10), (2, 2), (15, 7), (6, 21), (17, 4), (9, 16), (6, 16), (12, 7), (17, 22), (14, 8), (0, 11), (12, 11), (23, 20), (0, 15), (5, 17), (24, 8), (16, 7), (3, 5), (25, 22), (2, 5), (4, 11), (0, 10), (4, 24), (3, 20), (5, 8), (11, 24), (18, 12), (5, 7), (19, 19), (15, 0), (17, 17), (18, 5), (0, 13), (19, 2), (12, 23), (13, 0), (25, 6), (14, 24), (12, 25), (15, 20), (6, 23), (4, 17), (8, 11), (2, 25), (3, 23), (0, 12), (10, 4), (9, 12), (18, 7), (0, 19), (20, 18), (4, 0), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530028", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), 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), (14, 15), (13, 5), (4, 9), (16, 1), (0, 2), (8, 4), (18, 19), (6, 15), (3, 21), (8, 10), (1, 1), (8, 23), (17, 11), (4, 4), (8, 17), (12, 10), (11, 4), (15, 7), (1, 7), (5, 11), (8, 5), (11, 2), (7, 12), (1, 20), (18, 22), (17, 2), (0, 6), (8, 3), (18, 15), (17, 1), (2, 5), (4, 6), (7, 23), (4, 19), (5, 5), (16, 17), (0, 8), (12, 21), (2, 2), (16, 10), (19, 7), (6, 8), (15, 16), (11, 13), (12, 16), (12, 22), (8, 15), (15, 2), (5, 23), (15, 8), (3, 17), (4, 0), (6, 14), (15, 10), (13, 9), (9, 19), (12, 19), (3, 11), (19, 11), (11, 12), (17, 17), (17, 7), (15, 9), (12, 3), (11, 3), (18, 6), (9, 7), (12, 0), (20, 17), (3, 22), (14, 6), (16, 8), (4, 1), (10, 6), (3, 7), (21, 11), (10, 22), (14, 17), (0, 3), (4, 3), (3, 14), (19, 21), (10, 20), (17, 12), (12, 20), (19, 0), (14, 22), (1, 21), (21, 5), (1, 9), (20, 4), (8, 6), (15, 0), (19, 23), (4, 12), (1, 18), (8, 0), (17, 20), (8, 1), (14, 8), (7, 3), (0, 22), (10, 19), (2, 18), (15, 12), (7, 19), (17, 19), (17, 8), (1, 8), (5, 1), (21, 21), (19, 20), (19, 14), (1, 13), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325120", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 4), (15, 0), (15, 2), (10, 10), (20, 23), (8, 20), (16, 22), (9, 12), (5, 6), (15, 14), (12, 9), (9, 4), (0, 15), (14, 5), (7, 15), (0, 1), (10, 17), (10, 15), (11, 10), (21, 17), (9, 6), (15, 23), (2, 3), (18, 6), (7, 6), (5, 11), (11, 5), (22, 15), (4, 3), (9, 8), (12, 20), (6, 6), (21, 1), (19, 21), (6, 14), (19, 1), (20, 5), (16, 1), (2, 9), (9, 11), (12, 11), (10, 0), (3, 4), (2, 1), (11, 18), (8, 16), (12, 18), (6, 21), (14, 23), (18, 16), (17, 14), (1, 19), (19, 2), (21, 24), (7, 20), (18, 14), (0, 2), (19, 24), (6, 22), (15, 20), (2, 23), (18, 20), (15, 3), (0, 18), (8, 1), (8, 22), (17, 24), (22, 6), (7, 18), (20, 18), (11, 24), (2, 10), (18, 13), (15, 10), (5, 20), (19, 8), (0, 14), (20, 10), (3, 3), (9, 16), (9, 15), (22, 17), (17, 3), (4, 20), (1, 18), (11, 6), (11, 17), (5, 5), (12, 0), (4, 17), (15, 16), (2, 24), (6, 17), (3, 20), (16, 13), (12, 17), (7, 19), (14, 10), (22, 5), (11, 4), (16, 4), (11, 13), (17, 13), (8, 2), (4, 23), (16, 15), (6, 15), (8, 13), (18, 21), (7, 12), (19, 12), (20, 22), (18, 3), (20, 12), (10, 11), (7, 3), (2, 20), (14, 4), (21, 23), (17, 12), (8, 14), (4, 15), (16, 16), (8, 9), (7, 11), (7, 0), (9, 2), (19, 14), (21, 3), (6, 19), (17, 16), (5, 18), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732998", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 26), (20, 8), (25, 2), (6, 13), (18, 5), (23, 12), (7, 10), (10, 9), (4, 1), (5, 6), (19, 5), (12, 18), (7, 24), (9, 13), (11, 27), (12, 8), (16, 5), (5, 22), (3, 23), (22, 17), (11, 11), (16, 20), (4, 25), (4, 17), (24, 0), (8, 8), (21, 3), (8, 22), (2, 22), (1, 11), (20, 15), (0, 16), (23, 10), (17, 6), (7, 4), (3, 5), (11, 14), (7, 16), (9, 15), (9, 14), (18, 7), (17, 7), (25, 22), (20, 12), (13, 9), (8, 10), (10, 21), (19, 27), (2, 23), (5, 19), (17, 25), (16, 6), (25, 26), (18, 20), (13, 10), (15, 2), (24, 22), (7, 8), (20, 10), (25, 6), (2, 19), (19, 6), (8, 18), (16, 14), (18, 15), (14, 17), (11, 17), (5, 21), (20, 0), (6, 5), (1, 5), (25, 10), (12, 22), (3, 17), (15, 4), (14, 26), (4, 12), (19, 9), (23, 11), (21, 9), (4, 27), (13, 15), (15, 3), (7, 2), (24, 15), (10, 17), (19, 16), (18, 25), (11, 19), (23, 13), (2, 10), (4, 26), (18, 13), (12, 12), (21, 7), (8, 19), (23, 21), (2, 17), (21, 13), (10, 20), (22, 27), (19, 18), (22, 19), (14, 4), (0, 26), (8, 5), (13, 0), (11, 26), (4, 9), (9, 21), (23, 16), (6, 19), (1, 22), (16, 7), (9, 27), (21, 10), (7, 20), (25, 9), (19, 14), (5, 13), (8, 3), (4, 20), (20, 7), (16, 17), (9, 17), (21, 20), (3, 18), (14, 10), (0, 4), (14, 21), (0, 27), (19, 3), (25, 8), (21, 1), (17, 0), (22, 13), (6, 25), (19, 1), (4, 13), (22, 25), (22, 16), (18, 19), (5, 4), (23, 7), (22, 18), (19, 15), (9, 4), (21, 25), (4, 22), (23, 3), (3, 7), (17, 5), (22, 20), (14, 11), (3, 16), (9, 2), (13, 4), (9, 1), (21, 17), (7, 11), (5, 2), (15, 16), (14, 19), (19, 21), (9, 26), (23, 27), (22, 0), (11, 1), (5, 8), (19, 4), (8, 24), (5, 12), (9, 8), (5, 23), (11, 3), (9, 7), (21, 23), (9, 22), (12, 9), (3, 27), (23, 4), (3, 22), (6, 22), (10, 22), (0, 23), (23, 25), (0, 13), (13, 24), (9, 19), (15, 26), (12, 0), (4, 0), (24, 4), (11, 23), (17, 16), (4, 10), (20, 3), (9, 18), (16, 12), (8, 17), (17, 23), (10, 3), (3, 12), (14, 23), (22, 11), (2, 8), (0, 25), (12, 14), (1, 12), (21, 19), (24, 11), (1, 10), (3, 11), (22, 7), (7, 25), (15, 9), (1, 9), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502944", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 15), (3, 4), (14, 12), (18, 20), (4, 8), (5, 6), (3, 8), (2, 0), (13, 9), (17, 1), (12, 21), (6, 3), (6, 1), (7, 14), (15, 12), (5, 3), (19, 9), (18, 0), (6, 20), (16, 7), (13, 0), (21, 17), (13, 11), (21, 3), (0, 21), (8, 14), (1, 1), (17, 7), (10, 15), (7, 21), (18, 5), (0, 9), (9, 1), (4, 15), (8, 21), (7, 16), (6, 19), (15, 5), (20, 15), (10, 12), (14, 9), (21, 0), (14, 5), (17, 19), (16, 6), (5, 13), (10, 4), (20, 21), (3, 3), (3, 20), (14, 18), (7, 10), (6, 0), (16, 8), (17, 9), (16, 20), (1, 17), (16, 19), (15, 10), (12, 3), (4, 4), (19, 15), (18, 14), (21, 14), (19, 7), (13, 16), (14, 4), (20, 12), (14, 10), (21, 1), (7, 11), (20, 6), (15, 6), (19, 1), (11, 3), (15, 9), (19, 16), (15, 18), (14, 6), (20, 10), (7, 6), (4, 21), (9, 6), (5, 5), (13, 8), (21, 11), (15, 0), (21, 19), (13, 4), (5, 9), (0, 15), (9, 13), (14, 22), (3, 10), (16, 18), (2, 17), (14, 1), (20, 2), (14, 19), (14, 0), (20, 4), (21, 16), (2, 10), (4, 17), (6, 14), (7, 0), (18, 1), (10, 9), (20, 20), (3, 2), (5, 1), (5, 20), (9, 5), (14, 20), (4, 0), (15, 19), (2, 4), (12, 1), (5, 19), (4, 22), (20, 9), (9, 0), (12, 4), (16, 14), (10, 18), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "389470", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 23), (11, 19), (5, 10), (13, 19), (10, 5), (14, 16), (8, 8), (21, 20), (11, 20), (5, 23), (3, 4), (12, 25), (10, 26), (23, 19), (4, 26), (11, 13), (15, 19), (5, 6), (21, 14), (19, 17), (15, 15), (18, 21), (4, 16), (20, 1), (7, 2), (20, 14), (17, 17), (7, 6), (10, 22), (2, 14), (17, 4), (10, 2), (8, 6), (3, 14), (17, 21), (16, 0), (8, 9), (3, 6), (12, 9), (9, 2), (6, 15), (15, 21), (14, 9), (21, 0), (12, 14), (18, 16), (5, 4), (18, 6), (1, 9), (18, 14), (1, 22), (3, 1), (5, 9), (17, 1), (22, 7), (4, 1), (2, 2), (12, 22), (14, 8), (15, 10), (13, 11), (20, 20), (2, 1), (13, 23), (4, 6), (23, 3), (3, 12), (13, 7), (4, 19), (24, 20), (4, 5), (7, 21), (4, 24), (6, 12), (23, 24), (6, 14), (11, 4), (19, 19), (15, 6), (9, 14), (11, 6), (8, 22), (5, 24), (14, 24), (2, 13), (22, 1), (11, 15), (20, 25), (10, 0), (9, 23), (4, 18), (13, 15), (23, 18), (7, 16), (3, 26), (22, 5), (18, 17), (9, 12), (17, 6), (15, 5), (8, 10), (2, 5), (21, 19), (23, 22), (24, 12), (7, 18), (9, 20), (0, 2), (6, 16), (8, 12), (2, 22), (0, 8), (11, 17), (6, 21), (1, 23), (11, 22), (7, 24), (6, 22), (7, 1), (17, 24), (23, 14), (15, 7), (13, 4), (11, 26), (3, 19), (10, 6), (14, 22), (20, 19), (19, 10), (14, 5), (6, 10), (12, 12), (9, 11), (0, 21), (5, 3), (3, 7), (18, 3), (1, 21), (9, 5), (1, 20), (3, 2), (22, 16), (22, 11), (10, 25), (12, 1), (20, 3), (11, 5), (24, 15), (9, 16), (7, 20), (11, 25), (7, 26), (18, 0), (11, 9), (19, 1), (1, 15), (15, 16), (18, 1), (21, 18), (17, 10), (2, 21), (21, 10), (22, 21), (16, 19), (10, 17), (24, 19), (3, 3), (0, 11), (7, 8), (19, 25), (19, 26), (20, 0), (13, 18), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803262", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 19), (18, 19), (14, 25), (8, 22), (9, 11), (11, 9), (7, 5), (13, 14), (17, 6), (11, 13), (2, 3), (12, 21), (11, 15), (1, 22), (5, 7), (17, 23), (14, 19), (18, 21), (0, 8), (11, 24), (1, 11), (2, 22), (16, 13), (3, 18), (15, 5), (13, 4), (19, 24), (19, 15), (1, 4), (14, 6), (8, 19), (16, 4), (14, 7), (20, 6), (12, 10), (6, 16), (13, 22), (14, 13), (0, 26), (3, 19), (4, 12), (12, 26), (7, 19), (20, 11), (12, 15), (13, 10), (16, 25), (9, 2), (1, 0), (14, 9), (9, 10), (13, 18), (4, 19), (15, 19), (11, 18), (13, 11), (16, 7), (1, 6), (18, 0), (2, 5), (10, 20), (12, 24), (20, 13), (14, 16), (6, 13), (3, 12), (0, 19), (19, 5), (15, 16), (14, 15), (8, 16), (8, 26), (16, 19), (20, 26), (2, 8), (12, 16), (1, 21), (2, 9), (18, 8), (8, 17), (19, 25), (2, 23), (1, 19), (3, 9), (10, 11), (1, 14), (4, 3), (11, 17), (21, 14), (21, 8), (4, 1), (0, 23), (11, 25), (9, 23), (4, 17), (7, 2), (20, 8), (11, 10), (20, 21), (18, 26), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226868", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), 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), (21, 14), (1, 18), (11, 15), (3, 1), (25, 9), (12, 17), (7, 3), (22, 11), (9, 11), (25, 6), (26, 13), (3, 3), (13, 4), (11, 13), (17, 1), (10, 19), (15, 19), (17, 18), (14, 8), (3, 8), (1, 21), (12, 2), (16, 20), (10, 14), (7, 17), (4, 6), (22, 1), (12, 11), (15, 10), (20, 11), (22, 15), (10, 18), (6, 14), (7, 8), (13, 3), (18, 14), (4, 16), (16, 17), (23, 8), (5, 15), (16, 0), (15, 0), (17, 17), (1, 1), (14, 2), (24, 3), (17, 3), (3, 12), (20, 19), (22, 8), (13, 7), (4, 14), (16, 4), (18, 21), (23, 11), (14, 17), (3, 21), (19, 8), (2, 1), (6, 7), (1, 11), (6, 12), (12, 1), (21, 3), (24, 4), (19, 1), (2, 11), (23, 19), (15, 20), (5, 9), (20, 8), (7, 14), (17, 15), (16, 3), (13, 8), (8, 8), (0, 21), (14, 14), (9, 19), (22, 12), (16, 10), (25, 7), (26, 17), (11, 2), (21, 2), (14, 4), (11, 21), (0, 18), (14, 5), (19, 0), (2, 21), (5, 21), (23, 5), (13, 13), (6, 1), (13, 2), (9, 10), (23, 13), (2, 16), (18, 11), (24, 8), (21, 5), (15, 12), (23, 4), (9, 17), (20, 1), (16, 14), (18, 12), (25, 5), (9, 8), (15, 18), (19, 20), (2, 13), (5, 10), (4, 21), (12, 21), (5, 6), (10, 7), (19, 9), (9, 18), (8, 14), (3, 19), (8, 18), (17, 0), (10, 16), (6, 16), (14, 0), (24, 11), (0, 19), (20, 7), (19, 15), (21, 8), (15, 8), (19, 14), (19, 3), (13, 6), (25, 18), (24, 17), (3, 16), (26, 14), (4, 9), (5, 20), (24, 9), (21, 7), (8, 20), (11, 16), (19, 16), (16, 19), (6, 15), (22, 16), (16, 1), (24, 5), (10, 9), (9, 13), (21, 19), (9, 0), (18, 2), (14, 15), (1, 17), (16, 16), (7, 0), (21, 21), (4, 19), (7, 13), (8, 0), (20, 18), (16, 15), (20, 3), (8, 6), (22, 17), (19, 4), (3, 17), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562176", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), 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), (2, 14), (22, 15), (6, 15), (3, 22), (13, 17), (18, 1), (14, 2), (22, 5), (10, 3), (1, 18), (4, 7), (8, 2), (4, 23), (17, 19), (22, 20), (3, 19), (12, 0), (14, 10), (15, 9), (5, 19), (4, 16), (17, 12), (18, 20), (8, 17), (7, 17), (6, 5), (8, 4), (5, 21), (10, 17), (22, 13), (11, 10), (2, 0), (17, 15), (11, 6), (14, 15), (5, 17), (9, 17), (22, 3), (10, 13), (6, 21), (6, 19), (13, 4), (12, 9), (4, 4), (17, 21), (0, 20), (21, 2), (14, 0), (20, 7), (17, 2), (19, 21), (16, 9), (20, 23), (3, 8), (15, 14), (16, 20), (16, 8), (8, 9), (1, 13), (2, 20), (15, 1), (9, 9), (5, 8), (8, 0), (17, 5), (1, 9), (20, 22), (3, 16), (19, 3), (4, 3), (21, 14), (1, 5), (0, 17), (10, 2), (22, 11), (11, 0), (15, 4), (12, 5), (19, 9), (22, 4), (16, 21), (8, 11), (21, 23), (5, 6), (21, 21), (14, 6), (6, 4), (15, 22), (16, 4), (23, 5), (12, 22), (18, 16), (6, 9), (9, 23), (20, 10), (6, 3), (23, 16), (7, 14), (21, 5), (13, 14), (17, 11), (14, 17), (2, 18), (0, 9), (4, 22), (1, 7), (7, 12), (20, 13), (8, 13), (13, 20), (17, 9), (19, 22), (17, 23), (3, 12), (10, 5), (2, 21), (11, 19), (2, 8), (2, 7), (0, 13), (22, 2), (14, 11), (2, 1), (3, 0), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540789", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 0), (13, 12), (6, 11), (1, 10), (10, 10), (11, 14), (7, 6), (15, 12), (18, 11), (7, 1), (14, 14), (5, 0), (1, 0), (10, 11), (13, 9), (7, 11), (4, 1), (16, 10), (26, 15), (19, 3), (12, 9), (10, 8), (7, 16), (24, 16), (5, 14), (7, 13), (17, 5), (19, 14), (7, 9), (2, 0), (5, 3), (21, 18), (3, 19), (17, 15), (15, 1), (6, 14), (10, 17), (8, 12), (14, 6), (2, 8), (21, 3), (14, 1), (18, 6), (17, 3), (6, 9), (0, 4), (17, 18), (14, 4), (17, 13), (25, 10), (16, 18), (0, 11), (26, 1), (10, 5), (8, 2), (25, 1), (9, 8), (4, 6), (12, 18), (18, 13), (13, 13), (4, 8), (1, 13), (23, 3), (0, 16), (3, 13), (18, 4), (13, 0), (15, 9), (1, 17), (15, 13), (23, 0), (12, 8), (0, 12), (21, 0), (4, 9), (22, 10), (14, 17), (16, 0), (17, 1), (14, 5), (18, 0), (23, 16), (25, 6), (23, 11), (3, 4), (13, 6), (24, 8), (21, 11), (25, 19), (7, 0), (10, 3), (17, 14), (16, 2), (26, 7), (0, 3), (20, 10), (24, 7), (9, 7), (2, 9), (12, 13), (13, 14), (20, 8), (26, 13), (9, 5), (9, 18), (8, 17), (26, 5), (13, 15), (3, 16), (9, 6), (16, 6), (25, 17), (22, 2), (1, 14), (6, 18), (9, 10), (11, 15), (16, 13), (1, 8), (23, 6), (1, 9), (0, 7), (3, 9), (0, 14), (22, 6), (5, 12), (8, 14), (15, 14), (18, 8), (11, 16), (5, 6), (18, 3), (12, 15), (8, 11), (1, 12), (10, 18), (0, 2), (14, 8), (21, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636880", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 11), (18, 3), (12, 12), (20, 14), (6, 3), (2, 24), (16, 9), (16, 17), (3, 15), (5, 15), (9, 24), (16, 13), (21, 9), (9, 16), (7, 25), (16, 3), (14, 10), (15, 11), (3, 20), (11, 18), (15, 16), (22, 17), (22, 10), (9, 12), (20, 21), (5, 7), (22, 19), (14, 12), (19, 19), (8, 23), (17, 22), (6, 18), (2, 20), (0, 11), (1, 10), (18, 20), (0, 9), (5, 24), (2, 19), (16, 14), (19, 1), (12, 17), (4, 21), (12, 1), (11, 10), (16, 1), (20, 9), (1, 11), (17, 19), (7, 0), (7, 15), (4, 4), (7, 19), (1, 14), (8, 13), (12, 24), (19, 6), (19, 22), (16, 15), (18, 10), (17, 14), (19, 12), (18, 8), (14, 3), (12, 5), (3, 9), (4, 13), (11, 11), (3, 25), (16, 19), (22, 7), (23, 10), (20, 25), (12, 15), (14, 1), (16, 6), (23, 2), (8, 20), (9, 19), (10, 3), (4, 19), (7, 14), (14, 4), (18, 17), (13, 5), (10, 12), (22, 20), (2, 2), (4, 2), (10, 6), (13, 12), (6, 23), (17, 0), (22, 0), (8, 10), (22, 15), (18, 14), (2, 18), (12, 20), (4, 1), (8, 7), (8, 9), (15, 3), (7, 23), (14, 23), (21, 25), (23, 19), (18, 2), (20, 16), (12, 0), (12, 16), (17, 5), (9, 0), (0, 20), (15, 13), (23, 12), (17, 21), (12, 25), (20, 4), (9, 1), (10, 19), (2, 17), (15, 20), (17, 16), (5, 8), (2, 4), (20, 24), (14, 7), (21, 5), (11, 17), (23, 14), (23, 7), (8, 22), (5, 1), (19, 16), (19, 21), (20, 18), (4, 7), (2, 1), (8, 3), (21, 22), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944610", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), 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), (10, 11), (20, 3), (5, 9), (4, 15), (15, 0), (0, 20), (23, 3), (15, 1), (27, 20), (19, 3), (22, 3), (17, 11), (4, 18), (22, 19), (12, 0), (15, 10), (5, 22), (13, 25), (9, 2), (21, 21), (22, 13), (5, 15), (15, 3), (8, 12), (19, 4), (22, 11), (8, 15), (0, 3), (15, 14), (10, 24), (15, 4), (10, 6), (20, 23), (26, 16), (7, 14), (18, 19), (14, 14), (7, 13), (26, 3), (7, 12), (12, 5), (12, 9), (21, 22), (3, 13), (2, 3), (2, 15), (1, 4), (27, 15), (21, 23), (27, 3), (26, 2), (22, 20), (5, 11), (11, 1), (13, 15), (25, 4), (24, 22), (25, 13), (17, 5), (7, 24), (25, 9), (19, 14), (7, 25), (27, 24), (0, 10), (5, 10), (6, 10), (15, 8), (0, 15), (7, 7), (21, 16), (15, 25), (25, 11), (13, 11), (5, 20), (4, 10), (27, 2), (15, 23), (3, 8), (14, 10), (3, 17), (18, 2), (20, 8), (3, 14), (8, 0), (22, 16), (21, 25), (20, 17), (12, 15), (1, 11), (14, 2), (23, 4), (7, 5), (25, 7), (10, 16), (20, 15), (23, 16), (25, 19), (13, 19), (11, 23), (10, 22), (23, 13), (23, 19), (21, 5), (2, 6), (10, 1), (24, 7), (26, 17), (7, 9), (17, 10), (10, 20), (17, 23), (24, 9), (3, 11), (19, 13), (24, 14), (25, 18), (14, 8), (13, 3), (10, 19), (1, 19), (4, 21), (22, 14), (0, 6), (15, 13), (3, 4), (27, 16), (19, 9), (15, 15), (19, 21), (0, 11), (27, 8), (11, 15), (13, 17), (24, 10), (18, 11), (16, 18), (21, 0), (22, 12), (27, 4), (8, 18), (10, 7), (18, 8), (14, 9), (18, 15), (13, 7), (2, 5), (1, 3), (12, 10), (9, 4), (25, 10), (17, 13), (18, 21), (14, 18), (20, 6), (16, 17), (24, 12), (27, 12), (10, 18), (17, 0), (16, 3), (21, 7), (13, 6), (16, 12), (16, 1), (5, 16), (3, 10), (11, 4), (3, 18), (2, 2), (2, 10), (21, 20), (26, 20), (14, 17), (17, 16), (11, 12), (15, 12), (2, 17), (19, 2), (20, 19), (14, 3), (27, 19), (17, 6), (4, 7), (12, 20), (7, 10), (20, 2), (7, 3), (15, 5), (12, 23), (21, 2), (9, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82080", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 15), (11, 16), (20, 11), (12, 17), (8, 0), (2, 13), (6, 23), (14, 7), (8, 22), (17, 0), (9, 1), (14, 15), (7, 6), (6, 21), (5, 15), (13, 18), (5, 1), (20, 22), (11, 22), (13, 12), (3, 2), (13, 9), (16, 19), (10, 23), (18, 4), (16, 13), (8, 17), (13, 16), (20, 1), (3, 12), (4, 5), (19, 2), (7, 12), (11, 18), (3, 11), (18, 17), (4, 14), (7, 21), (10, 4), (7, 19), (11, 6), (0, 17), (3, 0), (2, 19), (13, 21), (16, 9), (9, 10), (9, 21), (2, 7), (21, 17), (6, 5), (18, 11), (0, 15), (19, 19), (12, 11), (8, 1), (15, 0), (13, 10), (19, 9), (8, 15), (7, 10), (8, 7), (3, 6), (20, 14), (10, 11), (9, 15), (16, 15), (4, 17), (17, 18), (12, 16), (17, 3), (16, 16), (18, 3), (8, 8), (0, 8), (12, 4), (16, 20), (17, 7), (12, 6), (3, 22), (20, 18), (12, 5), (14, 20), (12, 9), (17, 10), (14, 0), (16, 21), (2, 3), (16, 17), (14, 23), (2, 15), (0, 16), (15, 18), (8, 6), (9, 7), (5, 21), (12, 15), (0, 5), (11, 0), (8, 21), (13, 19), (10, 0), (20, 5), (4, 2), (18, 6), (17, 14), (15, 9), (6, 2), (10, 1), (16, 12), (12, 12), (3, 19), (19, 17), (20, 9), (7, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474900", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), 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), (18, 17), (5, 6), (14, 4), (9, 1), (15, 15), (2, 24), (16, 12), (15, 20), (1, 16), (3, 1), (8, 8), (7, 28), (16, 23), (2, 18), (3, 28), (9, 28), (11, 20), (17, 5), (14, 28), (18, 15), (5, 24), (2, 28), (4, 2), (6, 9), (14, 6), (5, 23), (5, 18), (18, 27), (9, 20), (6, 15), (6, 4), (18, 3), (10, 8), (19, 3), (13, 2), (19, 21), (12, 0), (11, 23), (15, 7), (18, 21), (14, 25), (12, 20), (2, 27), (18, 10), (2, 2), (2, 12), (16, 7), (12, 28), (9, 11), (7, 5), (10, 24), (9, 3), (15, 18), (8, 22), (14, 16), (9, 6), (14, 26), (3, 24), (12, 23), (1, 27), (13, 5), (15, 25), (13, 21), (18, 19), (17, 19), (4, 15), (2, 1), (2, 22), (3, 21), (4, 17), (17, 25), (3, 17), (1, 22), (12, 3), (2, 11), (0, 4), (19, 2), (19, 25), (7, 21), (17, 7), (1, 7), (11, 8), (17, 24), (4, 26), (11, 12), (6, 2), (8, 0), (17, 14), (8, 27), (15, 2), (16, 10), (9, 22), (15, 1), (12, 13), (10, 0), (15, 6), (19, 15), (3, 25), (4, 6), (14, 7), (8, 19), (19, 16), (14, 15), (7, 4), (18, 12), (10, 20), (2, 26), (3, 7), (6, 21), (19, 6), (4, 20), (0, 12), (19, 26), (1, 18), (4, 3), (1, 21), (16, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77184", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), 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), (2, 6), (8, 1), (8, 16), (19, 18), (2, 21), (26, 19), (28, 10), (26, 12), (2, 9), (14, 20), (12, 0), (18, 0), (6, 7), (25, 0), (22, 14), (0, 3), (6, 11), (4, 8), (21, 11), (28, 20), (0, 19), (22, 11), (19, 7), (17, 4), (15, 1), (23, 20), (23, 14), (13, 0), (5, 7), (6, 16), (26, 17), (20, 3), (6, 13), (27, 0), (23, 21), (9, 21), (6, 6), (26, 2), (21, 10), (28, 17), (28, 3), (27, 14), (12, 14), (21, 6), (10, 6), (16, 12), (11, 5), (25, 5), (20, 7), (7, 16), (11, 4), (15, 13), (1, 16), (4, 6), (0, 10), (4, 2), (16, 9), (4, 10), (24, 15), (5, 1), (15, 7), (13, 5), (13, 15), (20, 10), (6, 14), (8, 21), (2, 18), (7, 3), (23, 11), (17, 5), (0, 15), (8, 14), (12, 5), (0, 1), (19, 8), (6, 3), (0, 2), (24, 2), (10, 10), (14, 10), (13, 20), (15, 11), (18, 7), (8, 7), (14, 9), (2, 1), (17, 0), (9, 8), (12, 20), (23, 10), (23, 1), (8, 3), (11, 9), (5, 3), (6, 0), (18, 19), (20, 12), (7, 8), (11, 3), (24, 20), (27, 1), (2, 7), (1, 3), (18, 11), (22, 19), (9, 9), (0, 7), (8, 10), (8, 15), (18, 6), (26, 13), (28, 13), (17, 11), (4, 20), (15, 14), (3, 11), (6, 21), (16, 20), (10, 15), (17, 14), (9, 12), (10, 7), (19, 5), (18, 10), (10, 12), (19, 1), (28, 6), (25, 10), (27, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954045", "dataset": "MATH"}
{"messages": [{"content": "In a 28x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 1), (23, 11), (2, 15), (15, 12), (24, 11), (13, 24), (22, 24), (14, 22), (20, 0), (24, 13), (8, 17), (24, 4), (17, 10), (13, 26), (3, 18), (15, 20), (5, 4), (16, 1), (20, 22), (16, 14), (27, 24), (7, 4), (10, 11), (1, 13), (17, 2), (1, 23), (4, 15), (7, 21), (12, 19), (0, 15), (24, 15), (17, 15), (19, 6), (27, 0), (16, 16), (26, 9), (16, 21), (14, 21), (5, 8), (25, 9), (10, 8), (25, 26), (10, 20), (26, 20), (20, 20), (15, 15), (2, 12), (5, 11), (14, 2), (24, 2), (25, 5), (14, 7), (11, 23), (7, 0), (8, 18), (3, 24), (5, 9), (19, 17), (3, 3), (3, 19), (18, 26), (20, 26), (4, 6), (5, 26), (5, 7), (4, 12), (15, 18), (14, 20), (10, 23), (8, 20), (23, 5), (3, 5), (7, 25), (25, 23), (20, 23), (10, 7), (10, 19), (5, 12), (3, 13), (27, 21), (14, 8), (24, 22), (6, 5), (21, 9), (18, 3), (20, 21), (14, 1), (26, 4), (9, 17), (5, 19), (1, 12), (25, 24), (17, 24), (17, 4), (25, 17), (27, 9), (8, 25), (21, 15), (22, 16), (26, 23), (0, 2), (25, 15), (16, 4), (7, 24), (7, 15), (13, 10), (20, 17), (2, 13), (1, 24), (12, 18), (14, 5), (15, 10), (13, 23), (7, 22), (3, 20), (19, 3), (11, 15), (20, 12), (5, 17), (9, 4), (8, 22), (24, 20), (18, 4), (16, 25), (1, 7), (8, 8), (0, 4), (4, 24), (14, 3), (16, 13), (18, 2), (8, 10), (17, 19), (19, 13), (8, 6), (2, 3), (1, 21), (12, 2), (6, 11), (18, 7), (3, 12), (22, 20), (8, 24), (22, 18), (22, 5), (26, 14), (25, 1), (5, 5), (27, 22), (6, 9), (22, 4), (22, 23), (4, 4), (21, 23), (6, 23), (4, 2), (16, 8), (27, 5), (8, 15), (10, 21), (19, 1), (11, 4), (11, 2), (12, 5), (7, 17), (11, 9), (24, 21), (17, 17), (13, 20), (14, 26), (18, 22), (4, 21), (4, 8), (25, 13), (21, 0), (20, 19), (6, 0), (8, 9), (13, 6), (10, 9), (12, 26), (21, 16), (18, 21), (9, 5), (18, 6), (23, 23), (15, 7), (3, 25), (0, 22), (13, 19), (11, 26), (2, 17), (18, 15), (26, 6), (24, 14), (17, 21), (12, 25), (2, 24), (27, 12), (21, 19), (22, 3), (17, 1), (6, 2), (4, 5), (26, 12), (8, 3), (21, 5), (14, 15), (19, 7), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818748", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (22, 23), (17, 2), (12, 5), (9, 15), (17, 27), (17, 24), (18, 15), (23, 1), (20, 2), (19, 17), (1, 2), (22, 28), (13, 11), (21, 11), (4, 25), (24, 14), (19, 28), (24, 7), (0, 26), (18, 21), (14, 3), (0, 19), (3, 7), (23, 17), (0, 5), (15, 21), (2, 25), (24, 5), (3, 24), (15, 20), (12, 0), (0, 12), (13, 3), (3, 12), (9, 9), (2, 19), (11, 12), (19, 14), (20, 7), (4, 7), (19, 8), (12, 15), (11, 3), (15, 6), (20, 20), (6, 10), (7, 13), (9, 26), (6, 12), (22, 17), (3, 9), (19, 7), (25, 10), (10, 15), (17, 28), (17, 16), (14, 15), (19, 10), (5, 19), (8, 19), (13, 21), (18, 1), (12, 24), (0, 23), (22, 19), (18, 14), (4, 17), (1, 9), (16, 5), (9, 21), (16, 0), (18, 23), (15, 8), (2, 20), (1, 17), (20, 24), (20, 0), (10, 13), (16, 8), (13, 27), (16, 18), (9, 13), (5, 9), (2, 13), (21, 24), (21, 5), (16, 14), (13, 16), (5, 3), (23, 21), (24, 15), (13, 0), (8, 4), (5, 13), (8, 18), (4, 19), (1, 24), (11, 7), (3, 23), (20, 21), (12, 13), (5, 1), (4, 27), (20, 18), (16, 21), (17, 14), (14, 8), (1, 18), (14, 19), (3, 10), (3, 21), (22, 21), (5, 16), (9, 8), (2, 26), (20, 14), (22, 26), (1, 4), (18, 5), (24, 4), (4, 10), (14, 26), (12, 22), (3, 26), (16, 6), (17, 3), (5, 28), (9, 7), (1, 5), (18, 13), (8, 27), (3, 1), (25, 15), (19, 6), (23, 2), (2, 9), (5, 25), (17, 20), (17, 0), (6, 4), (6, 9), (21, 18), (12, 26), (17, 10), (10, 4), (19, 2), (15, 13), (1, 7), (12, 1), (15, 28), (16, 10), (19, 5), (11, 5), (25, 19), (16, 13), (0, 9), (25, 9), (5, 21), (20, 6), (17, 25), (24, 6), (8, 2), (23, 8), (5, 2), (24, 16), (8, 10), (24, 28), (4, 15), (14, 4), (11, 2), (22, 10), (24, 13), (9, 14), (0, 13), (8, 11), (4, 22), (7, 6), (2, 21), (19, 4), (4, 14), (11, 1), (23, 20), (13, 17), (16, 17), (13, 9), (21, 2), (15, 7), (1, 27), (21, 23), (18, 12), (6, 1), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654240", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 4), (6, 1), (17, 0), (21, 18), (16, 19), (13, 5), (17, 13), (0, 20), (13, 20), (21, 19), (14, 10), (18, 0), (3, 23), (13, 16), (0, 8), (10, 16), (2, 7), (15, 2), (1, 5), (6, 13), (15, 17), (16, 9), (10, 19), (11, 8), (21, 16), (1, 0), (10, 15), (12, 11), (6, 16), (7, 23), (0, 7), (2, 16), (13, 11), (5, 13), (1, 2), (11, 6), (16, 3), (8, 2), (11, 16), (20, 7), (10, 7), (3, 20), (6, 19), (13, 19), (4, 15), (20, 3), (17, 2), (7, 11), (19, 2), (16, 13), (9, 6), (4, 10), (8, 9), (19, 5), (7, 0), (4, 19), (4, 9), (9, 9), (4, 22), (6, 2), (6, 11), (6, 9), (16, 17), (20, 11), (2, 10), (16, 0), (5, 22), (0, 11), (16, 11), (10, 12), (3, 12), (20, 15), (20, 17), (19, 8), (1, 9), (4, 6), (5, 12), (14, 11), (19, 11), (14, 22), (8, 18), (1, 17), (14, 7), (20, 20), (20, 18), (10, 2), (5, 1), (6, 14), (18, 24), (3, 15), (15, 22), (9, 21), (13, 21), (7, 15), (11, 14), (3, 16), (21, 23), (12, 2), (20, 16), (4, 0), (8, 5), (8, 21), (10, 14), (15, 13), (14, 15), (18, 21), (2, 14), (11, 11), (1, 18), (7, 19), (11, 9), (14, 3), (11, 23), (3, 1), (4, 17), (10, 22), (14, 2), (11, 19), (19, 9), (8, 19), (9, 19), (12, 14), (21, 22), (0, 6), (18, 15), (10, 6), (21, 3), (5, 24), (10, 17), (0, 12), (2, 12), (3, 5), (21, 6), (19, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497648", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), 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), (4, 2), (16, 13), (15, 16), (12, 6), (14, 25), (10, 25), (22, 23), (22, 21), (3, 3), (7, 2), (1, 20), (2, 3), (0, 18), (3, 24), (19, 18), (8, 5), (12, 5), (14, 3), (4, 10), (5, 25), (7, 12), (5, 2), (17, 6), (11, 9), (8, 23), (20, 13), (4, 28), (0, 5), (20, 18), (15, 20), (6, 6), (16, 19), (16, 15), (1, 17), (15, 19), (7, 28), (20, 14), (16, 5), (3, 9), (5, 16), (10, 27), (13, 3), (10, 12), (18, 16), (19, 3), (0, 6), (21, 24), (1, 12), (22, 22), (15, 10), (17, 3), (11, 0), (10, 20), (22, 14), (14, 6), (6, 4), (18, 17), (3, 10), (10, 4), (15, 12), (21, 28), (15, 6), (12, 20), (14, 28), (1, 5), (4, 21), (16, 26), (10, 8), (10, 16), (4, 13), (14, 13), (3, 14), (5, 4), (8, 4), (6, 12), (4, 14), (12, 28), (11, 26), (17, 16), (1, 11), (21, 26), (5, 12), (22, 4), (7, 15), (15, 17), (19, 9), (20, 0), (4, 6), (1, 14), (11, 25), (21, 1), (13, 5), (14, 18), (22, 3), (0, 3), (9, 18), (21, 7), (8, 6), (13, 9), (22, 8), (22, 15), (3, 23), (2, 6), (22, 26), (18, 9), (10, 15), (20, 11), (10, 1), (9, 10), (1, 22), (6, 21), (13, 6), (18, 6), (6, 11), (7, 26), (13, 19), (16, 17), (6, 27), (22, 11), (9, 19), (7, 1), (7, 23), (17, 7), (6, 25), (10, 24), (9, 22), (13, 14), (18, 24), (9, 28), (6, 2), (6, 9), (9, 17), (17, 2), (11, 16), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618324", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 25), (11, 4), (20, 12), (11, 3), (23, 6), (18, 2), (3, 16), (21, 5), (14, 13), (21, 8), (10, 1), (8, 14), (21, 26), (14, 23), (12, 26), (3, 5), (13, 12), (22, 22), (11, 22), (14, 19), (8, 2), (10, 18), (22, 1), (24, 12), (1, 18), (7, 3), (17, 25), (15, 16), (22, 15), (18, 23), (14, 10), (14, 24), (8, 11), (25, 20), (13, 24), (12, 1), (16, 9), (3, 7), (22, 10), (23, 25), (0, 19), (6, 4), (20, 18), (16, 11), (18, 0), (20, 2), (9, 4), (7, 5), (6, 21), (8, 0), (9, 16), (19, 0), (14, 16), (24, 6), (5, 25), (18, 18), (13, 25), (16, 2), (0, 9), (23, 5), (21, 16), (24, 8), (19, 24), (14, 5), (18, 11), (0, 2), (9, 23), (0, 22), (4, 7), (3, 2), (22, 12), (3, 6), (3, 0), (25, 15), (6, 7), (0, 17), (9, 15), (16, 10), (15, 5), (17, 12), (14, 26), (9, 6), (19, 26), (15, 26), (2, 5), (23, 26), (15, 0), (6, 24), (16, 15), (10, 16), (2, 16), (20, 9), (0, 23), (1, 15), (7, 26), (1, 5), (17, 16), (23, 21), (0, 8), (17, 23), (24, 21), (16, 20), (17, 2), (9, 11), (19, 2), (21, 12), (7, 0), (14, 20), (24, 10), (14, 0), (13, 6), (0, 12), (22, 7), (23, 17), (18, 7), (2, 8), (17, 17), (21, 19), (25, 19), (25, 2), (16, 22), (15, 10), (11, 15), (25, 3), (23, 12), (16, 3), (1, 2), (16, 14), (24, 23), (15, 25), (11, 11), (4, 11), (21, 15), (0, 15), (4, 25), (24, 22), (19, 8), (1, 16), (20, 4), (17, 0), (3, 26), (21, 20), (21, 21), (1, 23), (25, 5), (24, 7), (1, 22), (6, 10), (8, 3), (21, 13), (7, 20), (9, 17), (5, 4), (25, 6), (1, 24), (0, 25), (18, 26), (14, 14), (14, 2), (15, 11), (9, 1), (15, 19), (20, 21), (23, 22), (9, 7), (1, 6), (18, 15), (12, 8), (17, 19), (17, 3), (17, 7), (21, 25), (1, 8), (11, 14), (15, 3), (12, 24), (2, 24), (12, 0), (23, 11), (23, 19), (11, 7), (3, 14), (14, 18), (4, 12), (19, 20), (19, 23), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941220", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 23), (15, 15), (7, 16), (0, 17), (3, 10), (3, 15), (17, 25), (13, 2), (19, 26), (7, 8), (16, 19), (15, 24), (11, 15), (16, 1), (21, 14), (20, 8), (2, 6), (9, 25), (1, 23), (20, 4), (8, 24), (8, 9), (6, 12), (20, 1), (18, 27), (0, 8), (0, 13), (13, 1), (2, 22), (11, 14), (11, 19), (8, 11), (10, 9), (0, 16), (12, 25), (2, 1), (12, 23), (4, 6), (17, 17), (9, 20), (20, 9), (19, 22), (13, 23), (21, 18), (20, 12), (9, 5), (18, 24), (10, 3), (1, 22), (15, 14), (20, 11), (0, 24), (19, 25), (7, 5), (17, 21), (21, 24), (18, 3), (15, 27), (5, 17), (16, 21), (7, 24), (14, 3), (19, 12), (20, 3), (20, 18), (9, 12), (15, 13), (17, 10), (13, 20), (13, 21), (4, 27), (3, 12), (9, 11), (13, 19), (20, 14), (13, 17), (16, 0), (7, 23), (21, 9), (16, 6), (6, 20), (17, 22), (21, 6), (5, 12), (1, 19), (15, 16), (15, 18), (19, 1), (9, 18), (1, 17), (16, 17), (7, 2), (12, 27), (15, 4), (8, 8), (11, 8), (13, 4), (14, 12), (20, 20), (17, 20), (0, 22), (12, 9), (4, 18), (18, 5), (8, 22), (6, 25), (9, 8), (16, 13), (17, 1), (18, 4), (16, 10), (9, 22), (10, 14), (5, 25), (8, 15), (7, 17), (17, 0), (4, 8), (20, 16), (12, 19), (19, 6), (1, 15), (12, 13), (16, 22), (11, 4), (18, 12), (3, 25), (6, 16), (4, 21), (5, 27), (15, 1), (11, 23), (13, 3), (10, 27), (6, 4), (21, 5), (8, 5), (9, 16), (5, 18), (20, 5), (21, 20), (20, 10), (21, 17), (1, 1), (10, 8), (2, 14), (6, 3), (11, 20), (16, 20), (2, 18), (19, 13), (0, 12), (7, 1), (4, 2), (2, 21), (14, 17), (13, 18), (0, 4), (16, 5), (12, 14), (19, 7), (11, 1), (11, 2), (8, 21), (16, 16), (1, 16), (13, 16), (6, 21), (10, 6), (10, 5), (16, 3), (3, 20), (3, 16), (9, 23), (18, 22), (13, 27), (6, 19), (14, 8), (10, 10), (12, 2), (3, 13), (21, 12), (19, 14), (8, 10), (5, 8), (13, 14), (12, 16), (13, 25), (12, 3), (14, 15), (9, 4), (2, 7), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866664", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 24), (6, 10), (0, 16), (5, 25), (1, 1), (11, 25), (1, 18), (11, 23), (21, 5), (11, 9), (10, 15), (12, 11), (22, 0), (7, 1), (1, 6), (15, 11), (15, 3), (5, 12), (19, 25), (2, 23), (7, 12), (21, 7), (2, 20), (7, 5), (8, 19), (8, 17), (5, 5), (7, 21), (9, 23), (5, 16), (6, 1), (6, 23), (2, 24), (3, 25), (10, 2), (10, 7), (0, 21), (9, 10), (1, 16), (18, 0), (18, 3), (4, 25), (3, 15), (1, 23), (19, 1), (16, 25), (0, 24), (22, 23), (22, 14), (5, 23), (8, 20), (6, 15), (1, 14), (21, 2), (13, 10), (6, 9), (20, 4), (18, 14), (3, 18), (17, 25), (7, 17), (11, 1), (4, 16), (15, 18), (22, 13), (21, 10), (14, 17), (1, 13), (22, 3), (15, 5), (2, 5), (12, 6), (15, 16), (14, 1), (15, 24), (16, 24), (7, 26), (9, 19), (4, 23), (4, 17), (20, 10), (18, 1), (9, 12), (17, 10), (16, 17), (13, 5), (11, 13), (16, 0), (9, 8), (6, 11), (21, 17), (13, 0), (14, 21), (7, 2), (6, 0), (7, 3), (15, 4), (15, 8), (1, 19), (10, 4), (17, 14), (4, 14), (3, 17), (6, 14), (7, 18), (1, 11), (20, 9), (17, 1), (0, 12), (19, 18), (0, 10), (3, 0), (14, 16), (20, 26), (12, 9), (13, 2), (21, 26), (22, 21), (18, 4), (17, 24), (10, 0), (2, 16), (7, 16), (5, 22), (2, 11), (16, 3), (19, 15), (18, 7), (8, 7), (9, 15), (19, 3), (21, 14), (19, 14), (21, 21), (2, 17), (17, 23), (11, 12), (6, 13), (10, 17), (16, 6), (13, 25), (22, 20), (11, 10), (12, 3), (20, 19), (18, 25), (19, 26), (5, 3), (10, 16), (7, 0), (12, 0), (14, 14), (17, 19), (9, 9), (13, 13), (3, 6), (7, 13), (12, 2), (8, 18), (20, 1), (22, 22), (18, 15), (13, 19), (10, 21), (3, 13), (12, 15), (17, 11), (14, 25), (0, 14), (6, 21), (19, 11), (9, 2), (19, 16), (16, 12), (16, 26), (21, 23), (19, 23), (17, 16), (18, 11), (18, 12), (19, 4), (15, 13), (5, 18), (5, 19), (13, 7), (0, 19), (14, 6), (21, 12), (9, 14), (18, 2), (14, 7), (19, 17), (8, 12), (7, 15), (13, 11), (6, 4), (11, 3), (1, 10), (18, 9), (0, 22), (15, 15), (6, 26), (22, 11), (17, 13), (7, 20), (7, 19), (11, 4), (14, 22), (9, 5), (12, 25), (20, 11), (15, 1), (13, 6), (17, 15), (18, 20), (22, 1), (14, 0), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907440", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 18), (12, 15), (22, 6), (13, 20), (10, 13), (12, 3), (10, 5), (23, 18), (19, 4), (8, 14), (16, 14), (2, 10), (21, 4), (11, 8), (25, 15), (13, 9), (17, 18), (23, 4), (16, 21), (6, 16), (19, 2), (3, 9), (26, 11), (19, 13), (1, 19), (1, 7), (8, 3), (8, 19), (26, 15), (7, 15), (24, 18), (20, 1), (22, 14), (11, 7), (1, 3), (6, 3), (9, 18), (10, 7), (5, 11), (2, 8), (26, 12), (10, 8), (8, 9), (25, 4), (5, 16), (7, 7), (7, 12), (9, 21), (6, 13), (4, 21), (22, 3), (14, 0), (4, 12), (14, 8), (23, 3), (4, 2), (7, 16), (3, 6), (19, 1), (12, 6), (25, 9), (2, 12), (20, 11), (12, 2), (23, 7), (18, 11), (3, 14), (8, 12), (4, 9), (26, 13), (8, 13), (13, 4), (11, 0), (21, 3), (7, 3), (17, 4), (14, 20), (12, 12), (2, 19), (2, 2), (14, 11), (4, 16), (11, 11), (21, 6), (16, 13), (5, 1), (24, 21), (18, 21), (11, 20), (24, 5), (18, 12), (18, 18), (3, 15), (19, 10), (19, 8), (16, 0), (15, 0), (19, 7), (23, 17), (14, 12), (8, 0), (15, 20), (11, 16), (20, 7), (25, 18), (0, 19), (6, 19), (14, 3), (10, 0), (17, 16), (7, 4), (15, 10), (9, 15), (1, 18), (24, 11), (16, 20), (9, 13), (16, 15), (1, 4), (17, 21), (2, 0), (21, 9), (12, 18), (15, 7), (0, 7), (5, 2), (10, 18), (16, 16), (8, 15), (11, 18), (16, 5), (3, 11), (20, 10), (4, 15), (12, 21), (26, 1), (18, 13), (10, 4), (16, 7), (3, 3), (9, 10), (5, 19), (14, 10), (17, 11), (17, 20), (13, 0), (23, 15), (15, 6), (23, 0), (22, 20), (10, 15), (17, 7), (6, 11), (25, 21), (3, 16), (1, 21), (20, 2), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810960", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (15, 16), (0, 3), (13, 7), (10, 12), (21, 7), (24, 18), (1, 5), (21, 8), (17, 17), (6, 16), (26, 7), (6, 8), (23, 14), (12, 8), (3, 16), (16, 9), (13, 0), (13, 11), (14, 1), (12, 16), (12, 20), (13, 14), (9, 6), (20, 0), (21, 17), (1, 4), (15, 19), (0, 10), (7, 0), (4, 12), (12, 0), (2, 6), (16, 1), (21, 19), (14, 5), (10, 5), (15, 10), (23, 5), (16, 16), (25, 7), (9, 9), (5, 19), (13, 17), (15, 3), (4, 8), (20, 8), (10, 16), (4, 15), (4, 1), (13, 9), (7, 20), (18, 11), (14, 9), (6, 7), (18, 13), (22, 8), (4, 5), (9, 1), (3, 20), (14, 0), (26, 6), (12, 17), (23, 15), (11, 8), (0, 8), (11, 5), (23, 20), (17, 18), (16, 3), (26, 4), (19, 0), (18, 12), (19, 7), (25, 1), (16, 5), (11, 4), (5, 11), (8, 14), (0, 14), (19, 13), (11, 3), (12, 3), (11, 12), (23, 6), (16, 2), (13, 10), (7, 10), (8, 0), (1, 14), (2, 13), (4, 17), (6, 12), (17, 15), (25, 17), (9, 4), (2, 4), (21, 5), (0, 16), (9, 8), (8, 2), (12, 13), (8, 3), (13, 19), (24, 19), (15, 8), (6, 3), (13, 2), (15, 20), (26, 5), (22, 20), (26, 0), (23, 9), (19, 2), (0, 7), (19, 15), (3, 15), (9, 12), (19, 11), (7, 9), (10, 3), (18, 4), (2, 17), (24, 0), (10, 1), (2, 0), (11, 15), (13, 8), (0, 12), (18, 5), (18, 15), (3, 13), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "846582", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (14, 14), (1, 4), (23, 11), (13, 1), (23, 26), (6, 7), (21, 25), (10, 4), (24, 22), (10, 20), (20, 9), (4, 14), (2, 0), (24, 18), (13, 6), (7, 5), (1, 11), (22, 4), (11, 14), (6, 18), (26, 7), (6, 11), (0, 22), (4, 0), (22, 2), (15, 24), (8, 6), (19, 0), (18, 26), (7, 10), (14, 0), (6, 8), (17, 21), (6, 23), (24, 25), (18, 9), (2, 6), (8, 5), (6, 20), (1, 27), (8, 0), (10, 18), (23, 10), (3, 25), (9, 20), (27, 22), (4, 23), (1, 1), (8, 1), (10, 19), (20, 7), (22, 23), (3, 16), (26, 17), (3, 2), (8, 3), (1, 6), (1, 26), (11, 17), (3, 5), (2, 2), (18, 12), (11, 23), (4, 11), (12, 12), (2, 4), (0, 7), (13, 9), (22, 8), (8, 17), (1, 22), (26, 10), (8, 22), (21, 9), (27, 17), (19, 25), (23, 25), (24, 14), (0, 10), (27, 2), (12, 25), (6, 2), (2, 10), (10, 24), (23, 20), (25, 13), (24, 17), (17, 4), (16, 12), (22, 21), (18, 24), (6, 17), (2, 15), (0, 11), (3, 13), (26, 23), (22, 18), (22, 15), (13, 13), (21, 5), (25, 23), (7, 23), (15, 17), (15, 23), (26, 16), (4, 9), (22, 24), (13, 8), (20, 24), (20, 23), (14, 27), (1, 24), (24, 8), (12, 1), (0, 15), (14, 17), (0, 6), (9, 18), (15, 15), (8, 18), (10, 11), (5, 9), (18, 2), (13, 14), (27, 11), (14, 10), (24, 2), (14, 19), (21, 2), (23, 0), (0, 27), (14, 2), (19, 7), (1, 2), (12, 24), (15, 12), (5, 20), (27, 8), (22, 22), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175440", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), 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, 21), (9, 27), (25, 25), (13, 22), (17, 20), (23, 12), (16, 21), (15, 24), (27, 21), (21, 8), (18, 12), (18, 26), (11, 27), (25, 14), (23, 18), (25, 9), (27, 9), (4, 16), (17, 22), (3, 0), (6, 14), (10, 4), (17, 4), (8, 17), (15, 11), (10, 11), (7, 17), (6, 7), (15, 7), (5, 1), (24, 8), (22, 24), (8, 11), (0, 20), (17, 11), (11, 12), (6, 12), (8, 26), (5, 4), (18, 8), (1, 4), (22, 3), (24, 0), (14, 19), (5, 0), (1, 18), (6, 1), (2, 9), (19, 10), (20, 25), (3, 22), (0, 9), (4, 7), (25, 18), (9, 24), (26, 7), (14, 27), (6, 15), (11, 25), (15, 20), (20, 6), (26, 18), (10, 19), (6, 0), (3, 27), (2, 23), (13, 19), (25, 0), (18, 0), (11, 9), (16, 24), (12, 26), (12, 23), (5, 12), (11, 21), (15, 0), (13, 20), (19, 4), (0, 19), (22, 22), (1, 23), (22, 21), (22, 20), (24, 18), (1, 13), (20, 26), (24, 25), (27, 19), (23, 16), (26, 12), (27, 5), (23, 11), (22, 10), (1, 22), (22, 2), (1, 20), (21, 25), (12, 16), (19, 6), (23, 27), (0, 18), (6, 6), (1, 25), (27, 16), (14, 23), (0, 7), (1, 2), (12, 7), (12, 19), (20, 5), (27, 10), (16, 26), (12, 25), (2, 1), (23, 26), (3, 19), (11, 6), (10, 3), (13, 10), (15, 4), (2, 26), (15, 6), (19, 12), (24, 21), (3, 4), (23, 20), (11, 19), (6, 22), (20, 2), (2, 18), (4, 3), (4, 6), (8, 9), (17, 6), (19, 25), (9, 19), (12, 14), (15, 3), (12, 2), (12, 12), (0, 24), (1, 24), (20, 22), (1, 10), (0, 26), (4, 20), (18, 18), (16, 15), (27, 8), (10, 5), (22, 18), (11, 20), (21, 1), (22, 16), (5, 3), (20, 3), (9, 17), (9, 21), (17, 10), (21, 24), (25, 16), (14, 7), (12, 20), (5, 19), (21, 26), (22, 7), (11, 15), (8, 12), (8, 3), (25, 3), (7, 3), (7, 13), (24, 22), (19, 8), (5, 6), (0, 4), (15, 25), (6, 21), (8, 23), (26, 6), (9, 10), (15, 17), (11, 22), (27, 14), (22, 26), (3, 6), (25, 26), (6, 16), (19, 14), (5, 9), (20, 11), (18, 13), (3, 18), (11, 13), (11, 2), (13, 11), (2, 16), (21, 2), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34020", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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), (20, 13), (19, 25), (9, 16), (17, 25), (19, 15), (2, 23), (16, 22), (13, 24), (12, 25), (10, 4), (11, 15), (12, 24), (15, 13), (18, 23), (12, 0), (6, 24), (6, 4), (10, 1), (3, 13), (12, 19), (16, 6), (12, 13), (15, 14), (6, 9), (20, 26), (5, 11), (9, 11), (5, 21), (0, 21), (2, 22), (19, 3), (5, 6), (18, 17), (21, 15), (12, 7), (18, 24), (8, 9), (8, 4), (8, 18), (5, 1), (0, 14), (15, 23), (9, 14), (16, 5), (12, 2), (15, 4), (0, 26), (14, 5), (17, 24), (9, 24), (18, 5), (18, 12), (15, 20), (19, 18), (14, 3), (21, 8), (14, 2), (17, 26), (6, 26), (11, 4), (20, 7), (16, 19), (3, 22), (8, 26), (21, 2), (5, 19), (9, 25), (13, 2), (14, 9), (5, 8), (17, 6), (6, 15), (13, 10), (4, 24), (19, 4), (0, 15), (21, 16), (7, 5), (13, 5), (7, 10), (12, 22), (18, 26), (19, 9), (3, 6), (8, 2), (4, 10), (21, 22), (16, 15), (19, 23), (10, 3), (17, 17), (16, 7), (7, 4), (11, 26), (12, 5), (15, 2), (5, 3), (8, 23), (18, 4), (21, 3), (16, 26), (10, 17), (15, 6), (10, 19), (15, 1), (17, 1), (18, 21), (0, 18), (5, 24), (21, 20), (9, 26), (11, 24), (1, 13), (19, 20), (19, 12), (9, 6), (20, 18), (21, 17), (19, 8), (2, 3), (21, 1), (2, 7), (20, 24), (7, 3), (7, 14), (17, 22), (21, 0), (6, 6), (7, 13), (13, 1), (3, 12), (8, 21), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978656", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 15), (10, 14), (12, 4), (14, 7), (5, 9), (4, 3), (12, 12), (13, 20), (5, 18), (1, 18), (21, 10), (21, 2), (21, 8), (19, 8), (10, 0), (14, 6), (14, 20), (13, 4), (5, 7), (9, 4), (3, 6), (0, 5), (5, 8), (3, 0), (12, 11), (21, 11), (3, 14), (10, 7), (18, 6), (13, 1), (13, 17), (3, 5), (17, 13), (20, 0), (6, 17), (3, 13), (13, 3), (21, 9), (6, 16), (5, 10), (5, 6), (0, 6), (7, 3), (21, 0), (0, 14), (15, 1), (20, 14), (21, 5), (7, 13), (7, 17), (18, 19), (13, 18), (4, 14), (19, 17), (5, 12), (16, 3), (9, 0), (14, 12), (18, 12), (6, 12), (20, 19), (5, 16), (4, 12), (5, 14), (8, 20), (17, 17), (18, 2), (8, 13), (6, 3), (0, 7), (10, 1), (3, 10), (7, 16), (18, 5), (13, 13), (1, 16), (7, 6), (20, 5), (5, 13), (11, 17), (10, 2), (7, 1), (14, 4), (9, 13), (2, 8), (4, 10), (1, 4), (5, 19), (18, 16), (19, 6), (18, 10), (17, 0), (8, 8), (4, 17), (7, 20), (19, 19), (21, 3), (11, 4), (12, 2), (11, 2), (16, 17), (6, 0), (12, 10), (11, 15), (20, 12), (0, 16), (16, 8), (19, 4), (1, 6), (20, 20), (5, 0), (2, 10), (1, 10), (1, 1), (21, 4), (20, 7), (20, 17), (15, 11), (16, 15), (8, 12), (0, 19), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708484", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 26), (13, 13), (0, 19), (7, 0), (2, 14), (15, 24), (18, 2), (9, 18), (1, 1), (1, 21), (1, 12), (6, 10), (2, 2), (8, 22), (6, 9), (8, 10), (13, 6), (1, 15), (14, 6), (15, 22), (11, 16), (6, 1), (19, 12), (4, 0), (15, 2), (19, 0), (4, 10), (16, 1), (16, 0), (3, 25), (3, 9), (13, 0), (11, 10), (8, 15), (6, 14), (19, 6), (17, 24), (13, 24), (3, 12), (4, 3), (0, 23), (4, 11), (17, 26), (2, 1), (8, 19), (3, 16), (8, 6), (12, 15), (8, 5), (17, 8), (17, 19), (5, 12), (3, 14), (19, 24), (4, 6), (18, 7), (9, 12), (19, 19), (19, 11), (19, 1), (13, 15), (14, 25), (12, 26), (17, 1), (1, 0), (0, 4), (7, 11), (2, 12), (9, 22), (7, 21), (13, 23), (17, 18), (9, 21), (3, 24), (10, 7), (15, 13), (18, 26), (12, 1), (13, 25), (9, 14), (3, 3), (7, 13), (16, 9), (16, 12), (14, 1), (2, 23), (18, 15), (11, 11), (5, 24), (0, 24), (6, 15), (15, 16), (12, 6), (10, 2), (10, 14), (17, 5), (2, 8), (15, 26), (9, 25), (18, 13), (5, 14), (15, 9), (13, 12), (16, 4), (16, 8), (2, 3), (7, 2), (3, 8), (9, 6), (9, 3), (15, 12), (5, 5), (12, 12), (1, 18), (12, 17), (19, 15), (18, 18), (14, 23), (3, 18), (11, 24), (9, 2), (19, 21), (17, 2), (11, 25), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964418", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 13), (0, 7), (0, 18), (21, 16), (9, 1), (18, 14), (19, 23), (22, 25), (21, 1), (24, 15), (17, 23), (8, 25), (23, 21), (20, 13), (20, 0), (14, 2), (0, 5), (12, 0), (14, 10), (8, 8), (2, 4), (24, 23), (3, 0), (6, 5), (14, 25), (27, 2), (18, 2), (1, 21), (3, 23), (9, 9), (10, 5), (3, 10), (26, 4), (17, 19), (8, 2), (23, 3), (21, 12), (26, 23), (15, 9), (24, 11), (0, 13), (17, 4), (26, 20), (27, 6), (25, 3), (23, 6), (27, 25), (7, 14), (16, 20), (20, 22), (13, 1), (7, 4), (26, 10), (21, 17), (21, 20), (4, 2), (18, 7), (8, 12), (3, 15), (24, 27), (16, 8), (3, 9), (8, 3), (23, 11), (12, 23), (24, 7), (7, 23), (17, 17), (24, 24), (1, 12), (4, 18), (17, 21), (21, 9), (11, 8), (8, 11), (26, 14), (1, 26), (10, 24), (20, 1), (6, 24), (20, 16), (25, 9), (27, 12), (25, 23), (0, 8), (24, 5), (8, 28), (16, 17), (9, 18), (21, 21), (1, 25), (23, 4), (12, 24), (26, 3), (7, 15), (15, 25), (3, 20), (5, 8), (0, 12), (14, 21), (26, 25), (16, 26), (27, 20), (11, 14), (4, 22), (14, 24), (20, 18), (8, 10), (18, 12), (10, 11), (8, 20), (23, 15), (9, 25), (21, 10), (18, 21), (11, 12), (24, 4), (26, 5), (2, 18), (18, 18), (20, 17), (22, 22), (19, 17), (1, 8), (2, 14), (15, 13), (12, 9), (13, 16), (2, 0), (23, 18), (27, 18), (24, 13), (0, 19), (20, 20), (22, 4), (9, 28), (23, 22), (0, 27), (1, 24), (3, 18), (4, 25), (1, 2), (27, 9), (12, 1), (14, 1), (0, 23), (25, 18), (16, 25), (25, 12), (10, 1), (7, 11), (17, 18), (15, 2), (7, 20), (7, 19), (7, 22), (8, 5), (15, 0), (5, 20), (18, 6), (22, 24), (19, 12), (17, 24), (10, 28), (9, 16), (13, 15), (7, 12), (15, 28), (17, 25), (27, 24), (11, 0), (11, 4), (2, 23), (5, 27), (19, 14), (20, 2), (11, 1), (24, 0), (13, 14), (15, 6), (7, 16), (12, 28), (4, 23), (10, 0), (24, 6), (19, 13), (0, 21), (17, 12), (27, 3), (2, 16), (10, 4), (16, 1), (10, 15), (11, 27), (13, 19), (9, 19), (19, 8), (13, 18), (3, 6), (11, 21), (8, 23), (0, 16), (15, 16), (19, 27), (27, 11), (0, 6), (12, 18), (4, 11), (12, 15), (18, 25), (18, 17), (16, 3), (2, 26), (18, 9), (19, 4), (21, 8), (1, 1), (9, 22), (27, 22), (8, 1), (4, 17), (24, 2), (7, 21), (6, 3), (17, 3), (15, 14), (3, 21), (26, 8), (8, 19), (9, 4), (14, 27), (4, 0), (6, 20), (17, 28), (5, 4), (13, 4), (11, 2), (8, 0), (20, 24), (7, 6), (22, 14), (27, 19), (24, 19), (23, 28), (20, 12), (6, 6), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920808", "dataset": "MATH"}
{"messages": [{"content": "In a 27x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 20), 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), (26, 9), (0, 15), (23, 17), (25, 12), (6, 13), (9, 17), (6, 20), (13, 10), (1, 6), (24, 16), (4, 0), (11, 19), (0, 7), (6, 4), (15, 15), (9, 13), (2, 6), (0, 4), (1, 4), (10, 13), (3, 10), (17, 16), (0, 6), (8, 7), (1, 1), (0, 14), (0, 12), (18, 13), (17, 3), (16, 17), (2, 11), (20, 2), (14, 1), (26, 15), (4, 13), (6, 16), (0, 20), (5, 9), (6, 9), (24, 2), (17, 19), (15, 14), (19, 7), (20, 14), (3, 12), (8, 6), (21, 7), (21, 14), (3, 20), (17, 18), (26, 13), (8, 1), (23, 0), (26, 2), (13, 15), (18, 10), (16, 19), (8, 2), (9, 10), (9, 5), (8, 16), (7, 12), (26, 4), (9, 8), (17, 10), (2, 8), (14, 6), (2, 18), (0, 19), (13, 1), (16, 15), (10, 3), (22, 7), (24, 8), (2, 17), (18, 15), (8, 14), (0, 5), (4, 18), (0, 10), (7, 0), (22, 15), (11, 16), (24, 13), (2, 12), (21, 11), (15, 19), (17, 11), (26, 12), (2, 1), (22, 11), (11, 8), (8, 13), (1, 14), (13, 8), (19, 16), (15, 4), (18, 3), (24, 4), (8, 17), (12, 3), (10, 11), (4, 11), (16, 16), (15, 2), (12, 5), (9, 4), (12, 16), (10, 16), (26, 1), (22, 4), (21, 9), (2, 7), (9, 6), (26, 11), (11, 12), (10, 17), (15, 3), (26, 16), (2, 4), (12, 12), (8, 5), (23, 20), (19, 4), (10, 15), (18, 18), (15, 12), (4, 7), (5, 13), (7, 6), (20, 20), (21, 13), (7, 16), (13, 18), (11, 11), (13, 19), (2, 3), (20, 19), (21, 2), (22, 14), (18, 0), (12, 19), (16, 6), (10, 14), (22, 10), (25, 18), (8, 10), (7, 4), (11, 13), (13, 3), (23, 9), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430320", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 17), (17, 10), (9, 25), (9, 4), (4, 15), (7, 14), (18, 8), (15, 18), (10, 8), (26, 19), (0, 16), (17, 24), (19, 15), (6, 14), (18, 17), (15, 17), (11, 23), (25, 5), (20, 4), (21, 15), (15, 0), (9, 16), (27, 13), (2, 14), (26, 16), (12, 9), (8, 6), (24, 6), (13, 18), (0, 25), (21, 10), (11, 7), (0, 9), (12, 11), (19, 20), (10, 15), (17, 19), (12, 22), (8, 25), (8, 1), (2, 2), (15, 11), (16, 0), (21, 1), (15, 20), (12, 0), (9, 3), (1, 18), (10, 0), (9, 8), (16, 4), (18, 0), (12, 16), (19, 2), (9, 1), (17, 15), (14, 5), (10, 22), (18, 13), (17, 7), (0, 24), (14, 21), (22, 2), (15, 19), (18, 25), (10, 1), (4, 13), (15, 25), (27, 0), (1, 21), (13, 2), (22, 22), (1, 16), (25, 11), (16, 13), (14, 14), (22, 8), (0, 2), (19, 23), (8, 9), (22, 19), (18, 18), (12, 14), (23, 13), (0, 1), (6, 1), (19, 16), (7, 16), (22, 25), (8, 15), (1, 12), (12, 18), (7, 11), (24, 18), (13, 25), (19, 5), (26, 1), (14, 4), (9, 13), (10, 14), (13, 0), (16, 22), (17, 25), (21, 3), (6, 9), (7, 15), (27, 20), (4, 22), (16, 3), (5, 15), (14, 1), (25, 17), (10, 20), (11, 8), (26, 3), (0, 11), (18, 24), (7, 12), (16, 9), (10, 9), (4, 25), (5, 0), (25, 24), (21, 8), (22, 17), (24, 2), (26, 11), (21, 11), (16, 6), (24, 13), (3, 17), (22, 20), (27, 24), (3, 22), (14, 0), (3, 0), (13, 6), (7, 9), (21, 21), (3, 19), (19, 3), (6, 20), (20, 12), (13, 19), (20, 20), (24, 21), (7, 24), (21, 4), (7, 19), (6, 4), (24, 3), (4, 6), (13, 16), (2, 0), (16, 25), (20, 25), (10, 3), (1, 13), (15, 21), (3, 5), (20, 2), (5, 4), (16, 12), (19, 10), (14, 6), (1, 6), (10, 11), (16, 14), (4, 24), (11, 17), (5, 19), (7, 13), (2, 3), (25, 18), (22, 14), (0, 22), (18, 14), (6, 16), (2, 13), (7, 7), (24, 4), (18, 1), (4, 2), (5, 7), (18, 5), (3, 7), (14, 15), (22, 16), (8, 19), (27, 7), (19, 7), (13, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712644", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), 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), (15, 18), (6, 15), (7, 14), (8, 14), (16, 11), (6, 9), (16, 5), (18, 15), (2, 10), (19, 11), (13, 20), (11, 15), (8, 17), (14, 16), (11, 3), (7, 8), (15, 5), (12, 11), (2, 8), (16, 6), (2, 12), (3, 3), (12, 6), (5, 5), (6, 10), (3, 15), (17, 4), (0, 18), (14, 15), (9, 3), (15, 12), (19, 13), (20, 2), (18, 2), (18, 18), (15, 3), (7, 16), (2, 3), (19, 4), (11, 4), (19, 9), (8, 7), (13, 16), (1, 10), (10, 6), (16, 9), (8, 1), (2, 1), (6, 7), (6, 3), (9, 9), (14, 9), (12, 13), (16, 20), (14, 6), (3, 11), (16, 14), (16, 3), (19, 20), (6, 16), (0, 10), (20, 4), (19, 5), (9, 8), (3, 9), (11, 7), (8, 3), (8, 15), (9, 11), (5, 12), (1, 3), (15, 8), (0, 6), (7, 20), (13, 4), (12, 7), (13, 15), (17, 2), (15, 1), (17, 6), (0, 11), (18, 0), (18, 13), (17, 12), (10, 1), (4, 20), (19, 0), (6, 4), (7, 18), (4, 11), (14, 14), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "668176", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 3), (0, 13), (6, 1), (2, 19), (17, 15), (8, 11), (8, 10), (2, 12), (8, 21), (13, 21), (11, 13), (21, 10), (0, 20), (22, 19), (5, 12), (2, 20), (19, 6), (15, 18), (3, 21), (22, 12), (17, 12), (13, 26), (20, 6), (4, 10), (4, 22), (20, 26), (13, 3), (8, 14), (14, 24), (0, 21), (16, 1), (0, 12), (15, 23), (3, 11), (18, 14), (9, 23), (25, 6), (7, 5), (26, 13), (0, 3), (4, 8), (4, 16), (26, 11), (12, 23), (4, 24), (8, 6), (4, 14), (16, 17), (17, 21), (20, 3), (11, 22), (26, 22), (14, 21), (1, 17), (8, 7), (11, 25), (24, 6), (23, 18), (3, 17), (8, 0), (8, 15), (13, 19), (14, 16), (19, 14), (14, 19), (7, 6), (12, 19), (25, 14), (1, 13), (21, 17), (4, 0), (15, 17), (5, 21), (24, 7), (22, 18), (3, 25), (10, 24), (25, 7), (17, 17), (9, 11), (18, 5), (0, 11), (23, 12), (20, 2), (2, 1), (8, 19), (6, 18), (10, 13), (26, 15), (9, 7), (11, 15), (14, 7), (20, 20), (13, 10), (19, 11), (2, 0), (26, 7), (18, 18), (14, 10), (15, 2), (4, 6), (24, 25), (16, 18), (6, 17), (7, 10), (4, 11), (17, 6), (13, 17), (11, 11), (4, 23), (20, 10), (24, 14), (17, 11), (13, 15), (10, 8), (5, 16), (22, 6), (12, 5), (10, 0), (20, 22), (3, 15), (17, 19), (6, 0), (23, 26), (11, 26), (18, 26), (2, 10), (16, 9), (18, 10), (15, 12), (15, 6), (21, 1), (3, 6), (21, 6), (24, 12), (5, 17), (18, 21), (25, 9), (5, 13), (0, 25), (25, 24), (3, 24), (19, 4), (22, 21), (1, 16), (16, 21), (8, 3), (8, 18), (5, 5), (23, 17), (10, 12), (21, 20), (10, 7), (6, 21), (25, 21), (11, 6), (26, 20), (23, 3), (13, 4), (23, 11), (15, 15), (3, 10), (18, 17), (16, 12), (25, 13), (13, 16), (0, 24), (15, 8), (12, 18), (1, 10), (19, 19), (4, 17), (14, 1), (17, 9), (20, 25), (1, 24), (16, 23), (18, 11), (20, 19), (4, 3), (3, 5), (6, 6), (5, 8), (26, 0), (24, 4), (11, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410166", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), 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, 19), (19, 22), (12, 25), (15, 0), (6, 0), (15, 17), (12, 24), (22, 6), (14, 4), (12, 23), (6, 3), (15, 19), (14, 5), (18, 5), (1, 4), (10, 25), (16, 9), (1, 9), (9, 19), (18, 23), (21, 2), (18, 14), (22, 7), (19, 10), (15, 9), (19, 0), (6, 14), (13, 1), (17, 0), (2, 0), (20, 13), (1, 18), (15, 11), (5, 13), (9, 5), (13, 2), (22, 1), (18, 0), (20, 1), (21, 0), (9, 25), (4, 25), (16, 10), (2, 21), (20, 16), (14, 22), (15, 7), (4, 24), (2, 6), (15, 3), (11, 18), (13, 13), (2, 25), (6, 8), (3, 3), (2, 16), (11, 7), (9, 17), (13, 16), (22, 8), (2, 11), (4, 12), (19, 7), (14, 24), (11, 19), (9, 1), (3, 25), (16, 5), (8, 4), (5, 18), (14, 6), (20, 4), (10, 18), (15, 15), (21, 15), (18, 21), (17, 9), (8, 21), (19, 2), (0, 10), (8, 19), (6, 7), (5, 12), (7, 8), (15, 12), (17, 3), (15, 1), (21, 13), (21, 20), (18, 24), (21, 18), (21, 6), (7, 10), (5, 1), (13, 22), (7, 25), (21, 8), (9, 12), (8, 2), (7, 21), (7, 2), (21, 19), (4, 18), (19, 16), (4, 4), (5, 9), (4, 21), (8, 13), (6, 15), (13, 14), (1, 3), (1, 12), (11, 0), (17, 8), (13, 18), (18, 13), (16, 15), (9, 18), (12, 6), (17, 1), (10, 11), (18, 1), (0, 6), (11, 23), (20, 7), (16, 8), (3, 14), (4, 1), (5, 19), (0, 5), (1, 0), (13, 19), (4, 11), (18, 17), (12, 4), (13, 4), (11, 2), (22, 15), (14, 21), (0, 12), (15, 25), (12, 3), (6, 1), (21, 3), (11, 15), (10, 4), (20, 24), (14, 1), (4, 0), (10, 23), (16, 11), (12, 19), (19, 19), (0, 2), (9, 22), (19, 5), (4, 22), (0, 20), (16, 1), (1, 10), (3, 20), (3, 24), (15, 20), (12, 2), (9, 10), (13, 7), (12, 11), (2, 2), (14, 14), (11, 21), (0, 16), (15, 2), (3, 21), (13, 10), (12, 10), (19, 13), (20, 18), (0, 21), (8, 14), (12, 17), (17, 5), (7, 24), (17, 23), (19, 17), (7, 23), (8, 20), (7, 0), (22, 11), (22, 5), (0, 4), (10, 2), (4, 8), (0, 23), (20, 2), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281808", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), 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), (8, 0), (10, 3), (21, 6), (24, 3), (11, 7), (12, 3), (0, 18), (23, 21), (21, 17), (13, 6), (22, 5), (13, 17), (7, 0), (24, 4), (22, 11), (5, 8), (4, 22), (6, 3), (10, 11), (21, 18), (3, 8), (0, 7), (18, 21), (17, 13), (18, 7), (15, 10), (14, 23), (10, 13), (8, 3), (19, 6), (10, 6), (23, 12), (0, 23), (3, 10), (13, 2), (16, 19), (16, 22), (22, 16), (6, 17), (11, 22), (15, 5), (5, 21), (22, 20), (11, 4), (16, 10), (8, 8), (5, 6), (18, 9), (23, 20), (3, 16), (21, 19), (11, 21), (2, 10), (17, 3), (19, 22), (24, 16), (20, 22), (24, 10), (5, 16), (11, 18), (19, 4), (5, 23), (25, 14), (16, 4), (14, 19), (11, 14), (15, 20), (19, 3), (5, 10), (10, 20), (23, 16), (2, 6), (16, 13), (5, 12), (24, 15), (20, 12), (21, 13), (5, 15), (16, 11), (0, 14), (1, 2), (20, 16), (11, 13), (8, 11), (6, 0), (11, 1), (2, 21), (19, 12), (17, 18), (8, 5), (3, 5), (5, 1), (22, 23), (23, 7), (22, 0), (20, 21), (25, 12), (13, 16), (16, 20), (2, 14), (15, 2), (1, 11), (4, 23), (22, 4), (3, 21), (9, 11), (5, 20), (1, 1), (15, 18), (5, 22), (25, 18), (24, 11), (14, 7), (23, 23), (20, 17), (17, 20), (4, 0), (19, 1), (25, 9), (19, 14), (11, 6), (18, 3), (15, 4), (18, 11), (10, 23), (16, 15), (2, 3), (18, 19), (13, 21), (1, 20), (15, 23), (2, 15), (14, 0), (17, 8), (9, 15), (14, 15), (4, 20), (9, 7), (11, 19), (6, 8), (6, 1), (7, 16), (0, 1), (14, 21), (10, 21), (7, 11), (3, 1), (2, 17), (10, 8), (23, 5), (12, 22), (12, 12), (23, 4), (20, 19), (16, 23), (2, 9), (3, 12), (19, 13), (15, 6), (8, 23), (9, 17), (12, 17), (15, 3), (4, 21), (22, 18), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483720", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (20, 6), (4, 24), (14, 20), (20, 13), (10, 3), (10, 0), (2, 4), (19, 5), (12, 1), (9, 2), (22, 20), (20, 5), (1, 26), (10, 8), (11, 19), (17, 8), (23, 13), (20, 20), (1, 17), (12, 2), (21, 16), (13, 13), (12, 22), (2, 10), (3, 11), (4, 1), (1, 2), (10, 10), (16, 1), (12, 21), (20, 22), (10, 25), (4, 18), (23, 5), (4, 5), (14, 2), (23, 7), (18, 19), (6, 16), (13, 25), (7, 11), (20, 0), (18, 28), (14, 10), (9, 9), (17, 10), (23, 23), (21, 11), (15, 14), (23, 10), (23, 4), (16, 0), (11, 20), (3, 12), (21, 2), (20, 19), (11, 18), (6, 13), (5, 4), (10, 4), (13, 19), (12, 25), (14, 23), (18, 20), (7, 2), (11, 17), (20, 12), (23, 1), (15, 0), (8, 6), (2, 5), (4, 2), (4, 13), (11, 24), (5, 21), (14, 12), (0, 14), (18, 27), (12, 17), (15, 3), (9, 25), (9, 24), (22, 2), (0, 18), (7, 9), (4, 22), (7, 20), (10, 13), (23, 17), (12, 19), (14, 26), (14, 6), (22, 14), (7, 27), (8, 12), (19, 27), (21, 10), (17, 7), (4, 28), (21, 14), (17, 0), (20, 8), (9, 19), (9, 23), (5, 19), (6, 14), (22, 22), (15, 11), (1, 9), (23, 0), (2, 23), (15, 18), (1, 4), (14, 5), (18, 17), (4, 7), (0, 13), (15, 2), (11, 10), (1, 13), (22, 0), (14, 1), (7, 21), (22, 10), (19, 8), (16, 24), (16, 13), (6, 18), (1, 16), (22, 9), (7, 13), (17, 28), (13, 24), (2, 13), (8, 20), (18, 14), (8, 11), (20, 10), (15, 22), (19, 20), (15, 21), (15, 15), (7, 3), (12, 24), (17, 9), (3, 18), (4, 19), (23, 24), (11, 16), (11, 2), (3, 25), (20, 25), (4, 11), (21, 9), (6, 6), (17, 26), (6, 23), (12, 26), (16, 23), (7, 17), (3, 6), (3, 7), (23, 22), (8, 28), (11, 14), (11, 5), (21, 17), (6, 24), (19, 4), (15, 25), (14, 24), (23, 26), (17, 11), (17, 6), (20, 23), (16, 3), (1, 23), (16, 5), (23, 11), (5, 28), (0, 2), (18, 5), (12, 0), (10, 21), (4, 26), (23, 20), (10, 24), (10, 18), (1, 14), (22, 19), (19, 25), (21, 0), (8, 27), (18, 7), (2, 25), (8, 7), (22, 13), (2, 3), (7, 25), (10, 7), (14, 21), (22, 24), (8, 4), (21, 20), (19, 24), (8, 25), (10, 15), (17, 17), (15, 9), (7, 1), (16, 9), (20, 4), (5, 7), (17, 18), (14, 25), (5, 27), (1, 25), (2, 28), (3, 1), (18, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187698", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 28), (23, 3), (3, 7), (19, 1), (22, 19), (4, 23), (0, 1), (14, 9), (10, 13), (10, 15), (1, 15), (17, 2), (10, 26), (16, 24), (1, 16), (22, 9), (13, 5), (11, 26), (3, 5), (17, 9), (1, 23), (21, 5), (20, 18), (18, 3), (13, 1), (8, 27), (17, 8), (12, 5), (14, 28), (12, 11), (11, 13), (7, 7), (22, 27), (20, 20), (8, 7), (4, 20), (15, 15), (16, 21), (23, 7), (19, 21), (22, 17), (11, 10), (22, 6), (22, 14), (18, 8), (5, 12), (16, 27), (5, 21), (3, 14), (15, 10), (9, 9), (5, 7), (15, 9), (9, 7), (8, 26), (13, 10), (3, 11), (12, 4), (14, 18), (7, 12), (21, 21), (15, 2), (15, 28), (8, 0), (21, 22), (20, 21), (12, 18), (18, 5), (5, 14), (0, 27), (9, 19), (4, 10), (23, 18), (17, 10), (12, 3), (17, 11), (13, 22), (22, 1), (10, 8), (13, 25), (2, 11), (1, 6), (20, 7), (8, 1), (6, 2), (15, 11), (0, 21), (18, 12), (21, 25), (12, 15), (14, 8), (7, 9), (6, 10), (23, 21), (5, 27), (0, 20), (6, 14), (21, 9), (16, 16), (23, 12), (8, 2), (4, 18), (7, 11), (5, 10), (0, 11), (2, 7), (17, 3), (16, 26), (1, 27), (14, 17), (23, 2), (5, 1), (16, 28), (19, 25), (11, 20), (0, 26), (6, 15), (19, 24), (14, 23), (22, 24), (2, 14), (3, 25), (10, 27), (3, 27), (10, 20), (23, 6), (13, 14), (20, 27), (1, 14), (13, 7), (21, 24), (19, 22), (8, 5), (20, 28), (18, 20), (14, 10), (16, 22), (15, 12), (10, 11), (8, 16), (0, 13), (2, 4), (3, 9), (12, 2), (16, 12), (6, 3), (12, 27), (5, 0), (15, 5), (12, 17), (19, 27), (13, 12), (0, 7), (8, 22), (19, 7), (17, 14), (9, 4), (23, 22), (1, 20), (18, 4), (11, 14), (18, 19), (4, 9), (17, 4), (5, 13), (10, 3), (8, 25), (8, 13), (15, 27), (9, 2), (2, 5), (19, 0), (17, 6), (10, 23), (2, 21), (9, 26), (0, 23), (10, 6), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388710", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 2), (15, 9), (17, 6), (24, 3), (2, 20), (10, 14), (4, 8), (26, 1), (26, 6), (16, 0), (18, 15), (13, 4), (3, 22), (11, 2), (4, 14), (11, 10), (23, 11), (20, 21), (18, 22), (18, 21), (11, 0), (19, 0), (5, 17), (4, 19), (22, 15), (2, 2), (8, 2), (18, 11), (18, 20), (4, 0), (21, 20), (22, 14), (12, 23), (22, 4), (20, 19), (13, 3), (8, 7), (13, 19), (22, 10), (22, 13), (22, 0), (28, 13), (11, 22), (17, 17), (9, 11), (26, 21), (2, 10), (3, 5), (9, 15), (19, 17), (22, 18), (27, 11), (16, 2), (26, 15), (19, 21), (20, 6), (24, 4), (27, 9), (7, 2), (15, 3), (24, 18), (23, 13), (15, 20), (1, 13), (14, 14), (26, 20), (2, 7), (2, 22), (13, 7), (2, 4), (15, 7), (28, 8), (16, 1), (4, 2), (14, 21), (18, 13), (13, 11), (9, 0), (1, 23), (16, 21), (17, 0), (2, 16), (18, 9), (2, 5), (5, 4), (16, 7), (27, 7), (3, 2), (9, 19), (5, 6), (5, 7), (8, 4), (10, 23), (2, 17), (10, 11), (21, 0), (28, 2), (28, 16), (26, 14), (4, 17), (24, 20), (13, 12), (13, 18), (8, 9), (4, 10), (18, 1), (22, 19), (25, 0), (27, 0), (13, 8), (20, 1), (13, 20), (24, 1), (9, 4), (20, 15), (24, 21), (27, 23), (11, 16), (11, 14), (9, 13), (15, 4), (5, 5), (15, 16), (16, 15), (17, 22), (2, 6), (19, 15), (12, 0), (5, 3), (9, 22), (6, 5), (19, 6), (8, 1), (23, 8), (21, 8), (20, 8), (11, 4), (13, 14), (7, 19), (15, 17), (24, 13), (12, 6), (23, 23), (18, 17), (24, 8), (1, 1), (4, 15), (13, 6), (8, 5), (12, 18), (0, 13), (25, 22), (11, 8), (23, 6), (23, 2), (15, 19), (10, 10), (0, 22), (17, 10), (3, 19), (10, 4), (17, 2), (10, 7), (22, 17), (14, 16), (12, 10), (9, 21), (23, 3), (0, 18), (8, 21), (13, 13), (9, 18), (11, 15), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520172", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 18), (10, 22), (8, 8), (2, 10), (15, 15), (7, 6), (16, 21), (20, 16), (5, 7), (20, 0), (16, 17), (13, 19), (8, 14), (15, 1), (12, 3), (15, 5), (0, 24), (15, 8), (12, 15), (9, 2), (14, 24), (15, 24), (18, 14), (5, 25), (2, 19), (14, 1), (13, 14), (8, 3), (15, 19), (7, 4), (9, 19), (14, 2), (13, 21), (9, 12), (12, 11), (13, 23), (6, 5), (16, 3), (1, 15), (4, 22), (14, 23), (21, 21), (12, 23), (8, 17), (9, 14), (7, 5), (13, 20), (2, 0), (21, 4), (5, 12), (4, 15), (18, 9), (17, 22), (8, 0), (21, 0), (21, 3), (11, 18), (6, 13), (6, 17), (1, 24), (0, 20), (5, 1), (22, 14), (12, 5), (9, 4), (17, 20), (0, 23), (4, 24), (0, 16), (21, 16), (6, 23), (21, 8), (3, 15), (11, 10), (5, 20), (11, 1), (9, 25), (19, 19), (3, 8), (4, 21), (6, 24), (12, 20), (10, 7), (1, 0), (2, 7), (6, 4), (16, 12), (21, 12), (8, 11), (1, 4), (4, 4), (8, 6), (22, 10), (18, 22), (16, 16), (9, 3), (20, 3), (15, 2), (14, 11), (22, 19), (15, 3), (15, 6), (20, 2), (1, 1), (13, 1), (0, 21), (1, 16), (11, 3), (8, 15), (10, 17), (5, 6), (5, 13), (5, 11), (18, 25), (14, 5), (10, 12), (8, 4), (0, 18), (16, 10), (8, 1), (17, 23), (14, 18), (5, 9), (16, 22), (15, 23), (4, 11), (19, 0), (16, 2), (11, 23), (13, 12), (11, 12), (19, 3), (20, 11), (6, 22), (16, 18), (5, 23), (15, 17), (14, 22), (12, 6), (14, 12), (12, 10), (22, 9), (12, 21), (20, 19), (15, 12), (3, 23), (9, 20), (7, 15), (18, 1), (16, 23), (10, 8), (18, 24), (22, 1), (22, 7), (22, 5), (0, 7), (20, 6), (16, 6), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840156", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), 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), (6, 5), (25, 12), (3, 19), (16, 7), (4, 13), (25, 17), (6, 1), (21, 7), (14, 3), (14, 10), (10, 11), (25, 9), (3, 1), (2, 9), (2, 11), (24, 10), (17, 18), (19, 6), (19, 11), (2, 2), (22, 1), (12, 13), (0, 6), (1, 6), (11, 10), (1, 4), (25, 8), (4, 9), (5, 16), (17, 14), (8, 13), (7, 2), (17, 11), (22, 9), (12, 16), (14, 20), (13, 4), (20, 4), (3, 2), (20, 9), (19, 18), (11, 1), (6, 0), (0, 7), (13, 17), (20, 19), (17, 0), (17, 13), (10, 17), (5, 13), (10, 16), (7, 18), (11, 15), (7, 4), (12, 1), (0, 9), (18, 8), (14, 7), (23, 6), (8, 15), (16, 13), (20, 18), (23, 13), (15, 8), (23, 9), (7, 17), (1, 18), (16, 17), (9, 7), (18, 6), (16, 2), (14, 6), (18, 16), (4, 2), (8, 8), (10, 1), (1, 19), (22, 15), (22, 7), (20, 6), (13, 15), (16, 3), (20, 13), (6, 16), (2, 4), (13, 19), (8, 19), (15, 0), (24, 17), (19, 0), (23, 14), (25, 10), (13, 2), (11, 4), (19, 1), (19, 3), (5, 2), (10, 7), (23, 8), (24, 8), (6, 2), (8, 1), (19, 13), (7, 12), (16, 12), (17, 15), (17, 19), (15, 7), (9, 17), (3, 18), (19, 14), (19, 15), (18, 0), (20, 15), (7, 11), (25, 14), (18, 7), (4, 12), (23, 0), (19, 7), (20, 12), (16, 0), (15, 20), (24, 3), (22, 18), (3, 15), (19, 8), (22, 10), (8, 17), (12, 8), (20, 14), (7, 3), (2, 0), (11, 20), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322082", "dataset": "MATH"}
{"messages": [{"content": "In a 21x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 15), (16, 2), (19, 22), (13, 26), (7, 3), (13, 21), (8, 24), (18, 25), (9, 22), (17, 16), (12, 3), (7, 8), (20, 7), (8, 16), (6, 25), (8, 12), (17, 22), (12, 23), (15, 23), (8, 4), (3, 13), (20, 1), (1, 2), (13, 6), (8, 28), (1, 26), (13, 14), (16, 1), (19, 19), (9, 2), (4, 25), (20, 27), (9, 19), (0, 5), (16, 19), (9, 1), (8, 8), (9, 17), (13, 15), (15, 17), (13, 1), (9, 5), (14, 17), (8, 2), (10, 9), (7, 28), (3, 9), (2, 3), (11, 24), (10, 11), (7, 13), (20, 11), (1, 27), (15, 20), (18, 8), (5, 13), (11, 5), (16, 14), (8, 25), (1, 17), (17, 24), (18, 4), (3, 7), (9, 14), (1, 6), (11, 4), (3, 0), (12, 16), (12, 12), (16, 3), (5, 8), (1, 12), (2, 14), (18, 28), (11, 15), (11, 26), (14, 19), (19, 15), (12, 22), (7, 20), (7, 14), (10, 21), (14, 2), (6, 3), (13, 28), (4, 23), (17, 27), (11, 18), (17, 14), (19, 7), (19, 26), (14, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571968", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 20), (5, 11), (6, 11), (22, 16), (10, 17), (17, 20), (17, 1), (10, 13), (5, 14), (23, 12), (10, 8), (5, 6), (19, 20), (3, 1), (1, 19), (16, 8), (17, 21), (8, 10), (4, 21), (24, 10), (24, 13), (13, 17), (1, 5), (4, 10), (2, 11), (23, 11), (21, 7), (10, 15), (21, 17), (23, 7), (12, 9), (7, 2), (3, 19), (11, 4), (15, 20), (3, 2), (14, 8), (14, 19), (9, 23), (17, 4), (15, 23), (18, 0), (20, 21), (1, 24), (14, 7), (15, 7), (4, 9), (11, 2), (3, 17), (6, 0), (22, 2), (14, 1), (20, 18), (6, 22), (1, 1), (7, 3), (9, 7), (2, 17), (8, 19), (13, 3), (1, 22), (5, 17), (22, 24), (13, 7), (24, 4), (24, 0), (2, 20), (20, 15), (13, 21), (20, 16), (9, 9), (8, 5), (15, 10), (4, 12), (17, 9), (23, 22), (23, 24), (2, 10), (1, 11), (4, 8), (0, 1), (14, 16), (8, 2), (6, 1), (12, 13), (1, 14), (13, 16), (17, 7), (24, 6), (18, 12), (6, 12), (2, 8), (10, 11), (7, 14), (9, 3), (7, 22), (15, 24), (12, 4), (16, 21), (12, 23), (16, 11), (13, 15), (8, 3), (12, 12), (17, 16), (23, 18), (20, 0), (10, 7), (0, 2), (20, 22), (20, 19), (6, 9), (11, 24), (16, 0), (24, 21), (4, 17), (19, 8), (23, 2), (7, 21), (5, 0), (8, 6), (3, 4), (19, 4), (23, 13), (24, 8), (14, 9), (6, 20), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883458", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), 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), (11, 4), (17, 17), (7, 1), (22, 10), (2, 20), (20, 9), (0, 12), (17, 22), (11, 10), (14, 16), (10, 9), (6, 20), (13, 8), (5, 10), (4, 18), (13, 0), (20, 12), (15, 19), (10, 21), (20, 21), (3, 6), (3, 16), (16, 16), (19, 3), (5, 16), (12, 20), (14, 6), (5, 5), (7, 13), (19, 6), (4, 4), (7, 2), (21, 1), (13, 14), (15, 14), (7, 10), (18, 4), (11, 3), (20, 5), (1, 9), (21, 2), (13, 21), (16, 8), (6, 23), (11, 13), (6, 17), (2, 5), (7, 18), (16, 9), (15, 16), (11, 7), (0, 9), (12, 18), (18, 9), (17, 15), (18, 10), (8, 6), (17, 7), (4, 8), (22, 2), (17, 3), (17, 20), (5, 17), (10, 6), (5, 12), (16, 17), (7, 5), (3, 1), (2, 15), (9, 5), (18, 17), (7, 8), (7, 7), (22, 15), (22, 0), (5, 3), (20, 4), (17, 11), (12, 22), (2, 4), (15, 0), (1, 5), (22, 17), (13, 18), (14, 14), (9, 12), (17, 10), (0, 11), (4, 7), (7, 12), (9, 0), (12, 16), (21, 23), (22, 14), (3, 9), (12, 8), (12, 5), (20, 18), (14, 11), (0, 14), (5, 7), (14, 5), (4, 20), (17, 5), (8, 2), (14, 8), (15, 5), (13, 2), (6, 15), (2, 14), (8, 20), (9, 16), (1, 22), (6, 19), (12, 11), (3, 23), (17, 21), (10, 1), (4, 9), (11, 23), (1, 2), (2, 7), (3, 8), (6, 13), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "833386", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 24), (19, 15), (10, 8), (4, 28), (2, 14), (15, 4), (4, 17), (18, 23), (21, 7), (22, 26), (20, 2), (22, 18), (16, 13), (4, 18), (2, 16), (8, 26), (15, 20), (6, 9), (4, 9), (18, 16), (15, 25), (1, 8), (7, 25), (7, 6), (1, 12), (11, 20), (16, 28), (19, 25), (20, 21), (4, 14), (4, 22), (3, 14), (12, 7), (8, 18), (11, 10), (6, 0), (14, 13), (16, 21), (2, 17), (18, 5), (11, 16), (0, 25), (5, 16), (19, 11), (17, 25), (7, 22), (17, 9), (10, 19), (22, 27), (1, 27), (16, 2), (13, 24), (19, 19), (1, 13), (2, 24), (4, 13), (10, 20), (5, 27), (10, 7), (7, 3), (13, 18), (22, 20), (3, 13), (12, 25), (11, 28), (14, 10), (3, 0), (0, 14), (14, 12), (19, 27), (1, 19), (9, 23), (20, 23), (22, 0), (18, 10), (15, 11), (11, 3), (10, 23), (1, 15), (2, 0), (16, 26), (9, 25), (4, 5), (4, 3), (12, 9), (15, 18), (8, 27), (10, 6), (13, 9), (17, 1), (19, 21), (18, 2), (21, 5), (6, 20), (9, 28), (7, 10), (3, 18), (9, 6), (8, 7), (2, 1), (7, 19), (10, 24), (10, 2), (4, 4), (22, 6), (2, 7), (12, 19), (1, 14), (22, 25), (11, 19), (0, 26), (6, 2), (2, 28), (15, 24), (12, 11), (6, 23), (17, 6), (11, 5), (22, 15), (20, 0), (20, 24), (9, 17), (7, 18), (19, 22), (1, 25), (11, 9), (22, 11), (9, 15), (4, 16), (3, 19), (13, 11), (16, 7), (9, 13), (8, 5), (0, 11), (17, 2), (17, 8), (13, 6), (19, 3), (15, 2), (7, 2), (19, 10), (14, 8), (21, 13), (5, 12), (21, 15), (5, 21), (11, 14), (16, 6), (14, 0), (10, 0), (8, 9), (14, 14), (7, 15), (13, 14), (4, 12), (7, 14), (14, 2), (21, 6), (22, 10), (21, 18), (6, 10), (7, 21), (14, 6), (6, 3), (7, 1), (16, 22), (2, 3), (13, 8), (5, 25), (6, 13), (16, 5), (11, 15), (18, 0), (18, 12), (1, 22), (9, 11), (17, 22), (5, 24), (1, 23), (18, 4), (2, 10), (0, 2), (2, 4), (18, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847998", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 16), (7, 0), (9, 1), (7, 7), (15, 6), (19, 18), (19, 2), (14, 16), (1, 9), (5, 12), (12, 17), (17, 8), (1, 14), (8, 21), (12, 20), (15, 19), (7, 19), (6, 7), (2, 18), (8, 7), (12, 14), (0, 16), (23, 2), (13, 9), (1, 4), (13, 7), (17, 3), (21, 21), (2, 17), (0, 1), (19, 12), (1, 15), (13, 6), (0, 4), (2, 14), (10, 2), (19, 8), (15, 14), (6, 8), (10, 6), (3, 16), (7, 2), (0, 19), (13, 2), (9, 14), (11, 9), (6, 1), (7, 11), (16, 0), (8, 15), (9, 4), (23, 19), (20, 15), (19, 4), (11, 7), (8, 18), (21, 2), (2, 0), (22, 13), (1, 7), (7, 14), (21, 4), (16, 20), (9, 2), (8, 0), (17, 2), (3, 17), (17, 16), (21, 8), (19, 15), (17, 9), (5, 16), (11, 14), (5, 5), (12, 12), (19, 6), (15, 16), (15, 20), (16, 17), (0, 17), (4, 12), (0, 10), (9, 3), (18, 12), (10, 1), (2, 11), (18, 2), (11, 17), (18, 3), (11, 8), (3, 10), (11, 4), (10, 3), (6, 15), (6, 17), (16, 7), (18, 6), (19, 14), (10, 10), (7, 21), (11, 12), (13, 4), (9, 11), (1, 16), (5, 15), (14, 6), (1, 2), (3, 5), (20, 13), (8, 6), (23, 11), (9, 16), (12, 3), (6, 9), (11, 13), (2, 7), (14, 11), (5, 8), (4, 13), (23, 17), (2, 2), (0, 9), (0, 12), (14, 5), (2, 16), (18, 11), (21, 10), (3, 18), (15, 2), (9, 7), (1, 20), (12, 16), (5, 11), (11, 19), (10, 18), (12, 2), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784412", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 2), (16, 8), (11, 18), (16, 0), (18, 3), (21, 14), (12, 10), (21, 10), (22, 8), (11, 4), (7, 3), (2, 8), (12, 18), (5, 0), (7, 13), (8, 5), (22, 20), (17, 10), (9, 20), (10, 1), (4, 22), (12, 20), (1, 14), (13, 5), (13, 16), (21, 3), (13, 21), (21, 17), (21, 15), (13, 8), (23, 23), (0, 1), (18, 13), (5, 12), (17, 26), (22, 14), (6, 21), (23, 16), (21, 24), (23, 21), (4, 17), (7, 23), (22, 25), (22, 7), (16, 4), (12, 12), (6, 3), (18, 0), (17, 13), (4, 15), (4, 13), (11, 5), (14, 17), (7, 1), (7, 5), (10, 8), (17, 17), (10, 5), (21, 11), (18, 17), (5, 11), (20, 0), (21, 26), (15, 12), (10, 13), (16, 21), (5, 17), (4, 9), (10, 9), (23, 6), (4, 23), (14, 1), (14, 2), (9, 1), (6, 10), (19, 23), (23, 14), (11, 14), (15, 24), (21, 1), (15, 8), (20, 24), (14, 16), (17, 19), (5, 3), (6, 17), (18, 22), (10, 17), (23, 2), (2, 0), (5, 8), (4, 2), (7, 12), (15, 7), (0, 3), (23, 19), (8, 15), (11, 6), (22, 16), (5, 18), (6, 6), (13, 11), (12, 4), (16, 26), (7, 25), (11, 17), (16, 9), (12, 21), (8, 13), (22, 6), (14, 6), (22, 26), (20, 8), (3, 24), (19, 20), (8, 3), (15, 18), (7, 2), (7, 6), (5, 10), (6, 25), (12, 7), (9, 4), (5, 24), (23, 5), (0, 24), (7, 15), (11, 24), (6, 14), (17, 24), (8, 26), (9, 26), (4, 18), (7, 17), (19, 7), (19, 18), (8, 20), (20, 1), (6, 5), (15, 9), (13, 10), (20, 14), (12, 2), (0, 6), (1, 16), (19, 17), (14, 20), (8, 14), (19, 26), (16, 15), (18, 10), (2, 13), (15, 23), (21, 4), (23, 20), (17, 4), (1, 12), (5, 16), (5, 6), (5, 14), (8, 8), (17, 15), (3, 17), (15, 14), (4, 12), (9, 3), (1, 4), (10, 25), (9, 25), (7, 26), (6, 23), (20, 26), (16, 18), (11, 1), (1, 24), (20, 10), (15, 10), (7, 14), (17, 22), (8, 21), (16, 3), (11, 20), (9, 24), (6, 2), (21, 25), (22, 19), (6, 19), (10, 3), (10, 22), (1, 6), (2, 26), (21, 20), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417960", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 19), (19, 15), (15, 5), (18, 17), (7, 24), (5, 20), (18, 14), (18, 10), (3, 7), (10, 3), (9, 24), (8, 11), (1, 12), (5, 23), (5, 10), (3, 15), (5, 12), (16, 16), (13, 1), (18, 2), (2, 5), (12, 18), (15, 12), (3, 0), (5, 17), (12, 24), (3, 4), (10, 15), (18, 22), (14, 24), (19, 24), (8, 20), (16, 11), (1, 6), (7, 4), (20, 26), (14, 22), (12, 7), (16, 10), (12, 8), (11, 18), (0, 13), (0, 14), (7, 22), (20, 4), (20, 18), (14, 5), (12, 25), (15, 3), (18, 5), (17, 17), (11, 16), (6, 14), (13, 12), (12, 17), (12, 16), (13, 20), (2, 3), (10, 8), (2, 25), (13, 10), (1, 8), (1, 24), (15, 20), (14, 1), (12, 9), (2, 11), (13, 11), (11, 25), (17, 5), (20, 5), (17, 18), (18, 16), (17, 4), (16, 20), (15, 13), (0, 16), (3, 21), (18, 13), (10, 17), (19, 0), (4, 11), (2, 20), (15, 23), (8, 10), (20, 15), (6, 26), (11, 7), (13, 14), (1, 22), (14, 12), (6, 21), (16, 0), (17, 10), (7, 16), (7, 7), (6, 3), (13, 0), (13, 16), (12, 2), (6, 12), (14, 10), (19, 8), (19, 14), (15, 14), (5, 4), (14, 21), (13, 21), (17, 7), (12, 11), (8, 6), (15, 27), (8, 24), (14, 18), (19, 26), (10, 5), (15, 26), (14, 27), (20, 2), (11, 1), (5, 0), (6, 23), (14, 7), (16, 26), (4, 17), (15, 8), (16, 7), (13, 24), (15, 1), (2, 4), (3, 19), (9, 5), (13, 27), (4, 18), (13, 7), (15, 0), (4, 15), (18, 15), (6, 27), (12, 22), (3, 17), (19, 22), (2, 21), (11, 11), (6, 19), (2, 24), (4, 2), (10, 26), (19, 19), (16, 21), (20, 8), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66150", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), 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), (5, 18), (11, 17), (0, 17), (19, 5), (6, 0), (5, 6), (11, 15), (22, 7), (21, 21), (22, 21), (9, 20), (3, 20), (1, 19), (14, 11), (14, 16), (20, 1), (3, 2), (17, 11), (12, 2), (22, 1), (6, 5), (0, 22), (19, 10), (4, 21), (1, 12), (12, 19), (17, 14), (10, 3), (11, 19), (16, 11), (15, 18), (14, 13), (7, 10), (5, 3), (17, 7), (15, 11), (4, 19), (4, 15), (10, 10), (18, 3), (6, 21), (17, 1), (0, 13), (14, 22), (21, 7), (19, 4), (12, 22), (0, 2), (5, 8), (12, 17), (22, 14), (3, 13), (7, 8), (20, 15), (2, 2), (3, 15), (21, 8), (20, 13), (19, 17), (4, 5), (15, 17), (20, 2), (15, 15), (13, 21), (20, 7), (1, 13), (18, 1), (3, 4), (6, 16), (3, 6), (10, 16), (3, 14), (9, 14), (0, 10), (22, 12), (5, 2), (9, 0), (14, 10), (15, 22), (4, 7), (7, 6), (1, 4), (13, 12), (21, 16), (16, 10), (8, 1), (1, 0), (7, 14), (20, 11), (1, 5), (15, 6), (16, 19), (19, 18), (12, 20), (1, 7), (7, 7), (9, 4), (12, 4), (0, 19), (16, 7), (22, 18), (14, 20), (22, 9), (13, 20), (9, 5), (19, 21), (10, 4), (8, 2), (11, 2), (12, 1), (10, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999240", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 8), (10, 5), (17, 1), (5, 15), (17, 3), (11, 15), (22, 20), (19, 6), (11, 5), (15, 2), (13, 2), (9, 12), (13, 17), (17, 11), (9, 17), (2, 22), (18, 10), (6, 13), (14, 4), (2, 6), (14, 3), (15, 7), (0, 9), (16, 10), (14, 21), (22, 16), (13, 12), (16, 11), (7, 12), (1, 11), (10, 17), (15, 3), (5, 17), (20, 7), (13, 19), (20, 15), (18, 16), (20, 13), (18, 21), (22, 2), (1, 18), (2, 4), (6, 7), (17, 6), (15, 14), (21, 7), (13, 21), (10, 19), (14, 2), (11, 0), (11, 20), (8, 4), (17, 15), (4, 2), (5, 13), (21, 12), (11, 2), (19, 8), (9, 20), (9, 6), (7, 17), (21, 6), (19, 18), (2, 1), (4, 20), (6, 1), (21, 11), (11, 9), (10, 16), (18, 14), (2, 7), (15, 16), (19, 10), (15, 13), (16, 20), (7, 7), (11, 22), (0, 8), (22, 21), (14, 5), (3, 13), (1, 20), (5, 0), (18, 15), (8, 11), (14, 13), (6, 3), (7, 2), (16, 2), (5, 19), (2, 9), (19, 1), (17, 19), (7, 5), (17, 12), (22, 9), (0, 4), (5, 4), (21, 18), (4, 1), (14, 12), (1, 22), (7, 6), (1, 6), (20, 21), (6, 10), (14, 22), (11, 8), (1, 10), (16, 16), (15, 12), (1, 12), (5, 5), (13, 1), (2, 5), (18, 12), (9, 5), (11, 18), (18, 2), (14, 10), (22, 11), (19, 5), (0, 3), (18, 6), (0, 6), (1, 21), (17, 10), (10, 6), (12, 21), (10, 20), (21, 3), (14, 17), (19, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259600", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (2, 7), (5, 8), (20, 20), (1, 20), (7, 15), (10, 25), (6, 5), (4, 2), (6, 23), (11, 17), (13, 22), (20, 25), (4, 20), (5, 14), (7, 21), (15, 12), (11, 4), (1, 6), (14, 23), (11, 8), (10, 1), (16, 17), (18, 6), (5, 24), (10, 19), (11, 1), (12, 21), (7, 24), (0, 11), (12, 1), (15, 0), (5, 3), (7, 13), (8, 11), (4, 0), (18, 11), (19, 15), (1, 12), (14, 24), (19, 1), (1, 5), (14, 3), (12, 22), (17, 0), (18, 12), (18, 4), (17, 15), (19, 11), (1, 16), (8, 14), (0, 18), (7, 22), (9, 12), (9, 25), (9, 20), (14, 17), (0, 20), (12, 10), (18, 15), (18, 0), (11, 14), (15, 4), (8, 1), (19, 21), (8, 15), (15, 17), (7, 10), (19, 9), (9, 17), (11, 0), (7, 4), (11, 6), (18, 2), (3, 3), (11, 16), (7, 3), (15, 18), (1, 13), (11, 5), (6, 11), (2, 25), (10, 7), (14, 14), (14, 2), (3, 4), (20, 12), (11, 3), (3, 2), (6, 2), (8, 8), (20, 14), (17, 3), (0, 17), (1, 15), (10, 17), (16, 16), (6, 4), (1, 2), (4, 16), (19, 8), (5, 4), (1, 14), (3, 0), (0, 4), (3, 22), (20, 10), (1, 23), (3, 18), (15, 3), (18, 20), (6, 8), (5, 9), (16, 7), (18, 23), (13, 7), (20, 3), (2, 22), (16, 12), (15, 15), (3, 7), (15, 21), (3, 23), (20, 6), (7, 16), (6, 10), (6, 20), (21, 22), (14, 1), (20, 8), (5, 13), (9, 18), (19, 23), (19, 20), (17, 8), (6, 22), (21, 11), (10, 14), (3, 21), (20, 11), (17, 17), (9, 14), (9, 2), (18, 10), (6, 16), (0, 24), (8, 5), (2, 12), (8, 7), (21, 4), (19, 24), (8, 17), (2, 24), (13, 15), (8, 21), (15, 22), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413856", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), 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), (1, 11), (7, 15), (5, 11), (1, 2), (13, 10), (2, 22), (14, 1), (8, 22), (1, 17), (11, 18), (18, 19), (6, 5), (13, 1), (7, 7), (8, 7), (17, 2), (4, 17), (7, 2), (15, 11), (7, 3), (20, 10), (14, 18), (17, 23), (16, 23), (0, 4), (8, 12), (6, 14), (20, 4), (12, 8), (7, 6), (15, 20), (4, 24), (17, 7), (18, 14), (3, 0), (1, 0), (16, 18), (5, 20), (8, 17), (5, 18), (6, 3), (6, 19), (19, 17), (12, 23), (8, 9), (4, 3), (6, 8), (16, 20), (14, 7), (11, 9), (1, 7), (12, 2), (2, 21), (5, 21), (14, 14), (20, 1), (17, 11), (6, 7), (11, 12), (5, 8), (13, 22), (18, 12), (7, 1), (13, 14), (7, 11), (10, 20), (11, 4), (8, 3), (13, 13), (19, 22), (15, 2), (17, 19), (20, 20), (20, 14), (9, 16), (7, 12), (12, 9), (18, 11), (5, 3), (12, 10), (18, 16), (17, 10), (2, 19), (12, 0), (1, 13), (15, 21), (4, 1), (9, 18), (8, 14), (10, 17), (16, 0), (16, 16), (20, 9), (6, 11), (7, 16), (13, 23), (4, 10), (17, 5), (7, 19), (19, 24), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "815803", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 21), (18, 7), (7, 13), (26, 0), (0, 19), (8, 10), (15, 11), (15, 1), (4, 20), (16, 17), (8, 9), (3, 22), (14, 16), (20, 15), (2, 20), (11, 10), (12, 18), (15, 15), (7, 8), (15, 16), (27, 11), (0, 13), (16, 10), (0, 4), (23, 8), (12, 15), (3, 21), (21, 21), (1, 16), (2, 18), (20, 12), (3, 17), (11, 15), (23, 13), (23, 19), (10, 8), (10, 19), (7, 1), (3, 10), (26, 9), (16, 13), (17, 18), (27, 15), (19, 2), (19, 9), (13, 5), (8, 19), (2, 17), (11, 11), (6, 18), (6, 6), (27, 7), (21, 12), (16, 14), (12, 20), (9, 19), (0, 21), (20, 9), (5, 15), (16, 0), (6, 17), (20, 16), (2, 8), (8, 1), (21, 16), (7, 9), (13, 10), (6, 11), (19, 15), (3, 0), (4, 2), (21, 9), (25, 22), (21, 2), (5, 4), (6, 0), (22, 22), (7, 5), (22, 18), (11, 4), (11, 6), (7, 16), (13, 12), (13, 17), (15, 14), (8, 5), (5, 8), (13, 4), (5, 20), (22, 4), (14, 0), (21, 6), (19, 8), (3, 2), (25, 8), (23, 17), (19, 3), (25, 19), (8, 16), (14, 14), (20, 13), (15, 7), (12, 12), (12, 14), (4, 18), (12, 11), (2, 4), (14, 20), (16, 7), (27, 17), (10, 14), (22, 19), (27, 9), (25, 18), (7, 11), (3, 1), (8, 4), (3, 12), (15, 21), (19, 14), (27, 16), (21, 3), (2, 19), (19, 18), (18, 22), (10, 4), (21, 17), (10, 22), (21, 7), (2, 15), (8, 20), (1, 21), (2, 2), (11, 12), (11, 3), (10, 18), (8, 8), (7, 6), (12, 16), (25, 15), (2, 16), (11, 7), (6, 7), (19, 16), (6, 16), (20, 14), (6, 2), (23, 5), (6, 15), (3, 5), (15, 6), (21, 1), (23, 7), (13, 11), (20, 2), (10, 3), (3, 11), (9, 6), (6, 5), (15, 10), (25, 4), (9, 18), (8, 17), (5, 13), (4, 21), (2, 13), (6, 1), (14, 5), (3, 16), (10, 9), (27, 6), (4, 13), (5, 14), (6, 21), (22, 12), (22, 10), (19, 11), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515056", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 23), (2, 7), (5, 0), (15, 17), (0, 5), (0, 7), (1, 4), (8, 8), (8, 17), (16, 3), (7, 22), (15, 21), (7, 3), (13, 2), (20, 16), (5, 9), (19, 16), (8, 6), (8, 19), (3, 16), (18, 15), (7, 2), (0, 10), (14, 12), (3, 3), (2, 11), (14, 18), (12, 14), (14, 0), (10, 8), (10, 5), (13, 16), (9, 18), (12, 0), (0, 17), (6, 23), (19, 12), (2, 16), (18, 2), (11, 14), (19, 7), (4, 12), (15, 11), (14, 19), (7, 20), (12, 18), (14, 9), (7, 0), (20, 22), (4, 19), (6, 4), (17, 12), (8, 1), (3, 15), (12, 3), (9, 1), (10, 2), (5, 15), (5, 18), (17, 3), (10, 21), (18, 9), (2, 12), (16, 14), (18, 19), (12, 7), (1, 21), (16, 5), (4, 22), (11, 12), (15, 0), (11, 13), (12, 5), (11, 16), (11, 9), (13, 17), (7, 7), (10, 23), (2, 15), (5, 11), (20, 12), (16, 2), (13, 7), (0, 13), (10, 18), (20, 20), (20, 9), (2, 8), (12, 1), (5, 7), (18, 0), (12, 11), (15, 5), (3, 11), (5, 13), (14, 5), (19, 6), (9, 17), (1, 2), (12, 9), (11, 3), (19, 14), (5, 2), (2, 17), (20, 17), (3, 19), (4, 18), (19, 4), (5, 3), (19, 5), (7, 18), (2, 0), (9, 11), (17, 22), (0, 6), (16, 19), (17, 20), (18, 10), (2, 4), (5, 14), (20, 13), (10, 3), (10, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337662", "dataset": "MATH"}
{"messages": [{"content": "In a 26x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 19), 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), (15, 17), (22, 19), (19, 10), (12, 12), (15, 18), (24, 14), (19, 17), (24, 5), (4, 17), (1, 16), (16, 12), (9, 0), (10, 9), (12, 4), (4, 7), (5, 11), (14, 3), (11, 7), (10, 18), (0, 7), (2, 17), (23, 10), (3, 17), (3, 14), (13, 1), (9, 19), (14, 6), (13, 4), (22, 12), (0, 16), (2, 2), (11, 6), (2, 12), (23, 11), (0, 11), (3, 0), (6, 0), (12, 11), (9, 10), (2, 4), (12, 5), (6, 9), (25, 11), (24, 19), (16, 3), (6, 11), (4, 10), (9, 18), (20, 12), (1, 13), (4, 6), (8, 16), (1, 15), (19, 13), (15, 0), (23, 7), (1, 9), (13, 17), (14, 4), (15, 3), (5, 18), (14, 13), (6, 6), (17, 4), (13, 14), (24, 6), (18, 10), (13, 5), (0, 2), (9, 13), (14, 9), (24, 17), (2, 13), (23, 19), (20, 7), (11, 11), (14, 14), (3, 8), (22, 3), (21, 15), (9, 3), (7, 1), (1, 18), (4, 8), (14, 0), (16, 8), (21, 5), (12, 10), (22, 5), (2, 19), (25, 3), (18, 3), (13, 10), (21, 19), (6, 8), (13, 0), (1, 10), (16, 19), (24, 3), (24, 13), (7, 14), (8, 8), (15, 15), (2, 1), (10, 19), (12, 19), (18, 7), (17, 8), (4, 19), (17, 0), (21, 1), (12, 6), (2, 16), (10, 14), (13, 13), (21, 2), (24, 15), (20, 14), (11, 18), (25, 1), (22, 10), (2, 6), (3, 18), (3, 12), (5, 16), (14, 5), (22, 11), (17, 14), (14, 15), (19, 18), (10, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "982032", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 20), (16, 3), (1, 11), (19, 9), (13, 12), (9, 8), (16, 24), (12, 0), (15, 4), (6, 15), (9, 17), (12, 15), (17, 1), (3, 20), (10, 19), (12, 3), (9, 1), (11, 9), (18, 20), (8, 19), (8, 25), (3, 23), (15, 24), (0, 22), (11, 17), (1, 16), (13, 21), (0, 19), (17, 14), (8, 16), (0, 7), (9, 7), (2, 4), (16, 5), (18, 2), (11, 10), (15, 5), (13, 22), (4, 11), (11, 22), (0, 17), (13, 7), (1, 14), (2, 1), (0, 12), (19, 20), (3, 8), (3, 21), (11, 24), (4, 21), (19, 7), (19, 6), (8, 11), (10, 17), (4, 15), (15, 11), (0, 21), (9, 12), (2, 14), (15, 22), (11, 1), (0, 8), (1, 4), (7, 17), (8, 18), (3, 2), (4, 10), (18, 22), (18, 23), (2, 2), (8, 22), (7, 8), (13, 8), (14, 19), (16, 25), (6, 17), (9, 21), (8, 4), (1, 24), (2, 12), (13, 25), (8, 6), (4, 7), (13, 18), (7, 25), (16, 21), (17, 18), (10, 25), (2, 24), (8, 10), (11, 19), (8, 15), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "630882", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (6, 11), (11, 3), (17, 15), (21, 14), (4, 18), (13, 18), (10, 0), (16, 20), (19, 24), (12, 6), (14, 10), (6, 14), (7, 25), (11, 6), (19, 12), (7, 4), (7, 17), (16, 16), (18, 13), (2, 10), (0, 24), (3, 18), (10, 14), (21, 21), (8, 17), (12, 23), (1, 7), (19, 6), (9, 7), (13, 4), (11, 14), (17, 1), (19, 19), (3, 16), (19, 13), (3, 2), (15, 5), (15, 3), (2, 7), (10, 7), (3, 11), (5, 11), (8, 18), (19, 10), (7, 8), (9, 10), (19, 20), (16, 21), (2, 11), (16, 25), (0, 17), (9, 14), (12, 5), (7, 1), (21, 22), (6, 8), (4, 2), (19, 17), (14, 9), (11, 19), (9, 1), (12, 21), (16, 13), (10, 17), (14, 18), (21, 2), (19, 9), (13, 15), (10, 6), (18, 10), (14, 19), (20, 23), (8, 15), (20, 4), (17, 11), (18, 3), (9, 20), (7, 15), (14, 7), (16, 3), (13, 8), (21, 20), (6, 25), (21, 16), (14, 8), (14, 6), (19, 22), (14, 20), (18, 20), (21, 0), (21, 10), (11, 9), (11, 1), (20, 2), (1, 23), (4, 11), (4, 8), (12, 8), (3, 8), (11, 8), (10, 22), (0, 18), (20, 0), (1, 13), (3, 4), (12, 12), (3, 19), (20, 3), (14, 15), (17, 18), (6, 16), (11, 24), (15, 7), (17, 21), (8, 6), (15, 16), (3, 21), (12, 20), (1, 20), (20, 15), (1, 14), (19, 7), (18, 7), (3, 20), (13, 16), (4, 24), (20, 7), (19, 0), (3, 1), (11, 2), (21, 8), (0, 15), (9, 23), (14, 14), (0, 20), (20, 12), (20, 14), (20, 13), (15, 9), (14, 16), (2, 19), (6, 23), (0, 16), (14, 13), (3, 14), (17, 22), (8, 9), (7, 24), (16, 2), (6, 15), (13, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439684", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 7), (4, 13), (17, 12), (11, 9), (23, 19), (13, 13), (26, 23), (5, 7), (16, 13), (1, 18), (23, 25), (10, 4), (20, 23), (4, 1), (13, 20), (18, 9), (14, 14), (8, 10), (25, 2), (6, 24), (14, 18), (8, 0), (4, 18), (15, 4), (25, 1), (22, 14), (25, 8), (17, 25), (12, 10), (4, 25), (21, 16), (0, 10), (14, 27), (25, 25), (16, 12), (21, 17), (23, 27), (8, 22), (19, 4), (3, 0), (20, 5), (26, 20), (17, 27), (22, 12), (16, 23), (10, 18), (16, 25), (4, 26), (13, 10), (24, 12), (16, 9), (5, 19), (15, 16), (5, 15), (0, 25), (10, 7), (7, 20), (1, 11), (1, 14), (3, 14), (0, 26), (13, 1), (15, 19), (8, 8), (13, 18), (0, 8), (9, 2), (8, 23), (21, 12), (3, 11), (18, 12), (12, 4), (19, 24), (18, 23), (21, 25), (11, 15), (17, 13), (24, 11), (22, 8), (6, 17), (12, 23), (8, 5), (8, 21), (3, 8), (9, 22), (10, 16), (6, 23), (5, 11), (7, 9), (3, 3), (16, 27), (6, 3), (4, 21), (22, 25), (10, 15), (21, 22), (12, 2), (12, 1), (20, 13), (6, 22), (2, 16), (19, 17), (7, 13), (22, 5), (13, 16), (22, 1), (21, 0), (2, 3), (18, 4), (15, 15), (5, 13), (1, 4), (11, 1), (12, 8), (0, 14), (24, 13), (23, 18), (9, 17), (13, 0), (18, 0), (26, 26), (17, 10), (15, 13), (10, 20), (10, 17), (18, 17), (6, 15), (0, 9), (15, 6), (0, 20), (4, 16), (2, 6), (13, 21), (7, 21), (23, 10), (8, 2), (17, 16), (9, 15), (2, 25), (0, 22), (0, 23), (23, 6), (14, 11), (10, 0), (9, 7), (19, 3), (0, 13), (25, 3), (3, 4), (26, 1), (17, 14), (24, 19), (17, 9), (3, 24), (2, 11), (10, 10), (1, 22), (18, 1), (6, 4), (25, 13), (15, 23), (22, 27), (5, 23), (1, 26), (13, 3), (18, 16), (4, 15), (25, 26), (9, 10), (18, 5), (14, 10), (0, 12), (9, 13), (14, 13), (20, 17), (16, 24), (14, 19), (5, 2), (23, 9), (17, 18), (7, 15), (19, 6), (4, 11), (22, 16), (24, 8), (19, 14), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803190", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (17, 14), (19, 16), (20, 9), (13, 10), (22, 6), (1, 4), (23, 20), (0, 6), (5, 21), (0, 18), (10, 8), (27, 6), (6, 19), (17, 9), (8, 13), (20, 8), (6, 15), (10, 14), (24, 19), (12, 5), (11, 1), (26, 6), (9, 10), (14, 19), (4, 1), (21, 6), (9, 13), (17, 2), (6, 1), (20, 11), (5, 15), (19, 7), (16, 18), (4, 16), (6, 16), (13, 8), (15, 19), (12, 19), (19, 20), (25, 7), (12, 7), (12, 4), (12, 6), (21, 8), (9, 2), (10, 21), (3, 11), (27, 10), (24, 7), (15, 8), (16, 17), (16, 0), (1, 8), (25, 17), (27, 13), (10, 12), (15, 16), (1, 21), (14, 8), (18, 11), (3, 5), (0, 12), (7, 19), (16, 21), (27, 5), (9, 3), (8, 11), (19, 1), (23, 10), (16, 11), (5, 2), (8, 14), (23, 0), (5, 0), (24, 20), (1, 13), (27, 11), (11, 9), (2, 1), (11, 19), (7, 4), (2, 2), (25, 5), (16, 2), (21, 3), (5, 10), (4, 0), (3, 20), (20, 16), (9, 17), (27, 16), (17, 10), (26, 9), (13, 16), (7, 16), (12, 3), (15, 14), (6, 12), (20, 1), (20, 12), (13, 17), (9, 4), (22, 16), (10, 19), (3, 8), (3, 12), (18, 1), (20, 0), (2, 6), (9, 19), (13, 7), (14, 2), (15, 7), (2, 11), (11, 16), (16, 4), (22, 9), (22, 13), (10, 11), (22, 4), (8, 8), (15, 2), (0, 4), (18, 3), (19, 2), (17, 17), (24, 16), (2, 21), (7, 1), (14, 3), (17, 16), (9, 15), (16, 19), (18, 4), (14, 18), (14, 1), (17, 0), (16, 1), (27, 4), (13, 19), (15, 3), (4, 4), (8, 5), (8, 9), (15, 17), (6, 9), (21, 15), (11, 20), (25, 14), (14, 4), (15, 13), (11, 4), (7, 5), (14, 16), (4, 17), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "671880", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), 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), (20, 1), (8, 26), (15, 11), (22, 10), (10, 23), (10, 1), (19, 6), (13, 14), (23, 14), (18, 23), (9, 14), (23, 17), (15, 22), (13, 24), (6, 19), (7, 13), (0, 3), (11, 17), (12, 20), (22, 16), (0, 16), (12, 8), (22, 7), (4, 22), (2, 19), (16, 23), (5, 7), (19, 25), (20, 0), (1, 8), (19, 19), (1, 16), (18, 16), (4, 16), (6, 17), (11, 7), (2, 23), (16, 22), (22, 20), (5, 16), (15, 20), (11, 12), (15, 23), (6, 21), (5, 3), (3, 26), (17, 26), (20, 25), (14, 9), (17, 10), (5, 8), (11, 4), (5, 25), (14, 13), (7, 7), (14, 19), (3, 10), (23, 8), (18, 4), (21, 9), (2, 3), (1, 18), (19, 0), (4, 10), (8, 25), (10, 11), (6, 14), (15, 12), (1, 13), (15, 6), (17, 3), (11, 2), (10, 2), (9, 22), (4, 4), (15, 0), (11, 25), (2, 1), (21, 18), (23, 22), (22, 8), (3, 5), (6, 7), (23, 19), (21, 23), (6, 5), (20, 7), (8, 15), (21, 21), (21, 20), (0, 18), (1, 14), (19, 1), (7, 10), (10, 4), (4, 19), (20, 15), (7, 16), (10, 25), (19, 7), (5, 26), (23, 6), (8, 9), (9, 25), (20, 23), (21, 19), (20, 2), (10, 14), (11, 1), (16, 10), (22, 25), (17, 21), (5, 1), (19, 23), (8, 6), (2, 17), (11, 8), (6, 18), (0, 20), (9, 6), (11, 9), (2, 24), (23, 2), (15, 13), (0, 24), (23, 13), (7, 2), (16, 2), (4, 6), (0, 2), (20, 19), (12, 0), (17, 24), (1, 5), (2, 18), (7, 3), (11, 23), (9, 19), (9, 12), (1, 10), (14, 18), (1, 15), (17, 4), (11, 19), (19, 26), (0, 7), (1, 20), (1, 21), (18, 0), (8, 3), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139392", "dataset": "MATH"}
{"messages": [{"content": "In a 25x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (0, 5), (16, 4), (8, 17), (0, 19), (6, 10), (12, 15), (24, 0), (23, 18), (8, 2), (23, 4), (22, 1), (15, 10), (21, 20), (17, 15), (2, 9), (19, 20), (18, 18), (15, 12), (23, 17), (9, 20), (3, 17), (7, 15), (6, 8), (12, 10), (20, 10), (4, 6), (3, 7), (5, 4), (6, 17), (14, 1), (17, 3), (3, 9), (23, 0), (21, 17), (10, 18), (0, 10), (11, 17), (4, 14), (3, 1), (19, 2), (7, 9), (9, 18), (0, 2), (14, 15), (6, 15), (14, 16), (10, 6), (2, 13), (24, 9), (2, 2), (16, 9), (8, 15), (2, 0), (11, 12), (3, 8), (19, 4), (3, 13), (19, 14), (4, 13), (0, 1), (16, 18), (14, 14), (18, 9), (24, 3), (10, 4), (13, 18), (1, 4), (5, 16), (8, 7), (0, 18), (17, 16), (11, 10), (14, 10), (14, 9), (10, 7), (19, 16), (4, 0), (1, 13), (23, 19), (10, 1), (4, 7), (11, 6), (14, 18), (22, 13), (2, 4), (11, 19), (4, 15), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685590", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 17), (16, 11), (13, 7), (2, 19), (19, 20), (3, 20), (14, 0), (9, 5), (12, 12), (4, 6), (5, 8), (0, 16), (1, 11), (8, 11), (0, 2), (5, 12), (8, 19), (4, 15), (8, 4), (13, 20), (8, 9), (11, 21), (11, 3), (0, 11), (1, 18), (18, 14), (0, 15), (8, 17), (12, 14), (5, 16), (19, 19), (19, 17), (12, 8), (4, 12), (11, 20), (12, 2), (5, 0), (2, 21), (12, 0), (3, 5), (0, 12), (3, 0), (14, 12), (10, 11), (0, 18), (13, 12), (2, 13), (11, 7), (15, 20), (13, 2), (11, 5), (7, 11), (18, 13), (4, 13), (13, 10), (6, 6), (8, 13), (18, 12), (2, 12), (2, 10), (0, 1), (13, 5), (6, 0), (17, 20), (10, 8), (16, 10), (13, 3), (2, 15), (8, 2), (13, 18), (5, 21), (14, 2), (18, 15), (13, 15), (3, 15), (18, 6), (5, 1), (6, 7), (11, 15), (5, 10), (9, 0), (5, 18), (10, 15), (19, 13), (7, 0), (1, 20), (16, 19), (6, 15), (0, 20), (0, 14), (7, 10), (0, 7), (17, 11), (4, 10), (0, 5), (7, 12), (7, 4), (2, 9), (14, 8), (19, 6), (2, 5), (13, 21), (18, 4), (3, 19), (14, 21), (17, 10), (4, 11), (0, 8), (16, 9), (17, 5), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516322", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (5, 13), (2, 17), (17, 15), (5, 15), (1, 17), (16, 3), (17, 21), (7, 17), (15, 17), (20, 1), (4, 17), (19, 17), (19, 1), (0, 20), (8, 12), (5, 2), (20, 7), (9, 4), (0, 4), (15, 0), (20, 8), (13, 8), (6, 19), (3, 18), (14, 0), (14, 19), (6, 4), (17, 12), (16, 21), (12, 10), (17, 0), (15, 10), (15, 11), (0, 19), (11, 17), (15, 2), (18, 18), (9, 7), (5, 0), (0, 25), (8, 5), (12, 7), (20, 11), (0, 1), (6, 18), (19, 21), (3, 12), (8, 24), (16, 6), (12, 25), (11, 4), (18, 19), (12, 18), (2, 6), (5, 22), (2, 0), (6, 9), (10, 15), (16, 18), (16, 9), (8, 15), (10, 17), (17, 24), (3, 19), (15, 19), (13, 11), (15, 24), (7, 1), (17, 19), (0, 21), (11, 21), (7, 2), (4, 8), (0, 2), (19, 19), (10, 18), (2, 22), (12, 6), (0, 24), (17, 5), (15, 14), (13, 24), (1, 9), (13, 23), (20, 19), (4, 5), (14, 13), (0, 14), (14, 7), (11, 19), (7, 6), (7, 8), (20, 12), (6, 1), (20, 16), (20, 10), (14, 3), (4, 9), (9, 8), (7, 3), (17, 14), (8, 4), (14, 4), (8, 16), (20, 2), (19, 5), (19, 20), (3, 13), (10, 2), (12, 8), (13, 2), (1, 2), (15, 15), (4, 7), (1, 6), (8, 3), (16, 4), (11, 11), (12, 23), (16, 25), (6, 23), (3, 24), (13, 7), (13, 13), (7, 9), (6, 10), (11, 1), (18, 12), (5, 18), (10, 5), (9, 6), (6, 6), (11, 13), (11, 16), (6, 22), (0, 5), (1, 11), (15, 16), (1, 21), (9, 12), (17, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591440", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), 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), (19, 19), (12, 5), (8, 13), (12, 14), (4, 15), (0, 20), (24, 7), (11, 4), (7, 7), (24, 12), (24, 1), (1, 19), (7, 4), (12, 13), (23, 21), (8, 9), (0, 13), (20, 11), (9, 5), (13, 19), (10, 4), (18, 6), (22, 0), (8, 4), (19, 21), (2, 5), (4, 1), (23, 9), (9, 6), (10, 0), (9, 4), (0, 7), (1, 3), (23, 14), (22, 6), (0, 2), (9, 2), (8, 16), (7, 13), (8, 22), (18, 21), (25, 20), (10, 10), (3, 16), (22, 21), (26, 13), (7, 17), (8, 6), (23, 6), (2, 19), (20, 3), (5, 14), (3, 0), (22, 5), (23, 7), (12, 16), (19, 14), (14, 12), (14, 11), (0, 15), (25, 11), (20, 18), (10, 3), (11, 12), (13, 5), (12, 19), (14, 10), (23, 19), (26, 3), (0, 1), (21, 1), (16, 1), (26, 10), (9, 16), (20, 0), (17, 11), (17, 0), (2, 0), (3, 4), (17, 3), (23, 17), (20, 13), (4, 10), (18, 5), (11, 1), (6, 4), (1, 4), (25, 22), (4, 8), (8, 11), (26, 11), (8, 18), (2, 1), (9, 17), (10, 15), (20, 7), (5, 18), (24, 0), (5, 8), (17, 20), (6, 1), (22, 20), (24, 13), (21, 9), (20, 8), (8, 0), (18, 20), (24, 3), (11, 19), (15, 12), (14, 1), (0, 16), (1, 11), (3, 17), (3, 1), (24, 11), (5, 13), (12, 10), (22, 18), (18, 14), (6, 10), (16, 0), (14, 17), (13, 13), (17, 12), (17, 8), (0, 21), (2, 8), (12, 20), (6, 16), (15, 3), (5, 3), (12, 21), (12, 17), (24, 9), (8, 2), (12, 0), (16, 4), (7, 19), (14, 3), (3, 22), (15, 18), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353511", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (11, 16), (13, 2), (4, 16), (13, 11), (7, 9), (13, 7), (17, 14), (0, 1), (10, 17), (8, 0), (0, 10), (17, 16), (6, 14), (10, 5), (15, 2), (5, 7), (11, 4), (11, 0), (3, 14), (3, 23), (7, 23), (7, 16), (9, 16), (13, 17), (17, 2), (9, 3), (4, 20), (1, 22), (19, 12), (20, 14), (2, 20), (20, 22), (8, 9), (18, 15), (18, 16), (12, 8), (7, 10), (15, 16), (4, 7), (5, 21), (18, 20), (5, 22), (5, 24), (6, 13), (9, 1), (19, 14), (7, 18), (7, 22), (13, 24), (1, 2), (13, 12), (14, 24), (11, 9), (12, 10), (1, 14), (3, 8), (3, 21), (20, 10), (10, 21), (9, 17), (17, 24), (15, 22), (2, 17), (7, 24), (9, 22), (8, 1), (1, 8), (15, 14), (7, 2), (9, 0), (7, 21), (3, 15), (1, 3), (17, 19), (18, 7), (3, 13), (12, 12), (18, 2), (14, 2), (18, 19), (7, 7), (3, 17), (17, 21), (4, 8), (1, 24), (17, 15), (20, 11), (10, 1), (15, 0), (7, 6), (14, 11), (14, 9), (4, 6), (14, 18), (19, 18), (9, 2), (5, 1), (3, 11), (17, 12), (1, 7), (14, 23), (19, 15), (13, 3), (14, 7), (19, 19), (18, 14), (19, 16), (2, 4), (15, 5), (4, 24), (3, 24), (19, 4), (9, 19), (13, 18), (10, 11), (1, 20), (15, 19), (12, 19), (1, 10), (15, 6), (1, 1), (16, 1), (4, 9), (12, 17), (12, 1), (0, 6), (16, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295020", "dataset": "MATH"}
{"messages": [{"content": "In a 25x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 0), (17, 0), (17, 16), (19, 22), (20, 20), (0, 15), (13, 14), (7, 7), (18, 6), (15, 12), (4, 5), (11, 23), (23, 22), (17, 9), (21, 2), (19, 11), (3, 5), (22, 6), (16, 2), (13, 13), (8, 17), (18, 19), (0, 8), (12, 1), (9, 11), (18, 8), (3, 13), (23, 3), (24, 15), (18, 21), (15, 1), (24, 8), (2, 3), (16, 12), (22, 9), (0, 14), (2, 18), (3, 16), (24, 3), (7, 15), (13, 23), (22, 18), (9, 1), (3, 20), (24, 9), (4, 2), (24, 12), (11, 0), (5, 3), (21, 11), (15, 3), (15, 4), (22, 13), (1, 4), (15, 5), (21, 6), (17, 13), (3, 12), (16, 0), (23, 15), (5, 13), (23, 11), (5, 14), (13, 15), (3, 8), (12, 10), (5, 16), (8, 22), (12, 2), (8, 23), (14, 1), (7, 9), (18, 17), (13, 17), (9, 8), (13, 3), (8, 16), (8, 5), (18, 0), (2, 8), (18, 13), (0, 20), (6, 5), (12, 12), (7, 13), (17, 6), (6, 2), (11, 8), (23, 10), (1, 0), (8, 19), (6, 23), (6, 11), (22, 19), (6, 20), (4, 13), (4, 1), (3, 1), (2, 13), (20, 10), (20, 16), (12, 8), (3, 0), (21, 9), (19, 1), (12, 23), (23, 23), (2, 1), (22, 11), (12, 19), (23, 19), (2, 14), (7, 11), (13, 5), (16, 8), (11, 16), (5, 6), (2, 17), (10, 13), (23, 16), (3, 22), (9, 6), (24, 7), (19, 14), (4, 10), (7, 16), (2, 9), (19, 8), (5, 17), (22, 2), (13, 0), (14, 0), (16, 6), (17, 18), (6, 19), (23, 14), (6, 17), (7, 18), (10, 23), (17, 2), (18, 10), (9, 20), (11, 22), (16, 21), (8, 11), (9, 0), (3, 17), (14, 19), (1, 15), (10, 22), (15, 8), (4, 6), (23, 7), (18, 5), (6, 14), (23, 17), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "873221", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), 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), (21, 4), (22, 14), (18, 16), (1, 13), (14, 25), (13, 12), (19, 26), (13, 15), (11, 17), (20, 17), (18, 15), (10, 7), (10, 22), (4, 8), (17, 12), (18, 6), (1, 19), (6, 9), (1, 5), (0, 2), (17, 18), (5, 9), (17, 1), (14, 4), (8, 1), (14, 15), (7, 15), (21, 26), (14, 0), (15, 20), (0, 9), (15, 12), (20, 15), (4, 11), (21, 6), (1, 2), (22, 20), (4, 25), (0, 18), (1, 16), (2, 11), (21, 17), (3, 22), (11, 4), (5, 25), (22, 6), (6, 23), (20, 24), (18, 20), (14, 3), (16, 15), (10, 1), (4, 20), (20, 7), (8, 28), (2, 8), (9, 28), (14, 22), (15, 8), (3, 24), (16, 18), (4, 7), (16, 20), (4, 5), (11, 3), (8, 21), (11, 18), (9, 12), (11, 24), (20, 3), (5, 3), (2, 28), (0, 4), (21, 18), (16, 19), (14, 16), (4, 24), (20, 16), (10, 5), (10, 14), (8, 7), (17, 28), (17, 17), (17, 16), (22, 9), (17, 5), (13, 3), (7, 9), (10, 28), (19, 2), (6, 6), (9, 27), (8, 3), (21, 5), (0, 11), (21, 2), (19, 22), (19, 9), (7, 26), (9, 20), (8, 23), (16, 12), (1, 15), (11, 14), (21, 1), (5, 12), (13, 10), (8, 27), (12, 1), (14, 26), (1, 28), (13, 27), (18, 8), (4, 28), (10, 2), (2, 18), (11, 20), (8, 0), (14, 6), (3, 6), (16, 4), (9, 7), (9, 0), (10, 25), (12, 20), (20, 26), (3, 16), (6, 11), (13, 19), (20, 5), (4, 6), (15, 6), (1, 18), (11, 13), (2, 14), (17, 3), (4, 15), (5, 5), (17, 26), (8, 25), (22, 18), (19, 23), (21, 27), (6, 14), (9, 11), (20, 10), (5, 26), (9, 22), (13, 20), (3, 10), (13, 9), (17, 22), (22, 17), (11, 2), (14, 2), (12, 26), (15, 17), (20, 13), (4, 22), (13, 6), (22, 4), (9, 10), (8, 26), (16, 1), (12, 24), (9, 16), (2, 21), (11, 16), (10, 9), (7, 7), (16, 7), (12, 6), (21, 25), (18, 23), (17, 0), (10, 26), (18, 5), (6, 13), (14, 19), (21, 22), (3, 21), (14, 20), (9, 2), (3, 25), (6, 17), (12, 17), (2, 13), (12, 14), (3, 2), (6, 1), (1, 25), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "668280", "dataset": "MATH"}
{"messages": [{"content": "In a 24x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 9), (7, 14), (14, 23), (18, 6), (9, 15), (10, 6), (9, 8), (9, 21), (9, 23), (22, 19), (7, 19), (18, 23), (13, 7), (10, 19), (7, 15), (18, 8), (7, 22), (21, 9), (21, 11), (22, 23), (21, 20), (5, 9), (14, 18), (13, 11), (3, 8), (20, 17), (14, 6), (19, 16), (5, 20), (18, 0), (2, 8), (17, 8), (23, 13), (17, 19), (20, 14), (22, 8), (20, 21), (11, 23), (15, 6), (8, 8), (1, 6), (14, 16), (3, 15), (8, 3), (11, 3), (13, 12), (9, 6), (16, 17), (21, 15), (8, 13), (15, 20), (16, 1), (23, 6), (22, 1), (3, 6), (1, 3), (6, 20), (15, 5), (2, 22), (6, 8), (3, 13), (16, 9), (14, 1), (18, 22), (11, 6), (15, 17), (2, 16), (21, 2), (13, 1), (18, 20), (19, 5), (18, 18), (22, 5), (17, 4), (1, 12), (6, 13), (22, 20), (14, 21), (1, 0), (20, 11), (0, 9), (2, 23), (9, 4), (9, 13), (18, 9), (6, 15), (15, 21), (2, 12), (19, 22), (20, 8), (3, 5), (10, 5), (8, 0), (1, 19), (19, 1), (1, 21), (6, 0), (14, 13), (12, 14), (6, 12), (18, 21), (9, 22), (3, 18), (20, 20), (0, 10), (19, 19), (16, 14), (6, 6), (4, 10), (21, 13), (7, 10), (15, 18), (23, 1), (23, 7), (17, 14), (7, 23), (1, 7), (0, 4), (16, 21), (8, 14), (1, 22), (7, 13), (20, 3), (6, 18), (16, 23), (4, 12), (11, 12), (10, 23), (2, 15), (10, 18), (6, 7), (16, 10), (14, 0), (3, 23), (17, 21), (23, 2), (18, 2), (0, 23), (4, 7), (16, 18), (19, 3), (20, 23), (16, 15), (6, 23), (3, 10), (18, 11), (13, 9), (14, 20), (10, 12), (20, 0), (15, 2), (2, 13), (11, 21), (10, 20), (8, 11), (1, 1), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142610", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 0), (20, 20), (15, 8), (4, 5), (0, 13), (14, 17), (15, 4), (3, 7), (20, 26), (28, 15), (5, 23), (28, 17), (25, 2), (26, 14), (18, 17), (19, 21), (22, 12), (4, 9), (23, 3), (24, 20), (25, 21), (3, 16), (2, 0), (8, 9), (14, 12), (7, 26), (9, 17), (20, 22), (1, 10), (25, 20), (20, 8), (6, 15), (4, 0), (2, 17), (18, 16), (19, 13), (11, 19), (8, 23), (5, 20), (7, 23), (25, 3), (23, 26), (16, 12), (24, 23), (1, 7), (13, 13), (6, 8), (28, 3), (6, 17), (25, 17), (18, 15), (16, 24), (26, 7), (10, 8), (17, 5), (21, 23), (23, 7), (27, 6), (22, 25), (6, 22), (17, 12), (14, 13), (0, 23), (10, 7), (19, 24), (25, 25), (11, 0), (15, 13), (27, 4), (14, 1), (28, 14), (1, 25), (1, 6), (8, 26), (11, 2), (5, 26), (3, 25), (1, 23), (7, 25), (2, 18), (15, 7), (20, 10), (22, 24), (13, 9), (16, 16), (17, 0), (3, 11), (24, 11), (0, 14), (20, 9), (13, 17), (25, 13), (6, 6), (15, 3), (15, 5), (26, 25), (0, 7), (20, 6), (27, 25), (15, 14), (25, 12), (21, 2), (6, 11), (0, 8), (16, 23), (17, 13), (9, 23), (25, 16), (4, 20), (9, 1), (20, 12), (17, 17), (22, 5), (28, 13), (14, 23), (27, 20), (23, 0), (4, 15), (25, 22), (21, 10), (5, 15), (3, 8), (26, 10), (20, 7), (19, 12), (11, 5), (12, 14), (4, 18), (23, 4), (10, 3), (21, 3), (26, 13), (0, 11), (9, 6), (2, 3), (21, 21), (11, 17), (10, 12), (17, 11), (22, 10), (23, 16), (12, 8), (23, 5), (28, 9), (0, 19), (3, 22), (15, 17), (16, 15), (6, 0), (2, 14), (8, 2), (12, 24), (0, 9), (13, 16), (10, 11), (28, 1), (1, 13), (9, 3), (3, 1), (14, 26), (13, 3), (19, 22), (19, 20), (13, 2), (1, 8), (16, 18), (4, 19), (17, 9), (7, 19), (22, 3), (23, 25), (13, 11), (6, 4), (4, 23), (3, 23), (3, 26), (22, 16), (12, 25), (19, 26), (27, 23), (5, 22), (0, 12), (14, 4), (26, 17), (15, 9), (23, 11), (26, 18), (15, 23), (0, 26), (19, 7), (8, 18), (28, 2), (4, 2), (12, 2), (24, 1), (2, 15), (9, 18), (10, 25), (5, 14), (27, 2), (22, 18), (15, 2), (12, 26), (23, 10), (3, 14), (4, 22), (13, 21), (9, 21), (28, 23), (4, 3), (26, 8), (9, 0), (20, 21), (26, 21), (1, 14), (2, 23), (11, 16), (3, 2), (13, 1), (23, 8), (2, 25), (8, 1), (20, 11), (13, 10), (18, 13), (25, 9), (16, 7), (28, 20), (11, 24), (8, 6), (10, 10), (22, 6), (22, 13), (22, 1), (21, 15), (22, 2), (14, 5), (17, 15), (6, 24), (4, 8), (9, 19), (6, 25), (19, 18), (25, 15), (0, 16), (20, 18), (22, 26), (21, 5), (27, 16), (27, 19), (20, 24), (26, 3), (16, 22), (24, 9), (28, 12), (27, 15), (6, 19), (28, 18), (15, 1), (18, 7), (20, 2), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908424", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), 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), (10, 8), (20, 5), (20, 16), (16, 10), (4, 4), (7, 22), (21, 6), (24, 11), (20, 7), (20, 21), (14, 25), (15, 0), (12, 16), (16, 15), (0, 23), (11, 13), (10, 4), (1, 16), (16, 21), (18, 14), (17, 11), (10, 25), (22, 25), (9, 8), (1, 3), (23, 16), (17, 20), (9, 25), (20, 10), (10, 11), (10, 0), (17, 23), (12, 25), (13, 16), (18, 25), (4, 19), (17, 6), (1, 10), (15, 10), (23, 21), (7, 18), (11, 18), (24, 21), (11, 15), (4, 17), (15, 22), (12, 22), (22, 4), (12, 19), (14, 16), (3, 22), (10, 16), (24, 1), (7, 6), (16, 13), (17, 1), (9, 24), (24, 0), (2, 23), (18, 13), (0, 12), (22, 20), (22, 12), (23, 14), (2, 24), (18, 4), (6, 12), (11, 9), (3, 16), (22, 14), (11, 4), (23, 23), (19, 5), (7, 13), (5, 17), (3, 14), (1, 8), (19, 18), (0, 20), (24, 5), (10, 3), (12, 18), (3, 0), (0, 11), (12, 4), (20, 13), (1, 23), (19, 7), (17, 17), (17, 5), (14, 24), (3, 13), (5, 18), (11, 5), (15, 14), (12, 21), (18, 3), (11, 7), (17, 18), (14, 14), (5, 4), (19, 13), (6, 13), (22, 23), (1, 0), (12, 10), (3, 3), (7, 5), (10, 18), (7, 24), (1, 11), (0, 19), (0, 15), (18, 10), (15, 24), (3, 12), (5, 10), (3, 11), (1, 21), (24, 16), (0, 18), (5, 13), (10, 13), (16, 22), (4, 22), (16, 16), (5, 7), (24, 19), (0, 5), (22, 8), (21, 19), (0, 14), (2, 6), (22, 3), (24, 2), (18, 9), (1, 17), (22, 2), (19, 19), (19, 12), (1, 25), (3, 19), (21, 21), (13, 22), (12, 7), (21, 0), (9, 10), (2, 18), (23, 11), (13, 2), (1, 5), (5, 22), (12, 9), (14, 1), (18, 1), (22, 16), (16, 9), (12, 11), (19, 16), (13, 14), (2, 13), (21, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "659823", "dataset": "MATH"}
{"messages": [{"content": "In a 22x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 19), 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), (12, 15), (19, 10), (19, 1), (9, 6), (14, 10), (12, 4), (5, 17), (16, 14), (14, 18), (8, 8), (3, 12), (21, 5), (14, 3), (1, 1), (5, 15), (9, 19), (4, 4), (11, 8), (2, 4), (17, 9), (5, 2), (21, 13), (19, 17), (3, 17), (19, 16), (10, 5), (10, 1), (15, 8), (3, 10), (7, 17), (8, 7), (5, 10), (16, 3), (17, 2), (15, 13), (20, 19), (1, 16), (4, 3), (1, 3), (6, 5), (10, 15), (21, 14), (12, 3), (21, 11), (7, 12), (17, 10), (15, 16), (12, 11), (2, 9), (8, 17), (21, 1), (19, 7), (4, 1), (18, 0), (21, 8), (4, 14), (3, 19), (18, 3), (16, 10), (12, 17), (18, 13), (1, 15), (13, 7), (2, 18), (20, 15), (16, 13), (5, 4), (21, 17), (9, 15), (7, 1), (0, 7), (1, 14), (9, 2), (6, 18), (11, 16), (21, 3), (15, 4), (4, 15), (20, 0), (3, 5), (11, 1), (8, 15), (4, 5), (7, 16), (18, 7), (14, 2), (7, 13), (3, 1), (13, 8), (5, 14), (8, 19), (15, 10), (6, 13), (9, 8), (9, 13), (6, 19), (13, 12), (7, 10), (8, 12), (10, 9), (15, 11), (1, 10), (0, 6), (1, 18), (18, 5), (21, 0), (13, 4), (19, 6), (18, 14), (19, 8), (7, 18), (7, 14), (15, 0), (4, 17), (5, 6), (0, 9), (3, 18), (7, 7), (10, 19), (13, 5), (2, 17), (3, 3), (14, 13), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987844", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 26), (16, 26), (0, 9), (3, 23), (7, 5), (19, 26), (19, 5), (4, 3), (8, 20), (8, 19), (11, 22), (4, 20), (19, 7), (7, 15), (16, 13), (15, 18), (14, 3), (13, 12), (11, 2), (7, 14), (15, 1), (5, 10), (18, 23), (10, 2), (6, 26), (16, 11), (4, 4), (9, 19), (2, 3), (8, 21), (14, 20), (19, 15), (2, 9), (12, 22), (15, 6), (2, 7), (5, 19), (19, 1), (15, 5), (2, 11), (4, 5), (13, 27), (5, 14), (4, 0), (6, 21), (8, 26), (18, 6), (4, 15), (15, 9), (0, 19), (10, 8), (8, 1), (13, 11), (18, 21), (4, 7), (11, 14), (19, 8), (12, 8), (13, 17), (10, 28), (5, 12), (9, 25), (15, 16), (0, 13), (8, 14), (13, 9), (16, 8), (8, 8), (10, 10), (7, 9), (1, 8), (10, 23), (10, 11), (3, 21), (12, 9), (18, 2), (13, 24), (18, 12), (16, 23), (8, 27), (15, 19), (3, 24), (10, 1), (7, 13), (14, 21), (15, 12), (4, 13), (2, 23), (18, 13), (2, 4), (17, 19), (2, 10), (14, 2), (7, 19), (0, 18), (9, 2), (3, 26), (17, 0), (12, 7), (15, 23), (6, 6), (8, 5), (1, 9), (15, 27), (6, 18), (4, 12), (7, 4), (9, 24), (19, 6), (11, 28), (2, 6), (11, 16), (18, 28), (14, 5), (16, 17), (17, 2), (6, 5), (3, 12), (17, 26), (11, 7), (9, 18), (12, 20), (0, 12), (3, 25), (8, 12), (15, 11), (16, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "674664", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 5), (18, 3), (16, 26), (14, 24), (14, 15), (0, 8), (1, 2), (7, 28), (6, 14), (13, 28), (21, 7), (24, 8), (5, 19), (5, 14), (21, 17), (4, 27), (18, 6), (6, 17), (4, 3), (13, 15), (10, 0), (11, 8), (8, 27), (7, 14), (8, 26), (19, 14), (20, 6), (0, 4), (23, 28), (8, 13), (1, 13), (1, 20), (11, 18), (8, 21), (9, 4), (6, 18), (18, 23), (5, 18), (16, 23), (11, 17), (19, 11), (23, 15), (24, 13), (13, 25), (23, 17), (16, 4), (24, 2), (11, 13), (2, 24), (14, 28), (1, 25), (20, 24), (15, 14), (11, 25), (20, 18), (10, 8), (0, 27), (16, 15), (8, 16), (5, 8), (15, 24), (0, 7), (7, 15), (6, 20), (11, 9), (20, 16), (22, 18), (19, 13), (15, 2), (7, 6), (8, 15), (22, 15), (19, 28), (1, 7), (3, 16), (15, 7), (14, 7), (16, 24), (24, 4), (9, 14), (13, 11), (2, 8), (19, 18), (9, 16), (13, 7), (19, 4), (19, 7), (12, 18), (6, 8), (21, 27), (23, 24), (17, 5), (12, 4), (20, 14), (2, 12), (22, 7), (4, 14), (22, 1), (14, 21), (24, 16), (15, 11), (8, 4), (9, 7), (0, 2), (10, 2), (19, 17), (23, 3), (20, 9), (15, 22), (23, 16), (21, 5), (14, 5), (8, 25), (20, 7), (2, 18), (5, 9), (10, 4), (7, 27), (22, 19), (22, 25), (12, 17), (5, 1), (5, 23), (11, 7), (0, 22), (15, 20), (7, 23), (17, 9), (1, 28), (12, 20), (13, 24), (20, 12), (24, 3), (19, 20), (24, 9), (17, 22), (7, 12), (18, 2), (6, 7), (3, 1), (8, 10), (4, 26), (10, 10), (12, 6), (20, 4), (1, 21), (11, 3), (3, 28), (8, 17), (12, 26), (12, 27), (20, 2), (13, 16), (16, 1), (19, 6), (24, 21), (10, 14), (13, 20), (5, 12), (4, 23), (21, 14), (2, 1), (11, 20), (21, 13), (22, 3), (19, 25), (21, 12), (16, 7), (23, 5), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "761320", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 18), (5, 21), (1, 7), (13, 4), (18, 26), (10, 15), (4, 28), (10, 22), (14, 2), (7, 26), (5, 2), (13, 2), (9, 14), (9, 27), (19, 5), (19, 11), (10, 3), (5, 25), (10, 16), (18, 0), (6, 2), (19, 17), (5, 3), (6, 23), (1, 21), (4, 23), (0, 14), (9, 6), (16, 24), (19, 21), (2, 11), (4, 10), (2, 15), (19, 27), (7, 8), (18, 21), (4, 14), (11, 26), (1, 26), (8, 25), (9, 9), (12, 13), (7, 3), (17, 1), (7, 22), (1, 12), (16, 7), (5, 28), (12, 18), (13, 12), (4, 20), (11, 19), (16, 22), (4, 3), (7, 20), (16, 10), (0, 20), (12, 2), (6, 25), (2, 20), (6, 24), (17, 27), (10, 20), (3, 23), (5, 23), (11, 7), (18, 1), (5, 7), (4, 15), (14, 4), (4, 27), (15, 2), (14, 14), (6, 28), (17, 11), (14, 3), (11, 4), (18, 27), (18, 15), (0, 2), (2, 27), (4, 6), (10, 11), (13, 9), (3, 5), (19, 10), (11, 20), (9, 7), (12, 28), (12, 9), (16, 12), (7, 0), (9, 12), (1, 2), (7, 28), (7, 19), (16, 27), (15, 27), (8, 14), (11, 1), (7, 1), (12, 25), (15, 19), (7, 14), (5, 19), (2, 22), (3, 13), (17, 19), (11, 12), (8, 27), (8, 17), (15, 24), (19, 22), (12, 23), (15, 20), (3, 11), (13, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696466", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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, 15), (0, 18), (14, 16), (3, 11), (11, 9), (19, 19), (3, 14), (2, 0), (13, 22), (22, 11), (22, 3), (19, 6), (3, 15), (22, 10), (13, 6), (19, 14), (8, 21), (8, 7), (2, 3), (18, 5), (13, 5), (7, 9), (12, 23), (7, 16), (10, 4), (21, 23), (6, 24), (20, 6), (3, 24), (18, 15), (13, 16), (9, 15), (20, 16), (10, 5), (12, 0), (2, 12), (5, 12), (2, 2), (18, 4), (20, 14), (5, 6), (22, 21), (11, 23), (7, 0), (20, 17), (0, 24), (2, 8), (5, 14), (6, 6), (20, 3), (19, 5), (12, 5), (22, 9), (1, 2), (3, 17), (14, 3), (14, 13), (7, 12), (0, 1), (5, 19), (21, 20), (23, 2), (14, 6), (17, 20), (14, 8), (23, 1), (15, 11), (16, 2), (8, 0), (9, 1), (18, 22), (19, 3), (5, 18), (20, 10), (3, 7), (5, 5), (9, 17), (7, 14), (0, 2), (9, 2), (7, 4), (3, 16), (7, 23), (21, 12), (1, 24), (15, 8), (6, 3), (5, 20), (5, 0), (21, 9), (12, 21), (14, 17), (3, 19), (17, 4), (1, 10), (2, 7), (19, 4), (9, 10), (18, 16), (5, 8), (22, 13), (19, 15), (19, 16), (11, 20), (3, 22), (8, 2), (10, 20), (17, 22), (22, 14), (15, 9), (4, 1), (19, 23), (16, 7), (15, 18), (4, 3), (12, 8), (18, 21), (4, 6), (12, 6), (3, 10), (13, 23), (8, 8), (10, 21), (8, 10), (16, 12), (11, 10), (1, 14), (12, 24), (15, 10), (11, 16), (20, 22), (8, 3), (21, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981024", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (15, 11), (6, 20), (8, 10), (0, 23), (15, 19), (21, 25), (6, 13), (11, 4), (17, 23), (20, 3), (17, 16), (11, 26), (14, 1), (5, 21), (6, 26), (3, 9), (18, 16), (2, 27), (19, 5), (9, 6), (18, 24), (13, 11), (18, 27), (12, 15), (9, 5), (9, 8), (23, 21), (22, 15), (19, 4), (14, 8), (0, 2), (10, 22), (19, 3), (23, 6), (13, 13), (15, 4), (1, 22), (10, 7), (2, 10), (1, 11), (16, 9), (1, 4), (14, 24), (10, 27), (7, 19), (2, 7), (23, 26), (8, 24), (6, 23), (6, 1), (18, 11), (14, 26), (5, 17), (7, 21), (19, 20), (18, 15), (12, 19), (16, 21), (17, 14), (15, 15), (3, 3), (13, 2), (9, 27), (22, 0), (19, 0), (19, 15), (5, 11), (8, 11), (23, 8), (4, 19), (7, 7), (9, 26), (2, 22), (1, 13), (4, 25), (19, 26), (5, 4), (15, 9), (9, 18), (10, 14), (21, 8), (9, 3), (20, 25), (0, 16), (4, 7), (0, 3), (13, 8), (10, 8), (21, 2), (2, 5), (2, 2), (23, 4), (3, 10), (12, 23), (12, 1), (7, 18), (7, 9), (15, 8), (18, 26), (5, 16), (8, 17), (14, 27), (4, 16), (23, 24), (10, 1), (9, 10), (11, 27), (2, 9), (0, 18), (11, 8), (12, 9), (10, 3), (16, 24), (7, 23), (3, 27), (19, 11), (15, 20), (13, 12), (18, 25), (1, 25), (17, 6), (4, 5), (19, 24), (10, 9), (4, 11), (4, 2), (23, 9), (18, 13), (23, 2), (12, 14), (6, 14), (20, 0), (5, 15), (13, 20), (5, 14), (15, 16), (23, 19), (10, 21), (20, 7), (16, 5), (9, 22), (7, 27), (6, 12), (3, 25), (18, 5), (8, 26), (21, 13), (1, 26), (14, 5), (3, 12), (8, 6), (7, 11), (17, 15), (9, 0), (11, 14), (9, 7), (11, 22), (15, 24), (21, 26), (21, 1), (20, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609714", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 15), (18, 21), (4, 25), (14, 16), (8, 21), (15, 9), (10, 22), (19, 13), (16, 9), (12, 14), (3, 2), (12, 0), (11, 25), (16, 8), (16, 27), (5, 9), (2, 24), (12, 19), (19, 6), (1, 2), (10, 6), (4, 23), (10, 20), (17, 10), (13, 15), (5, 3), (4, 21), (3, 21), (9, 15), (13, 6), (3, 13), (3, 15), (0, 17), (7, 15), (12, 17), (7, 1), (0, 8), (3, 8), (5, 1), (6, 2), (11, 20), (12, 23), (9, 16), (17, 13), (0, 9), (13, 9), (2, 23), (8, 28), (13, 8), (9, 22), (14, 3), (10, 5), (10, 4), (14, 23), (1, 9), (6, 13), (8, 0), (11, 3), (16, 1), (1, 25), (2, 7), (18, 5), (17, 6), (10, 28), (11, 16), (3, 4), (7, 3), (1, 12), (13, 27), (18, 14), (14, 10), (5, 12), (18, 3), (19, 17), (9, 1), (3, 17), (5, 16), (15, 5), (18, 2), (6, 12), (7, 5), (10, 16), (0, 14), (12, 21), (17, 5), (8, 5), (10, 14), (2, 27), (4, 7), (19, 21), (11, 24), (8, 13), (14, 2), (1, 16), (2, 22), (19, 2), (7, 2), (3, 0), (8, 24), (12, 11), (2, 5), (14, 13), (17, 23), (14, 24), (16, 3), (12, 20), (3, 22), (11, 0), (5, 20), (11, 1), (14, 4), (4, 1), (18, 15), (16, 6), (4, 24), (16, 12), (6, 23), (8, 20), (19, 20), (4, 10), (17, 12), (12, 15), (15, 22), (18, 18), (18, 23), (9, 20), (3, 10), (18, 9), (5, 17), (11, 14), (13, 3), (7, 16), (18, 22), (0, 12), (19, 1), (4, 18), (11, 28), (14, 1), (18, 27), (3, 5), (6, 8), (13, 20), (1, 4), (10, 26), (3, 14), (12, 28), (19, 4), (8, 23), (10, 3), (1, 11), (3, 25), (6, 28), (13, 10), (7, 0), (13, 13), (10, 2), (8, 4), (15, 27), (14, 26), (16, 4), (7, 21), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998205", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 7), (13, 15), (10, 18), (21, 5), (13, 14), (26, 5), (24, 9), (27, 2), (16, 14), (8, 18), (27, 3), (26, 16), (26, 17), (17, 21), (26, 11), (24, 1), (0, 9), (20, 8), (26, 9), (19, 5), (25, 7), (17, 16), (10, 13), (16, 8), (13, 9), (10, 20), (19, 20), (7, 15), (15, 7), (13, 0), (23, 7), (26, 21), (7, 9), (21, 4), (13, 4), (24, 24), (8, 2), (15, 6), (22, 23), (26, 2), (27, 4), (26, 4), (23, 1), (22, 5), (24, 16), (17, 13), (18, 5), (23, 16), (25, 1), (6, 7), (13, 2), (2, 23), (1, 1), (20, 7), (15, 17), (13, 23), (26, 8), (13, 17), (18, 8), (13, 19), (2, 9), (19, 18), (27, 17), (5, 6), (18, 2), (22, 18), (5, 2), (25, 12), (19, 1), (18, 20), (12, 15), (21, 11), (21, 9), (12, 18), (12, 9), (8, 23), (11, 10), (26, 23), (11, 5), (23, 24), (22, 3), (7, 6), (27, 13), (3, 15), (26, 7), (21, 12), (18, 0), (9, 3), (14, 14), (0, 16), (4, 22), (20, 20), (27, 20), (2, 21), (3, 20), (7, 5), (17, 0), (10, 4), (7, 13), (23, 9), (8, 5), (23, 13), (21, 2), (23, 10), (15, 16), (20, 19), (2, 15), (27, 21), (9, 9), (26, 20), (23, 4), (10, 0), (14, 21), (4, 24), (0, 10), (0, 17), (0, 1), (17, 23), (11, 1), (18, 9), (3, 17), (23, 23), (18, 16), (0, 5), (14, 13), (23, 11), (21, 7), (5, 15), (25, 23), (11, 0), (2, 22), (10, 21), (0, 12), (23, 17), (14, 4), (25, 13), (3, 11), (1, 2), (22, 20), (16, 18), (16, 17), (12, 6), (3, 2), (4, 18), (5, 22), (15, 3), (23, 2), (27, 9), (9, 22), (1, 4), (20, 0), (4, 23), (6, 22), (7, 17), (16, 12), (24, 8), (22, 6), (11, 8), (18, 13), (22, 0), (24, 21), (4, 1), (21, 22), (15, 14), (19, 9), (19, 12), (7, 8), (5, 18), (6, 9), (6, 17), (21, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648870", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 17), (5, 22), (17, 18), (16, 22), (14, 3), (3, 2), (12, 17), (14, 17), (1, 18), (10, 4), (17, 20), (1, 20), (8, 20), (14, 1), (12, 11), (3, 18), (9, 18), (13, 13), (0, 21), (11, 13), (2, 9), (12, 0), (12, 21), (19, 21), (9, 4), (1, 2), (5, 19), (12, 9), (9, 16), (10, 20), (20, 21), (9, 9), (18, 10), (11, 22), (19, 8), (5, 23), (21, 0), (8, 11), (0, 6), (7, 14), (21, 8), (19, 14), (16, 12), (19, 1), (20, 3), (3, 22), (12, 6), (11, 3), (10, 23), (6, 5), (2, 21), (2, 18), (6, 21), (18, 6), (0, 23), (1, 11), (20, 8), (9, 15), (12, 16), (3, 3), (11, 7), (7, 5), (5, 11), (15, 17), (1, 21), (9, 6), (15, 2), (1, 9), (17, 2), (7, 16), (0, 4), (2, 3), (1, 15), (2, 6), (14, 15), (11, 0), (8, 3), (2, 17), (17, 21), (1, 8), (18, 4), (0, 18), (18, 13), (13, 17), (13, 18), (19, 17), (15, 23), (13, 2), (17, 5), (2, 11), (6, 14), (14, 2), (3, 7), (21, 16), (10, 7), (19, 6), (3, 5), (17, 15), (1, 23), (21, 10), (6, 0), (18, 7), (2, 16), (21, 17), (6, 13), (2, 8), (4, 13), (10, 14), (21, 15), (16, 11), (10, 21), (10, 16), (5, 20), (8, 14), (19, 9), (2, 20), (21, 22), (4, 17), (7, 21), (3, 12), (18, 5), (9, 10), (15, 10), (11, 21), (12, 23), (3, 20), (7, 2), (11, 1), (7, 7), (13, 0), (6, 16), (19, 12), (14, 7), (0, 15), (20, 16), (17, 16), (15, 3), (3, 9), (8, 19), (4, 15), (18, 9), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987270", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 14), (11, 6), (16, 20), (13, 5), (20, 11), (4, 12), (9, 12), (0, 10), (15, 13), (0, 19), (25, 1), (1, 0), (15, 14), (18, 18), (20, 16), (10, 10), (25, 6), (16, 6), (7, 9), (22, 13), (23, 5), (15, 8), (23, 10), (10, 0), (19, 0), (19, 8), (12, 3), (16, 1), (15, 4), (24, 14), (3, 4), (11, 10), (18, 10), (1, 2), (10, 6), (2, 3), (6, 10), (21, 4), (9, 14), (11, 1), (3, 5), (23, 3), (12, 20), (23, 4), (4, 2), (21, 11), (21, 13), (10, 15), (17, 15), (14, 12), (21, 7), (18, 9), (9, 7), (11, 4), (19, 1), (10, 1), (12, 16), (7, 20), (0, 15), (14, 6), (17, 9), (21, 16), (25, 10), (6, 20), (15, 1), (13, 1), (10, 8), (7, 2), (9, 2), (5, 20), (18, 5), (12, 13), (9, 9), (17, 5), (16, 16), (15, 12), (2, 6), (6, 3), (10, 20), (15, 3), (13, 12), (3, 1), (21, 2), (11, 19), (0, 7), (6, 19), (6, 4), (6, 6), (7, 12), (25, 19), (12, 8), (6, 8), (18, 0), (13, 6), (24, 11), (7, 11), (13, 2), (24, 6), (7, 13), (10, 12), (14, 11), (3, 17), (6, 14), (9, 16), (24, 16), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "679350", "dataset": "MATH"}
{"messages": [{"content": "In a 28x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 7), (19, 18), (16, 27), (5, 2), (13, 7), (0, 24), (17, 24), (5, 10), (14, 22), (27, 20), (18, 12), (3, 19), (9, 2), (3, 9), (2, 0), (17, 21), (27, 21), (16, 12), (6, 8), (7, 13), (4, 3), (17, 0), (0, 7), (20, 4), (6, 14), (10, 16), (19, 16), (15, 3), (22, 27), (15, 2), (23, 20), (11, 22), (20, 6), (2, 17), (9, 19), (6, 5), (16, 10), (26, 22), (20, 20), (22, 3), (21, 26), (10, 27), (24, 0), (24, 5), (22, 5), (20, 13), (5, 5), (13, 21), (17, 3), (19, 0), (3, 8), (7, 5), (2, 9), (11, 7), (10, 19), (27, 19), (20, 9), (3, 16), (5, 21), (2, 18), (19, 4), (25, 17), (9, 0), (23, 18), (1, 20), (2, 14), (24, 7), (0, 14), (25, 9), (2, 13), (23, 7), (22, 10), (4, 10), (8, 7), (12, 11), (25, 14), (18, 0), (17, 18), (13, 8), (11, 17), (24, 14), (27, 7), (25, 4), (10, 15), (15, 14), (10, 3), (7, 26), (5, 4), (12, 13), (27, 10), (25, 25), (27, 0), (3, 10), (17, 4), (15, 12), (12, 17), (11, 8), (13, 3), (16, 2), (15, 27), (4, 14), (16, 0), (15, 1), (25, 21), (7, 15), (26, 18), (17, 11), (3, 22), (16, 13), (14, 20), (9, 4), (10, 7), (6, 16), (19, 6), (11, 26), (25, 8), (14, 14), (20, 22), (8, 1), (6, 11), (14, 17), (4, 11), (8, 23), (18, 2), (5, 7), (17, 7), (26, 3), (7, 18), (11, 5), (25, 10), (4, 5), (18, 21), (8, 11), (12, 12), (9, 10), (23, 8), (26, 25), (25, 1), (1, 2), (18, 16), (6, 22), (16, 8), (25, 16), (10, 22), (11, 27), (0, 13), (12, 2), (3, 18), (10, 4), (19, 21), (6, 13), (17, 25), (13, 1), (12, 3), (3, 26), (12, 14), (0, 8), (16, 7), (8, 19), (25, 5), (24, 1), (22, 11), (13, 27), (26, 27), (14, 16), (8, 24), (23, 16), (24, 10), (8, 18), (8, 14), (11, 9), (17, 22), (5, 6), (8, 3), (19, 20), (4, 12), (4, 25), (22, 15), (26, 2), (25, 23), (4, 17), (12, 7), (7, 14), (3, 15), (11, 13), (24, 9), (26, 21), (23, 11), (7, 24), (26, 1), (5, 0), (16, 19), (23, 10), (19, 1), (13, 5), (26, 7), (20, 24), (17, 13), (10, 18), (14, 18), (24, 3), (27, 8), (26, 24), (3, 23), (11, 3), (14, 25), (21, 4), (21, 15), (19, 17), (13, 12), (20, 3), (24, 16), (3, 11), (3, 5), (3, 25), (5, 1), (13, 24), (16, 17), (2, 27), (6, 24), (7, 21), (19, 13), (0, 23), (4, 20), (18, 11), (12, 5), (15, 4), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132096", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), 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), (18, 0), (24, 14), (6, 19), (16, 4), (20, 21), (7, 1), (12, 19), (21, 13), (4, 6), (18, 20), (13, 22), (2, 2), (13, 3), (18, 17), (25, 15), (24, 19), (8, 22), (1, 17), (2, 10), (9, 15), (21, 5), (5, 7), (14, 10), (4, 21), (11, 10), (3, 19), (22, 16), (24, 3), (23, 2), (8, 7), (15, 0), (0, 5), (13, 5), (11, 11), (26, 3), (1, 18), (12, 15), (25, 11), (16, 3), (23, 14), (17, 6), (19, 3), (5, 19), (9, 9), (24, 21), (6, 10), (2, 15), (11, 17), (12, 9), (12, 8), (7, 11), (19, 6), (25, 10), (25, 3), (21, 0), (1, 4), (5, 15), (23, 23), (1, 9), (3, 21), (5, 11), (7, 21), (4, 7), (6, 16), (26, 9), (1, 14), (20, 2), (26, 20), (3, 20), (1, 13), (3, 9), (25, 0), (14, 5), (16, 15), (17, 16), (19, 21), (5, 20), (22, 8), (8, 12), (24, 13), (6, 15), (26, 11), (26, 5), (10, 17), (16, 9), (22, 4), (5, 2), (9, 17), (11, 6), (10, 16), (26, 7), (4, 23), (13, 16), (0, 14), (11, 19), (11, 20), (10, 18), (13, 17), (9, 23), (23, 11), (2, 22), (24, 7), (13, 20), (8, 15), (6, 6), (22, 20), (16, 19), (16, 10), (9, 22), (13, 8), (3, 8), (19, 8), (19, 22), (18, 4), (24, 23), (6, 13), (25, 6), (10, 8), (23, 12), (26, 1), (2, 19), (16, 8), (14, 9), (4, 1), (26, 12), (16, 22), (25, 18), (16, 12), (19, 14), (9, 8), (8, 3), (7, 6), (9, 11), (26, 0), (0, 12), (10, 11), (4, 12), (19, 5), (12, 4), (10, 2), (14, 1), (21, 23), (22, 13), (9, 21), (10, 20), (6, 7), (22, 9), (21, 2), (19, 23), (20, 1), (13, 12), (23, 3), (24, 6), (4, 16), (20, 14), (25, 8), (3, 18), (5, 1), (17, 21), (13, 4), (19, 0), (21, 16), (17, 17), (5, 6), (19, 7), (17, 3), (21, 9), (15, 6), (19, 1), (1, 11), (17, 12), (5, 3), (5, 13), (6, 3), (7, 7), (13, 0), (16, 23), (19, 17), (4, 13), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "762039", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 13), (12, 10), (13, 5), (12, 15), (18, 6), (14, 13), (21, 1), (3, 6), (5, 10), (21, 12), (12, 20), (20, 0), (2, 3), (6, 18), (11, 1), (9, 15), (14, 12), (5, 0), (18, 20), (9, 12), (6, 5), (17, 5), (17, 3), (1, 10), (18, 11), (8, 3), (18, 3), (16, 14), (11, 9), (13, 3), (10, 8), (7, 12), (20, 13), (11, 5), (12, 18), (15, 18), (21, 15), (19, 6), (12, 9), (12, 8), (6, 19), (3, 1), (13, 11), (14, 8), (7, 4), (19, 11), (6, 3), (8, 14), (0, 13), (2, 19), (5, 2), (20, 10), (11, 13), (20, 20), (18, 4), (1, 19), (6, 16), (6, 20), (5, 5), (20, 1), (12, 3), (1, 11), (7, 7), (5, 12), (3, 14), (19, 3), (4, 5), (22, 8), (13, 0), (5, 20), (3, 3), (2, 15), (13, 17), (17, 19), (19, 10), (20, 12), (10, 18), (3, 12), (14, 20), (19, 15), (12, 6), (19, 13), (2, 2), (5, 7), (0, 4), (11, 8), (4, 14), (4, 19), (22, 14), (15, 7), (14, 14), (3, 0), (4, 4), (11, 12), (18, 18), (6, 12), (2, 10), (6, 13), (3, 4), (10, 2), (16, 9), (5, 18), (7, 8), (1, 2), (0, 6), (6, 11), (6, 8), (4, 20), (10, 10), (14, 2), (9, 9), (20, 5), (3, 20), (3, 17), (10, 0), (10, 7), (4, 3), (16, 19), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38280", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (2, 23), (0, 22), (20, 26), (11, 12), (11, 10), (14, 14), (3, 19), (16, 7), (8, 0), (20, 1), (4, 25), (17, 10), (0, 20), (7, 23), (8, 16), (22, 25), (15, 8), (7, 1), (19, 14), (14, 25), (24, 5), (9, 16), (23, 16), (21, 4), (1, 26), (14, 26), (6, 2), (20, 4), (16, 20), (5, 3), (0, 7), (10, 15), (22, 14), (1, 19), (18, 17), (24, 0), (5, 8), (3, 10), (14, 13), (4, 0), (4, 18), (3, 7), (8, 3), (12, 21), (11, 0), (2, 13), (1, 17), (14, 11), (19, 25), (24, 1), (23, 7), (0, 23), (12, 18), (9, 3), (11, 19), (11, 7), (11, 27), (12, 14), (3, 27), (9, 12), (4, 14), (18, 14), (7, 17), (3, 2), (2, 20), (7, 26), (15, 15), (0, 13), (13, 1), (3, 23), (1, 10), (22, 7), (6, 27), (11, 3), (17, 11), (12, 23), (1, 16), (24, 22), (23, 21), (14, 17), (19, 22), (21, 14), (17, 7), (12, 20), (24, 18), (7, 22), (18, 20), (18, 3), (22, 11), (7, 8), (17, 12), (2, 7), (15, 23), (22, 21), (0, 4), (11, 22), (10, 13), (20, 20), (22, 6), (13, 11), (16, 8), (11, 15), (1, 21), (2, 10), (1, 15), (20, 7), (14, 27), (21, 12), (2, 18), (15, 11), (24, 3), (0, 17), (7, 20), (6, 24), (5, 9), (13, 7), (19, 26), (24, 17), (14, 8), (17, 17), (5, 11), (11, 26), (19, 17), (20, 6), (17, 19), (0, 19), (6, 19), (24, 9), (10, 7), (6, 13), (10, 23), (4, 26), (20, 14), (8, 24), (10, 17), (23, 0), (19, 4), (8, 25), (8, 10), (21, 22), (21, 1), (15, 16), (7, 24), (16, 3), (11, 8), (4, 3), (0, 3), (0, 21), (18, 12), (19, 12), (6, 15), (13, 14), (4, 19), (23, 20), (11, 24), (13, 22), (16, 9), (21, 19), (24, 2), (23, 6), (4, 24), (10, 16), (10, 6), (18, 0), (15, 18), (23, 17), (20, 11), (20, 13), (8, 9), (18, 16), (13, 18), (5, 15), (2, 24), (10, 12), (10, 11), (16, 5), (24, 10), (22, 13), (15, 17), (16, 23), (9, 2), (22, 1), (0, 8), (4, 10), (5, 26), (20, 10), (21, 18), (0, 26), (4, 9), (8, 22), (17, 4), (6, 3), (13, 26), (13, 21), (8, 17), (12, 12), (16, 0), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513648", "dataset": "MATH"}
{"messages": [{"content": "In a 28x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 3), (13, 22), (0, 2), (10, 11), (26, 1), (17, 8), (23, 16), (26, 11), (27, 12), (3, 22), (12, 13), (5, 17), (9, 22), (6, 19), (5, 7), (23, 9), (5, 16), (13, 17), (3, 7), (14, 17), (11, 15), (18, 7), (1, 8), (22, 1), (1, 12), (27, 18), (16, 22), (24, 18), (5, 5), (2, 21), (18, 17), (0, 7), (23, 13), (3, 19), (4, 14), (15, 17), (9, 21), (10, 3), (23, 19), (5, 12), (18, 3), (17, 2), (17, 18), (13, 11), (14, 3), (1, 6), (20, 19), (20, 20), (27, 16), (11, 1), (21, 4), (8, 19), (12, 12), (5, 18), (0, 3), (15, 5), (25, 8), (10, 6), (14, 0), (24, 8), (27, 2), (22, 11), (0, 19), (24, 7), (26, 6), (21, 18), (14, 22), (4, 22), (25, 12), (18, 15), (0, 14), (3, 15), (10, 2), (0, 17), (18, 2), (0, 20), (20, 11), (16, 4), (2, 12), (25, 19), (17, 15), (26, 10), (8, 13), (4, 18), (8, 20), (20, 12), (2, 17), (21, 17), (11, 11), (16, 16), (22, 13), (1, 1), (13, 6), (16, 19), (6, 13), (4, 1), (8, 22), (12, 18), (3, 17), (3, 21), (13, 5), (10, 10), (24, 1), (18, 21), (8, 4), (25, 10), (17, 10), (17, 13), (12, 17), (25, 3), (5, 21), (18, 5), (14, 19), (9, 15), (22, 16), (24, 0), (15, 11), (17, 17), (26, 19), (23, 0), (6, 22), (23, 12), (27, 20), (9, 6), (21, 19), (16, 1), (18, 1), (14, 16), (23, 14), (13, 19), (23, 2), (20, 15), (26, 22), (7, 18), (2, 9), (7, 1), (1, 20), (11, 10), (6, 0), (17, 12), (21, 1), (15, 6), (23, 17), (14, 9), (9, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973731", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 19), (18, 14), (5, 5), (12, 0), (8, 18), (7, 13), (10, 15), (8, 4), (11, 4), (12, 15), (17, 13), (7, 18), (9, 2), (6, 17), (5, 9), (14, 11), (16, 7), (3, 20), (9, 6), (14, 3), (13, 20), (3, 16), (1, 9), (8, 20), (6, 5), (19, 8), (2, 16), (13, 10), (10, 20), (2, 1), (14, 6), (9, 14), (9, 3), (4, 9), (5, 16), (6, 2), (3, 9), (10, 11), (10, 18), (13, 18), (11, 11), (7, 11), (0, 8), (12, 17), (18, 10), (3, 19), (11, 5), (0, 13), (18, 18), (17, 6), (9, 13), (17, 12), (13, 7), (10, 3), (9, 0), (5, 10), (3, 5), (6, 6), (16, 2), (8, 17), (1, 18), (4, 14), (0, 16), (9, 20), (2, 19), (13, 3), (8, 15), (0, 19), (6, 8), (7, 7), (4, 1), (8, 10), (18, 11), (5, 14), (9, 11), (2, 0), (16, 0), (19, 9), (14, 5), (12, 2), (9, 10), (6, 10), (6, 13), (0, 11), (2, 14), (11, 19), (1, 8), (17, 0), (15, 5), (9, 8), (0, 2), (19, 2), (19, 18), (3, 18), (13, 13), (18, 3), (3, 17), (12, 1), (6, 19), (6, 7), (5, 19), (11, 8), (18, 8), (15, 4), (12, 4), (14, 19), (1, 20), (4, 2), (17, 2), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924432", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (8, 15), (18, 6), (2, 5), (3, 4), (7, 15), (9, 20), (5, 14), (8, 3), (14, 8), (3, 1), (7, 8), (5, 7), (3, 16), (11, 5), (17, 15), (10, 12), (12, 20), (13, 20), (3, 12), (14, 16), (2, 8), (10, 21), (11, 7), (17, 5), (14, 21), (15, 10), (5, 5), (2, 0), (14, 20), (10, 1), (7, 9), (6, 19), (1, 14), (1, 0), (4, 19), (7, 10), (16, 17), (7, 4), (9, 8), (3, 21), (6, 6), (6, 18), (7, 12), (13, 7), (7, 3), (15, 15), (11, 4), (1, 11), (15, 1), (10, 19), (8, 10), (16, 19), (11, 15), (18, 3), (0, 2), (3, 3), (10, 14), (11, 21), (12, 9), (13, 3), (8, 5), (10, 4), (9, 13), (3, 2), (3, 11), (4, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799871", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 4), (13, 12), (13, 3), (11, 18), (14, 17), (16, 5), (15, 8), (18, 23), (8, 9), (2, 5), (14, 2), (4, 18), (16, 8), (21, 8), (14, 20), (15, 19), (8, 4), (13, 1), (7, 20), (19, 3), (6, 15), (1, 18), (18, 19), (18, 11), (12, 0), (9, 12), (7, 4), (1, 11), (7, 17), (20, 23), (1, 21), (10, 5), (2, 9), (19, 13), (7, 22), (4, 0), (2, 10), (9, 22), (19, 2), (4, 10), (9, 1), (8, 19), (10, 23), (21, 12), (2, 13), (13, 22), (3, 1), (16, 15), (14, 14), (6, 7), (5, 1), (12, 7), (10, 3), (22, 7), (7, 19), (9, 2), (22, 9), (12, 13), (14, 21), (19, 18), (2, 11), (5, 6), (16, 10), (0, 20), (3, 5), (3, 4), (22, 18), (20, 19), (18, 15), (15, 16), (14, 5), (12, 20), (20, 15), (1, 15), (3, 16), (6, 18), (4, 13), (21, 7), (22, 13), (17, 15), (22, 15), (20, 2), (10, 6), (5, 2), (16, 6), (2, 18), (17, 10), (6, 10), (10, 19), (15, 14), (0, 17), (8, 12), (14, 11), (13, 21), (13, 20), (1, 5), (11, 9), (14, 10), (19, 14), (12, 17), (0, 19), (11, 1), (21, 3), (20, 20), (13, 19), (21, 15), (7, 6), (12, 2), (10, 1), (14, 1), (13, 14), (5, 20), (9, 13), (20, 12), (17, 8), (18, 8), (11, 10), (8, 0), (7, 23), (10, 2), (21, 5), (12, 5), (6, 8), (1, 2), (3, 17), (12, 4), (5, 12), (4, 20), (7, 15), (22, 20), (16, 12), (0, 23), (22, 2), (11, 4), (13, 15), (1, 8), (10, 8), (17, 4), (6, 11), (8, 3), (14, 8), (18, 2), (17, 7), (17, 3), (16, 1), (11, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899674", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), 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), (10, 12), (23, 19), (3, 4), (25, 3), (12, 17), (8, 9), (7, 18), (2, 5), (23, 5), (11, 19), (14, 20), (0, 10), (3, 17), (24, 16), (16, 2), (3, 20), (9, 7), (17, 1), (18, 19), (14, 10), (21, 18), (14, 19), (16, 4), (6, 12), (18, 16), (21, 10), (9, 2), (16, 6), (4, 12), (19, 18), (7, 19), (20, 0), (2, 19), (5, 14), (16, 5), (1, 20), (13, 1), (22, 3), (22, 4), (11, 3), (17, 9), (12, 2), (11, 11), (12, 4), (12, 10), (2, 3), (15, 14), (5, 11), (10, 6), (18, 1), (6, 4), (19, 20), (0, 16), (18, 2), (3, 10), (8, 10), (13, 19), (3, 15), (2, 11), (15, 6), (0, 17), (19, 14), (11, 6), (0, 19), (10, 20), (2, 13), (24, 6), (21, 1), (4, 19), (2, 17), (14, 18), (15, 16), (21, 15), (24, 2), (1, 11), (20, 1), (6, 1), (9, 20), (17, 2), (24, 5), (2, 8), (20, 2), (22, 13), (17, 20), (9, 10), (12, 6), (14, 1), (0, 14), (18, 5), (9, 0), (25, 18), (2, 18), (4, 17), (24, 4), (25, 14), (0, 13), (20, 18), (17, 4), (4, 13), (21, 19), (21, 13), (0, 12), (13, 4), (13, 20), (10, 9), (22, 12), (22, 2), (3, 16), (13, 5), (14, 2), (4, 18), (15, 12), (21, 12), (21, 4), (24, 13), (14, 0), (0, 20), (7, 9), (1, 17), (19, 0), (23, 1), (6, 3), (5, 9), (12, 15), (19, 4), (16, 18), (25, 11), (6, 14), (10, 14), (0, 9), (23, 3), (7, 16), (0, 4), (10, 3), (5, 17), (4, 20), (18, 7), (21, 16), (7, 15), (11, 12), (2, 4), (19, 2), (21, 0), (13, 0), (19, 5), (6, 10), (12, 14), (6, 13), (22, 7), (19, 19), (18, 11), (23, 8), (21, 8), (12, 19), (11, 10), (12, 9), (21, 2), (9, 17), (11, 4), (16, 15), (21, 14), (5, 19), (1, 10), (12, 20), (13, 10), (5, 16), (24, 19), (9, 18), (11, 15), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "703725", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 12), (18, 20), (14, 14), (7, 24), (6, 25), (2, 13), (5, 15), (15, 15), (24, 19), (27, 21), (19, 16), (27, 8), (8, 10), (14, 3), (1, 22), (12, 2), (10, 10), (20, 16), (7, 15), (5, 23), (14, 8), (14, 10), (23, 14), (12, 20), (14, 12), (24, 17), (1, 4), (22, 7), (0, 25), (26, 16), (14, 5), (5, 13), (11, 2), (24, 0), (18, 16), (9, 0), (8, 7), (24, 18), (11, 20), (8, 22), (0, 18), (17, 4), (24, 7), (12, 1), (25, 14), (12, 11), (18, 25), (17, 21), (7, 8), (23, 10), (26, 25), (0, 10), (26, 24), (22, 13), (17, 12), (25, 17), (13, 15), (26, 15), (24, 5), (24, 11), (3, 17), (10, 12), (0, 14), (17, 23), (0, 17), (5, 25), (13, 6), (21, 0), (25, 19), (13, 2), (2, 10), (25, 8), (4, 16), (22, 11), (8, 20), (8, 5), (15, 13), (27, 9), (13, 16), (13, 19), (6, 24), (20, 18), (27, 1), (1, 7), (22, 9), (13, 10), (5, 14), (13, 4), (17, 2), (14, 0), (18, 6), (17, 5), (21, 10), (7, 14), (4, 20), (14, 20), (22, 20), (13, 24), (1, 6), (5, 3), (27, 4), (5, 10), (11, 10), (0, 21), (0, 5), (11, 3), (1, 12), (22, 23), (22, 5), (12, 21), (5, 5), (17, 10), (11, 6), (26, 13), (27, 22), (2, 1), (21, 23), (24, 3), (22, 4), (16, 16), (10, 14), (26, 12), (15, 20), (19, 18), (15, 3), (8, 23), (24, 10), (9, 10), (8, 12), (2, 19), (14, 23), (10, 21), (23, 3), (9, 15), (26, 18), (9, 9), (20, 14), (3, 20), (27, 20), (5, 19), (3, 0), (16, 0), (23, 17), (19, 8), (5, 1), (15, 12), (18, 5), (10, 1), (4, 19), (23, 9), (10, 9), (26, 17), (18, 7), (9, 8), (17, 9), (19, 14), (13, 25), (10, 24), (27, 0), (20, 2), (0, 8), (4, 18), (16, 23), (2, 25), (21, 16), (7, 3), (9, 6), (9, 19), (1, 14), (24, 16), (11, 24), (9, 13), (25, 18), (20, 19), (19, 25), (5, 24), (19, 15), (17, 0), (11, 19), (15, 5), (13, 23), (16, 17), (6, 4), (19, 20), (5, 22), (19, 2), (27, 15), (13, 5), (21, 4), (7, 23), (0, 7), (8, 11), (11, 18), (17, 8), (1, 3), (3, 18), (0, 23), (3, 13), (25, 16), (4, 0), (0, 16), (18, 11), (22, 19), (12, 6), (11, 12), (18, 8), (16, 7), (3, 22), (26, 6), (11, 1), (6, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "639138", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 19), (2, 9), (0, 5), (2, 18), (14, 12), (5, 15), (17, 9), (13, 16), (20, 10), (14, 18), (15, 12), (8, 10), (3, 1), (9, 7), (9, 8), (21, 0), (5, 13), (17, 0), (16, 13), (11, 14), (7, 1), (3, 20), (7, 19), (6, 2), (6, 3), (1, 4), (20, 7), (7, 16), (13, 6), (7, 11), (12, 1), (2, 3), (3, 13), (12, 16), (4, 19), (7, 14), (19, 14), (3, 15), (18, 11), (5, 11), (8, 5), (6, 13), (15, 9), (1, 13), (0, 8), (16, 10), (21, 13), (10, 0), (7, 8), (12, 14), (2, 10), (1, 11), (13, 11), (15, 6), (17, 5), (6, 10), (13, 10), (5, 16), (15, 5), (6, 14), (17, 15), (10, 6), (11, 19), (17, 14), (19, 12), (10, 3), (10, 2), (20, 4), (15, 3), (5, 18), (5, 20), (18, 1), (8, 16), (4, 11), (6, 20), (21, 6), (10, 9), (10, 10), (5, 8), (7, 5), (11, 17), (0, 7), (10, 4), (18, 17), (11, 13), (13, 14), (20, 16), (12, 5), (11, 2), (1, 10), (10, 14), (13, 9), (8, 12), (8, 0), (16, 11), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "379321", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), 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, 16), (25, 26), (2, 25), (24, 9), (0, 14), (13, 24), (6, 18), (4, 0), (21, 10), (14, 22), (12, 21), (15, 12), (17, 3), (19, 8), (5, 17), (11, 5), (14, 23), (19, 15), (18, 17), (15, 26), (12, 6), (21, 18), (17, 2), (18, 28), (19, 27), (23, 1), (8, 15), (10, 13), (13, 8), (4, 24), (15, 13), (26, 14), (19, 7), (0, 8), (15, 22), (3, 8), (3, 7), (20, 11), (24, 19), (13, 15), (12, 15), (8, 3), (24, 8), (5, 4), (7, 10), (7, 4), (10, 17), (26, 13), (25, 23), (22, 12), (7, 20), (1, 5), (0, 2), (8, 17), (12, 20), (4, 25), (11, 16), (3, 11), (17, 8), (25, 24), (9, 23), (6, 14), (10, 4), (10, 27), (20, 2), (24, 26), (6, 24), (26, 23), (0, 21), (5, 15), (14, 27), (19, 5), (4, 12), (8, 9), (26, 8), (10, 23), (4, 26), (9, 13), (13, 28), (21, 12), (10, 25), (2, 13), (18, 7), (17, 7), (18, 21), (21, 21), (22, 16), (9, 6), (23, 11), (21, 17), (6, 16), (0, 13), (10, 7), (9, 1), (4, 14), (8, 28), (20, 6), (7, 18), (20, 12), (15, 15), (7, 17), (12, 10), (7, 22), (16, 11), (4, 16), (10, 6), (16, 23), (23, 23), (2, 9), (18, 1), (17, 9), (3, 20), (19, 2), (22, 4), (18, 26), (7, 5), (7, 7), (8, 21), (16, 17), (22, 1), (17, 11), (3, 26), (0, 1), (5, 10), (17, 14), (20, 1), (8, 12), (23, 24), (9, 7), (12, 16), (9, 12), (15, 16), (25, 14), (26, 9), (20, 26), (8, 2), (4, 6), (19, 13), (24, 11), (21, 9), (9, 26), (8, 10), (4, 20), (1, 23), (25, 7), (22, 9), (18, 5), (19, 9), (1, 24), (20, 13), (1, 7), (4, 19), (2, 4), (18, 23), (16, 7), (25, 28), (24, 27), (24, 20), (8, 25), (23, 25), (7, 15), (26, 10), (8, 4), (17, 18), (1, 14), (8, 8), (1, 10), (16, 25), (23, 18), (5, 18), (22, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "666792", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 18), (6, 16), (4, 1), (22, 7), (6, 17), (15, 19), (20, 10), (1, 16), (23, 12), (0, 8), (10, 0), (1, 10), (16, 2), (18, 0), (15, 18), (17, 12), (20, 3), (20, 5), (12, 3), (8, 12), (11, 10), (9, 14), (0, 13), (21, 15), (17, 2), (5, 13), (16, 12), (14, 4), (20, 11), (12, 9), (6, 20), (13, 8), (12, 0), (0, 16), (22, 19), (11, 15), (0, 20), (17, 0), (3, 7), (11, 20), (6, 2), (16, 19), (19, 19), (11, 0), (23, 19), (3, 12), (0, 14), (7, 0), (2, 18), (14, 14), (12, 12), (7, 7), (16, 4), (13, 15), (1, 19), (7, 8), (4, 20), (2, 19), (2, 1), (18, 20), (15, 14), (22, 10), (17, 7), (14, 16), (12, 6), (14, 6), (12, 19), (16, 1), (21, 11), (18, 12), (13, 13), (4, 16), (1, 18), (7, 9), (15, 13), (22, 1), (3, 13), (13, 20), (16, 17), (15, 5), (21, 18), (7, 14), (19, 13), (2, 6), (3, 10), (14, 19), (9, 7), (2, 5), (5, 12), (7, 4), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617590", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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), (17, 9), (15, 17), (9, 23), (2, 16), (15, 18), (12, 21), (5, 7), (9, 22), (14, 20), (17, 8), (14, 5), (12, 16), (5, 4), (12, 1), (17, 10), (2, 19), (11, 14), (11, 2), (12, 13), (19, 19), (3, 24), (1, 18), (1, 24), (18, 15), (7, 14), (18, 0), (10, 14), (6, 2), (14, 8), (4, 18), (3, 1), (10, 23), (15, 6), (16, 15), (1, 16), (0, 18), (0, 10), (1, 8), (17, 17), (13, 14), (0, 20), (17, 16), (5, 13), (12, 18), (19, 3), (4, 22), (10, 11), (6, 13), (12, 24), (3, 23), (17, 18), (13, 17), (6, 10), (19, 21), (17, 5), (1, 0), (3, 22), (10, 12), (8, 4), (1, 21), (11, 20), (0, 2), (18, 6), (3, 4), (0, 14), (11, 4), (13, 10), (6, 1), (2, 1), (8, 13), (19, 17), (2, 24), (3, 18), (14, 23), (16, 24), (0, 8), (16, 19), (10, 18), (8, 3), (9, 1), (16, 20), (3, 2), (10, 9), (18, 4), (8, 15), (15, 12), (12, 7), (11, 13), (17, 21), (10, 2), (13, 23), (15, 14), (4, 20), (13, 16), (1, 7), (18, 14), (6, 3), (13, 21), (16, 8), (17, 22), (5, 9), (5, 18), (8, 14), (4, 23), (17, 13), (11, 17), (15, 23), (10, 3), (18, 7), (14, 4), (8, 21), (4, 1), (7, 24), (15, 1), (7, 20), (11, 5), (18, 9), (19, 20), (16, 7), (10, 1), (18, 1), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769776", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), 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), (21, 17), (3, 18), (18, 0), (21, 6), (24, 12), (4, 21), (25, 11), (6, 19), (7, 0), (3, 17), (18, 7), (14, 18), (7, 5), (21, 0), (16, 17), (13, 22), (14, 2), (22, 2), (16, 13), (1, 0), (21, 2), (0, 14), (15, 11), (17, 7), (12, 22), (21, 22), (16, 7), (24, 3), (25, 18), (22, 17), (23, 15), (21, 8), (20, 10), (4, 5), (12, 8), (20, 21), (12, 4), (17, 1), (22, 9), (19, 8), (12, 15), (7, 7), (23, 14), (17, 12), (11, 20), (12, 19), (24, 7), (15, 2), (18, 16), (22, 1), (8, 12), (4, 8), (21, 13), (17, 8), (4, 3), (3, 12), (25, 15), (22, 12), (9, 20), (10, 9), (15, 22), (21, 19), (18, 15), (25, 10), (6, 21), (10, 15), (5, 10), (19, 21), (18, 1), (21, 1), (23, 2), (23, 11), (11, 12), (0, 17), (10, 10), (23, 10), (19, 20), (6, 15), (1, 19), (16, 21), (6, 11), (17, 13), (12, 18), (2, 21), (22, 3), (4, 10), (25, 9), (6, 0), (0, 11), (12, 10), (6, 4), (15, 1), (11, 9), (4, 2), (16, 19), (5, 12), (5, 0), (17, 19), (15, 10), (20, 2), (23, 17), (10, 6), (18, 5), (23, 19), (9, 5), (6, 6), (20, 17), (3, 1), (14, 20), (24, 9), (5, 5), (8, 22), (8, 6), (23, 0), (1, 8), (9, 14), (4, 18), (23, 6), (16, 10), (1, 9), (8, 1), (2, 7), (4, 16), (4, 22), (25, 13), (9, 0), (8, 15), (13, 19), (3, 16), (8, 3), (24, 18), (19, 4), (8, 14), (13, 0), (2, 12), (5, 2), (4, 1), (6, 17), (20, 1), (17, 3), (10, 14), (6, 13), (1, 15), (24, 10), (3, 22), (8, 5), (18, 10), (16, 5), (23, 9), (25, 6), (15, 17), (15, 13), (4, 9), (4, 11), (22, 16), (2, 0), (10, 12), (2, 22), (10, 8), (6, 12), (9, 10), (18, 17), (19, 2), (15, 3), (24, 16), (13, 8), (23, 4), (10, 7), (22, 20), (9, 1), (5, 14), (10, 18), (3, 3), (11, 22), (22, 4), (16, 1), (21, 9), (14, 9), (1, 17), (16, 18), (17, 9), (2, 8), (19, 5), (21, 5), (19, 14), (16, 14), (0, 21), (0, 15), (20, 22), (8, 19), (12, 12), (14, 21), (12, 1), (23, 20), (6, 7), (14, 22), (2, 10), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719364", "dataset": "MATH"}
{"messages": [{"content": "In a 28x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 19), 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), (17, 7), (16, 1), (18, 12), (17, 14), (22, 12), (26, 12), (20, 1), (13, 14), (7, 18), (8, 17), (15, 15), (8, 15), (20, 5), (23, 15), (12, 1), (1, 11), (21, 9), (1, 9), (12, 4), (6, 5), (19, 7), (4, 14), (15, 19), (24, 6), (0, 14), (19, 4), (7, 5), (22, 14), (26, 3), (23, 1), (24, 10), (25, 3), (6, 10), (25, 8), (14, 0), (26, 9), (26, 4), (20, 12), (15, 18), (21, 1), (24, 15), (10, 8), (20, 6), (1, 4), (7, 9), (24, 5), (7, 16), (2, 2), (10, 3), (27, 11), (21, 7), (8, 12), (0, 7), (9, 7), (21, 11), (19, 8), (21, 4), (16, 2), (10, 12), (1, 19), (9, 14), (20, 14), (26, 5), (27, 2), (14, 14), (3, 14), (0, 12), (22, 13), (6, 16), (9, 11), (9, 12), (20, 9), (12, 17), (19, 5), (24, 8), (9, 0), (20, 4), (7, 12), (18, 13), (17, 18), (7, 11), (23, 5), (20, 10), (13, 1), (13, 7), (16, 15), (22, 18), (16, 10), (14, 10), (0, 3), (18, 19), (0, 15), (1, 10), (1, 14), (10, 16), (12, 8), (18, 8), (27, 5), (14, 2), (12, 19), (8, 19), (8, 8), (4, 15), (3, 12), (18, 15), (23, 19), (20, 8), (18, 1), (26, 13), (16, 19), (16, 13), (23, 18), (17, 12), (16, 16), (9, 15), (15, 2), (19, 2), (12, 5), (23, 10), (27, 15), (24, 2), (6, 11), (26, 8), (11, 2), (16, 0), (17, 5), (22, 4), (26, 1), (17, 15), (24, 13), (11, 3), (19, 10), (8, 2), (23, 7), (14, 16), (6, 18), (25, 12), (2, 18), (22, 3), (11, 12), (6, 12), (10, 11), (6, 13), (20, 11), (14, 9), (8, 16), (14, 7), (3, 17), (19, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332760", "dataset": "MATH"}
{"messages": [{"content": "In a 21x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 24), (3, 9), (5, 7), (3, 15), (17, 8), (14, 1), (9, 6), (15, 13), (13, 4), (10, 1), (16, 7), (12, 7), (18, 11), (8, 16), (3, 5), (3, 8), (13, 15), (20, 14), (0, 19), (9, 10), (17, 4), (14, 7), (5, 10), (19, 21), (7, 15), (15, 0), (8, 20), (8, 12), (5, 18), (4, 16), (4, 18), (0, 2), (2, 20), (8, 23), (9, 21), (15, 23), (17, 19), (20, 19), (20, 2), (3, 0), (11, 7), (5, 16), (3, 18), (11, 10), (11, 18), (12, 16), (10, 22), (17, 2), (7, 17), (16, 9), (0, 13), (9, 7), (18, 23), (15, 7), (9, 13), (9, 23), (9, 2), (17, 21), (19, 5), (3, 12), (6, 19), (10, 13), (18, 18), (6, 14), (9, 0), (10, 2), (9, 4), (12, 1), (4, 22), (6, 21), (19, 11), (2, 4), (19, 19), (16, 21), (20, 4), (11, 23), (6, 12), (11, 22), (6, 22), (16, 4), (9, 24), (13, 14), (1, 12), (7, 16), (11, 3), (7, 1), (3, 14), (17, 3), (18, 12), (2, 24), (9, 9), (12, 5), (7, 14), (11, 0), (19, 18), (0, 7), (10, 16), (9, 11), (8, 19), (20, 17), (4, 14), (10, 10), (3, 7), (1, 23), (10, 21), (13, 19), (7, 18), (0, 3), (18, 17), (1, 7), (10, 8), (14, 14), (10, 6), (2, 21), (15, 18), (8, 24), (19, 1), (14, 11), (20, 16), (11, 20), (5, 3), (11, 13), (14, 18), (6, 2), (19, 9), (4, 8), (5, 20), (2, 0), (6, 18), (17, 14), (13, 9), (15, 2), (10, 14), (6, 16), (4, 23), (12, 6), (1, 17), (12, 8), (11, 11), (5, 12), (4, 19), (3, 10), (17, 18), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570648", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 20), (19, 7), (0, 16), (18, 5), (23, 1), (7, 23), (18, 19), (3, 27), (6, 2), (18, 8), (11, 0), (6, 9), (1, 13), (14, 2), (1, 9), (11, 10), (24, 18), (8, 10), (15, 26), (28, 14), (28, 23), (1, 20), (14, 23), (24, 11), (28, 16), (7, 3), (16, 15), (17, 27), (21, 15), (19, 18), (11, 3), (15, 0), (5, 19), (28, 12), (8, 23), (8, 17), (13, 9), (6, 23), (6, 14), (21, 17), (26, 26), (8, 6), (8, 3), (3, 24), (18, 2), (13, 18), (12, 4), (6, 15), (14, 19), (6, 16), (19, 17), (8, 9), (8, 0), (9, 10), (19, 14), (20, 2), (3, 20), (18, 25), (23, 21), (5, 5), (19, 1), (14, 14), (3, 3), (10, 24), (8, 5), (13, 19), (16, 2), (23, 4), (4, 5), (16, 9), (16, 18), (25, 7), (15, 2), (22, 18), (11, 21), (7, 14), (27, 27), (14, 4), (11, 13), (9, 2), (2, 11), (22, 2), (22, 13), (3, 0), (7, 18), (9, 4), (18, 1), (13, 27), (24, 17), (3, 19), (13, 21), (0, 1), (21, 5), (21, 16), (6, 11), (6, 8), (9, 17), (7, 15), (7, 25), (25, 13), (4, 3), (24, 10), (0, 6), (4, 13), (16, 8), (22, 1), (21, 13), (5, 23), (16, 24), (18, 20), (22, 6), (10, 14), (13, 8), (23, 22), (10, 16), (12, 17), (28, 20), (13, 2), (20, 11), (5, 9), (26, 6), (8, 24), (24, 4), (15, 9), (2, 3), (5, 0), (28, 22), (9, 5), (10, 15), (11, 20), (10, 27), (6, 26), (13, 7), (9, 6), (3, 8), (13, 0), (9, 8), (6, 5), (20, 16), (22, 19), (13, 3), (23, 7), (28, 9), (28, 24), (12, 13), (16, 20), (6, 18), (8, 2), (21, 18), (2, 27), (11, 7), (25, 23), (22, 12), (5, 16), (9, 20), (15, 12), (19, 24), (11, 24), (2, 18), (11, 12), (9, 16), (27, 22), (25, 5), (20, 22), (27, 20), (10, 4), (0, 26), (12, 10), (17, 14), (12, 2), (20, 3), (6, 10), (17, 26), (19, 13), (15, 6), (13, 13), (20, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803176", "dataset": "MATH"}
{"messages": [{"content": "In a 22x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 4), (15, 7), (19, 16), (10, 3), (14, 7), (7, 17), (11, 15), (10, 6), (20, 4), (2, 5), (19, 18), (2, 18), (12, 4), (10, 5), (14, 18), (11, 6), (21, 9), (2, 8), (8, 0), (19, 10), (17, 9), (9, 0), (5, 14), (17, 5), (4, 2), (0, 3), (4, 11), (17, 18), (3, 17), (10, 11), (15, 17), (17, 19), (13, 8), (21, 6), (7, 14), (1, 9), (16, 13), (0, 16), (13, 14), (6, 13), (6, 6), (8, 12), (13, 10), (4, 6), (13, 16), (19, 15), (17, 0), (16, 15), (6, 1), (3, 5), (4, 0), (16, 19), (15, 9), (17, 7), (14, 2), (7, 19), (20, 5), (0, 1), (6, 9), (9, 4), (9, 7), (18, 14), (15, 18), (0, 6), (4, 10), (4, 13), (15, 10), (6, 12), (6, 0), (6, 18), (11, 1), (10, 17), (3, 6), (15, 16), (10, 16), (16, 3), (3, 4), (16, 16), (15, 12), (15, 19), (5, 4), (14, 10), (9, 9), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "910918", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (25, 3), (5, 20), (12, 5), (3, 22), (7, 17), (2, 1), (25, 4), (13, 22), (9, 23), (0, 21), (18, 9), (9, 2), (19, 21), (27, 1), (4, 11), (10, 2), (5, 1), (7, 11), (3, 4), (24, 14), (3, 7), (27, 16), (12, 19), (23, 16), (2, 2), (7, 14), (24, 6), (3, 13), (3, 10), (5, 9), (0, 4), (20, 11), (15, 6), (22, 7), (20, 5), (10, 24), (26, 0), (25, 20), (14, 21), (23, 12), (9, 10), (12, 24), (24, 0), (25, 19), (10, 16), (1, 19), (20, 16), (8, 13), (23, 23), (6, 0), (27, 5), (9, 13), (16, 11), (27, 7), (15, 15), (10, 18), (22, 4), (6, 23), (1, 22), (9, 6), (7, 19), (15, 11), (2, 18), (7, 6), (26, 18), (17, 3), (13, 6), (0, 19), (11, 14), (13, 14), (12, 16), (24, 19), (22, 9), (20, 17), (13, 3), (23, 14), (27, 2), (4, 0), (21, 22), (26, 7), (6, 10), (22, 22), (8, 11), (27, 6), (25, 14), (21, 6), (6, 8), (26, 1), (21, 8), (18, 7), (16, 4), (15, 14), (14, 7), (7, 8), (20, 6), (23, 20), (3, 23), (27, 4), (22, 6), (27, 22), (14, 10), (2, 21), (13, 20), (15, 21), (25, 22), (7, 16), (24, 2), (27, 10), (15, 13), (17, 9), (22, 20), (22, 15), (5, 3), (18, 22), (17, 15), (12, 18), (12, 6), (26, 11), (16, 3), (2, 13), (25, 1), (0, 12), (0, 7), (20, 8), (15, 18), (10, 17), (9, 7), (8, 7), (18, 16), (10, 0), (24, 18), (22, 17), (14, 8), (11, 8), (22, 18), (21, 21), (5, 18), (0, 24), (13, 17), (4, 16), (5, 2), (19, 4), (2, 4), (17, 5), (9, 21), (11, 23), (21, 14), (2, 10), (7, 0), (12, 3), (25, 21), (9, 1), (26, 5), (26, 8), (24, 1), (4, 22), (15, 16), (9, 15), (1, 0), (8, 24), (24, 23), (11, 7), (17, 7), (2, 23), (11, 21), (9, 16), (20, 18), (25, 23), (4, 24), (18, 5), (11, 19), (15, 23), (13, 7), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268395", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), 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), (15, 8), (19, 6), (12, 7), (2, 3), (1, 8), (18, 18), (13, 11), (18, 3), (2, 0), (7, 11), (9, 10), (6, 9), (10, 7), (16, 18), (16, 4), (14, 22), (3, 6), (0, 17), (7, 9), (19, 22), (21, 13), (21, 6), (5, 9), (11, 6), (5, 8), (15, 16), (2, 10), (13, 19), (2, 16), (8, 4), (6, 16), (1, 16), (0, 6), (12, 20), (17, 4), (18, 13), (11, 15), (21, 5), (20, 0), (9, 19), (5, 4), (12, 8), (2, 6), (7, 6), (15, 7), (1, 14), (18, 0), (11, 5), (1, 21), (20, 17), (15, 18), (15, 4), (9, 9), (0, 11), (14, 17), (20, 14), (14, 21), (20, 15), (21, 15), (5, 2), (11, 3), (19, 12), (14, 6), (2, 22), (19, 15), (8, 11), (16, 19), (2, 2), (12, 19), (19, 20), (19, 2), (16, 5), (16, 7), (1, 9), (14, 5), (1, 17), (0, 8), (6, 13), (17, 7), (17, 16), (16, 13), (10, 16), (19, 4), (10, 6), (16, 21), (19, 7), (18, 17), (9, 11), (8, 2), (1, 22), (6, 1), (18, 22), (17, 13), (17, 10), (1, 12), (12, 5), (8, 17), (3, 10), (2, 12), (1, 20), (6, 12), (18, 2), (2, 19), (10, 20), (1, 7), (5, 3), (0, 10), (10, 0), (3, 12), (14, 3), (19, 8), (0, 7), (12, 11), (1, 11), (2, 11), (16, 9), (13, 12), (13, 0), (4, 1), (17, 1), (7, 13), (0, 13), (2, 4), (14, 16), (13, 7), (18, 6), (16, 12), (2, 17), (16, 2), (10, 18), (4, 15), (15, 0), (20, 9), (1, 0), (6, 17), (4, 18), (21, 16), (10, 3), (9, 1), (11, 22), (17, 18), (12, 3), (3, 16), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "733865", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 19), (23, 10), (11, 15), (18, 11), (4, 2), (22, 7), (2, 10), (8, 0), (20, 13), (8, 1), (7, 11), (20, 18), (4, 15), (19, 18), (5, 16), (14, 1), (22, 11), (23, 0), (14, 14), (14, 9), (20, 16), (11, 12), (21, 4), (11, 3), (10, 17), (9, 3), (12, 16), (14, 20), (19, 6), (16, 17), (23, 1), (18, 0), (13, 6), (15, 13), (12, 20), (7, 19), (19, 11), (18, 8), (7, 16), (7, 6), (12, 2), (8, 9), (14, 15), (15, 11), (9, 9), (12, 5), (2, 3), (3, 7), (23, 16), (0, 5), (5, 18), (10, 12), (19, 16), (7, 10), (23, 19), (10, 19), (1, 12), (19, 5), (22, 10), (13, 13), (22, 18), (2, 20), (6, 10), (20, 1), (8, 11), (6, 5), (13, 17), (6, 6), (3, 16), (1, 11), (9, 6), (13, 11), (19, 14), (21, 1), (12, 8), (9, 15), (0, 17), (10, 0), (22, 19), (14, 3), (14, 10), (19, 17), (4, 10), (2, 14), (17, 3), (14, 12), (13, 7), (3, 10), (15, 18), (22, 4), (16, 15), (16, 13), (11, 2), (16, 11), (23, 11), (19, 13), (11, 8), (21, 7), (9, 16), (8, 2), (14, 6), (16, 12), (15, 3), (14, 11), (21, 18), (15, 16), (12, 11), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942644", "dataset": "MATH"}
{"messages": [{"content": "In a 29x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 19), (11, 14), (21, 10), (15, 15), (17, 8), (8, 17), (23, 4), (0, 5), (2, 17), (21, 0), (19, 18), (20, 13), (7, 12), (12, 9), (9, 0), (13, 15), (3, 7), (27, 4), (10, 23), (8, 20), (19, 22), (10, 9), (13, 18), (28, 8), (16, 6), (8, 13), (9, 7), (9, 6), (4, 1), (2, 22), (4, 21), (25, 12), (12, 11), (25, 23), (4, 13), (9, 11), (16, 15), (26, 2), (26, 13), (2, 24), (3, 0), (13, 7), (3, 6), (24, 12), (18, 18), (21, 22), (20, 19), (3, 20), (23, 1), (7, 22), (5, 22), (13, 21), (11, 22), (15, 10), (26, 7), (27, 18), (25, 7), (18, 23), (16, 0), (8, 4), (7, 13), (5, 2), (22, 3), (25, 14), (13, 22), (6, 3), (8, 12), (5, 7), (16, 5), (7, 3), (22, 19), (25, 8), (23, 5), (4, 12), (26, 19), (24, 4), (18, 19), (24, 14), (1, 11), (0, 22), (0, 16), (12, 21), (25, 24), (2, 14), (25, 10), (15, 21), (2, 2), (14, 17), (16, 3), (1, 5), (11, 16), (6, 23), (5, 17), (24, 11), (17, 19), (27, 3), (14, 15), (3, 3), (23, 14), (14, 23), (19, 15), (24, 18), (24, 1), (12, 23), (1, 18), (27, 11), (5, 6), (18, 21), (12, 3), (25, 17), (20, 12), (2, 16), (3, 4), (16, 14), (9, 4), (17, 22), (23, 20), (1, 17), (9, 18), (12, 18), (14, 9), (22, 2), (27, 9), (5, 11), (28, 4), (4, 3), (28, 18), (8, 10), (14, 16), (5, 16), (8, 0), (9, 12), (23, 2), (8, 23), (20, 22), (18, 13), (21, 24), (26, 9), (7, 11), (22, 10), (28, 7), (2, 11), (25, 22), (23, 3), (1, 2), (26, 1), (8, 9), (27, 22), (8, 8), (1, 9), (2, 23), (1, 1), (21, 14), (11, 0), (10, 6), (20, 4), (0, 8), (27, 7), (10, 17), (3, 13), (10, 22), (21, 9), (0, 12), (9, 13), (5, 9), (19, 11), (14, 18), (22, 18), (28, 1), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "747984", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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), (17, 4), (25, 14), (4, 4), (19, 18), (7, 17), (21, 2), (10, 6), (27, 2), (3, 8), (21, 9), (10, 13), (25, 11), (23, 18), (16, 10), (7, 12), (14, 0), (2, 4), (8, 3), (18, 6), (9, 7), (5, 9), (5, 18), (16, 11), (26, 17), (7, 11), (10, 3), (8, 0), (16, 15), (22, 0), (2, 14), (27, 20), (5, 11), (9, 9), (0, 10), (10, 5), (13, 9), (14, 15), (6, 8), (6, 7), (7, 8), (12, 3), (14, 18), (14, 16), (7, 1), (4, 7), (11, 9), (15, 4), (21, 16), (20, 13), (3, 11), (6, 14), (18, 16), (19, 11), (16, 1), (13, 7), (21, 1), (1, 19), (1, 9), (2, 13), (5, 14), (9, 8), (24, 9), (12, 19), (1, 14), (20, 6), (17, 19), (1, 12), (10, 2), (24, 0), (23, 4), (26, 12), (22, 11), (21, 8), (14, 17), (21, 18), (18, 18), (13, 18), (20, 10), (19, 10), (2, 19), (23, 8), (16, 7), (24, 1), (8, 9), (19, 2), (11, 3), (22, 14), (15, 0), (12, 13), (3, 4), (0, 11), (4, 12), (22, 19), (4, 15), (6, 18), (4, 20), (25, 6), (9, 2), (6, 13), (7, 5), (26, 19), (12, 17), (22, 3), (5, 8), (5, 21), (12, 0), (8, 7), (3, 15), (14, 8), (16, 13), (14, 7), (0, 6), (19, 8), (15, 18), (14, 11), (5, 5), (26, 9), (16, 4), (22, 17), (23, 16), (8, 1), (18, 4), (8, 19), (15, 17), (4, 16), (0, 18), (25, 2), (12, 9), (17, 21), (21, 17), (22, 13), (12, 21), (23, 2), (9, 10), (26, 3), (23, 10), (9, 16), (0, 21), (19, 5), (7, 20), (19, 1), (21, 20), (8, 14), (14, 4), (12, 1), (13, 10), (2, 6), (22, 8), (26, 14), (26, 8), (23, 5), (12, 4), (15, 19), (24, 19), (27, 3), (19, 0), (10, 16), (1, 0), (26, 5), (24, 11), (21, 13), (4, 11), (13, 1), (15, 15), (6, 15), (8, 20), (16, 18), (5, 6), (14, 14), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918534", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 18), (9, 17), (4, 2), (6, 23), (18, 1), (7, 12), (12, 9), (10, 15), (16, 17), (20, 1), (8, 17), (15, 3), (0, 10), (7, 7), (19, 22), (6, 7), (13, 15), (5, 3), (11, 22), (3, 5), (6, 5), (3, 16), (8, 2), (2, 8), (6, 17), (5, 24), (11, 1), (19, 17), (2, 4), (8, 25), (0, 7), (2, 23), (12, 23), (13, 16), (20, 13), (11, 20), (17, 10), (20, 24), (6, 24), (12, 25), (6, 0), (9, 9), (9, 21), (5, 11), (17, 13), (14, 5), (5, 0), (16, 11), (13, 20), (7, 22), (0, 23), (18, 10), (12, 13), (10, 22), (6, 18), (15, 7), (9, 0), (14, 23), (18, 18), (2, 16), (20, 14), (14, 6), (16, 20), (0, 17), (16, 18), (0, 24), (19, 16), (13, 4), (11, 24), (19, 19), (3, 14), (10, 16), (0, 18), (17, 25), (8, 12), (3, 1), (15, 25), (7, 19), (5, 19), (11, 13), (19, 14), (9, 7), (12, 22), (11, 0), (10, 18), (16, 1), (9, 19), (4, 18), (19, 9), (8, 5), (3, 9), (4, 25), (19, 8), (4, 1), (0, 3), (13, 7), (4, 7), (12, 1), (7, 15), (3, 20), (6, 10), (17, 24), (7, 6), (19, 20), (18, 11), (2, 0), (15, 21), (9, 1), (15, 16), (8, 4), (0, 20), (10, 20), (2, 7), (11, 18), (14, 10), (6, 14), (11, 16), (2, 24), (12, 3), (3, 0), (10, 23), (0, 22), (10, 7), (16, 24), (7, 3), (17, 15), (11, 19), (7, 25), (9, 4), (9, 23), (18, 21), (16, 23), (12, 11), (6, 20), (16, 16), (20, 2), (20, 10), (1, 3), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "852480", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (16, 6), (2, 10), (0, 21), (19, 19), (10, 11), (8, 5), (6, 15), (16, 1), (5, 22), (13, 16), (16, 14), (11, 17), (12, 2), (7, 5), (18, 2), (18, 1), (3, 19), (16, 13), (6, 5), (5, 18), (8, 9), (6, 4), (4, 19), (0, 14), (1, 2), (1, 15), (4, 5), (6, 7), (1, 10), (11, 13), (7, 4), (19, 9), (3, 5), (8, 12), (6, 6), (18, 4), (5, 7), (4, 7), (18, 9), (19, 14), (6, 10), (2, 9), (12, 14), (7, 17), (4, 17), (2, 5), (5, 11), (5, 21), (18, 18), (8, 1), (7, 22), (18, 6), (6, 8), (17, 4), (4, 9), (13, 8), (8, 3), (7, 2), (18, 19), (5, 6), (11, 7), (14, 8), (19, 7), (4, 21), (16, 0), (0, 11), (2, 13), (19, 16), (10, 22), (4, 12), (3, 14), (8, 13), (8, 6), (16, 2), (19, 10), (1, 11), (19, 8), (13, 6), (3, 3), (5, 16), (10, 21), (14, 12), (3, 21), (2, 4), (15, 10), (2, 3), (8, 8), (15, 20), (19, 20), (17, 2), (7, 9), (9, 18), (14, 9), (10, 18), (18, 17), (15, 2), (6, 17), (0, 1), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992437", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), 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), (6, 7), (4, 3), (2, 14), (12, 5), (0, 9), (11, 13), (18, 12), (19, 11), (3, 3), (17, 15), (13, 11), (8, 10), (1, 2), (2, 13), (17, 19), (1, 8), (17, 1), (2, 10), (4, 6), (11, 10), (15, 17), (12, 12), (12, 3), (16, 15), (16, 10), (7, 15), (10, 5), (7, 3), (3, 5), (3, 11), (13, 3), (12, 10), (0, 11), (14, 5), (16, 9), (8, 15), (12, 19), (0, 12), (16, 5), (12, 4), (10, 6), (6, 8), (15, 3), (6, 14), (9, 16), (2, 15), (7, 7), (13, 6), (12, 13), (9, 9), (4, 17), (1, 12), (1, 16), (19, 4), (2, 11), (6, 19), (15, 4), (16, 8), (18, 11), (19, 6), (8, 8), (19, 18), (0, 17), (16, 3), (15, 18), (8, 3), (6, 0), (18, 3), (7, 10), (17, 14), (0, 18), (10, 12), (5, 5), (7, 4), (17, 7), (15, 8), (16, 11), (15, 19), (3, 8), (17, 12), (19, 16), (9, 5), (2, 12), (0, 13), (10, 17), (1, 0), (18, 15), (19, 9), (7, 14), (5, 16), (6, 3), (4, 10), (1, 18), (9, 17), (1, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "910056", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (15, 14), (2, 6), (2, 13), (4, 0), (3, 12), (18, 15), (18, 19), (14, 13), (4, 19), (7, 20), (4, 1), (8, 4), (10, 12), (9, 2), (2, 2), (11, 15), (15, 1), (15, 18), (13, 12), (2, 20), (18, 8), (4, 20), (19, 6), (19, 11), (5, 15), (14, 16), (8, 15), (5, 16), (14, 6), (1, 9), (8, 17), (14, 7), (3, 18), (18, 9), (13, 8), (2, 9), (14, 20), (6, 12), (8, 8), (9, 20), (15, 10), (13, 4), (7, 2), (17, 7), (17, 8), (1, 5), (17, 0), (15, 13), (1, 19), (12, 9), (18, 1), (6, 6), (3, 14), (11, 17), (19, 5), (6, 10), (1, 12), (10, 6), (5, 7), (1, 2), (0, 12), (14, 9), (8, 11), (1, 7), (5, 9), (14, 3), (19, 15), (12, 1), (12, 5), (10, 14), (17, 6), (12, 7), (11, 4), (18, 5), (4, 16), (7, 12), (8, 12), (18, 4), (0, 17), (12, 6), (18, 18), (17, 4), (17, 14), (14, 14), (12, 3), (1, 16), (3, 7), (17, 2), (18, 2), (7, 15), (15, 4), (19, 13), (11, 10), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "772786", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 14), (6, 15), (20, 21), (12, 6), (10, 10), (16, 3), (1, 14), (11, 4), (11, 2), (9, 19), (17, 12), (11, 0), (13, 13), (16, 17), (6, 17), (1, 3), (7, 10), (4, 2), (13, 9), (18, 14), (0, 17), (9, 4), (10, 19), (4, 16), (10, 18), (0, 8), (15, 8), (2, 17), (21, 1), (14, 16), (7, 23), (19, 14), (0, 2), (0, 18), (1, 21), (0, 22), (9, 18), (14, 19), (19, 12), (14, 5), (5, 0), (11, 10), (0, 13), (7, 1), (1, 2), (20, 6), (6, 21), (7, 4), (2, 22), (20, 3), (5, 12), (18, 6), (9, 9), (19, 6), (10, 22), (12, 7), (4, 15), (5, 21), (13, 5), (2, 6), (17, 0), (21, 0), (4, 12), (17, 2), (4, 17), (4, 9), (14, 6), (15, 0), (10, 5), (4, 14), (20, 0), (8, 5), (14, 4), (15, 6), (9, 12), (21, 2), (17, 21), (21, 18), (8, 6), (16, 8), (19, 17), (17, 7), (1, 8), (10, 21), (16, 20), (16, 6), (19, 21), (17, 4), (12, 5), (5, 9), (10, 1), (2, 1), (6, 22), (4, 11), (17, 10), (19, 13), (3, 14), (1, 22), (14, 3), (10, 17), (10, 20), (1, 4), (8, 23), (19, 1), (0, 1), (10, 23), (8, 18), (15, 15), (18, 2), (4, 13), (7, 18), (21, 7), (8, 4), (10, 6), (7, 3), (9, 1), (10, 2), (7, 9), (18, 0), (4, 7), (20, 5), (18, 7), (4, 21), (13, 2), (20, 8), (15, 12), (20, 11), (12, 19), (12, 20), (2, 5), (4, 6), (7, 2), (0, 5), (19, 11), (1, 16), (16, 22), (8, 12), (15, 14), (1, 20), (15, 9), (19, 16), (21, 17), (13, 14), (10, 16), (14, 22), (14, 20), (18, 23), (13, 8), (19, 15), (8, 14), (20, 20), (2, 12), (19, 22), (17, 8), (7, 20), (16, 12), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844968", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 13), (10, 15), (4, 19), (18, 3), (13, 1), (0, 15), (7, 19), (22, 0), (5, 7), (9, 0), (0, 21), (13, 17), (19, 1), (21, 3), (12, 13), (8, 5), (23, 5), (14, 5), (25, 20), (25, 14), (22, 3), (1, 16), (9, 17), (24, 3), (13, 14), (16, 0), (22, 13), (17, 20), (10, 0), (15, 5), (13, 8), (21, 6), (17, 4), (1, 2), (15, 20), (10, 11), (23, 3), (3, 10), (16, 8), (20, 21), (19, 9), (0, 17), (5, 17), (13, 4), (24, 1), (24, 14), (17, 8), (18, 19), (1, 19), (20, 17), (26, 13), (18, 20), (5, 16), (11, 19), (18, 2), (22, 11), (1, 5), (15, 19), (21, 14), (7, 2), (9, 18), (23, 16), (21, 20), (17, 16), (7, 20), (3, 21), (17, 15), (14, 20), (17, 9), (15, 9), (22, 5), (8, 10), (18, 17), (7, 4), (14, 4), (19, 4), (19, 10), (4, 17), (0, 4), (11, 15), (6, 11), (6, 4), (26, 3), (6, 9), (10, 14), (23, 9), (24, 17), (9, 14), (7, 8), (16, 12), (10, 12), (1, 21), (5, 21), (3, 15), (22, 16), (18, 21), (1, 9), (8, 1), (8, 0), (0, 14), (13, 10), (0, 16), (10, 20), (14, 21), (19, 0), (7, 1), (19, 19), (22, 18), (10, 19), (24, 8), (2, 8), (0, 9), (21, 4), (7, 12), (9, 1), (9, 3), (12, 14), (26, 8), (21, 18), (14, 12), (2, 13), (5, 10), (1, 10), (17, 19), (17, 18), (20, 14), (20, 8), (13, 21), (22, 20), (22, 8), (4, 3), (15, 18), (3, 9), (14, 6), (22, 4), (23, 15), (24, 13), (12, 15), (7, 15), (13, 9), (11, 21), (13, 15), (11, 10), (22, 2), (25, 16), (6, 19), (0, 1), (23, 21), (11, 7), (17, 21), (3, 2), (17, 12), (4, 7), (21, 11), (21, 5), (1, 6), (26, 0), (2, 17), (2, 1), (1, 12), (16, 3), (13, 0), (26, 18), (8, 16), (20, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545805", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 11), (19, 2), (5, 21), (10, 6), (10, 2), (5, 0), (1, 2), (16, 2), (1, 5), (15, 7), (0, 8), (18, 17), (14, 12), (17, 18), (7, 8), (10, 4), (5, 10), (6, 15), (9, 13), (14, 10), (11, 5), (4, 0), (16, 16), (11, 11), (16, 19), (5, 4), (5, 18), (14, 14), (12, 2), (10, 12), (7, 1), (19, 1), (0, 9), (3, 8), (9, 12), (14, 3), (14, 18), (16, 21), (15, 8), (11, 6), (12, 7), (10, 15), (0, 7), (1, 1), (14, 15), (7, 17), (17, 9), (19, 9), (17, 13), (7, 14), (9, 19), (13, 1), (14, 16), (18, 0), (18, 21), (12, 1), (2, 7), (5, 5), (16, 1), (9, 20), (20, 20), (6, 1), (14, 1), (15, 2), (2, 0), (9, 21), (16, 20), (5, 12), (3, 21), (13, 7), (8, 16), (12, 16), (16, 5), (7, 19), (1, 11), (0, 10), (15, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719864", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), 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), (11, 10), (4, 24), (10, 10), (6, 24), (18, 9), (10, 26), (7, 18), (14, 0), (1, 16), (8, 4), (17, 10), (4, 5), (1, 21), (9, 20), (5, 15), (17, 18), (8, 26), (19, 6), (12, 4), (10, 1), (10, 2), (12, 20), (18, 4), (18, 15), (4, 13), (16, 17), (18, 3), (13, 15), (7, 27), (0, 19), (10, 13), (2, 16), (10, 7), (4, 0), (13, 8), (9, 19), (17, 9), (5, 3), (14, 11), (18, 13), (9, 27), (4, 22), (5, 20), (8, 16), (3, 17), (0, 22), (5, 6), (8, 13), (19, 11), (0, 17), (13, 3), (11, 17), (9, 10), (16, 18), (11, 20), (18, 27), (13, 14), (2, 20), (7, 4), (12, 16), (12, 26), (14, 3), (19, 1), (7, 9), (13, 22), (13, 11), (17, 13), (6, 27), (9, 14), (0, 27), (3, 10), (7, 22), (15, 24), (17, 15), (8, 25), (16, 5), (4, 8), (3, 13), (0, 15), (6, 18), (12, 24), (3, 0), (11, 12), (1, 8), (16, 0), (0, 23), (3, 6), (0, 25), (1, 6), (1, 5), (3, 12), (9, 11), (19, 3), (13, 4), (18, 10), (16, 3), (11, 8), (16, 11), (2, 10), (14, 18), (6, 19), (3, 14), (18, 19), (19, 18), (7, 24), (13, 20), (0, 3), (15, 7), (13, 24), (17, 11), (2, 9), (15, 6), (16, 24), (16, 1), (3, 23), (19, 15), (17, 2), (11, 22), (12, 0), (19, 23), (1, 27), (0, 4), (7, 7), (6, 20), (8, 5), (16, 19), (4, 6), (17, 22), (11, 27), (7, 20), (0, 9), (18, 7), (9, 0), (17, 7), (10, 21), (11, 11), (12, 1), (15, 25), (9, 6), (12, 10), (16, 13), (16, 16), (5, 21), (15, 22), (3, 24), (14, 24), (1, 17), (14, 12), (12, 27), (10, 4), (0, 12), (5, 17), (15, 12), (1, 9), (1, 22), (18, 18), (12, 18), (10, 8), (8, 7), (1, 7), (8, 9), (5, 11), (3, 8), (0, 26), (4, 9), (9, 9), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255312", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 11), (7, 10), (23, 3), (11, 9), (18, 6), (18, 23), (0, 5), (18, 15), (25, 7), (4, 21), (17, 0), (6, 16), (1, 24), (6, 1), (12, 12), (23, 24), (21, 28), (12, 28), (5, 0), (7, 18), (3, 13), (19, 8), (19, 19), (13, 22), (24, 5), (17, 4), (23, 4), (7, 19), (18, 7), (20, 13), (15, 22), (14, 0), (13, 9), (6, 9), (9, 9), (3, 8), (6, 6), (2, 18), (22, 8), (15, 20), (24, 10), (0, 15), (21, 2), (24, 4), (20, 10), (21, 5), (20, 15), (22, 3), (5, 9), (22, 18), (21, 16), (14, 16), (25, 23), (15, 0), (13, 8), (1, 13), (5, 22), (0, 28), (24, 27), (18, 14), (20, 1), (15, 26), (20, 22), (14, 21), (11, 24), (4, 10), (22, 11), (7, 14), (22, 22), (7, 28), (20, 9), (19, 20), (24, 1), (10, 21), (4, 13), (9, 17), (1, 16), (20, 6), (4, 3), (23, 23), (16, 26), (15, 1), (7, 7), (23, 13), (19, 24), (24, 9), (10, 25), (19, 6), (14, 26), (14, 17), (17, 6), (25, 11), (8, 18), (6, 22), (0, 26), (20, 3), (8, 25), (10, 20), (4, 19), (11, 20), (12, 23), (10, 16), (8, 21), (9, 15), (13, 23), (13, 18), (25, 15), (2, 23), (19, 25), (23, 11), (17, 18), (23, 28), (19, 0), (4, 1), (4, 17), (18, 21), (1, 14), (13, 25), (4, 16), (17, 10), (15, 7), (23, 10), (4, 0), (6, 17), (12, 25), (15, 2), (24, 22), (6, 0), (8, 15), (5, 7), (11, 26), (10, 1), (0, 4), (24, 19), (10, 18), (14, 7), (15, 9), (21, 4), (13, 26), (10, 9), (3, 4), (14, 9), (0, 18), (9, 12), (20, 19), (7, 12), (2, 26), (21, 10), (25, 5), (7, 11), (22, 10), (18, 1), (21, 20), (9, 8), (23, 0), (14, 2), (10, 11), (5, 13), (9, 3), (6, 25), (23, 27), (11, 5), (10, 0), (16, 8), (2, 27), (6, 7), (16, 10), (14, 15), (23, 5), (3, 17), (11, 21), (2, 6), (13, 0), (5, 18), (8, 2), (9, 2), (12, 1), (12, 14), (7, 23), (5, 1), (6, 10), (21, 24), (0, 19), (1, 15), (10, 27), (4, 9), (16, 1), (25, 3), (9, 16), (8, 7), (24, 20), (1, 23), (21, 12), (0, 27), (11, 8), (2, 16), (15, 24), (19, 7), (7, 5), (25, 2), (19, 2), (18, 22), (2, 7), (3, 0), (24, 12), (20, 28), (15, 15), (18, 16), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391440", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 27), (20, 23), (20, 15), (23, 0), (8, 18), (13, 25), (9, 24), (2, 26), (0, 11), (0, 14), (2, 18), (6, 20), (0, 12), (19, 11), (17, 24), (14, 9), (9, 3), (22, 19), (15, 12), (5, 26), (14, 14), (23, 9), (21, 8), (9, 21), (8, 6), (3, 12), (4, 17), (19, 4), (4, 8), (6, 13), (5, 10), (2, 8), (17, 23), (20, 1), (6, 16), (16, 16), (22, 1), (14, 17), (7, 20), (11, 16), (12, 21), (21, 17), (24, 2), (8, 7), (5, 27), (0, 8), (14, 4), (1, 5), (18, 12), (17, 22), (24, 8), (17, 10), (15, 20), (15, 16), (9, 12), (6, 1), (9, 27), (19, 16), (9, 1), (8, 11), (18, 3), (7, 2), (23, 13), (19, 21), (16, 15), (5, 13), (5, 22), (13, 5), (23, 22), (1, 26), (20, 21), (0, 9), (1, 24), (22, 7), (3, 19), (0, 1), (24, 11), (0, 15), (16, 21), (24, 25), (8, 4), (20, 0), (13, 21), (13, 7), (17, 8), (0, 20), (15, 22), (20, 8), (15, 26), (16, 5), (5, 8), (1, 8), (10, 5), (10, 27), (18, 23), (9, 7), (20, 2), (7, 9), (7, 21), (20, 14), (22, 27), (6, 0), (18, 16), (9, 10), (8, 12), (16, 26), (19, 14), (5, 18), (0, 3), (1, 13), (5, 12), (4, 27), (13, 18), (13, 15), (5, 16), (8, 0), (7, 13), (24, 4), (22, 20), (21, 25), (4, 9), (15, 7), (5, 5), (15, 3), (13, 27), (12, 14), (1, 27), (9, 8), (9, 19), (2, 14), (7, 27), (18, 24), (21, 16), (17, 26), (8, 8), (8, 14), (17, 2), (7, 6), (7, 18), (11, 7), (14, 1), (13, 9), (17, 9), (5, 4), (7, 4), (19, 5), (22, 24), (4, 3), (1, 21), (6, 12), (2, 1), (13, 8), (4, 11), (0, 23), (19, 26), (23, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165088", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 23), (13, 19), (4, 6), (18, 7), (16, 17), (14, 13), (22, 19), (12, 7), (16, 20), (20, 21), (21, 1), (14, 9), (13, 6), (12, 6), (1, 10), (4, 22), (8, 17), (22, 16), (18, 4), (21, 3), (19, 15), (14, 18), (15, 5), (15, 3), (22, 6), (13, 17), (19, 5), (12, 2), (3, 0), (12, 12), (3, 5), (21, 8), (16, 6), (4, 25), (1, 5), (3, 10), (17, 25), (3, 25), (23, 19), (2, 10), (16, 25), (14, 12), (21, 10), (19, 20), (16, 10), (3, 13), (9, 15), (2, 6), (21, 19), (12, 8), (8, 22), (6, 3), (23, 4), (0, 5), (12, 19), (5, 24), (3, 20), (15, 19), (13, 21), (4, 15), (0, 11), (18, 18), (4, 24), (9, 21), (5, 4), (14, 19), (7, 5), (11, 3), (19, 21), (16, 9), (16, 24), (20, 5), (5, 15), (19, 1), (22, 9), (18, 15), (20, 17), (23, 13), (2, 1), (15, 11), (12, 16), (21, 14), (22, 3), (4, 19), (5, 20), (13, 4), (19, 12), (16, 11), (1, 0), (20, 24), (11, 17), (15, 0), (3, 16), (18, 23), (10, 12), (4, 17), (23, 10), (19, 9), (5, 7), (7, 24), (16, 23), (5, 22), (12, 9), (7, 11), (10, 23), (13, 15), (3, 9), (11, 5), (15, 24), (22, 2), (19, 18), (18, 8), (20, 2), (8, 4), (15, 21), (14, 2), (15, 15), (10, 10), (2, 11), (11, 4), (5, 19), (21, 4), (10, 1), (18, 5), (10, 2), (11, 12), (6, 2), (3, 11), (14, 4), (6, 21), (15, 9), (10, 15), (6, 5), (11, 25), (9, 18), (17, 3), (21, 5), (7, 8), (7, 25), (23, 22), (13, 10), (13, 18), (6, 8), (22, 10), (7, 13), (14, 23), (7, 20), (9, 0), (12, 13), (3, 8), (23, 14), (9, 6), (6, 23), (13, 16), (11, 8), (18, 20), (11, 19), (22, 17), (12, 18), (13, 22), (17, 6), (5, 16), (14, 1), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717300", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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, 14), (10, 10), (18, 20), (16, 1), (18, 5), (9, 23), (7, 24), (17, 7), (2, 19), (14, 10), (19, 2), (3, 19), (4, 8), (19, 15), (6, 8), (1, 12), (17, 19), (4, 12), (0, 11), (3, 16), (0, 2), (3, 21), (0, 14), (0, 16), (8, 20), (19, 11), (4, 14), (6, 2), (3, 13), (12, 12), (6, 10), (17, 9), (16, 4), (9, 12), (0, 20), (10, 2), (15, 2), (8, 9), (0, 22), (8, 24), (12, 23), (8, 18), (3, 22), (3, 5), (11, 12), (0, 15), (19, 0), (0, 19), (1, 9), (2, 8), (3, 18), (8, 19), (4, 10), (5, 19), (9, 10), (9, 9), (15, 16), (0, 6), (5, 23), (1, 5), (9, 6), (16, 23), (5, 5), (5, 1), (2, 13), (10, 5), (3, 0), (18, 1), (4, 11), (15, 19), (16, 5), (12, 7), (14, 2), (5, 16), (13, 2), (19, 23), (17, 13), (16, 2), (4, 2), (12, 5), (3, 4), (10, 1), (5, 17), (12, 21), (10, 20), (18, 2), (16, 12), (6, 23), (11, 17), (12, 16), (15, 11), (14, 6), (15, 1), (6, 4), (10, 7), (3, 23), (0, 5), (0, 12), (9, 8), (4, 22), (9, 2), (19, 13), (16, 14), (4, 3), (17, 23), (7, 3), (4, 1), (0, 21), (0, 7), (18, 4), (19, 9), (0, 23), (13, 24), (14, 8), (18, 12), (12, 0), (18, 14), (6, 11), (17, 21), (9, 16), (14, 0), (19, 19), (11, 1), (6, 18), (17, 5), (17, 14), (15, 3), (7, 2), (17, 24), (5, 21), (11, 19), (12, 11), (12, 3), (17, 17), (14, 1), (9, 1), (7, 23), (5, 15), (4, 21), (13, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755082", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 15), (10, 15), (22, 12), (2, 14), (17, 9), (2, 11), (15, 4), (11, 19), (14, 3), (1, 1), (3, 9), (2, 1), (6, 0), (1, 12), (1, 9), (19, 18), (20, 10), (19, 8), (8, 2), (17, 18), (0, 8), (21, 13), (11, 12), (11, 5), (14, 2), (21, 19), (7, 5), (8, 19), (19, 7), (8, 14), (19, 10), (5, 4), (2, 9), (18, 16), (2, 3), (6, 9), (5, 18), (1, 0), (18, 17), (0, 10), (12, 10), (5, 8), (21, 3), (4, 4), (1, 13), (1, 5), (8, 8), (8, 7), (19, 3), (14, 12), (8, 16), (15, 15), (6, 8), (13, 12), (22, 16), (10, 2), (20, 16), (20, 20), (22, 17), (8, 13), (16, 15), (19, 4), (18, 1), (17, 4), (8, 3), (22, 11), (19, 19), (20, 4), (16, 14), (7, 13), (1, 8), (2, 20), (20, 7), (9, 2), (8, 6), (2, 19), (8, 0), (20, 1), (22, 15), (10, 19), (16, 5), (16, 8), (20, 15), (14, 11), (3, 1), (22, 7), (8, 12), (14, 17), (21, 10), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787230", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 19), (0, 5), (13, 19), (18, 4), (10, 17), (20, 9), (15, 4), (8, 22), (14, 19), (19, 22), (0, 25), (2, 5), (21, 24), (9, 13), (6, 10), (19, 7), (18, 18), (10, 11), (11, 15), (11, 4), (13, 3), (22, 6), (20, 7), (0, 18), (12, 4), (21, 16), (20, 26), (16, 2), (19, 10), (5, 23), (1, 18), (15, 16), (0, 14), (14, 16), (10, 5), (0, 8), (13, 8), (2, 9), (6, 13), (16, 18), (0, 15), (12, 22), (14, 12), (14, 10), (16, 5), (9, 22), (23, 21), (7, 14), (2, 23), (2, 0), (22, 18), (15, 24), (18, 13), (14, 9), (10, 4), (17, 19), (18, 15), (3, 21), (4, 6), (3, 10), (11, 17), (7, 1), (9, 6), (14, 26), (12, 26), (14, 6), (3, 13), (3, 4), (13, 6), (13, 24), (3, 6), (2, 24), (7, 22), (19, 26), (3, 14), (17, 12), (2, 17), (8, 26), (3, 15), (6, 18), (0, 21), (18, 10), (9, 21), (13, 10), (7, 4), (13, 14), (2, 13), (9, 19), (23, 20), (4, 12), (22, 3), (6, 16), (18, 12), (12, 3), (22, 11), (23, 2), (11, 5), (1, 3), (19, 14), (23, 1), (5, 19), (11, 10), (16, 8), (2, 3), (1, 8), (16, 3), (13, 9), (5, 12), (9, 9), (17, 22), (15, 22), (9, 8), (5, 5), (5, 6), (11, 19), (17, 7), (19, 4), (7, 21), (12, 13), (11, 8), (19, 25), (9, 1), (2, 6), (14, 25), (23, 24), (9, 3), (1, 20), (15, 25), (3, 18), (16, 15), (12, 5), (19, 2), (16, 13), (10, 15), (8, 7), (1, 5), (9, 16), (20, 19), (8, 23), (23, 15), (20, 10), (8, 3), (8, 25), (3, 24), (12, 16), (4, 24), (11, 1), (21, 5), (4, 15), (16, 16), (0, 20), (15, 12), (12, 10), (1, 2), (14, 24), (23, 25), (4, 4), (14, 3), (21, 25), (20, 16), (5, 1), (0, 26), (20, 1), (0, 13), (16, 17), (11, 9), (10, 19), (20, 12), (22, 9), (16, 21), (8, 16), (15, 6), (19, 19), (4, 10), (0, 3), (19, 9), (11, 3), (3, 3), (0, 9), (20, 23), (10, 2), (8, 4), (14, 8), (20, 0), (15, 11), (20, 5), (20, 4), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501120", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 19), (24, 4), (4, 19), (21, 20), (13, 15), (5, 17), (13, 9), (20, 12), (23, 17), (16, 1), (5, 1), (8, 9), (15, 8), (8, 20), (14, 16), (23, 24), (15, 20), (2, 16), (21, 4), (17, 19), (1, 22), (0, 24), (17, 12), (7, 17), (11, 2), (17, 6), (21, 7), (0, 3), (23, 22), (20, 1), (4, 1), (11, 9), (6, 16), (5, 5), (14, 10), (18, 18), (18, 3), (16, 7), (9, 11), (15, 6), (18, 17), (18, 8), (13, 17), (22, 7), (1, 19), (22, 20), (1, 10), (18, 5), (20, 3), (15, 22), (15, 0), (23, 7), (15, 24), (23, 3), (2, 24), (9, 17), (15, 13), (24, 19), (20, 11), (13, 1), (15, 7), (11, 0), (4, 20), (12, 1), (14, 8), (21, 1), (8, 22), (17, 14), (5, 19), (17, 4), (20, 14), (9, 6), (10, 20), (6, 0), (9, 22), (11, 5), (11, 14), (12, 8), (0, 7), (16, 10), (22, 13), (6, 7), (5, 13), (5, 8), (3, 9), (2, 21), (23, 15), (8, 6), (24, 20), (20, 22), (7, 4), (21, 11), (3, 22), (9, 10), (5, 18), (1, 13), (7, 0), (2, 0), (19, 21), (10, 2), (22, 2), (13, 19), (12, 7), (3, 7), (7, 5), (21, 2), (16, 16), (16, 22), (4, 0), (16, 18), (3, 20), (8, 21), (10, 24), (19, 15), (0, 11), (2, 6), (1, 16), (1, 15), (13, 7), (13, 18), (7, 11), (23, 12), (16, 15), (21, 13), (22, 10), (17, 13), (24, 21), (24, 22), (23, 11), (18, 13), (24, 14), (15, 16), (4, 10), (17, 11), (14, 2), (23, 21), (14, 7), (6, 20), (11, 22), (3, 17), (12, 24), (2, 13), (3, 1), (21, 19), (21, 10), (1, 20), (12, 16), (9, 16), (2, 7), (0, 19), (8, 16), (6, 5), (17, 21), (1, 5), (18, 15), (15, 21), (4, 14), (17, 18), (8, 7), (9, 4), (8, 23), (7, 22), (9, 1), (1, 12), (8, 17), (12, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613950", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), 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), (15, 13), (0, 9), (22, 10), (18, 22), (3, 19), (19, 22), (20, 22), (5, 19), (26, 21), (26, 0), (24, 22), (1, 4), (16, 11), (3, 10), (14, 11), (3, 2), (18, 3), (7, 22), (16, 12), (20, 11), (23, 2), (2, 13), (6, 22), (10, 10), (22, 2), (6, 3), (14, 21), (19, 10), (25, 11), (4, 9), (22, 21), (9, 11), (16, 13), (2, 19), (3, 15), (14, 18), (20, 10), (24, 6), (11, 19), (8, 0), (5, 4), (6, 11), (16, 6), (26, 6), (8, 17), (19, 4), (11, 16), (21, 1), (24, 4), (2, 15), (0, 19), (5, 6), (1, 9), (9, 1), (13, 12), (8, 19), (23, 12), (23, 19), (10, 13), (16, 15), (10, 21), (3, 1), (23, 21), (6, 19), (0, 23), (22, 12), (11, 2), (25, 9), (12, 20), (14, 16), (23, 7), (15, 10), (22, 11), (25, 10), (12, 14), (18, 6), (10, 12), (11, 10), (23, 5), (23, 22), (23, 14), (10, 18), (13, 11), (5, 18), (13, 9), (19, 1), (8, 18), (11, 13), (22, 7), (8, 3), (18, 19), (10, 5), (9, 3), (9, 5), (24, 1), (17, 12), (2, 12), (3, 16), (8, 1), (5, 9), (1, 2), (19, 21), (12, 23), (2, 6), (24, 14), (8, 23), (20, 5), (22, 22), (9, 9), (18, 10), (22, 17), (8, 9), (0, 20), (25, 1), (15, 12), (0, 5), (23, 20), (3, 18), (26, 8), (14, 14), (15, 7), (20, 8), (6, 1), (8, 13), (18, 4), (19, 20), (5, 22), (26, 11), (25, 7), (5, 0), (1, 21), (15, 9), (7, 4), (19, 9), (14, 17), (15, 5), (12, 10), (11, 17), (10, 3), (15, 1), (10, 17), (26, 4), (2, 0), (17, 4), (12, 7), (6, 5), (20, 18), (20, 1), (25, 16), (10, 15), (7, 18), (14, 3), (10, 8), (23, 10), (22, 3), (20, 2), (3, 13), (16, 2), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764829", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 17), (8, 7), (12, 12), (6, 0), (20, 26), (12, 11), (17, 11), (21, 12), (2, 14), (8, 8), (19, 17), (0, 21), (15, 12), (1, 8), (9, 17), (19, 2), (24, 12), (24, 8), (10, 2), (10, 19), (22, 2), (16, 9), (3, 1), (16, 14), (3, 13), (21, 19), (4, 24), (10, 21), (5, 3), (22, 15), (8, 25), (23, 12), (22, 5), (8, 13), (24, 20), (11, 13), (7, 1), (11, 2), (21, 24), (2, 26), (22, 13), (24, 5), (18, 15), (4, 7), (19, 5), (0, 25), (24, 18), (1, 21), (16, 4), (16, 16), (18, 10), (17, 9), (22, 10), (3, 5), (12, 13), (11, 4), (24, 7), (14, 17), (3, 7), (13, 1), (0, 24), (4, 18), (12, 4), (2, 20), (17, 18), (14, 13), (7, 23), (8, 2), (5, 22), (0, 26), (10, 7), (7, 2), (4, 15), (21, 2), (18, 9), (7, 22), (18, 3), (17, 6), (21, 1), (18, 13), (23, 22), (19, 22), (9, 19), (14, 8), (12, 18), (7, 19), (6, 1), (10, 16), (14, 24), (5, 8), (11, 9), (8, 0), (17, 5), (10, 24), (18, 11), (1, 4), (12, 17), (2, 13), (11, 1), (8, 3), (12, 15), (21, 5), (21, 8), (8, 20), (11, 20), (19, 15), (2, 12), (11, 15), (13, 0), (17, 16), (13, 5), (20, 22), (1, 15), (10, 6), (0, 7), (24, 21), (22, 12), (17, 14), (6, 15), (17, 21), (24, 19), (15, 6), (23, 4), (12, 14), (16, 0), (2, 11), (15, 15), (7, 13), (5, 23), (18, 5), (13, 24), (3, 23), (8, 17), (2, 4), (0, 12), (3, 11), (2, 1), (23, 26), (5, 10), (18, 8), (1, 19), (6, 20), (10, 4), (20, 21), (8, 4), (2, 21), (14, 20), (22, 16), (16, 11), (5, 18), (12, 20), (11, 3), (4, 23), (13, 6), (24, 10), (21, 9), (20, 1), (8, 12), (5, 14), (5, 20), (23, 19), (11, 8), (0, 17), (8, 5), (4, 11), (20, 16), (22, 24), (17, 25), (4, 5), (2, 23), (1, 5), (2, 3), (5, 7), (9, 2), (4, 12), (6, 2), (9, 16), (7, 20), (8, 6), (15, 4), (12, 7), (13, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19314", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), 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, 21), (18, 19), (10, 15), (21, 1), (9, 0), (21, 14), (12, 14), (0, 7), (3, 0), (18, 15), (20, 13), (20, 8), (21, 0), (17, 2), (16, 4), (0, 22), (18, 7), (10, 9), (19, 3), (18, 12), (16, 6), (15, 21), (14, 20), (6, 15), (6, 3), (7, 22), (9, 6), (21, 16), (12, 6), (10, 1), (2, 19), (12, 16), (15, 4), (2, 14), (2, 16), (4, 9), (16, 8), (14, 19), (4, 8), (18, 21), (5, 12), (3, 18), (11, 21), (11, 22), (12, 21), (20, 4), (14, 14), (9, 3), (17, 7), (17, 0), (15, 11), (14, 11), (2, 5), (7, 2), (7, 5), (0, 2), (12, 4), (18, 22), (12, 5), (16, 0), (6, 6), (10, 11), (17, 8), (10, 8), (16, 14), (2, 7), (9, 20), (12, 12), (19, 15), (21, 2), (4, 11), (19, 20), (21, 3), (11, 13), (11, 3), (11, 9), (5, 3), (6, 18), (21, 15), (21, 9), (14, 16), (9, 1), (19, 9), (20, 0), (8, 15), (14, 8), (1, 17), (9, 2), (12, 20), (4, 13), (11, 15), (17, 1), (13, 17), (16, 18), (8, 20), (15, 7), (13, 18), (11, 14), (17, 22), (7, 20), (20, 7), (20, 2), (11, 2), (4, 16), (11, 8), (19, 17), (9, 5), (16, 15), (9, 19), (7, 10), (19, 14), (12, 22), (10, 18), (2, 1), (5, 0), (0, 14), (21, 5), (6, 4), (2, 10), (13, 3), (4, 21), (10, 12), (4, 2), (6, 0), (14, 7), (0, 18), (7, 3), (2, 12), (12, 18), (15, 13), (8, 7), (5, 22), (16, 16), (20, 15), (19, 11), (4, 19), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "403200", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), 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), (17, 18), (10, 0), (3, 17), (15, 2), (7, 14), (6, 14), (19, 17), (18, 15), (16, 13), (12, 6), (14, 13), (14, 5), (11, 6), (11, 9), (4, 6), (3, 4), (2, 3), (5, 10), (18, 17), (8, 3), (9, 2), (17, 14), (7, 9), (14, 10), (10, 3), (5, 15), (20, 9), (2, 1), (9, 3), (9, 0), (9, 12), (6, 16), (16, 5), (12, 12), (19, 14), (3, 18), (16, 16), (16, 10), (0, 10), (3, 14), (2, 6), (5, 12), (0, 14), (0, 16), (15, 4), (10, 17), (5, 3), (7, 6), (15, 16), (13, 3), (5, 14), (1, 5), (3, 7), (8, 18), (6, 11), (14, 17), (11, 15), (15, 1), (3, 15), (8, 9), (18, 5), (16, 14), (13, 10), (2, 17), (1, 12), (14, 18), (14, 19), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872673", "dataset": "MATH"}
{"messages": [{"content": "In a 21x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 18), (7, 12), (12, 21), (6, 25), (15, 13), (8, 9), (0, 20), (16, 13), (7, 22), (15, 21), (8, 3), (20, 21), (16, 4), (18, 21), (5, 14), (9, 4), (16, 19), (4, 21), (16, 22), (18, 26), (14, 13), (11, 15), (2, 22), (8, 20), (13, 12), (15, 28), (8, 18), (12, 9), (15, 22), (1, 0), (11, 6), (4, 14), (8, 6), (7, 1), (16, 0), (9, 1), (14, 15), (8, 22), (15, 9), (4, 28), (17, 2), (3, 22), (13, 1), (9, 22), (17, 28), (10, 8), (8, 27), (0, 15), (0, 7), (4, 17), (14, 7), (4, 27), (3, 21), (10, 0), (2, 18), (14, 25), (19, 8), (7, 8), (6, 10), (4, 18), (13, 16), (8, 11), (17, 23), (17, 22), (6, 9), (19, 24), (18, 16), (10, 20), (4, 7), (18, 2), (10, 9), (11, 17), (19, 27), (14, 4), (0, 24), (0, 9), (9, 8), (2, 14), (9, 28), (14, 18), (13, 18), (10, 5), (9, 15), (5, 6), (12, 28), (14, 24), (13, 25), (9, 21), (4, 10), (1, 28), (1, 2), (18, 7), (3, 23), (14, 0), (7, 20), (20, 2), (11, 8), (16, 5), (16, 27), (20, 4), (7, 24), (18, 17), (18, 8), (4, 2), (18, 22), (10, 17), (15, 2), (3, 26), (4, 26), (17, 3), (5, 15), (6, 13), (7, 4), (4, 1), (5, 28), (2, 5), (16, 6), (18, 11), (10, 24), (2, 2), (9, 0), (0, 14), (19, 15), (7, 17), (12, 17), (14, 16), (17, 17), (11, 2), (16, 16), (2, 16), (11, 18), (20, 17), (4, 23), (5, 9), (5, 8), (16, 2), (1, 10), (5, 20), (0, 17), (11, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39240", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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, 18), (12, 8), (6, 12), (17, 0), (2, 13), (11, 2), (6, 6), (18, 11), (17, 15), (8, 6), (18, 9), (7, 16), (13, 4), (5, 18), (1, 1), (0, 17), (3, 7), (10, 14), (8, 20), (18, 18), (6, 11), (4, 3), (7, 20), (13, 11), (1, 9), (7, 12), (16, 6), (4, 9), (14, 9), (14, 7), (9, 18), (14, 17), (6, 18), (15, 20), (2, 0), (4, 5), (7, 3), (7, 9), (2, 1), (6, 5), (17, 10), (0, 8), (3, 0), (14, 20), (13, 2), (13, 1), (5, 11), (5, 7), (11, 10), (10, 10), (5, 6), (9, 10), (17, 8), (10, 18), (14, 12), (10, 20), (11, 1), (1, 4), (15, 4), (7, 2), (1, 14), (15, 14), (3, 17), (15, 6), (2, 9), (16, 9), (17, 14), (5, 1), (8, 14), (6, 17), (6, 14), (19, 12), (12, 17), (1, 20), (17, 5), (9, 9), (13, 5), (1, 16), (11, 5), (6, 4), (16, 2), (0, 14), (8, 2), (15, 1), (5, 12), (19, 9), (3, 9), (8, 5), (19, 10), (4, 4), (12, 16), (16, 5), (18, 17), (3, 5), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165042", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 16), (13, 26), (18, 7), (16, 17), (20, 6), (11, 14), (15, 25), (7, 6), (1, 25), (0, 15), (3, 3), (11, 16), (1, 21), (16, 15), (7, 21), (18, 26), (10, 16), (5, 19), (17, 6), (0, 13), (6, 13), (7, 3), (18, 8), (17, 17), (8, 19), (8, 26), (9, 24), (7, 12), (6, 17), (13, 8), (19, 7), (0, 18), (12, 10), (21, 15), (13, 21), (19, 12), (1, 12), (9, 21), (15, 20), (12, 11), (19, 8), (6, 23), (17, 19), (4, 17), (16, 25), (7, 7), (17, 18), (15, 3), (14, 22), (13, 5), (19, 24), (3, 12), (21, 9), (16, 0), (16, 4), (7, 9), (4, 14), (16, 5), (17, 14), (5, 2), (15, 15), (11, 2), (0, 25), (3, 21), (13, 14), (20, 12), (1, 1), (15, 21), (13, 15), (4, 3), (18, 20), (0, 6), (7, 24), (12, 25), (13, 7), (14, 14), (7, 11), (21, 0), (10, 12), (7, 10), (19, 3), (12, 19), (21, 17), (4, 21), (17, 23), (15, 4), (6, 14), (20, 15), (1, 15), (6, 4), (2, 24), (17, 7), (12, 12), (12, 24), (9, 6), (1, 19), (9, 12), (8, 25), (4, 5), (5, 13), (17, 1), (6, 7), (18, 25), (15, 0), (0, 14), (14, 9), (4, 9), (18, 15), (14, 11), (10, 21), (16, 18), (16, 7), (10, 11), (1, 4), (3, 24), (19, 22), (19, 6), (8, 23), (7, 13), (6, 24), (12, 26), (7, 2), (17, 16), (1, 18), (20, 3), (9, 9), (14, 23), (20, 22), (10, 5), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902528", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 20), (13, 12), (19, 5), (7, 16), (3, 21), (6, 24), (6, 10), (4, 1), (1, 21), (8, 16), (4, 0), (16, 13), (9, 3), (0, 10), (3, 20), (13, 16), (13, 23), (6, 7), (3, 3), (4, 16), (12, 8), (9, 14), (13, 3), (3, 14), (13, 2), (0, 23), (17, 14), (15, 19), (1, 22), (11, 18), (18, 7), (4, 10), (15, 17), (5, 19), (12, 16), (19, 18), (16, 3), (6, 3), (12, 4), (15, 25), (1, 23), (6, 2), (15, 6), (11, 8), (5, 21), (0, 6), (5, 18), (19, 3), (11, 23), (17, 15), (8, 10), (12, 17), (19, 6), (2, 23), (10, 14), (7, 4), (3, 6), (13, 10), (10, 6), (13, 5), (6, 6), (11, 16), (7, 8), (7, 23), (8, 25), (19, 13), (8, 0), (5, 10), (5, 23), (3, 12), (7, 17), (9, 1), (16, 4), (10, 24), (14, 25), (17, 10), (19, 17), (16, 14), (19, 12), (0, 13), (9, 10), (10, 15), (2, 11), (12, 15), (17, 20), (16, 2), (15, 2), (13, 14), (11, 24), (19, 22), (0, 25), (19, 14), (16, 23), (11, 21), (16, 8), (18, 10), (11, 10), (14, 22), (10, 25), (5, 3), (15, 12), (17, 25), (6, 19), (15, 4), (6, 14), (3, 24), (3, 4), (15, 21), (0, 7), (10, 10), (14, 7), (9, 9), (17, 2), (9, 15), (1, 0), (8, 8), (14, 10), (13, 20), (12, 10), (2, 24), (9, 19), (14, 5), (17, 11), (15, 18), (12, 2), (19, 11), (12, 22), (9, 2), (14, 12), (17, 24), (1, 13), (8, 1), (11, 14), (7, 0), (0, 3), (17, 6), (6, 20), (9, 11), (12, 0), (12, 7), (12, 23), (12, 12), (6, 1), (0, 21), (0, 4), (16, 12), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "693660", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), 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), (19, 23), (11, 27), (17, 16), (6, 24), (21, 6), (4, 6), (14, 15), (15, 22), (14, 2), (26, 3), (1, 17), (18, 4), (26, 1), (26, 11), (11, 5), (5, 19), (14, 13), (13, 10), (27, 25), (16, 13), (7, 28), (2, 23), (23, 21), (3, 15), (16, 25), (11, 19), (4, 12), (8, 2), (10, 2), (4, 22), (24, 25), (19, 0), (12, 0), (18, 3), (16, 14), (5, 11), (12, 8), (3, 9), (18, 6), (24, 23), (19, 19), (20, 27), (20, 5), (22, 28), (20, 9), (18, 19), (13, 15), (27, 4), (8, 27), (14, 24), (15, 5), (7, 3), (12, 21), (1, 13), (26, 21), (5, 16), (9, 26), (19, 4), (7, 11), (26, 24), (13, 21), (18, 10), (23, 20), (26, 22), (23, 8), (20, 23), (17, 21), (27, 8), (15, 2), (24, 5), (14, 0), (11, 20), (25, 21), (7, 1), (9, 0), (14, 22), (13, 1), (7, 5), (13, 26), (24, 21), (4, 16), (7, 15), (24, 3), (18, 9), (19, 20), (26, 14), (21, 24), (21, 10), (6, 6), (21, 5), (22, 15), (8, 3), (1, 2), (13, 23), (27, 5), (3, 13), (7, 0), (8, 22), (11, 9), (15, 16), (16, 21), (15, 27), (11, 28), (18, 17), (15, 25), (21, 2), (9, 3), (22, 26), (14, 10), (7, 13), (3, 4), (22, 4), (3, 1), (22, 18), (9, 16), (5, 18), (27, 23), (6, 4), (19, 9), (23, 14), (10, 13), (6, 11), (6, 14), (8, 13), (3, 27), (8, 15), (25, 4), (13, 7), (4, 19), (9, 10), (5, 0), (15, 9), (27, 6), (10, 19), (3, 18), (1, 16), (19, 14), (21, 8), (14, 25), (12, 24), (27, 0), (8, 24), (21, 11), (11, 12), (9, 25), (18, 23), (11, 0), (5, 2), (23, 13), (11, 14), (0, 27), (4, 24), (8, 0), (12, 6), (12, 14), (14, 5), (14, 17), (14, 9), (22, 27), (2, 20), (17, 0), (8, 6), (22, 14), (21, 12), (19, 25), (17, 9), (12, 25), (10, 8), (9, 8), (7, 19), (13, 13), (25, 28), (10, 11), (18, 26), (25, 0), (11, 8), (7, 9), (1, 27), (17, 26), (26, 25), (10, 5), (11, 4), (7, 25), (20, 13), (4, 25), (5, 25), (11, 6), (2, 12), (21, 22), (5, 20), (22, 17), (2, 4), (21, 27), (19, 24), (0, 14), (13, 17), (15, 26), (24, 17), (4, 2), (16, 6), (17, 25), (7, 6), (23, 18), (7, 16), (20, 24), (10, 16), (5, 6), (26, 16), (22, 11), (3, 11), (1, 10), (18, 25), (3, 12), (15, 28), (26, 9), (19, 10), (15, 24), (0, 18), (0, 9), (0, 12), (24, 20), (9, 6), (19, 15), (9, 4), (24, 9), (26, 19), (20, 4), (17, 13), (13, 25), (2, 17), (21, 19), (12, 22), (8, 4), (17, 23), (15, 13), (8, 28), (25, 5), (26, 27), (21, 4), (2, 28), (12, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743424", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 22), (18, 0), (9, 14), (7, 6), (20, 21), (4, 14), (4, 7), (25, 7), (2, 11), (20, 2), (8, 1), (26, 19), (21, 9), (11, 14), (21, 24), (18, 25), (24, 1), (22, 9), (14, 5), (12, 22), (25, 22), (21, 16), (10, 24), (11, 11), (7, 26), (15, 8), (20, 23), (4, 26), (16, 21), (17, 12), (20, 7), (6, 11), (6, 15), (12, 8), (11, 9), (11, 17), (20, 16), (14, 4), (17, 23), (22, 4), (13, 2), (14, 24), (17, 10), (21, 26), (19, 21), (19, 0), (4, 2), (2, 21), (12, 27), (3, 24), (1, 20), (20, 3), (4, 8), (12, 18), (11, 3), (13, 1), (26, 24), (18, 7), (2, 0), (6, 12), (15, 4), (22, 12), (22, 26), (2, 26), (14, 12), (2, 22), (9, 9), (0, 22), (2, 3), (13, 27), (6, 17), (7, 9), (2, 24), (12, 21), (17, 17), (21, 7), (10, 23), (17, 8), (20, 15), (11, 13), (23, 9), (12, 5), (2, 6), (5, 14), (24, 23), (5, 15), (8, 19), (24, 8), (5, 6), (1, 0), (11, 0), (18, 15), (22, 18), (9, 6), (4, 10), (0, 25), (5, 8), (0, 27), (9, 11), (21, 27), (7, 17), (23, 8), (24, 21), (3, 9), (1, 23), (25, 21), (10, 20), (20, 24), (18, 16), (17, 2), (5, 7), (18, 6), (15, 12), (22, 25), (4, 3), (20, 6), (8, 27), (2, 16), (19, 11), (9, 7), (11, 23), (1, 10), (2, 23), (2, 7), (14, 3), (3, 1), (25, 1), (6, 26), (23, 27), (11, 5), (4, 22), (14, 7), (5, 16), (24, 7), (24, 5), (22, 6), (11, 22), (10, 8), (22, 27), (23, 21), (21, 2), (18, 3), (17, 7), (23, 18), (9, 5), (13, 22), (15, 27), (15, 19), (24, 24), (2, 2), (10, 15), (9, 2), (3, 22), (7, 1), (15, 23), (24, 2), (16, 24), (14, 23), (23, 14), (4, 6), (5, 1), (12, 20), (6, 23), (22, 17), (13, 5), (11, 20), (19, 25), (0, 13), (24, 20), (21, 13), (13, 15), (3, 2), (15, 13), (12, 16), (15, 22), (26, 11), (15, 3), (21, 1), (13, 25), (17, 3), (5, 17), (14, 18), (7, 19), (9, 18), (8, 0), (23, 22), (5, 2), (1, 19), (14, 9), (3, 20), (26, 1), (15, 14), (24, 22), (19, 4), (24, 25), (5, 26), (22, 1), (26, 13), (19, 22), (20, 22), (14, 1), (22, 20), (24, 16), (6, 13), (12, 10), (16, 8), (6, 14), (15, 9), (8, 10), (0, 6), (25, 19), (26, 7), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "646236", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 19), (17, 0), (17, 25), (18, 20), (6, 7), (4, 4), (15, 5), (20, 1), (12, 10), (10, 26), (21, 10), (2, 12), (20, 10), (12, 19), (7, 1), (9, 17), (19, 21), (11, 15), (2, 10), (2, 11), (19, 1), (19, 24), (21, 21), (5, 7), (8, 6), (4, 13), (21, 15), (3, 8), (21, 24), (21, 1), (15, 8), (18, 10), (4, 3), (8, 12), (18, 26), (12, 6), (6, 21), (20, 13), (11, 18), (9, 11), (17, 8), (21, 2), (6, 2), (0, 3), (2, 2), (11, 1), (0, 7), (15, 20), (8, 20), (10, 14), (0, 2), (10, 24), (14, 7), (18, 13), (5, 19), (10, 6), (9, 18), (7, 15), (9, 12), (6, 15), (17, 20), (0, 16), (13, 16), (18, 11), (14, 16), (7, 27), (11, 3), (7, 11), (0, 14), (6, 11), (0, 17), (9, 27), (0, 5), (0, 18), (15, 12), (11, 10), (15, 25), (17, 23), (18, 5), (9, 5), (12, 12), (10, 16), (16, 23), (1, 16), (19, 15), (6, 27), (10, 18), (13, 0), (5, 9), (21, 26), (6, 26), (21, 12), (20, 2), (1, 23), (4, 22), (16, 20), (20, 14), (14, 25), (6, 16), (19, 10), (0, 22), (1, 3), (19, 13), (1, 27), (16, 26), (11, 20), (14, 17), (20, 17), (8, 5), (15, 0), (14, 20), (7, 6), (11, 16), (9, 22), (19, 0), (17, 5), (18, 14), (9, 14), (1, 8), (10, 9), (5, 21), (18, 9), (1, 13), (13, 14), (14, 24), (11, 27), (10, 8), (8, 23), (2, 16), (19, 8), (2, 3), (15, 2), (17, 22), (0, 27), (11, 0), (1, 26), (3, 15), (9, 0), (5, 2), (8, 26), (13, 1), (2, 13), (11, 7), (5, 20), (13, 2), (7, 10), (17, 4), (4, 20), (7, 3), (16, 2), (6, 20), (12, 3), (2, 21), (0, 11), (14, 0), (15, 24), (9, 24), (10, 23), (0, 1), (13, 12), (7, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994310", "dataset": "MATH"}
{"messages": [{"content": "In a 26x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 19), (21, 15), (7, 1), (19, 18), (17, 20), (23, 17), (12, 16), (18, 12), (1, 2), (2, 13), (5, 11), (18, 22), (8, 15), (10, 3), (6, 7), (9, 12), (6, 23), (13, 20), (10, 13), (14, 11), (20, 0), (9, 19), (16, 13), (3, 15), (11, 8), (24, 1), (16, 0), (2, 19), (17, 8), (6, 20), (4, 5), (3, 16), (20, 12), (5, 2), (23, 23), (0, 22), (21, 21), (5, 17), (2, 15), (9, 2), (5, 21), (1, 21), (18, 21), (11, 13), (16, 1), (22, 8), (15, 14), (15, 16), (6, 22), (10, 18), (2, 2), (11, 0), (9, 9), (2, 21), (14, 13), (21, 7), (15, 8), (25, 5), (19, 2), (24, 10), (1, 8), (22, 14), (21, 4), (20, 14), (15, 1), (15, 20), (24, 9), (0, 7), (3, 3), (6, 4), (15, 5), (18, 3), (20, 1), (5, 20), (22, 15), (17, 18), (9, 4), (1, 19), (2, 20), (21, 19), (12, 12), (3, 23), (2, 10), (2, 0), (20, 17), (18, 10), (25, 22), (5, 23), (4, 12), (16, 21), (1, 7), (12, 1), (17, 13), (23, 0), (11, 7), (7, 5), (12, 7), (10, 22), (13, 0), (10, 21), (21, 9), (3, 20), (18, 0), (20, 16), (17, 1), (10, 15), (25, 20), (15, 9), (17, 23), (19, 6), (25, 3), (2, 12), (11, 17), (19, 5), (12, 3), (6, 9), (24, 17), (24, 2), (17, 22), (14, 10), (22, 2), (2, 9), (21, 13), (24, 12), (18, 1), (6, 19), (8, 8), (4, 0), (1, 18), (9, 6), (4, 16), (25, 2), (19, 3), (2, 3), (1, 6), (25, 18), (0, 20), (7, 23), (0, 3), (15, 10), (7, 3), (25, 16), (9, 7), (16, 3), (13, 23), (2, 18), (0, 4), (11, 9), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18400", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 16), (3, 5), (5, 3), (7, 9), (1, 8), (0, 11), (19, 9), (3, 1), (3, 17), (0, 12), (21, 13), (13, 6), (20, 5), (19, 6), (13, 15), (10, 10), (20, 0), (21, 9), (20, 15), (14, 6), (11, 3), (18, 10), (12, 7), (15, 5), (9, 6), (2, 6), (2, 13), (21, 5), (6, 19), (16, 0), (5, 8), (18, 20), (4, 2), (0, 4), (8, 16), (10, 9), (11, 9), (11, 14), (19, 7), (19, 3), (10, 11), (15, 19), (1, 17), (14, 0), (12, 9), (2, 18), (6, 2), (9, 3), (14, 7), (11, 10), (7, 8), (0, 6), (12, 2), (14, 10), (8, 14), (0, 17), (2, 2), (5, 11), (19, 19), (7, 13), (20, 9), (8, 18), (6, 15), (1, 13), (20, 3), (14, 14), (9, 17), (10, 6), (2, 16), (10, 17), (11, 18), (9, 10), (20, 2), (6, 10), (19, 8), (20, 8), (4, 3), (5, 15), (11, 13), (6, 9), (21, 4), (8, 4), (21, 8), (17, 20), (10, 15), (13, 4), (18, 12), (1, 11), (16, 10), (17, 18), (12, 13), (14, 18), (13, 13), (6, 12), (13, 8), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770064", "dataset": "MATH"}
{"messages": [{"content": "In a 26x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 17), (5, 19), (9, 3), (11, 22), (17, 11), (22, 1), (7, 3), (6, 19), (8, 10), (15, 15), (1, 18), (25, 17), (14, 21), (12, 20), (1, 12), (5, 12), (14, 10), (10, 5), (24, 3), (9, 14), (21, 25), (0, 15), (4, 5), (12, 11), (6, 12), (8, 5), (18, 16), (17, 18), (13, 22), (13, 13), (4, 16), (21, 0), (25, 9), (3, 1), (0, 24), (3, 12), (19, 10), (16, 5), (8, 17), (14, 11), (6, 24), (23, 7), (0, 6), (8, 12), (15, 14), (10, 15), (2, 3), (9, 24), (7, 24), (7, 18), (0, 13), (18, 3), (8, 14), (2, 6), (13, 18), (22, 5), (3, 5), (10, 3), (23, 9), (22, 15), (24, 19), (9, 13), (2, 10), (22, 14), (9, 5), (14, 25), (15, 24), (21, 14), (20, 7), (24, 7), (6, 25), (11, 13), (9, 12), (5, 23), (23, 2), (21, 16), (15, 3), (11, 3), (17, 10), (22, 9), (3, 21), (10, 0), (6, 7), (19, 13), (7, 25), (13, 7), (1, 15), (21, 22), (24, 10), (11, 4), (21, 11), (21, 21), (16, 14), (23, 14), (23, 5), (25, 1), (2, 5), (13, 4), (13, 25), (2, 1), (8, 7), (13, 1), (2, 2), (14, 0), (15, 8), (19, 23), (22, 4), (15, 13), (11, 14), (8, 22), (5, 4), (19, 1), (20, 14), (14, 12), (16, 20), (20, 17), (11, 18), (25, 4), (2, 22), (14, 5), (7, 16), (21, 15), (4, 3), (20, 6), (17, 20), (24, 4), (2, 0), (24, 5), (5, 21), (24, 24), (24, 9), (5, 17), (7, 17), (19, 9), (14, 18), (8, 25), (6, 4), (5, 14), (13, 0), (10, 11), (5, 3), (20, 23), (24, 23), (16, 6), (0, 1), (20, 3), (14, 24), (2, 16), (18, 21), (10, 12), (16, 18), (9, 18), (12, 4), (23, 6), (21, 9), (22, 23), (23, 24), (13, 20), (5, 15), (10, 10), (25, 11), (4, 14), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451778", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 18), (4, 8), (8, 1), (5, 14), (14, 17), (7, 19), (19, 19), (7, 10), (16, 10), (6, 14), (22, 15), (16, 11), (3, 16), (2, 17), (6, 3), (11, 9), (7, 2), (2, 19), (11, 15), (1, 0), (14, 12), (12, 19), (8, 15), (0, 19), (13, 10), (4, 1), (3, 8), (14, 3), (2, 11), (9, 3), (22, 17), (2, 4), (10, 12), (21, 6), (7, 13), (6, 18), (10, 13), (3, 6), (22, 11), (4, 20), (1, 9), (10, 5), (5, 6), (22, 9), (15, 7), (12, 1), (11, 6), (14, 16), (5, 13), (11, 1), (8, 6), (22, 16), (3, 7), (13, 4), (3, 14), (16, 14), (4, 3), (3, 18), (17, 12), (13, 6), (12, 6), (16, 2), (20, 9), (17, 14), (7, 15), (10, 20), (13, 19), (2, 15), (7, 12), (16, 1), (18, 8), (8, 2), (0, 14), (13, 9), (22, 5), (21, 20), (19, 8), (18, 2), (6, 19), (12, 2), (14, 6), (9, 11), (13, 7), (9, 12), (18, 3), (20, 7), (13, 13), (2, 10), (9, 17), (22, 3), (8, 7), (12, 13), (15, 6), (0, 12), (0, 13), (10, 19), (8, 4), (11, 8), (13, 20), (4, 10), (3, 19), (17, 10), (4, 19), (1, 13), (14, 15), (5, 8), (12, 7), (14, 1), (21, 1), (3, 2), (16, 7), (3, 11), (5, 9), (7, 14), (21, 8), (1, 7), (6, 4), (11, 16), (15, 10), (8, 19), (5, 3), (17, 17), (18, 17), (5, 2), (0, 18), (0, 4), (10, 0), (6, 12), (13, 8), (21, 14), (10, 11), (13, 17), (0, 11), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177255", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 7), (23, 8), (10, 8), (7, 4), (6, 4), (17, 2), (9, 1), (17, 0), (5, 11), (25, 0), (19, 19), (10, 12), (4, 19), (18, 6), (6, 8), (1, 5), (14, 0), (10, 19), (20, 8), (21, 11), (8, 8), (2, 2), (26, 13), (12, 15), (27, 13), (25, 7), (6, 20), (17, 3), (13, 0), (22, 3), (7, 6), (4, 7), (19, 17), (15, 5), (23, 9), (16, 15), (22, 21), (22, 19), (18, 19), (12, 18), (7, 20), (22, 14), (24, 9), (16, 6), (11, 0), (0, 3), (14, 11), (13, 7), (3, 17), (0, 6), (18, 0), (21, 3), (0, 12), (8, 2), (6, 13), (20, 13), (3, 19), (19, 12), (4, 12), (2, 12), (0, 18), (20, 17), (24, 2), (24, 18), (7, 3), (23, 17), (26, 14), (25, 11), (1, 13), (10, 17), (27, 17), (15, 18), (21, 13), (15, 17), (19, 21), (18, 12), (8, 7), (13, 10), (18, 16), (7, 16), (10, 21), (3, 4), (3, 12), (2, 15), (13, 6), (22, 6), (5, 21), (23, 14), (5, 13), (9, 11), (15, 6), (20, 7), (12, 14), (21, 14), (10, 14), (15, 4), (3, 9), (11, 19), (8, 0), (8, 5), (3, 10), (21, 5), (23, 12), (15, 15), (8, 18), (23, 2), (7, 14), (4, 20), (11, 12), (6, 0), (16, 13), (11, 17), (22, 10), (4, 2), (19, 13), (27, 10), (24, 0), (2, 7), (10, 0), (3, 2), (16, 3), (21, 21), (25, 10), (21, 16), (27, 7), (27, 20), (16, 21), (25, 4), (5, 0), (20, 20), (24, 4), (17, 15), (0, 16), (19, 3), (3, 15), (6, 5), (2, 9), (3, 7), (1, 2), (27, 6), (0, 5), (12, 21), (9, 4), (4, 8), (21, 0), (21, 7), (17, 9), (12, 6), (19, 10), (20, 5), (8, 17), (17, 21), (2, 14), (24, 14), (12, 16), (23, 11), (22, 20), (16, 18), (25, 14), (21, 4), (26, 3), (18, 21), (14, 10), (16, 9), (2, 19), (3, 18), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963075", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (6, 12), (4, 9), (17, 8), (19, 6), (9, 10), (0, 3), (1, 10), (6, 13), (16, 13), (9, 0), (13, 8), (8, 18), (13, 2), (9, 1), (17, 20), (19, 11), (14, 4), (0, 12), (13, 17), (1, 9), (11, 17), (6, 20), (7, 19), (3, 6), (2, 14), (3, 9), (1, 7), (6, 10), (10, 3), (12, 11), (6, 19), (17, 3), (2, 19), (8, 12), (10, 12), (8, 6), (5, 5), (10, 4), (8, 20), (9, 4), (4, 1), (5, 9), (1, 15), (3, 16), (8, 2), (2, 15), (17, 4), (14, 9), (4, 8), (9, 17), (10, 6), (2, 6), (14, 7), (17, 19), (12, 10), (9, 16), (11, 8), (1, 5), (14, 13), (7, 13), (16, 12), (4, 2), (15, 17), (14, 16), (3, 13), (0, 13), (16, 7), (2, 5), (12, 4), (13, 14), (17, 11), (0, 5), (19, 7), (4, 10), (15, 7), (19, 12), (1, 0), (11, 7), (8, 3), (19, 13), (9, 18), (11, 6), (4, 11), (3, 20), (7, 7), (9, 9), (7, 1), (15, 8), (2, 0), (12, 20), (14, 20), (6, 0), (1, 3), (18, 20), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622380", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 23), (28, 18), (9, 7), (22, 17), (0, 21), (12, 10), (11, 13), (26, 20), (20, 8), (11, 5), (1, 23), (6, 17), (8, 24), (28, 10), (22, 18), (24, 15), (27, 23), (2, 8), (13, 21), (25, 15), (28, 3), (13, 11), (9, 14), (15, 2), (2, 24), (19, 4), (25, 6), (19, 24), (25, 8), (1, 4), (9, 3), (13, 5), (8, 13), (4, 0), (6, 10), (27, 17), (3, 18), (2, 3), (8, 23), (19, 8), (11, 19), (18, 24), (21, 24), (22, 16), (28, 8), (17, 3), (6, 24), (21, 6), (24, 2), (28, 9), (18, 3), (7, 16), (22, 13), (0, 9), (4, 6), (7, 13), (5, 22), (13, 1), (17, 1), (4, 8), (20, 10), (25, 11), (10, 15), (26, 10), (8, 8), (4, 17), (15, 17), (6, 22), (27, 25), (16, 21), (26, 25), (26, 14), (13, 13), (0, 3), (27, 11), (28, 19), (17, 6), (25, 2), (16, 7), (20, 11), (9, 16), (5, 9), (20, 24), (27, 3), (21, 4), (21, 10), (2, 14), (2, 22), (24, 3), (20, 4), (6, 2), (13, 25), (7, 11), (3, 3), (5, 7), (11, 14), (0, 10), (2, 10), (8, 20), (14, 24), (21, 16), (16, 3), (20, 0), (20, 22), (10, 17), (28, 6), (15, 13), (1, 25), (22, 22), (10, 9), (22, 6), (17, 5), (24, 1), (19, 19), (25, 3), (13, 10), (9, 15), (24, 12), (22, 10), (1, 18), (24, 23), (15, 12), (11, 18), (22, 1), (26, 19), (25, 12), (5, 1), (16, 4), (14, 6), (14, 25), (27, 5), (27, 21), (16, 9), (14, 21), (0, 18), (7, 17), (1, 8), (7, 24), (6, 18), (11, 21), (3, 20), (23, 7), (23, 2), (11, 25), (8, 5), (10, 22), (28, 5), (8, 4), (9, 2), (28, 15), (12, 6), (24, 6), (12, 24), (20, 16), (3, 9), (26, 2), (6, 4), (9, 17), (13, 4), (19, 7), (22, 14), (15, 11), (8, 19), (11, 17), (22, 2), (21, 3), (10, 20), (3, 0), (26, 17), (15, 10), (12, 19), (14, 16), (25, 19), (3, 7), (6, 9), (19, 12), (17, 0), (27, 16), (20, 19), (18, 12), (18, 15), (23, 25), (19, 2), (2, 7), (12, 20), (24, 7), (18, 18), (28, 2), (3, 5), (22, 19), (10, 18), (7, 10), (6, 25), (25, 16), (28, 7), (26, 3), (11, 8), (24, 25), (4, 10), (26, 12), (22, 20), (18, 0), (2, 20), (28, 16), (2, 23), (19, 23), (7, 4), (5, 19), (13, 16), (12, 23), (9, 18), (1, 9), (28, 0), (14, 7), (11, 9), (27, 15), (4, 9), (0, 24), (14, 4), (21, 14), (20, 20), (11, 6), (13, 20), (6, 12), (16, 10), (10, 16), (15, 22), (6, 5), (2, 18), (6, 15), (25, 5), (26, 24), (2, 5), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279168", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 22), (12, 4), (0, 4), (14, 5), (19, 0), (8, 22), (8, 1), (26, 15), (4, 2), (11, 19), (8, 3), (23, 9), (17, 6), (26, 4), (26, 23), (16, 0), (17, 3), (24, 3), (23, 2), (19, 22), (20, 18), (14, 15), (26, 16), (10, 25), (2, 22), (8, 26), (10, 13), (3, 12), (3, 16), (12, 13), (20, 12), (25, 25), (15, 18), (12, 0), (19, 15), (16, 19), (6, 27), (21, 3), (19, 17), (6, 18), (17, 16), (23, 3), (20, 7), (1, 15), (16, 23), (11, 22), (16, 9), (9, 24), (7, 18), (16, 2), (5, 6), (9, 17), (20, 24), (4, 14), (3, 17), (0, 20), (11, 14), (5, 1), (12, 3), (24, 12), (19, 8), (13, 22), (22, 21), (10, 6), (6, 13), (11, 12), (26, 0), (10, 24), (26, 3), (8, 21), (3, 5), (17, 1), (9, 25), (4, 10), (19, 4), (17, 14), (14, 27), (20, 25), (14, 13), (0, 6), (10, 22), (19, 6), (3, 9), (2, 25), (24, 18), (10, 27), (1, 21), (25, 7), (23, 16), (8, 2), (22, 24), (9, 19), (13, 9), (3, 18), (6, 1), (21, 26), (24, 0), (2, 4), (4, 9), (9, 1), (3, 1), (1, 5), (25, 15), (15, 1), (13, 4), (4, 24), (18, 0), (10, 15), (2, 5), (20, 6), (4, 8), (24, 7), (3, 25), (18, 6), (24, 8), (3, 15), (12, 18), (13, 14), (4, 16), (7, 26), (21, 23), (5, 17), (15, 12), (22, 26), (23, 8), (4, 21), (26, 13), (7, 0), (12, 24), (2, 21), (3, 24), (2, 14), (19, 2), (3, 8), (13, 7), (5, 0), (10, 0), (17, 11), (1, 22), (10, 10), (8, 16), (24, 1), (22, 13), (9, 7), (17, 27), (14, 4), (19, 19), (7, 23), (10, 8), (23, 25), (5, 27), (5, 13), (8, 19), (8, 20), (3, 11), (21, 8), (17, 13), (18, 22), (19, 26), (2, 20), (19, 20), (3, 2), (18, 11), (7, 9), (6, 0), (13, 15), (6, 17), (24, 6), (23, 10), (4, 15), (25, 13), (21, 22), (2, 0), (13, 11), (9, 0), (23, 17), (24, 17), (26, 7), (11, 5), (15, 9), (24, 5), (6, 26), (17, 5), (1, 2), (6, 2), (2, 6), (23, 1), (24, 24), (22, 5), (15, 16), (10, 17), (2, 26), (13, 16), (9, 27), (6, 24), (11, 4), (23, 15), (20, 23), (5, 8), (19, 25), (15, 25), (21, 27), (11, 11), (18, 18), (1, 14), (23, 27), (23, 12), (2, 11), (10, 23), (13, 12), (18, 27), (18, 21), (19, 16), (7, 5), (8, 0), (10, 3), (18, 20), (20, 10), (16, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "653640", "dataset": "MATH"}
{"messages": [{"content": "In a 21x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 26), 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, 4), (13, 16), (7, 0), (1, 15), (7, 5), (8, 17), (7, 15), (16, 14), (18, 5), (3, 8), (12, 21), (20, 2), (20, 19), (15, 20), (13, 6), (15, 19), (14, 16), (1, 20), (8, 10), (18, 1), (6, 6), (18, 3), (13, 12), (17, 20), (4, 2), (8, 22), (18, 14), (9, 14), (1, 4), (4, 15), (16, 26), (10, 24), (15, 24), (9, 19), (9, 2), (16, 0), (18, 22), (14, 22), (14, 12), (11, 8), (10, 5), (17, 22), (15, 5), (16, 24), (11, 24), (5, 0), (20, 25), (11, 4), (10, 26), (1, 8), (17, 3), (14, 8), (11, 25), (6, 21), (4, 4), (15, 22), (9, 13), (2, 26), (15, 2), (9, 11), (13, 4), (20, 11), (11, 21), (19, 6), (11, 20), (12, 18), (4, 13), (5, 16), (15, 23), (3, 26), (19, 24), (3, 7), (3, 2), (8, 2), (9, 23), (8, 19), (16, 18), (1, 13), (9, 12), (6, 7), (1, 18), (18, 7), (13, 17), (11, 13), (3, 15), (12, 0), (2, 20), (16, 22), (8, 5), (5, 13), (13, 24), (13, 7), (14, 7), (8, 6), (5, 3), (20, 20), (15, 26), (17, 24), (1, 26), (12, 8), (8, 21), (14, 24), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609768", "dataset": "MATH"}
{"messages": [{"content": "In a 21x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 23), (20, 11), (14, 22), (4, 2), (10, 18), (19, 8), (19, 20), (0, 2), (14, 27), (11, 24), (16, 2), (1, 18), (8, 28), (16, 24), (8, 8), (9, 9), (18, 18), (10, 3), (5, 11), (5, 4), (10, 8), (9, 19), (14, 15), (0, 18), (8, 5), (0, 25), (12, 22), (17, 24), (5, 5), (11, 25), (19, 11), (13, 6), (12, 5), (20, 23), (13, 11), (1, 5), (10, 21), (19, 6), (16, 25), (12, 12), (12, 0), (12, 8), (3, 5), (16, 13), (16, 19), (6, 13), (11, 5), (6, 21), (19, 5), (15, 24), (13, 16), (16, 23), (6, 7), (10, 7), (8, 27), (2, 22), (0, 7), (18, 19), (6, 16), (6, 9), (18, 26), (6, 6), (13, 27), (18, 10), (8, 3), (20, 4), (7, 10), (14, 28), (16, 18), (6, 12), (2, 11), (1, 11), (18, 6), (6, 25), (2, 14), (2, 4), (0, 15), (16, 11), (11, 6), (19, 13), (0, 9), (20, 8), (2, 17), (10, 12), (13, 1), (14, 9), (17, 1), (18, 11), (0, 10), (0, 27), (14, 25), (5, 8), (13, 3), (7, 16), (7, 19), (16, 7), (14, 17), (8, 1), (7, 5), (3, 17), (18, 5), (14, 18), (7, 8), (3, 10), (18, 24), (3, 3), (9, 5), (3, 11), (15, 25), (17, 23), (1, 26), (0, 22), (18, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "421950", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 7), (8, 1), (5, 11), (22, 3), (16, 5), (2, 0), (7, 4), (10, 3), (21, 19), (0, 8), (16, 17), (4, 14), (22, 7), (17, 15), (25, 16), (13, 10), (14, 17), (1, 18), (25, 19), (25, 17), (7, 12), (2, 21), (4, 16), (17, 4), (26, 7), (19, 14), (8, 18), (14, 4), (16, 2), (14, 8), (8, 3), (17, 20), (12, 17), (3, 18), (26, 11), (26, 1), (12, 22), (2, 8), (18, 1), (20, 7), (23, 22), (2, 1), (12, 18), (1, 4), (16, 18), (3, 0), (11, 2), (0, 9), (23, 17), (20, 12), (3, 11), (9, 9), (22, 13), (10, 1), (23, 19), (16, 20), (22, 9), (10, 0), (14, 12), (18, 12), (22, 17), (11, 12), (17, 0), (24, 14), (21, 10), (26, 20), (14, 15), (12, 21), (2, 6), (19, 15), (0, 13), (18, 13), (5, 10), (1, 17), (17, 11), (2, 10), (25, 21), (12, 10), (15, 5), (22, 16), (0, 16), (6, 22), (23, 14), (18, 4), (1, 0), (6, 15), (6, 13), (2, 14), (11, 13), (11, 5), (19, 17), (21, 12), (18, 15), (6, 9), (5, 18), (23, 10), (11, 17), (7, 17), (9, 20), (22, 0), (26, 2), (8, 4), (16, 0), (13, 5), (13, 8), (19, 5), (5, 4), (5, 21), (15, 22), (18, 10), (20, 22), (4, 20), (9, 16), (13, 20), (15, 4), (2, 9), (15, 8), (20, 6), (10, 2), (12, 5), (26, 16), (26, 13), (18, 18), (2, 2), (7, 5), (18, 17), (17, 13), (24, 4), (26, 9), (20, 18), (14, 5), (0, 18), (6, 6), (10, 7), (10, 12), (18, 3), (3, 5), (7, 15), (17, 16), (8, 8), (4, 21), (23, 11), (5, 1), (1, 16), (16, 10), (12, 14), (21, 16), (10, 13), (11, 22), (8, 16), (14, 6), (10, 16), (8, 6), (11, 10), (19, 6), (1, 10), (4, 2), (19, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601380", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 11), (2, 3), (2, 26), (13, 25), (4, 24), (3, 21), (0, 17), (4, 26), (13, 8), (13, 26), (9, 24), (19, 15), (16, 7), (1, 12), (10, 15), (5, 27), (19, 5), (9, 18), (17, 1), (12, 6), (15, 25), (6, 5), (2, 23), (13, 14), (14, 6), (4, 7), (2, 15), (3, 20), (8, 13), (10, 4), (16, 27), (7, 19), (6, 24), (1, 0), (13, 9), (16, 20), (6, 21), (13, 23), (5, 16), (11, 13), (16, 24), (2, 19), (16, 18), (4, 8), (15, 27), (17, 2), (6, 0), (9, 20), (7, 11), (4, 16), (9, 13), (19, 9), (6, 22), (18, 6), (17, 26), (8, 1), (9, 14), (10, 6), (19, 3), (15, 6), (11, 14), (4, 25), (7, 26), (9, 7), (19, 23), (5, 11), (6, 20), (16, 10), (10, 22), (1, 6), (1, 2), (18, 0), (5, 12), (5, 3), (12, 9), (17, 19), (11, 26), (0, 16), (10, 2), (4, 2), (4, 27), (15, 22), (14, 5), (9, 19), (14, 15), (10, 26), (0, 20), (9, 9), (5, 6), (14, 13), (5, 10), (3, 9), (11, 1), (14, 12), (5, 22), (0, 7), (4, 19), (9, 4), (8, 10), (17, 22), (0, 5), (17, 27), (4, 0), (18, 20), (12, 11), (5, 15), (14, 20), (5, 18), (1, 13), (9, 26), (0, 4), (1, 8), (14, 24), (17, 13), (0, 14), (3, 25), (13, 12), (9, 2), (15, 24), (4, 9), (0, 26), (6, 2), (6, 3), (4, 6), (3, 24), (15, 2), (2, 14), (16, 25), (5, 5), (16, 4), (11, 3), (4, 1), (17, 10), (7, 10), (11, 21), (9, 21), (13, 24), (18, 3), (12, 7), (13, 21), (14, 25), (0, 24), (1, 21), (19, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "756146", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 20), (19, 16), (5, 16), (18, 10), (21, 18), (20, 16), (13, 8), (15, 21), (6, 13), (11, 17), (0, 1), (6, 19), (21, 0), (19, 1), (6, 8), (16, 19), (5, 18), (17, 6), (3, 18), (5, 7), (9, 15), (15, 2), (8, 20), (20, 0), (20, 3), (20, 11), (3, 3), (14, 14), (11, 12), (19, 8), (5, 22), (17, 23), (11, 7), (3, 10), (3, 8), (5, 15), (0, 21), (17, 18), (4, 11), (4, 18), (2, 17), (13, 12), (7, 17), (2, 10), (5, 8), (14, 6), (0, 10), (20, 2), (18, 3), (2, 19), (20, 12), (9, 12), (2, 13), (2, 15), (2, 22), (6, 11), (7, 0), (16, 20), (8, 16), (19, 9), (3, 0), (14, 19), (5, 10), (6, 1), (14, 23), (20, 10), (20, 21), (15, 3), (6, 2), (21, 21), (0, 11), (13, 18), (7, 13), (17, 11), (8, 8), (10, 22), (8, 2), (16, 4), (6, 3), (7, 1), (20, 20), (20, 4), (13, 0), (13, 15), (9, 6), (4, 15), (9, 5), (8, 22), (21, 10), (14, 0), (16, 7), (5, 0), (12, 0), (15, 9), (6, 7), (14, 9), (21, 8), (21, 19), (17, 7), (3, 6), (16, 6), (3, 5), (2, 11), (4, 7), (17, 15), (3, 7), (5, 17), (7, 19), (2, 23), (7, 18), (19, 22), (15, 10), (8, 1), (14, 21), (7, 23), (4, 20), (8, 0), (15, 5), (21, 14), (8, 14), (19, 13), (4, 10), (13, 10), (1, 15), (19, 4), (17, 19), (9, 4), (15, 6), (5, 1), (14, 5), (16, 23), (0, 12), (10, 1), (19, 21), (7, 22), (20, 15), (9, 0), (8, 5), (0, 5), (15, 22), (10, 4), (0, 23), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48879", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), 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), (15, 0), (6, 17), (17, 16), (1, 14), (20, 14), (9, 7), (10, 18), (27, 1), (26, 19), (0, 1), (8, 8), (16, 1), (12, 18), (13, 17), (5, 6), (23, 4), (14, 5), (19, 20), (8, 5), (25, 15), (16, 3), (7, 11), (28, 11), (10, 7), (27, 3), (20, 3), (13, 7), (13, 6), (3, 19), (25, 17), (2, 20), (25, 16), (19, 6), (0, 12), (16, 15), (3, 10), (8, 10), (7, 10), (11, 3), (22, 6), (22, 8), (13, 4), (3, 15), (14, 9), (3, 13), (27, 8), (24, 12), (18, 16), (16, 12), (24, 8), (24, 20), (13, 12), (19, 4), (6, 10), (8, 0), (1, 1), (19, 16), (6, 16), (12, 14), (25, 19), (21, 7), (17, 0), (9, 14), (19, 10), (0, 10), (12, 15), (2, 9), (8, 15), (11, 6), (16, 18), (14, 1), (2, 1), (28, 14), (19, 11), (22, 2), (23, 16), (24, 15), (20, 6), (20, 0), (8, 6), (25, 2), (27, 2), (17, 12), (2, 13), (5, 1), (22, 11), (15, 16), (11, 7), (13, 16), (0, 16), (26, 20), (23, 19), (28, 9), (0, 18), (19, 7), (22, 17), (11, 12), (25, 4), (24, 11), (12, 17), (5, 14), (26, 2), (1, 17), (23, 6), (13, 19), (26, 0), (6, 4), (10, 5), (5, 12), (18, 0), (21, 11), (8, 9), (8, 2), (24, 9), (24, 14), (8, 16), (20, 13), (20, 20), (25, 13), (1, 13), (6, 5), (8, 3), (14, 14), (23, 15), (4, 10), (1, 15), (28, 8), (16, 0), (12, 6), (13, 15), (6, 11), (11, 14), (3, 12), (23, 20), (13, 1), (20, 16), (25, 11), (15, 12), (0, 13), (12, 12), (26, 5), (23, 1), (11, 15), (24, 17), (18, 11), (7, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956544", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 12), (12, 10), (1, 19), (10, 18), (11, 1), (1, 17), (12, 7), (7, 11), (2, 5), (16, 3), (19, 3), (3, 16), (2, 24), (19, 19), (2, 12), (1, 5), (0, 10), (10, 13), (9, 0), (3, 13), (11, 17), (8, 5), (1, 6), (13, 21), (4, 15), (19, 4), (7, 10), (19, 7), (2, 7), (18, 16), (15, 2), (2, 13), (18, 13), (15, 10), (18, 21), (17, 2), (12, 17), (0, 19), (6, 10), (15, 1), (14, 14), (3, 18), (0, 8), (11, 3), (2, 19), (6, 23), (9, 1), (12, 5), (9, 19), (13, 13), (10, 23), (17, 7), (16, 23), (18, 12), (11, 22), (17, 18), (17, 16), (1, 12), (4, 20), (12, 12), (0, 12), (1, 8), (13, 6), (4, 6), (10, 12), (15, 6), (13, 17), (14, 18), (13, 15), (17, 23), (2, 21), (18, 1), (5, 4), (13, 7), (3, 15), (0, 21), (14, 11), (11, 18), (13, 12), (5, 21), (11, 9), (5, 15), (16, 17), (6, 4), (14, 20), (7, 20), (7, 21), (5, 1), (0, 14), (9, 7), (10, 21), (18, 24), (18, 4), (8, 16), (19, 15), (15, 13), (19, 9), (10, 4), (17, 11), (10, 11), (8, 10), (5, 17), (9, 24), (11, 14), (17, 14), (5, 18), (12, 14), (0, 4), (16, 2), (1, 13), (0, 20), (15, 9), (17, 17), (14, 12), (1, 22), (6, 9), (2, 3), (9, 22), (17, 1), (2, 15), (0, 11), (5, 12), (15, 19), (5, 14), (1, 16), (0, 23), (14, 2), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987630", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), 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), (0, 3), (3, 3), (2, 2), (14, 3), (11, 12), (3, 8), (16, 3), (21, 7), (9, 7), (21, 19), (12, 3), (3, 11), (6, 20), (12, 15), (3, 9), (8, 7), (13, 5), (9, 10), (1, 4), (4, 15), (1, 19), (11, 18), (12, 10), (17, 1), (11, 11), (7, 10), (21, 21), (7, 9), (8, 10), (7, 11), (13, 18), (18, 22), (16, 17), (11, 8), (2, 5), (8, 17), (5, 13), (3, 13), (18, 8), (13, 8), (11, 5), (19, 21), (16, 18), (13, 20), (11, 6), (18, 4), (4, 18), (6, 22), (11, 2), (0, 18), (4, 1), (21, 5), (4, 12), (21, 15), (18, 17), (4, 2), (20, 4), (0, 5), (0, 8), (4, 5), (1, 6), (21, 4), (17, 0), (3, 1), (9, 4), (20, 12), (10, 15), (17, 9), (3, 7), (7, 0), (2, 10), (8, 6), (15, 22), (15, 17), (10, 16), (2, 0), (1, 15), (20, 8), (3, 21), (20, 15), (18, 12), (15, 9), (12, 6), (12, 17), (4, 11), (11, 17), (4, 20), (14, 7), (5, 22), (9, 5), (6, 10), (4, 8), (10, 22), (16, 10), (6, 8), (18, 0), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "546396", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), 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), (5, 13), (6, 8), (7, 8), (3, 23), (24, 13), (2, 9), (1, 11), (2, 3), (11, 9), (7, 12), (4, 16), (17, 2), (12, 9), (12, 15), (23, 18), (25, 13), (2, 6), (13, 0), (7, 6), (9, 20), (2, 7), (26, 16), (9, 3), (9, 11), (2, 4), (19, 19), (19, 6), (13, 15), (22, 20), (19, 14), (22, 13), (1, 14), (6, 14), (23, 17), (4, 3), (25, 21), (11, 2), (22, 9), (8, 6), (15, 4), (23, 23), (24, 3), (20, 13), (11, 12), (6, 6), (1, 19), (21, 17), (16, 4), (17, 17), (28, 21), (8, 9), (17, 5), (7, 3), (6, 11), (11, 20), (28, 20), (1, 1), (10, 6), (20, 2), (12, 7), (11, 22), (9, 6), (9, 2), (13, 9), (28, 16), (2, 22), (3, 5), (3, 3), (20, 12), (6, 7), (17, 7), (16, 21), (26, 8), (9, 10), (19, 12), (11, 19), (26, 5), (21, 9), (13, 21), (21, 18), (12, 4), (10, 16), (13, 18), (28, 19), (3, 21), (21, 14), (2, 19), (6, 5), (2, 1), (22, 14), (17, 23), (26, 6), (7, 11), (24, 21), (18, 18), (23, 13), (12, 21), (27, 21), (3, 13), (7, 23), (17, 14), (21, 5), (8, 4), (0, 20), (21, 3), (25, 18), (3, 17), (13, 8), (22, 23), (22, 21), (2, 15), (15, 6), (9, 19), (14, 9), (26, 7), (18, 19), (11, 14), (16, 22), (22, 4), (12, 2), (24, 22), (17, 21), (28, 14), (5, 21), (18, 22), (20, 6), (2, 16), (4, 21), (16, 0), (25, 5), (19, 18), (9, 23), (13, 1), (8, 22), (21, 4), (19, 22), (16, 8), (19, 4), (15, 23), (21, 12), (5, 3), (3, 9), (25, 23), (8, 1), (10, 8), (8, 7), (12, 13), (18, 17), (19, 9), (27, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755098", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 2), (13, 17), (18, 12), (15, 4), (13, 2), (9, 0), (6, 10), (11, 18), (13, 20), (25, 10), (9, 10), (12, 19), (25, 2), (23, 11), (1, 12), (21, 9), (11, 8), (0, 13), (14, 16), (20, 18), (10, 2), (17, 19), (19, 7), (3, 8), (2, 18), (0, 11), (14, 2), (19, 1), (21, 1), (13, 10), (16, 16), (23, 9), (9, 4), (0, 9), (10, 15), (10, 19), (22, 16), (19, 11), (5, 19), (7, 12), (8, 12), (11, 17), (18, 15), (1, 3), (0, 2), (9, 11), (6, 3), (0, 6), (20, 4), (21, 14), (13, 5), (17, 16), (24, 12), (7, 10), (20, 19), (16, 1), (2, 13), (5, 1), (18, 16), (25, 18), (21, 2), (3, 16), (24, 4), (21, 17), (6, 14), (4, 12), (9, 18), (5, 13), (25, 5), (3, 6), (7, 0), (9, 8), (1, 13), (16, 20), (12, 17), (14, 11), (3, 5), (12, 14), (16, 12), (24, 6), (17, 9), (5, 7), (24, 3), (9, 5), (1, 1), (6, 2), (16, 17), (8, 3), (1, 19), (19, 13), (5, 18), (17, 12), (10, 20), (13, 7), (10, 13), (18, 8), (23, 5), (3, 13), (9, 9), (8, 7), (19, 19), (16, 15), (9, 19), (11, 13), (11, 10), (9, 12), (12, 15), (1, 6), (17, 15), (10, 8), (2, 17), (11, 3), (8, 15), (14, 15), (23, 6), (22, 15), (25, 6), (11, 5), (12, 9), (2, 9), (14, 18), (25, 1), (15, 13), (10, 9), (18, 19), (12, 4), (6, 7), (9, 17), (3, 12), (22, 2), (8, 16), (1, 15), (9, 2), (4, 1), (9, 14), (16, 9), (25, 8), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892246", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 21), (11, 16), (3, 15), (9, 6), (6, 26), (3, 25), (21, 14), (0, 10), (16, 24), (14, 23), (22, 4), (24, 25), (8, 26), (13, 7), (24, 12), (10, 6), (24, 5), (11, 24), (12, 12), (14, 25), (10, 4), (10, 5), (20, 26), (2, 11), (11, 2), (14, 1), (11, 0), (12, 18), (19, 25), (8, 3), (5, 23), (11, 19), (5, 10), (7, 3), (13, 5), (10, 7), (19, 15), (5, 21), (1, 4), (22, 17), (20, 9), (18, 16), (24, 22), (16, 3), (0, 18), (4, 5), (12, 14), (11, 15), (17, 16), (17, 3), (24, 20), (2, 5), (6, 3), (19, 10), (17, 10), (19, 13), (25, 5), (3, 0), (22, 8), (9, 18), (18, 21), (14, 5), (20, 15), (13, 26), (2, 8), (5, 7), (13, 9), (5, 18), (7, 18), (14, 15), (14, 20), (3, 9), (25, 25), (7, 2), (23, 3), (17, 0), (18, 6), (16, 15), (16, 11), (3, 14), (8, 12), (16, 9), (14, 9), (15, 22), (5, 19), (6, 18), (22, 3), (19, 5), (10, 0), (13, 20), (19, 2), (5, 26), (4, 0), (5, 17), (18, 12), (24, 23), (11, 25), (9, 19), (16, 14), (20, 5), (8, 1), (8, 18), (1, 10), (6, 12), (7, 22), (0, 13), (17, 2), (23, 21), (19, 16), (13, 3), (0, 14), (18, 24), (22, 12), (8, 13), (14, 18), (0, 21), (18, 3), (17, 14), (15, 7), (25, 11), (11, 8), (15, 12), (22, 9), (8, 5), (1, 14), (2, 1), (15, 24), (25, 10), (3, 1), (16, 2), (12, 9), (4, 1), (2, 12), (14, 21), (22, 24), (7, 5), (21, 7), (8, 24), (16, 18), (23, 22), (24, 4), (2, 23), (19, 24), (24, 11), (19, 0), (13, 8), (24, 9), (9, 15), (13, 2), (6, 13), (8, 17), (16, 1), (24, 7), (10, 17), (21, 24), (1, 12), (22, 7), (7, 21), (22, 18), (6, 2), (6, 20), (0, 24), (12, 8), (9, 23), (17, 7), (14, 16), (1, 16), (21, 15), (18, 11), (1, 22), (8, 14), (6, 15), (10, 2), (17, 1), (23, 12), (15, 4), (22, 25), (14, 26), (12, 3), (10, 20), (24, 0), (9, 26), (5, 9), (25, 16), (5, 6), (23, 23), (9, 21), (0, 8), (13, 19), (3, 6), (8, 7), (22, 14), (21, 20), (0, 20), (19, 3), (23, 24), (10, 15), (23, 4), (6, 1), (9, 4), (20, 4), (20, 19), (2, 4), (24, 1), (2, 18), (17, 13), (4, 18), (8, 0), (18, 7), (5, 20), (16, 16), (23, 18), (9, 11), (18, 22), (0, 16), (14, 0), (25, 1), (7, 20), (6, 23), (15, 3), (23, 1), (0, 12), (25, 17), (10, 21), (7, 13), (22, 16), (19, 23), (17, 6), (15, 26), (2, 26), (20, 2), (15, 5), (2, 14), (18, 20), (7, 11), (13, 15), (7, 1), (4, 22), (23, 20), (9, 16), (20, 10), (15, 2), (24, 6), (9, 12), (4, 14), (12, 5), (18, 5), (17, 21), (4, 9), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159600", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), 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), (3, 12), (6, 8), (12, 7), (15, 19), (1, 14), (17, 1), (11, 9), (3, 5), (9, 10), (0, 9), (4, 9), (12, 18), (2, 9), (7, 9), (15, 3), (13, 1), (3, 19), (5, 16), (8, 1), (8, 4), (2, 7), (9, 9), (18, 17), (7, 17), (12, 3), (8, 8), (5, 3), (5, 1), (1, 12), (18, 18), (16, 12), (5, 17), (9, 12), (15, 17), (13, 9), (0, 5), (19, 7), (18, 15), (11, 11), (3, 14), (17, 3), (6, 3), (2, 15), (13, 8), (0, 15), (7, 13), (18, 14), (10, 1), (4, 12), (0, 12), (9, 13), (11, 3), (3, 2), (16, 4), (15, 0), (11, 5), (17, 5), (9, 4), (14, 10), (15, 5), (1, 1), (1, 4), (13, 3), (1, 7), (13, 18), (18, 1), (6, 12), (12, 19), (4, 18), (19, 6), (14, 17), (17, 11), (3, 1), (11, 17), (2, 14), (0, 2), (15, 8), (9, 6), (14, 9), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "809230", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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, 4), (6, 13), (1, 7), (6, 12), (19, 1), (17, 6), (1, 19), (8, 4), (8, 16), (11, 8), (5, 9), (6, 14), (1, 18), (17, 14), (18, 22), (0, 22), (2, 11), (11, 19), (9, 20), (16, 13), (19, 14), (11, 2), (18, 11), (7, 15), (13, 1), (10, 20), (16, 21), (18, 19), (17, 21), (14, 0), (19, 5), (2, 8), (10, 7), (11, 14), (14, 2), (10, 8), (10, 13), (0, 3), (16, 14), (5, 5), (2, 13), (4, 10), (8, 9), (10, 4), (7, 20), (9, 22), (19, 0), (19, 4), (1, 0), (4, 1), (18, 14), (6, 10), (1, 11), (7, 8), (2, 15), (5, 18), (19, 3), (3, 19), (5, 1), (13, 14), (17, 19), (8, 8), (1, 4), (12, 7), (4, 13), (16, 9), (3, 21), (17, 11), (10, 12), (17, 17), (8, 20), (2, 3), (4, 9), (12, 20), (5, 22), (12, 21), (11, 20), (16, 19), (13, 5), (7, 21), (4, 3), (15, 17), (19, 8), (12, 1), (4, 14), (18, 15), (15, 16), (12, 12), (15, 0), (3, 11), (13, 11), (1, 13), (11, 10), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345324", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 14), (9, 22), (11, 0), (25, 7), (16, 14), (6, 21), (15, 14), (18, 3), (3, 12), (10, 20), (18, 13), (12, 7), (4, 12), (24, 19), (10, 15), (6, 4), (21, 1), (12, 6), (6, 15), (18, 19), (14, 0), (0, 22), (15, 21), (7, 10), (13, 11), (7, 9), (4, 14), (25, 11), (17, 0), (3, 15), (19, 20), (16, 11), (15, 2), (7, 16), (4, 17), (1, 17), (2, 2), (24, 22), (24, 13), (10, 22), (6, 10), (10, 1), (8, 13), (13, 9), (16, 16), (10, 12), (8, 19), (2, 22), (3, 4), (7, 8), (14, 2), (24, 10), (14, 18), (22, 16), (18, 11), (0, 10), (3, 16), (14, 21), (13, 2), (7, 11), (23, 2), (3, 1), (0, 11), (21, 9), (5, 21), (24, 9), (14, 12), (5, 3), (1, 19), (9, 1), (13, 1), (11, 20), (17, 1), (9, 15), (24, 0), (19, 19), (9, 10), (1, 11), (20, 11), (13, 15), (22, 15), (14, 1), (18, 8), (11, 9), (9, 20), (6, 16), (18, 2), (1, 7), (20, 9), (14, 5), (14, 8), (1, 12), (13, 18), (19, 3), (16, 13), (18, 10), (4, 22), (5, 22), (23, 12), (3, 13), (2, 3), (3, 22), (5, 19), (2, 5), (8, 4), (22, 1), (19, 11), (21, 14), (1, 9), (23, 19), (10, 17), (5, 6), (0, 17), (11, 22), (0, 3), (6, 3), (14, 19), (5, 4), (11, 10), (5, 0), (6, 13), (23, 5), (13, 6), (24, 20), (25, 1), (0, 4), (17, 15), (7, 13), (24, 21), (8, 10), (1, 5), (0, 19), (12, 0), (8, 6), (3, 8), (21, 3), (15, 4), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998017", "dataset": "MATH"}
{"messages": [{"content": "In a 27x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 10), (7, 17), (2, 2), (14, 8), (19, 0), (17, 1), (3, 12), (7, 0), (14, 4), (3, 19), (4, 12), (7, 10), (26, 2), (14, 9), (2, 1), (24, 14), (16, 0), (11, 10), (8, 15), (23, 18), (5, 17), (25, 7), (5, 18), (17, 8), (19, 1), (3, 6), (21, 0), (11, 12), (7, 16), (12, 10), (13, 14), (22, 19), (3, 15), (14, 12), (19, 2), (4, 9), (25, 5), (18, 16), (15, 1), (20, 4), (4, 11), (13, 1), (16, 1), (23, 14), (17, 7), (4, 2), (4, 6), (13, 18), (10, 3), (6, 0), (17, 17), (6, 10), (6, 17), (6, 2), (22, 9), (17, 5), (2, 3), (13, 0), (26, 5), (21, 8), (1, 4), (11, 17), (4, 17), (13, 17), (19, 11), (18, 9), (13, 6), (20, 11), (9, 5), (0, 9), (1, 7), (9, 15), (17, 2), (7, 13), (10, 9), (9, 18), (8, 7), (22, 4), (26, 17), (9, 7), (10, 10), (11, 15), (17, 18), (10, 13), (0, 4), (15, 13), (17, 13), (0, 11), (17, 3), (25, 13), (20, 9), (19, 7), (2, 13), (19, 12), (8, 0), (5, 5), (26, 4), (2, 11), (10, 8), (0, 16), (7, 3), (5, 4), (11, 0), (7, 15), (4, 5), (12, 15), (25, 16), (16, 11), (20, 17), (12, 16), (11, 2), (26, 1), (9, 6), (15, 18), (18, 5), (10, 7), (2, 19), (13, 11), (9, 8), (3, 4), (13, 8), (1, 10), (16, 13), (18, 11), (26, 12), (3, 10), (13, 3), (15, 5), (20, 8), (24, 16), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223965", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 17), (20, 6), (3, 12), (7, 18), (13, 22), (6, 21), (20, 12), (4, 18), (10, 6), (18, 21), (1, 7), (10, 13), (17, 4), (22, 7), (15, 0), (22, 17), (2, 5), (1, 10), (1, 0), (15, 1), (9, 12), (8, 17), (16, 14), (21, 9), (3, 20), (2, 17), (16, 16), (12, 21), (19, 2), (18, 23), (2, 21), (2, 10), (15, 19), (10, 14), (9, 10), (7, 7), (17, 22), (22, 21), (16, 22), (9, 11), (21, 19), (9, 9), (13, 9), (15, 13), (6, 5), (18, 20), (1, 8), (4, 1), (10, 23), (17, 18), (1, 1), (13, 1), (12, 11), (19, 19), (19, 9), (15, 8), (17, 1), (14, 22), (14, 14), (17, 20), (11, 5), (17, 14), (7, 17), (15, 12), (17, 15), (9, 13), (16, 3), (1, 24), (10, 5), (11, 16), (0, 16), (20, 4), (5, 15), (10, 15), (10, 8), (9, 6), (17, 11), (8, 0), (22, 10), (19, 18), (12, 19), (19, 11), (11, 15), (12, 23), (13, 5), (10, 22), (17, 8), (13, 8), (17, 12), (2, 12), (8, 20), (12, 13), (12, 16), (0, 14), (7, 15), (14, 24), (3, 0), (15, 22), (8, 6), (13, 17), (7, 5), (3, 21), (18, 6), (0, 22), (13, 24), (21, 18), (13, 15), (19, 1), (0, 7), (21, 24), (13, 0), (7, 21), (16, 6), (5, 7), (19, 20), (22, 3), (9, 20), (15, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994350", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 14), (6, 16), (21, 8), (7, 11), (14, 18), (10, 0), (19, 19), (11, 19), (8, 21), (7, 13), (21, 9), (4, 10), (1, 17), (8, 2), (15, 10), (18, 13), (21, 19), (6, 2), (15, 3), (14, 11), (17, 2), (3, 0), (6, 8), (8, 14), (10, 7), (7, 3), (12, 2), (8, 5), (2, 1), (12, 3), (19, 7), (10, 15), (17, 6), (2, 17), (2, 5), (20, 11), (10, 8), (3, 11), (14, 21), (11, 10), (2, 2), (4, 14), (13, 17), (6, 12), (4, 7), (11, 17), (8, 20), (3, 17), (1, 21), (19, 1), (11, 8), (3, 21), (15, 14), (8, 19), (13, 1), (11, 1), (15, 5), (2, 8), (3, 6), (15, 4), (15, 22), (10, 2), (8, 6), (2, 16), (11, 18), (8, 15), (8, 12), (20, 17), (12, 9), (17, 5), (2, 3), (18, 0), (5, 12), (9, 16), (6, 19), (4, 11), (18, 14), (9, 17), (16, 1), (8, 1), (9, 6), (18, 22), (6, 0), (0, 4), (7, 9), (7, 6), (19, 12), (8, 4), (9, 10), (13, 12), (7, 0), (17, 19), (4, 1), (0, 13), (5, 8), (3, 15), (20, 22), (17, 10), (1, 20), (1, 10), (7, 21), (7, 15), (14, 2), (0, 22), (2, 7), (5, 21), (2, 14), (11, 5), (4, 3), (19, 15), (10, 1), (14, 20), (2, 10), (13, 6), (18, 6), (3, 10), (15, 17), (19, 20), (18, 7), (18, 19), (5, 20), (11, 6), (9, 9), (2, 11), (21, 6), (20, 0), (19, 4), (11, 2), (17, 9), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "702000", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 21), (2, 4), (3, 3), (21, 5), (9, 1), (6, 12), (3, 22), (10, 20), (10, 0), (14, 10), (8, 3), (17, 3), (23, 6), (20, 13), (21, 9), (12, 5), (19, 16), (17, 25), (0, 6), (24, 1), (20, 18), (14, 23), (22, 0), (18, 5), (15, 16), (22, 16), (28, 15), (16, 13), (26, 22), (9, 18), (22, 5), (22, 13), (17, 4), (11, 8), (15, 6), (8, 18), (9, 25), (18, 7), (20, 24), (20, 22), (6, 22), (18, 16), (28, 21), (19, 7), (1, 1), (0, 22), (27, 13), (1, 22), (10, 5), (5, 1), (23, 2), (6, 21), (11, 23), (19, 5), (24, 5), (1, 7), (25, 13), (18, 12), (11, 0), (4, 3), (10, 12), (3, 15), (13, 14), (4, 7), (25, 16), (16, 20), (24, 16), (15, 11), (11, 18), (28, 2), (12, 9), (9, 6), (16, 16), (1, 11), (28, 4), (17, 16), (22, 7), (23, 24), (27, 11), (18, 9), (3, 16), (14, 21), (7, 13), (19, 20), (19, 9), (17, 0), (23, 21), (18, 2), (28, 12), (16, 14), (13, 7), (28, 13), (25, 21), (16, 11), (18, 21), (23, 12), (26, 11), (14, 15), (9, 0), (24, 14), (27, 3), (23, 7), (8, 12), (2, 20), (13, 11), (6, 17), (3, 8), (4, 4), (27, 21), (15, 3), (4, 25), (5, 5), (13, 16), (18, 1), (25, 7), (18, 6), (18, 4), (27, 10), (9, 3), (7, 12), (4, 18), (4, 16), (25, 0), (3, 0), (0, 11), (17, 24), (7, 24), (2, 16), (5, 23), (17, 8), (13, 12), (6, 9), (18, 17), (4, 11), (26, 5), (21, 25), (17, 1), (4, 1), (13, 21), (23, 15), (9, 9), (14, 12), (24, 19), (16, 4), (24, 10), (28, 1), (24, 8), (21, 18), (5, 18), (11, 12), (15, 5), (10, 17), (6, 18), (21, 4), (11, 6), (28, 0), (2, 11), (5, 13), (14, 1), (16, 1), (6, 14), (1, 9), (25, 8), (23, 20), (12, 4), (3, 17), (28, 20), (25, 15), (22, 12), (14, 16), (7, 6), (9, 14), (22, 6), (24, 7), (4, 20), (17, 18), (28, 3), (27, 20), (0, 16), (2, 18), (24, 18), (9, 2), (19, 4), (7, 5), (7, 21), (10, 23), (17, 23), (4, 12), (15, 2), (0, 24), (16, 7), (14, 2), (9, 12), (10, 11), (22, 10), (3, 12), (26, 19), (17, 20), (1, 4), (18, 14), (12, 1), (16, 12), (10, 1), (12, 0), (16, 18), (13, 1), (5, 20), (26, 17), (23, 1), (19, 22), (4, 14), (6, 16), (11, 9), (16, 22), (13, 24), (26, 1), (7, 10), (27, 16), (12, 25), (4, 13), (6, 25), (17, 14), (1, 10), (10, 25), (28, 23), (21, 23), (21, 3), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800800", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (14, 1), (3, 19), (12, 20), (14, 25), (12, 11), (20, 25), (20, 7), (6, 9), (2, 28), (15, 12), (0, 22), (18, 7), (5, 5), (23, 4), (13, 15), (5, 10), (20, 20), (17, 13), (22, 16), (4, 14), (12, 24), (8, 19), (15, 9), (0, 6), (1, 10), (14, 20), (13, 8), (10, 3), (5, 8), (18, 26), (11, 8), (2, 14), (12, 26), (18, 13), (16, 0), (18, 2), (0, 10), (4, 5), (19, 6), (9, 13), (1, 24), (14, 23), (1, 18), (5, 21), (9, 6), (7, 6), (6, 2), (16, 13), (19, 14), (18, 11), (10, 28), (15, 24), (3, 15), (19, 22), (21, 23), (14, 4), (7, 19), (23, 7), (19, 11), (23, 2), (21, 15), (1, 19), (20, 0), (1, 0), (1, 25), (21, 20), (15, 10), (21, 25), (23, 11), (17, 17), (0, 19), (14, 22), (5, 25), (12, 16), (10, 26), (6, 18), (0, 17), (6, 0), (15, 17), (4, 24), (22, 25), (9, 12), (17, 1), (18, 28), (23, 0), (11, 3), (13, 18), (13, 20), (8, 7), (4, 26), (3, 5), (6, 12), (5, 19), (19, 0), (10, 4), (0, 16), (18, 9), (5, 17), (8, 4), (19, 17), (17, 7), (22, 4), (12, 28), (7, 28), (18, 21), (8, 6), (14, 6), (17, 21), (13, 26), (15, 7), (2, 21), (2, 6), (5, 22), (10, 1), (23, 3), (22, 3), (7, 11), (5, 23), (13, 10), (3, 10), (11, 20), (18, 17), (9, 23), (4, 2), (19, 24), (22, 7), (23, 27), (13, 27), (1, 14), (16, 11), (4, 1), (20, 8), (17, 10), (10, 19), (3, 4), (6, 25), (21, 28), (22, 19), (17, 26), (5, 28), (7, 14), (3, 1), (4, 8), (5, 4), (13, 2), (13, 22), (16, 22), (20, 3), (16, 5), (20, 16), (18, 15), (7, 9), (5, 26), (3, 2), (2, 7), (19, 15), (2, 11), (21, 17), (21, 24), (22, 22), (22, 23), (21, 1), (13, 12), (18, 27), (7, 10), (0, 26), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385632", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 10), (2, 17), (23, 9), (6, 5), (19, 4), (8, 7), (6, 20), (0, 16), (15, 10), (8, 1), (16, 8), (13, 9), (22, 20), (15, 12), (11, 20), (2, 16), (8, 3), (12, 16), (23, 4), (19, 5), (0, 5), (1, 7), (0, 20), (23, 14), (12, 2), (8, 9), (14, 13), (4, 9), (0, 1), (4, 13), (14, 8), (22, 10), (4, 19), (15, 20), (16, 16), (20, 1), (3, 6), (13, 16), (17, 11), (9, 21), (22, 19), (10, 1), (0, 15), (9, 16), (16, 15), (19, 10), (16, 4), (9, 4), (3, 10), (23, 17), (6, 19), (7, 9), (8, 8), (19, 17), (21, 10), (3, 17), (23, 7), (5, 16), (12, 14), (10, 17), (23, 13), (18, 6), (8, 17), (15, 17), (10, 0), (9, 3), (23, 2), (3, 3), (19, 9), (10, 10), (3, 11), (21, 0), (20, 5), (17, 4), (15, 1), (13, 2), (8, 11), (12, 3), (23, 10), (0, 6), (1, 12), (4, 4), (18, 4), (5, 12), (22, 2), (5, 10), (23, 15), (2, 19), (7, 13), (17, 18), (15, 14), (0, 2), (0, 11), (21, 5), (16, 11), (1, 19), (14, 20), (21, 16), (19, 8), (3, 13), (22, 15), (12, 8), (5, 13), (2, 15), (19, 2), (19, 11), (15, 11), (16, 10), (22, 17), (9, 7), (9, 19), (21, 17), (11, 12), (9, 9), (2, 18), (17, 13), (9, 18), (10, 12), (14, 6), (3, 19), (20, 12), (11, 14), (0, 14), (13, 1), (22, 8), (8, 14), (15, 2), (3, 15), (5, 9), (16, 9), (9, 5), (13, 19), (4, 6), (22, 12), (3, 12), (18, 2), (22, 6), (12, 10), (16, 14), (14, 18), (9, 12), (18, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21714", "dataset": "MATH"}
{"messages": [{"content": "In a 29x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 22), (12, 15), (25, 4), (3, 9), (27, 11), (15, 12), (22, 18), (23, 5), (4, 9), (24, 6), (7, 17), (3, 2), (7, 10), (19, 12), (27, 14), (14, 14), (10, 19), (6, 12), (28, 11), (24, 12), (22, 17), (18, 14), (0, 15), (24, 23), (13, 17), (25, 20), (21, 11), (19, 5), (9, 15), (17, 14), (11, 9), (2, 10), (12, 6), (18, 23), (28, 5), (25, 9), (1, 11), (20, 3), (13, 13), (25, 2), (1, 3), (15, 10), (8, 14), (25, 1), (27, 5), (21, 14), (11, 15), (5, 22), (16, 12), (19, 16), (8, 7), (1, 15), (23, 22), (10, 17), (2, 7), (19, 15), (28, 22), (23, 23), (17, 6), (28, 20), (26, 7), (23, 4), (28, 17), (21, 0), (11, 8), (1, 16), (1, 2), (12, 14), (2, 13), (12, 16), (27, 4), (11, 1), (12, 4), (1, 19), (20, 20), (20, 15), (18, 21), (5, 20), (15, 8), (23, 10), (20, 14), (15, 14), (0, 21), (19, 1), (15, 1), (28, 6), (11, 16), (5, 19), (22, 6), (27, 0), (9, 9), (13, 20), (26, 3), (9, 6), (4, 18), (6, 2), (5, 12), (3, 14), (14, 23), (10, 11), (25, 7), (21, 5), (11, 17), (12, 8), (28, 4), (4, 17), (7, 11), (25, 8), (4, 3), (13, 11), (11, 4), (8, 1), (3, 22), (18, 16), (13, 8), (16, 8), (14, 9), (21, 21), (2, 11), (24, 10), (22, 16), (17, 2), (5, 13), (28, 19), (1, 9), (14, 18), (27, 17), (1, 18), (6, 4), (20, 4), (27, 1), (4, 15), (10, 10), (6, 20), (2, 4), (20, 19), (17, 16), (14, 19), (22, 3), (0, 6), (23, 3), (19, 0), (21, 18), (1, 23), (11, 21), (15, 11), (24, 4), (24, 1), (3, 10), (10, 23), (9, 22), (25, 15), (0, 23), (13, 19), (16, 3), (21, 22), (2, 1), (18, 17), (6, 17), (18, 7), (18, 4), (7, 2), (12, 9), (2, 8), (28, 9), (17, 22), (1, 7), (19, 17), (19, 11), (12, 0), (20, 22), (4, 11), (16, 14), (12, 2), (13, 15), (13, 1), (19, 23), (1, 1), (26, 15), (4, 8), (20, 5), (23, 0), (16, 17), (16, 16), (10, 12), (21, 17), (28, 7), (0, 17), (16, 22), (16, 9), (14, 0), (8, 13), (24, 18), (25, 16), (22, 14), (19, 2), (17, 13), (0, 13), (28, 8), (1, 20), (17, 10), (7, 6), (13, 23), (6, 21), (12, 10), (3, 7), (2, 3), (26, 16), (24, 17), (16, 18), (18, 10), (17, 23), (18, 8), (27, 6), (24, 15), (26, 13), (18, 1), (9, 8), (5, 9), (13, 21), (3, 3), (9, 11), (26, 10), (9, 7), (4, 22), (18, 20), (18, 3), (23, 6), (4, 20), (5, 6), (22, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "446592", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 22), (1, 15), (19, 7), (0, 5), (1, 19), (17, 23), (19, 14), (4, 18), (19, 9), (10, 23), (3, 10), (17, 6), (1, 6), (0, 7), (1, 4), (7, 8), (1, 13), (4, 1), (7, 10), (5, 22), (13, 16), (0, 4), (10, 20), (12, 20), (4, 8), (18, 2), (5, 15), (3, 3), (20, 7), (21, 11), (5, 3), (5, 2), (2, 3), (14, 0), (13, 11), (2, 1), (8, 5), (11, 8), (9, 8), (19, 13), (6, 8), (7, 3), (14, 14), (10, 8), (16, 2), (15, 19), (18, 21), (8, 20), (21, 1), (9, 2), (9, 3), (6, 17), (20, 5), (7, 18), (16, 16), (6, 18), (0, 12), (7, 1), (10, 0), (14, 6), (13, 18), (9, 13), (8, 10), (3, 20), (13, 14), (19, 21), (0, 6), (10, 12), (20, 4), (7, 22), (9, 6), (3, 16), (13, 2), (17, 14), (15, 5), (8, 2), (15, 4), (18, 19), (3, 17), (17, 1), (8, 23), (18, 20), (4, 9), (0, 19), (20, 9), (16, 8), (12, 12), (21, 18), (2, 11), (5, 14), (19, 0), (5, 20), (4, 20), (19, 10), (8, 19), (16, 4), (18, 14), (15, 1), (21, 6), (14, 19), (9, 12), (0, 16), (15, 10), (12, 18), (6, 1), (12, 17), (20, 16), (4, 10), (5, 8), (13, 20), (14, 11), (0, 18), (16, 5), (0, 8), (10, 15), (3, 8), (1, 22), (17, 16), (2, 19), (17, 8), (10, 19), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "435498", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), 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, 0), (16, 18), (13, 13), (7, 17), (26, 18), (14, 6), (8, 0), (14, 7), (19, 11), (0, 10), (5, 6), (14, 3), (21, 7), (10, 6), (9, 19), (22, 22), (15, 8), (8, 12), (2, 4), (9, 14), (25, 9), (25, 22), (20, 16), (17, 0), (9, 22), (22, 20), (21, 5), (10, 9), (2, 15), (22, 11), (24, 12), (15, 16), (8, 16), (23, 6), (19, 16), (15, 6), (24, 10), (13, 14), (2, 7), (14, 22), (21, 13), (11, 6), (14, 1), (8, 3), (7, 5), (19, 14), (26, 9), (19, 12), (19, 18), (25, 2), (23, 10), (22, 12), (5, 4), (10, 15), (15, 10), (20, 0), (20, 18), (20, 5), (12, 9), (8, 22), (14, 8), (18, 1), (19, 5), (0, 9), (12, 17), (2, 12), (12, 18), (4, 7), (13, 3), (18, 16), (24, 18), (0, 3), (8, 11), (15, 18), (18, 17), (2, 1), (17, 11), (9, 15), (23, 17), (19, 9), (23, 5), (3, 2), (21, 15), (8, 6), (23, 20), (1, 18), (15, 3), (15, 7), (3, 3), (9, 4), (3, 9), (25, 1), (19, 6), (24, 4), (21, 20), (20, 10), (2, 11), (6, 9), (1, 5), (12, 12), (26, 20), (23, 9), (6, 13), (23, 13), (18, 15), (4, 17), (16, 22), (26, 4), (11, 17), (4, 22), (5, 11), (19, 3), (2, 9), (13, 1), (19, 13), (18, 14), (5, 17), (21, 0), (9, 21), (5, 12), (16, 13), (19, 0), (26, 11), (0, 12), (21, 21), (22, 10), (14, 0), (14, 2), (6, 8), (17, 15), (16, 8), (24, 5), (16, 3), (20, 9), (6, 7), (24, 16), (8, 13), (17, 5), (5, 5), (14, 5), (9, 7), (12, 0), (18, 7), (24, 3), (22, 21), (4, 20), (18, 0), (8, 20), (0, 13), (14, 19), (20, 2), (7, 13), (15, 4), (26, 7), (4, 18), (10, 22), (22, 6), (16, 19), (18, 3), (7, 11), (16, 1), (7, 0), (1, 13), (18, 11), (3, 12), (0, 18), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "772812", "dataset": "MATH"}
{"messages": [{"content": "In a 22x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 20), (8, 8), (3, 18), (3, 8), (20, 10), (18, 16), (11, 1), (16, 10), (8, 14), (18, 6), (11, 14), (4, 5), (0, 10), (19, 1), (21, 10), (12, 0), (6, 18), (6, 15), (20, 6), (12, 20), (16, 12), (7, 9), (2, 10), (17, 18), (13, 15), (3, 9), (9, 20), (16, 2), (6, 3), (11, 4), (3, 7), (10, 19), (12, 10), (20, 11), (17, 6), (11, 12), (14, 6), (16, 20), (18, 7), (8, 5), (13, 16), (14, 7), (19, 4), (20, 14), (5, 14), (8, 6), (1, 7), (19, 18), (12, 8), (7, 17), (2, 19), (21, 7), (14, 1), (21, 4), (15, 8), (5, 9), (16, 0), (20, 7), (14, 15), (19, 20), (6, 7), (20, 3), (13, 20), (7, 1), (11, 2), (18, 13), (17, 10), (11, 3), (20, 16), (2, 5), (13, 4), (7, 3), (4, 20), (21, 17), (8, 19), (11, 10), (13, 11), (13, 5), (14, 9), (10, 16), (16, 9), (20, 0), (11, 9), (19, 10), (16, 11), (0, 2), (11, 13), (8, 9), (6, 10), (8, 1), (0, 17), (9, 11), (20, 13), (11, 7), (15, 9), (12, 9), (15, 12), (14, 17), (1, 2), (4, 6), (14, 2), (10, 5), (5, 15), (3, 17), (1, 9), (0, 9), (10, 18), (12, 16), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "927422", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 26), (5, 23), (19, 9), (10, 6), (13, 18), (5, 11), (11, 25), (9, 21), (0, 20), (1, 27), (2, 20), (18, 27), (5, 25), (4, 13), (11, 23), (11, 27), (3, 19), (15, 16), (4, 22), (18, 20), (2, 15), (2, 14), (12, 10), (6, 10), (3, 24), (0, 12), (14, 25), (8, 0), (18, 19), (14, 9), (10, 21), (18, 9), (16, 15), (0, 25), (14, 27), (1, 14), (1, 2), (6, 15), (7, 23), (5, 14), (10, 0), (14, 26), (17, 22), (17, 7), (19, 11), (16, 2), (19, 2), (6, 5), (0, 2), (15, 19), (16, 17), (19, 14), (10, 18), (19, 10), (1, 19), (15, 15), (1, 15), (19, 6), (13, 22), (4, 19), (11, 7), (13, 27), (4, 23), (6, 21), (13, 23), (8, 4), (10, 24), (2, 25), (5, 12), (11, 3), (9, 0), (10, 26), (1, 13), (18, 18), (3, 1), (8, 21), (19, 7), (3, 17), (17, 26), (0, 23), (17, 15), (14, 19), (10, 14), (2, 3), (14, 2), (14, 13), (15, 17), (10, 15), (11, 17), (16, 27), (6, 23), (16, 19), (13, 4), (9, 7), (0, 5), (1, 11), (0, 6), (13, 6), (5, 26), (16, 6), (15, 3), (8, 10), (3, 18), (19, 24), (6, 20), (9, 10), (17, 24), (5, 18), (14, 0), (1, 20), (5, 4), (11, 13), (2, 8), (13, 14), (9, 25), (19, 19), (7, 0), (15, 26), (11, 20), (18, 6), (11, 2), (7, 19), (3, 10), (9, 1), (17, 9), (18, 12), (13, 1), (6, 24), (12, 26), (14, 23), (7, 13), (14, 7), (6, 14), (13, 26), (12, 1), (16, 22), (19, 5), (2, 16), (7, 17), (3, 16), (7, 2), (8, 16), (12, 23), (19, 15), (14, 17), (5, 15), (7, 6), (5, 19), (15, 12), (9, 20), (9, 27), (6, 8), (7, 14), (16, 11), (0, 9), (17, 18), (1, 9), (9, 24), (14, 6), (14, 10), (8, 20), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118000", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 18), (21, 5), (12, 9), (9, 19), (7, 7), (3, 12), (22, 14), (20, 3), (12, 11), (11, 15), (17, 9), (10, 0), (7, 19), (21, 4), (8, 18), (16, 7), (6, 12), (10, 18), (21, 11), (15, 2), (22, 4), (16, 4), (12, 18), (17, 16), (3, 2), (20, 1), (23, 3), (6, 16), (5, 14), (8, 15), (22, 13), (18, 5), (16, 10), (2, 12), (20, 20), (23, 17), (21, 14), (5, 16), (14, 20), (9, 18), (19, 0), (22, 16), (8, 0), (5, 3), (5, 7), (18, 7), (6, 14), (8, 6), (17, 14), (23, 16), (22, 7), (7, 17), (20, 14), (9, 3), (4, 13), (6, 4), (11, 19), (15, 14), (6, 11), (5, 20), (15, 13), (0, 17), (16, 16), (3, 6), (5, 8), (23, 9), (4, 3), (3, 10), (1, 20), (15, 10), (18, 13), (0, 15), (8, 3), (16, 12), (18, 16), (20, 0), (12, 13), (14, 10), (1, 4), (6, 2), (4, 11), (0, 5), (19, 3), (18, 10), (20, 4), (4, 19), (22, 15), (10, 14), (7, 16), (1, 14), (17, 0), (1, 13), (9, 17), (6, 3), (2, 3), (6, 10), (5, 18), (8, 17), (7, 9), (11, 13), (1, 2), (20, 15), (17, 8), (9, 12), (14, 13), (14, 7), (11, 2), (23, 4), (22, 19), (4, 8), (3, 17), (15, 16), (23, 0), (12, 5), (17, 2), (19, 20), (2, 5), (16, 3), (14, 19), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "953016", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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), (20, 23), (20, 19), (9, 23), (21, 13), (1, 23), (1, 9), (10, 2), (3, 12), (11, 6), (7, 5), (18, 6), (14, 23), (0, 22), (13, 4), (15, 0), (11, 21), (17, 24), (2, 3), (19, 13), (9, 26), (10, 13), (15, 5), (8, 6), (4, 5), (16, 24), (4, 15), (1, 2), (3, 17), (21, 17), (9, 21), (6, 10), (21, 9), (8, 14), (14, 8), (12, 6), (3, 16), (1, 7), (6, 9), (3, 20), (13, 13), (16, 0), (16, 3), (13, 16), (11, 9), (15, 18), (1, 8), (4, 24), (15, 19), (18, 22), (0, 25), (19, 22), (12, 26), (17, 0), (7, 16), (15, 20), (0, 19), (10, 16), (9, 18), (6, 20), (10, 6), (10, 1), (12, 11), (13, 15), (12, 12), (1, 12), (15, 14), (1, 11), (19, 10), (0, 11), (21, 23), (13, 7), (1, 24), (18, 12), (1, 25), (12, 22), (17, 4), (2, 20), (2, 6), (10, 5), (7, 8), (3, 7), (3, 25), (12, 21), (1, 15), (17, 8), (7, 9), (18, 0), (19, 16), (18, 19), (10, 18), (14, 14), (16, 10), (0, 8), (1, 4), (18, 5), (20, 2), (12, 23), (4, 18), (10, 19), (5, 8), (18, 1), (21, 3), (12, 17), (6, 17), (5, 25), (13, 14), (5, 7), (1, 5), (21, 18), (17, 23), (9, 10), (16, 19), (12, 5), (2, 14), (20, 7), (12, 3), (8, 22), (5, 12), (7, 4), (9, 14), (21, 8), (4, 10), (19, 5), (20, 13), (2, 13), (12, 9), (20, 18), (5, 26), (5, 23), (2, 7), (13, 5), (13, 18), (12, 25), (17, 22), (2, 24), (8, 20), (2, 23), (7, 0), (14, 5), (16, 11), (17, 1), (7, 2), (20, 20), (14, 4), (9, 3), (13, 24), (8, 9), (14, 24), (12, 2), (6, 12), (12, 15), (17, 12), (18, 3), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612045", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), 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), (25, 1), (5, 17), (22, 20), (14, 16), (9, 14), (15, 23), (7, 20), (0, 10), (22, 17), (15, 22), (24, 0), (20, 18), (8, 18), (23, 22), (18, 13), (5, 6), (10, 7), (2, 13), (18, 2), (7, 9), (9, 6), (12, 7), (6, 23), (21, 9), (22, 3), (19, 4), (7, 19), (11, 4), (5, 3), (5, 15), (0, 3), (12, 13), (9, 3), (21, 12), (8, 12), (25, 0), (16, 5), (11, 3), (16, 13), (6, 13), (14, 2), (19, 3), (8, 14), (9, 0), (15, 11), (11, 0), (24, 1), (21, 23), (25, 22), (16, 0), (18, 17), (23, 8), (14, 21), (8, 11), (25, 20), (13, 18), (24, 24), (6, 15), (10, 15), (2, 24), (15, 5), (14, 15), (10, 8), (7, 15), (15, 20), (2, 9), (22, 7), (24, 15), (7, 11), (5, 14), (2, 15), (0, 11), (24, 16), (19, 21), (21, 17), (17, 23), (8, 7), (8, 1), (10, 21), (14, 7), (10, 12), (18, 15), (16, 24), (24, 11), (7, 5), (18, 6), (18, 10), (17, 6), (24, 13), (12, 24), (13, 9), (23, 23), (4, 23), (21, 13), (1, 10), (2, 3), (4, 0), (13, 10), (22, 2), (1, 13), (19, 2), (8, 17), (1, 18), (23, 7), (3, 19), (20, 9), (6, 4), (2, 10), (21, 0), (13, 6), (23, 5), (6, 21), (19, 13), (6, 24), (9, 7), (17, 10), (3, 17), (19, 7), (19, 24), (11, 5), (8, 19), (13, 7), (11, 11), (24, 10), (3, 22), (10, 14), (9, 23), (7, 18), (23, 19), (13, 3), (17, 14), (13, 1), (21, 4), (17, 11), (5, 23), (8, 22), (11, 21), (17, 7), (1, 20), (6, 16), (3, 1), (9, 5), (14, 17), (3, 16), (14, 24), (18, 11), (14, 9), (6, 17), (3, 2), (5, 7), (24, 8), (21, 16), (9, 11), (4, 18), (2, 16), (8, 3), (8, 0), (19, 1), (14, 13), (4, 3), (7, 24), (5, 13), (8, 24), (19, 10), (3, 24), (13, 24), (16, 7), (0, 13), (1, 23), (20, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814635", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (0, 9), (10, 14), (0, 8), (18, 2), (12, 0), (13, 5), (6, 1), (19, 13), (0, 16), (3, 10), (16, 13), (10, 18), (6, 17), (7, 20), (11, 18), (19, 11), (13, 21), (4, 19), (9, 11), (5, 11), (9, 0), (4, 0), (5, 6), (19, 10), (2, 13), (5, 21), (9, 21), (6, 5), (8, 10), (18, 6), (18, 12), (13, 14), (11, 3), (7, 18), (2, 10), (8, 0), (19, 7), (14, 19), (3, 1), (14, 7), (17, 5), (14, 13), (11, 16), (2, 14), (5, 1), (2, 19), (5, 10), (13, 20), (14, 16), (18, 9), (18, 19), (11, 21), (13, 2), (17, 13), (4, 8), (16, 20), (2, 5), (12, 13), (16, 1), (15, 13), (5, 9), (19, 4), (9, 2), (18, 1), (1, 5), (3, 17), (18, 5), (6, 4), (8, 15), (14, 18), (5, 19), (14, 2), (13, 19), (7, 21), (3, 14), (5, 15), (10, 1), (19, 16), (7, 16), (19, 3), (19, 17), (14, 20), (13, 16), (17, 3), (2, 4), (17, 21), (13, 8), (0, 18), (9, 14), (12, 19), (16, 8), (7, 3), (11, 15), (8, 19), (7, 0), (19, 19), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "827232", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), 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), (8, 9), (10, 27), (9, 6), (9, 10), (4, 4), (12, 23), (16, 27), (6, 4), (6, 10), (12, 17), (3, 15), (1, 15), (14, 16), (4, 16), (4, 2), (12, 12), (15, 13), (7, 0), (4, 18), (3, 10), (17, 5), (0, 6), (4, 10), (4, 3), (19, 6), (14, 24), (12, 9), (10, 24), (9, 16), (15, 23), (6, 5), (19, 12), (17, 7), (6, 11), (17, 16), (11, 4), (18, 0), (13, 13), (18, 12), (9, 17), (14, 23), (6, 24), (13, 6), (18, 25), (18, 10), (18, 13), (3, 27), (17, 8), (10, 23), (19, 3), (4, 20), (19, 5), (15, 14), (11, 14), (7, 10), (8, 5), (4, 27), (2, 19), (19, 4), (3, 26), (1, 11), (16, 8), (10, 22), (11, 3), (6, 27), (2, 16), (4, 22), (2, 6), (13, 19), (8, 13), (3, 9), (3, 2), (1, 6), (7, 24), (8, 3), (2, 0), (4, 13), (14, 18), (13, 18), (10, 26), (11, 25), (9, 2), (18, 1), (19, 7), (6, 6), (10, 18), (12, 0), (11, 2), (18, 3), (2, 22), (4, 14), (1, 18), (0, 8), (16, 25), (7, 19), (17, 25), (19, 26), (14, 10), (19, 23), (9, 22), (1, 14), (19, 22), (16, 20), (17, 13), (2, 20), (9, 23), (14, 19), (13, 12), (11, 16), (5, 22), (16, 10), (1, 16), (0, 20), (6, 0), (19, 8), (12, 20), (9, 13), (5, 26), (10, 4), (13, 0), (10, 10), (3, 12), (19, 11), (10, 17), (8, 20), (6, 25), (14, 3), (5, 14), (11, 10), (2, 9), (10, 5), (14, 9), (7, 1), (5, 25), (10, 14), (5, 20), (0, 27), (4, 5), (7, 20), (2, 24), (15, 11), (18, 26), (16, 6), (19, 18), (1, 10), (5, 3), (2, 10), (4, 0), (13, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209754", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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, 0), (17, 11), (2, 17), (10, 15), (19, 6), (1, 9), (19, 17), (5, 2), (3, 11), (5, 0), (8, 11), (17, 2), (12, 11), (11, 14), (1, 11), (0, 15), (3, 17), (8, 10), (1, 0), (3, 18), (8, 12), (3, 19), (17, 5), (6, 20), (15, 20), (10, 8), (12, 4), (16, 9), (2, 5), (16, 18), (12, 0), (7, 3), (13, 20), (6, 4), (12, 3), (12, 12), (3, 9), (19, 14), (19, 0), (3, 2), (16, 1), (1, 10), (4, 15), (5, 9), (0, 9), (11, 5), (4, 5), (19, 19), (2, 9), (11, 2), (9, 13), (5, 14), (5, 17), (16, 15), (0, 6), (14, 2), (9, 0), (11, 0), (11, 15), (18, 6), (9, 6), (1, 1), (11, 3), (2, 2), (7, 10), (17, 6), (5, 3), (13, 10), (9, 4), (4, 16), (10, 14), (18, 13), (1, 6), (10, 7), (10, 11), (15, 15), (2, 11), (2, 1), (3, 8), (1, 4), (4, 9), (11, 11), (10, 13), (18, 2), (16, 20), (12, 8), (19, 9), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667644", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 10), (0, 3), (12, 12), (6, 17), (24, 10), (5, 19), (13, 14), (22, 22), (1, 24), (21, 17), (24, 13), (25, 23), (13, 10), (21, 19), (21, 4), (2, 21), (12, 11), (8, 10), (18, 17), (17, 11), (9, 22), (0, 18), (22, 21), (15, 13), (13, 20), (24, 15), (8, 8), (16, 5), (24, 5), (18, 14), (24, 11), (13, 1), (20, 14), (6, 0), (16, 0), (22, 2), (5, 3), (15, 15), (15, 21), (24, 9), (26, 9), (3, 0), (12, 14), (24, 20), (8, 3), (25, 22), (19, 7), (19, 23), (24, 22), (15, 0), (8, 9), (6, 11), (17, 17), (11, 12), (10, 6), (18, 9), (9, 15), (25, 5), (21, 10), (24, 6), (3, 14), (6, 1), (24, 2), (13, 19), (5, 13), (11, 17), (7, 16), (18, 13), (27, 16), (19, 24), (11, 11), (17, 22), (3, 11), (25, 13), (17, 4), (12, 0), (15, 8), (24, 4), (13, 11), (6, 4), (26, 0), (15, 20), (4, 10), (5, 24), (23, 3), (27, 5), (4, 1), (6, 23), (23, 0), (10, 0), (10, 19), (26, 13), (25, 6), (0, 14), (3, 22), (20, 10), (4, 15), (13, 18), (1, 11), (8, 21), (1, 22), (25, 9), (17, 6), (5, 4), (20, 12), (25, 0), (24, 1), (0, 12), (14, 14), (16, 22), (13, 6), (14, 4), (10, 17), (26, 19), (22, 17), (3, 10), (18, 11), (9, 24), (1, 7), (3, 8), (26, 2), (6, 16), (11, 8), (9, 10), (9, 21), (21, 9), (15, 14), (5, 22), (10, 2), (25, 15), (6, 24), (27, 9), (5, 18), (14, 11), (0, 19), (20, 7), (2, 20), (7, 8), (13, 16), (8, 24), (7, 23), (25, 18), (19, 22), (4, 5), (13, 8), (7, 0), (14, 0), (6, 22), (11, 1), (14, 5), (26, 17), (10, 14), (17, 19), (3, 6), (20, 23), (11, 6), (12, 22), (7, 18), (22, 0), (22, 7), (20, 18), (9, 2), (4, 14), (5, 0), (22, 16), (1, 8), (27, 11), (4, 22), (26, 11), (26, 12), (5, 23), (14, 22), (24, 18), (12, 13), (25, 16), (3, 12), (12, 16), (9, 13), (15, 10), (27, 4), (17, 1), (6, 5), (14, 17), (1, 1), (23, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862884", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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, 14), (21, 17), (16, 19), (17, 3), (15, 17), (13, 18), (9, 22), (12, 9), (11, 14), (0, 19), (0, 13), (11, 24), (11, 0), (13, 1), (16, 13), (11, 21), (5, 17), (14, 21), (14, 18), (11, 23), (18, 6), (21, 12), (20, 9), (16, 3), (0, 2), (21, 2), (3, 14), (10, 3), (8, 22), (15, 3), (7, 24), (5, 20), (8, 13), (12, 16), (19, 24), (12, 8), (14, 24), (15, 1), (10, 11), (11, 9), (21, 11), (13, 20), (11, 13), (10, 10), (19, 7), (2, 20), (18, 23), (1, 13), (21, 5), (5, 2), (12, 18), (18, 18), (0, 4), (7, 3), (9, 17), (16, 11), (4, 20), (16, 5), (21, 1), (18, 17), (16, 17), (16, 7), (6, 7), (2, 12), (5, 11), (0, 10), (8, 3), (17, 12), (13, 21), (18, 15), (5, 19), (2, 9), (20, 4), (18, 19), (20, 10), (4, 3), (4, 15), (21, 22), (18, 21), (1, 7), (2, 23), (13, 5), (19, 12), (1, 19), (6, 21), (18, 8), (10, 12), (4, 5), (12, 1), (1, 9), (3, 4), (16, 20), (12, 7), (7, 18), (14, 6), (18, 5), (4, 11), (20, 19), (13, 7), (5, 5), (1, 21), (5, 10), (1, 6), (1, 16), (4, 19), (7, 8), (5, 15), (6, 22), (12, 22), (5, 24), (0, 23), (1, 14), (18, 10), (16, 9), (5, 7), (14, 19), (16, 23), (12, 5), (0, 6), (4, 17), (4, 7), (6, 23), (18, 0), (19, 17), (10, 9), (9, 5), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757584", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 15), (8, 5), (16, 4), (4, 3), (1, 11), (8, 3), (13, 16), (4, 4), (8, 6), (9, 15), (16, 3), (4, 14), (19, 8), (0, 14), (10, 13), (8, 8), (18, 8), (4, 6), (11, 12), (5, 16), (13, 13), (2, 8), (7, 16), (6, 7), (11, 15), (11, 2), (2, 10), (15, 13), (16, 2), (15, 19), (7, 9), (18, 2), (4, 0), (19, 18), (6, 19), (18, 17), (3, 17), (12, 7), (11, 3), (13, 0), (11, 10), (0, 17), (5, 17), (16, 9), (4, 13), (8, 7), (9, 3), (2, 3), (7, 2), (13, 14), (14, 12), (11, 9), (7, 0), (4, 15), (1, 0), (1, 15), (19, 0), (1, 10), (1, 3), (19, 3), (18, 14), (1, 12), (2, 7), (2, 0), (6, 1), (13, 18), (0, 11), (12, 0), (1, 7), (13, 12), (10, 0), (6, 3), (3, 2), (8, 13), (2, 13), (7, 1), (4, 19), (0, 12), (5, 6), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930004", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), 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, 0), (15, 9), (12, 19), (3, 17), (17, 13), (16, 18), (16, 12), (9, 11), (17, 15), (3, 21), (14, 3), (13, 5), (0, 11), (11, 5), (17, 9), (0, 4), (19, 16), (6, 12), (10, 9), (4, 14), (12, 5), (2, 15), (0, 10), (5, 18), (2, 12), (3, 18), (3, 20), (11, 21), (14, 6), (13, 1), (8, 7), (3, 9), (16, 1), (15, 21), (20, 11), (7, 20), (5, 11), (8, 17), (9, 1), (15, 11), (6, 18), (18, 9), (3, 13), (3, 5), (11, 13), (6, 1), (1, 17), (16, 17), (19, 10), (1, 21), (6, 20), (7, 0), (1, 19), (6, 4), (19, 15), (8, 10), (14, 0), (14, 17), (19, 9), (14, 20), (12, 8), (13, 17), (4, 21), (18, 11), (7, 13), (16, 5), (20, 12), (18, 14), (2, 4), (3, 19), (5, 5), (17, 21), (1, 5), (19, 8), (11, 8), (8, 11), (6, 16), (2, 7), (11, 14), (17, 6), (16, 10), (0, 2), (11, 0), (1, 4), (11, 1), (16, 15), (0, 13), (13, 14), (13, 0), (20, 1), (20, 0), (15, 17), (12, 13), (4, 19), (2, 18), (7, 3), (18, 19), (10, 14), (13, 22), (6, 17), (11, 9), (14, 22), (4, 1), (3, 15), (3, 7), (13, 6), (3, 1), (9, 22), (4, 0), (6, 2), (12, 6), (5, 12), (18, 16), (1, 10), (15, 0), (18, 3), (20, 13), (19, 4), (15, 4), (18, 21), (0, 21), (20, 10), (5, 0), (17, 18), (17, 22), (12, 11), (17, 0), (18, 5), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866640", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), 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, 18), (0, 11), (11, 21), (3, 0), (10, 9), (14, 20), (13, 7), (8, 2), (12, 5), (14, 13), (7, 0), (2, 5), (17, 15), (17, 4), (9, 5), (6, 8), (18, 19), (4, 4), (9, 19), (6, 24), (3, 4), (15, 10), (15, 9), (16, 22), (13, 14), (1, 5), (10, 13), (13, 6), (0, 20), (9, 10), (0, 2), (3, 11), (2, 6), (11, 9), (1, 10), (1, 8), (14, 2), (6, 21), (11, 12), (5, 24), (14, 4), (19, 14), (19, 17), (4, 5), (13, 15), (16, 16), (10, 8), (8, 4), (3, 20), (8, 9), (4, 0), (12, 7), (19, 12), (2, 24), (2, 21), (17, 14), (10, 22), (6, 17), (10, 10), (8, 19), (4, 16), (2, 14), (2, 3), (12, 8), (11, 18), (6, 0), (12, 13), (7, 9), (0, 7), (7, 8), (14, 6), (8, 5), (6, 4), (17, 0), (13, 21), (3, 18), (16, 24), (1, 16), (3, 24), (4, 19), (19, 9), (8, 15), (17, 11), (15, 7), (15, 3), (13, 3), (7, 4), (11, 6), (18, 0), (4, 13), (9, 2), (2, 16), (13, 11), (10, 14), (14, 7), (5, 10), (18, 3), (6, 2), (7, 14), (5, 18), (17, 9), (2, 11), (0, 15), (13, 4), (8, 7), (18, 17), (19, 0), (18, 5), (6, 7), (1, 0), (17, 7), (12, 18), (18, 15), (13, 22), (17, 12), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622224", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 16), (1, 15), (20, 15), (24, 9), (17, 27), (7, 26), (23, 1), (13, 14), (20, 22), (14, 22), (1, 8), (9, 14), (11, 0), (4, 8), (21, 15), (15, 5), (23, 19), (5, 25), (22, 4), (11, 10), (17, 20), (6, 27), (6, 0), (6, 15), (0, 15), (0, 8), (24, 12), (2, 15), (13, 25), (4, 1), (13, 17), (2, 16), (23, 25), (0, 23), (5, 17), (21, 23), (20, 20), (10, 3), (1, 11), (18, 1), (16, 18), (15, 22), (0, 21), (20, 5), (21, 14), (17, 11), (24, 15), (10, 2), (17, 5), (2, 21), (19, 1), (16, 25), (5, 21), (7, 17), (22, 15), (20, 16), (18, 3), (23, 3), (1, 26), (5, 15), (14, 16), (9, 13), (16, 10), (12, 25), (13, 0), (21, 7), (3, 11), (18, 5), (5, 14), (15, 3), (19, 13), (15, 6), (22, 1), (4, 6), (21, 11), (24, 26), (18, 20), (3, 22), (1, 13), (22, 9), (10, 6), (3, 0), (15, 2), (24, 0), (16, 20), (8, 0), (12, 23), (19, 26), (3, 14), (16, 1), (11, 12), (6, 13), (0, 4), (2, 0), (20, 1), (14, 14), (11, 20), (2, 20), (7, 19), (8, 10), (21, 5), (16, 27), (18, 0), (24, 17), (19, 22), (12, 21), (19, 0), (8, 16), (11, 23), (10, 27), (10, 0), (22, 11), (9, 0), (19, 23), (15, 20), (7, 25), (23, 18), (14, 23), (12, 9), (8, 19), (13, 3), (5, 8), (2, 1), (11, 17), (7, 23), (19, 24), (7, 3), (9, 11), (7, 0), (0, 11), (21, 22), (11, 5), (17, 14), (9, 19), (18, 22), (4, 18), (19, 7), (21, 17), (1, 17), (19, 12), (5, 26), (20, 13), (20, 6), (23, 10), (9, 25), (13, 2), (11, 11), (21, 12), (10, 9), (9, 17), (13, 10), (9, 23), (11, 27), (18, 18), (11, 1), (15, 1), (23, 12), (11, 19), (22, 5), (17, 7), (14, 13), (8, 3), (3, 27), (19, 21), (17, 2), (7, 16), (15, 13), (4, 0), (7, 20), (7, 24), (1, 24), (22, 17), (3, 2), (10, 18), (4, 4), (14, 21), (6, 5), (23, 4), (15, 19), (22, 8), (23, 14), (10, 5), (7, 2), (23, 20), (22, 14), (1, 7), (5, 10), (0, 22), (18, 12), (0, 19), (21, 0), (18, 16), (10, 14), (17, 25), (6, 9), (19, 19), (10, 25), (6, 19), (18, 8), (11, 7), (5, 9), (9, 16), (20, 14), (10, 22), (0, 7), (15, 16), (3, 23), (8, 21), (1, 19), (8, 26), (7, 10), (13, 24), (2, 3), (15, 23), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763392", "dataset": "MATH"}
{"messages": [{"content": "In a 29x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 22), (10, 21), (3, 1), (0, 9), (27, 7), (12, 16), (2, 18), (3, 12), (1, 15), (19, 24), (15, 0), (10, 24), (23, 9), (5, 18), (15, 5), (14, 2), (0, 19), (14, 1), (8, 21), (14, 10), (12, 24), (14, 17), (5, 6), (0, 2), (21, 7), (4, 10), (26, 24), (28, 2), (17, 25), (14, 22), (26, 22), (12, 11), (22, 7), (21, 12), (14, 24), (19, 11), (12, 6), (11, 24), (23, 2), (0, 15), (24, 12), (6, 9), (23, 24), (20, 13), (0, 4), (18, 23), (5, 19), (24, 10), (10, 20), (16, 25), (25, 8), (17, 10), (3, 15), (24, 9), (11, 20), (7, 14), (28, 5), (5, 23), (22, 17), (23, 12), (20, 11), (15, 18), (4, 11), (20, 15), (19, 1), (24, 0), (28, 21), (10, 19), (28, 18), (9, 20), (14, 14), (4, 9), (18, 4), (27, 10), (14, 12), (22, 22), (20, 4), (5, 17), (19, 16), (18, 11), (6, 7), (6, 3), (1, 25), (20, 9), (10, 6), (21, 15), (11, 8), (4, 0), (1, 7), (21, 14), (13, 9), (17, 16), (1, 16), (2, 14), (7, 23), (10, 8), (8, 2), (17, 19), (2, 13), (15, 24), (12, 20), (18, 3), (22, 4), (19, 2), (19, 0), (19, 8), (21, 21), (3, 3), (28, 13), (14, 0), (16, 19), (11, 13), (20, 23), (8, 19), (20, 5), (17, 15), (10, 14), (11, 6), (7, 22), (20, 10), (10, 16), (17, 5), (28, 12), (18, 13), (22, 20), (12, 23), (1, 12), (20, 8), (7, 24), (9, 8), (18, 7), (0, 22), (25, 11), (8, 7), (19, 4), (28, 15), (11, 7), (13, 25), (13, 14), (28, 4), (0, 20), (24, 14), (15, 23), (13, 17), (19, 10), (0, 7), (1, 23), (3, 13), (14, 4), (8, 15), (11, 21), (27, 2), (2, 21), (26, 23), (6, 1), (0, 10), (20, 2), (20, 18), (21, 3), (27, 8), (23, 7), (9, 16), (25, 5), (18, 14), (0, 5), (8, 14), (11, 4), (3, 7), (13, 1), (19, 21), (2, 9), (17, 6), (8, 1), (18, 10), (2, 3), (20, 25), (17, 22), (12, 13), (27, 9), (15, 1), (24, 6), (25, 14), (13, 6), (9, 18), (21, 8), (27, 4), (18, 1), (6, 13), (25, 6), (3, 9), (7, 15), (24, 5), (6, 8), (8, 8), (26, 5), (1, 21), (2, 4), (24, 13), (2, 1), (26, 17), (25, 24), (26, 0), (2, 12), (9, 2), (3, 5), (3, 14), (21, 19), (17, 2), (24, 16), (3, 23), (25, 13), (17, 12), (26, 16), (24, 20), (3, 21), (5, 16), (10, 15), (12, 1), (16, 6), (14, 6), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883296", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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), (17, 22), (9, 10), (16, 6), (20, 23), (1, 9), (17, 21), (10, 19), (16, 15), (15, 7), (3, 23), (5, 14), (10, 9), (10, 20), (16, 9), (8, 3), (7, 9), (6, 21), (20, 0), (0, 20), (16, 12), (5, 7), (12, 12), (10, 2), (16, 21), (6, 14), (17, 1), (10, 5), (12, 7), (19, 17), (17, 19), (7, 5), (1, 23), (16, 13), (4, 10), (21, 24), (3, 14), (1, 4), (4, 9), (8, 21), (3, 21), (0, 21), (5, 23), (2, 10), (8, 10), (4, 17), (19, 0), (22, 13), (15, 3), (3, 5), (16, 5), (1, 18), (21, 3), (20, 8), (18, 3), (1, 14), (3, 24), (22, 23), (14, 7), (7, 7), (18, 16), (3, 22), (8, 20), (7, 8), (17, 9), (21, 15), (4, 5), (13, 3), (16, 14), (12, 11), (10, 6), (15, 22), (11, 26), (14, 2), (3, 25), (7, 1), (2, 1), (9, 0), (18, 4), (2, 11), (18, 10), (7, 24), (14, 26), (18, 20), (12, 19), (11, 17), (21, 18), (0, 24), (3, 17), (13, 12), (4, 25), (12, 21), (9, 5), (8, 25), (15, 2), (0, 4), (8, 18), (13, 26), (19, 3), (12, 2), (21, 6), (18, 5), (10, 11), (14, 1), (15, 13), (21, 7), (0, 12), (11, 7), (0, 15), (18, 8), (18, 12), (13, 16), (3, 10), (13, 23), (1, 15), (12, 1), (9, 19), (19, 9), (10, 7), (20, 7), (2, 16), (20, 12), (6, 23), (9, 7), (5, 4), (15, 5), (14, 9), (16, 2), (19, 25), (9, 26), (17, 8), (4, 15), (21, 17), (6, 16), (2, 22), (7, 26), (17, 0), (8, 24), (17, 25), (4, 12), (7, 19), (17, 23), (0, 8), (16, 18), (5, 18), (14, 8), (21, 14), (18, 19), (8, 12), (11, 13), (12, 8), (10, 17), (4, 3), (8, 9), (8, 11), (15, 14), (15, 23), (7, 23), (12, 25), (13, 7), (1, 8), (7, 12), (2, 2), (22, 12), (13, 15), (18, 6), (1, 13), (18, 15), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922944", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 22), (2, 27), (3, 12), (22, 12), (11, 17), (14, 3), (17, 25), (28, 2), (6, 16), (23, 18), (11, 26), (23, 23), (4, 23), (19, 13), (15, 8), (27, 4), (9, 25), (2, 20), (18, 2), (19, 18), (23, 15), (22, 11), (12, 3), (2, 11), (14, 21), (14, 4), (22, 25), (27, 10), (27, 20), (13, 20), (1, 7), (5, 21), (8, 20), (3, 8), (28, 17), (15, 12), (3, 19), (11, 22), (3, 0), (22, 7), (28, 1), (5, 26), (20, 18), (4, 12), (0, 17), (25, 26), (7, 13), (17, 23), (15, 14), (26, 3), (3, 2), (9, 1), (25, 14), (27, 11), (13, 21), (4, 6), (12, 12), (14, 12), (5, 24), (18, 10), (5, 20), (20, 4), (10, 8), (24, 21), (10, 1), (10, 13), (27, 21), (2, 24), (20, 22), (4, 17), (1, 19), (24, 0), (21, 24), (23, 9), (16, 11), (23, 5), (19, 21), (11, 2), (11, 16), (12, 20), (21, 21), (4, 27), (11, 25), (22, 17), (19, 1), (1, 18), (3, 1), (23, 12), (13, 25), (13, 28), (21, 7), (11, 23), (11, 27), (16, 4), (11, 8), (15, 20), (23, 21), (1, 26), (20, 27), (4, 13), (2, 17), (25, 0), (2, 19), (19, 7), (25, 13), (15, 3), (16, 8), (7, 21), (15, 21), (10, 6), (15, 6), (0, 22), (25, 20), (10, 17), (3, 23), (12, 22), (2, 10), (26, 20), (13, 3), (16, 2), (27, 8), (3, 11), (19, 10), (23, 2), (3, 16), (28, 14), (5, 16), (2, 8), (13, 15), (12, 0), (0, 5), (9, 14), (14, 22), (15, 10), (23, 3), (24, 6), (0, 18), (8, 5), (22, 9), (10, 0), (4, 4), (8, 19), (13, 16), (28, 20), (23, 8), (20, 14), (14, 11), (24, 15), (4, 25), (4, 8), (14, 25), (4, 15), (19, 25), (14, 10), (14, 15), (5, 7), (12, 25), (9, 4), (18, 4), (7, 1), (9, 13), (23, 4), (20, 20), (2, 13), (7, 7), (20, 8), (7, 11), (20, 16), (15, 11), (18, 11), (4, 20), (25, 22), (9, 8), (1, 13), (7, 0), (3, 22), (23, 11), (19, 6), (19, 4), (20, 24), (19, 14), (16, 14), (25, 1), (17, 7), (26, 0), (12, 27), (18, 28), (22, 3), (26, 17), (6, 11), (24, 19), (25, 7), (2, 6), (12, 24), (22, 1), (6, 7), (21, 4), (2, 4), (25, 11), (20, 1), (1, 27), (25, 18), (9, 21), (8, 9), (5, 17), (25, 2), (15, 25), (10, 25), (4, 14), (14, 19), (26, 5), (3, 10), (15, 0), (0, 2), (14, 23), (9, 12), (18, 5), (9, 11), (24, 18), (12, 26), (13, 6), (22, 19), (18, 23), (22, 15), (28, 0), (10, 2), (11, 10), (7, 5), (22, 14), (11, 12), (14, 2), (19, 22), (4, 7), (14, 5), (14, 7), (25, 10), (16, 22), (16, 27), (24, 2), (27, 6), (4, 3), (7, 25), (17, 1), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224400", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), 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), (18, 17), (16, 2), (0, 12), (8, 5), (19, 1), (13, 7), (16, 15), (12, 12), (17, 12), (9, 12), (17, 20), (3, 11), (9, 19), (3, 12), (1, 10), (5, 5), (14, 21), (11, 3), (10, 14), (1, 6), (3, 21), (0, 16), (15, 20), (16, 19), (4, 21), (14, 6), (11, 21), (14, 2), (4, 19), (6, 13), (17, 3), (4, 13), (9, 5), (3, 10), (6, 5), (12, 6), (19, 15), (10, 8), (11, 17), (14, 16), (1, 14), (14, 13), (2, 8), (1, 15), (10, 7), (3, 2), (17, 14), (2, 17), (13, 3), (13, 15), (14, 20), (10, 2), (11, 11), (19, 12), (6, 6), (9, 9), (13, 17), (14, 19), (14, 1), (9, 16), (12, 3), (9, 8), (20, 18), (18, 1), (7, 14), (17, 4), (2, 13), (19, 16), (20, 7), (2, 15), (20, 20), (11, 16), (3, 14), (14, 22), (16, 5), (16, 1), (17, 22), (0, 14), (16, 12), (16, 13), (5, 7), (15, 9), (8, 18), (18, 21), (6, 4), (17, 17), (11, 18), (8, 9), (19, 19), (12, 13), (16, 10), (9, 2), (15, 14), (4, 18), (2, 22), (12, 18), (19, 3), (13, 1), (13, 19), (12, 16), (5, 14), (7, 19), (4, 14), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "596862", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), 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), (19, 16), (15, 24), (0, 19), (9, 8), (15, 17), (1, 1), (22, 9), (1, 19), (1, 9), (15, 11), (15, 10), (0, 6), (21, 10), (8, 3), (3, 19), (24, 17), (24, 11), (7, 12), (2, 11), (4, 17), (8, 9), (3, 7), (8, 0), (24, 12), (5, 4), (21, 18), (20, 2), (24, 19), (10, 0), (15, 9), (6, 0), (17, 15), (2, 8), (5, 2), (15, 0), (10, 13), (22, 6), (4, 13), (19, 9), (18, 12), (3, 20), (7, 19), (22, 19), (1, 6), (20, 19), (17, 5), (4, 5), (23, 22), (7, 1), (5, 9), (11, 17), (10, 10), (2, 13), (16, 19), (19, 7), (14, 6), (21, 14), (23, 6), (1, 22), (1, 3), (5, 23), (20, 3), (1, 14), (12, 19), (15, 7), (6, 17), (3, 10), (22, 23), (21, 19), (15, 12), (10, 7), (0, 16), (5, 14), (16, 24), (12, 6), (13, 0), (16, 2), (6, 22), (16, 6), (14, 17), (8, 4), (18, 13), (2, 5), (8, 2), (7, 24), (24, 7), (6, 14), (13, 17), (0, 10), (20, 13), (13, 3), (7, 4), (10, 11), (6, 12), (11, 24), (23, 13), (8, 6), (13, 12), (4, 24), (15, 4), (13, 23), (12, 13), (17, 0), (19, 8), (20, 10), (13, 20), (8, 11), (7, 9), (12, 23), (1, 11), (13, 6), (14, 7), (14, 22), (10, 20), (14, 16), (2, 6), (9, 21), (17, 14), (11, 1), (19, 12), (17, 4), (4, 12), (20, 9), (10, 4), (13, 4), (12, 10), (2, 22), (24, 21), (14, 14), (20, 0), (6, 3), (10, 18), (6, 19), (11, 14), (19, 5), (11, 6), (20, 22), (9, 5), (2, 16), (19, 14), (1, 10), (19, 4), (7, 0), (4, 0), (3, 16), (15, 8), (14, 5), (1, 4), (4, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "811024", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 16), (19, 23), (15, 6), (5, 25), (12, 15), (4, 25), (7, 19), (9, 23), (2, 7), (18, 1), (4, 15), (15, 18), (14, 8), (3, 12), (16, 10), (13, 20), (17, 15), (2, 4), (11, 9), (12, 0), (6, 26), (7, 1), (13, 9), (9, 18), (17, 2), (9, 17), (3, 6), (3, 15), (5, 8), (7, 17), (19, 24), (10, 16), (4, 6), (3, 25), (15, 1), (3, 13), (14, 11), (6, 16), (4, 9), (15, 17), (15, 7), (12, 11), (1, 7), (11, 5), (17, 11), (18, 7), (18, 23), (8, 3), (8, 16), (7, 26), (0, 22), (12, 20), (5, 6), (2, 22), (18, 17), (12, 23), (15, 20), (8, 0), (1, 3), (15, 23), (10, 19), (16, 14), (11, 21), (4, 14), (14, 3), (3, 2), (18, 26), (0, 15), (8, 2), (12, 19), (0, 18), (14, 26), (16, 3), (14, 18), (8, 12), (3, 23), (11, 22), (19, 11), (4, 2), (5, 24), (4, 16), (9, 8), (1, 12), (17, 4), (2, 5), (3, 14), (7, 21), (13, 3), (18, 8), (1, 18), (9, 1), (6, 14), (6, 5), (5, 23), (12, 17), (15, 3), (7, 10), (7, 4), (5, 5), (8, 4), (18, 10), (16, 2), (6, 1), (2, 14), (11, 12), (13, 8), (2, 1), (6, 8), (16, 13), (4, 5), (10, 23), (12, 24), (8, 20), (15, 8), (14, 12), (8, 23), (3, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749554", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), 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), (16, 17), (4, 2), (21, 0), (9, 22), (12, 6), (1, 24), (16, 7), (21, 23), (16, 1), (8, 24), (10, 21), (20, 13), (23, 6), (4, 20), (8, 15), (15, 1), (12, 9), (4, 10), (14, 6), (4, 27), (7, 21), (3, 17), (5, 1), (14, 22), (18, 0), (22, 21), (10, 2), (2, 27), (11, 19), (16, 0), (14, 27), (5, 7), (2, 11), (12, 5), (3, 21), (15, 22), (16, 24), (21, 10), (14, 3), (10, 8), (13, 22), (14, 20), (0, 22), (3, 6), (23, 13), (6, 6), (1, 5), (13, 12), (10, 23), (2, 22), (20, 12), (5, 27), (8, 8), (4, 12), (22, 0), (13, 2), (21, 15), (9, 3), (16, 3), (0, 4), (4, 18), (0, 25), (20, 4), (15, 25), (19, 8), (7, 4), (8, 11), (11, 7), (22, 1), (4, 22), (21, 1), (15, 11), (14, 23), (8, 7), (19, 3), (5, 22), (13, 8), (5, 23), (6, 17), (7, 1), (23, 23), (7, 0), (10, 18), (0, 19), (2, 21), (22, 14), (3, 8), (6, 14), (4, 0), (8, 10), (1, 17), (17, 21), (21, 19), (22, 25), (1, 7), (12, 11), (20, 7), (23, 10), (17, 8), (6, 9), (6, 10), (0, 16), (10, 17), (9, 26), (15, 13), (10, 0), (16, 20), (19, 16), (12, 19), (9, 14), (2, 18), (13, 9), (6, 27), (6, 16), (3, 10), (6, 3), (18, 17), (0, 15), (8, 27), (3, 14), (19, 24), (7, 8), (14, 16), (16, 12), (17, 13), (19, 13), (0, 24), (21, 11), (14, 8), (5, 19), (2, 12), (18, 12), (13, 26), (3, 16), (3, 27), (16, 2), (6, 25), (15, 17), (5, 0), (10, 3), (2, 3), (4, 7), (17, 6), (19, 17), (8, 9), (1, 25), (15, 9), (22, 16), (10, 6), (7, 17), (17, 16), (1, 2), (7, 16), (16, 26), (16, 25), (0, 5), (6, 18), (0, 7), (16, 11), (4, 24), (17, 18), (11, 21), (15, 6), (1, 18), (13, 21), (7, 13), (13, 14), (6, 8), (7, 12), (2, 13), (11, 11), (23, 14), (19, 15), (0, 11), (14, 14), (1, 1), (9, 17), (20, 26), (10, 16), (17, 5), (10, 25), (2, 19), (3, 20), (15, 27), (15, 14), (14, 5), (10, 19), (19, 22), (11, 16), (21, 12), (15, 23), (3, 11), (4, 19), (7, 19), (12, 2), (3, 13), (4, 15), (19, 14), (17, 11), (14, 9), (14, 11), (3, 3), (4, 5), (23, 9), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554346", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), 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), (22, 1), (15, 24), (5, 21), (21, 17), (12, 0), (10, 15), (5, 11), (11, 13), (22, 17), (9, 5), (16, 6), (10, 8), (1, 15), (11, 3), (6, 11), (8, 16), (1, 13), (16, 22), (19, 4), (5, 23), (17, 0), (22, 7), (17, 17), (2, 3), (18, 4), (15, 25), (12, 21), (16, 15), (2, 7), (9, 7), (14, 17), (6, 25), (22, 25), (0, 23), (12, 14), (6, 13), (21, 6), (5, 0), (22, 16), (4, 27), (22, 23), (20, 3), (20, 11), (13, 0), (6, 27), (1, 12), (21, 12), (2, 9), (19, 1), (16, 21), (12, 16), (20, 17), (15, 6), (13, 16), (10, 24), (10, 22), (13, 19), (16, 7), (16, 23), (9, 15), (11, 26), (8, 22), (19, 24), (13, 23), (20, 4), (10, 23), (0, 12), (15, 0), (2, 8), (16, 10), (11, 8), (7, 26), (13, 5), (7, 12), (19, 16), (16, 2), (22, 6), (3, 5), (21, 20), (12, 7), (10, 12), (1, 0), (8, 12), (11, 2), (17, 26), (15, 20), (16, 0), (18, 27), (3, 1), (15, 5), (18, 25), (1, 16), (20, 8), (15, 3), (4, 16), (8, 9), (3, 2), (18, 17), (17, 14), (5, 7), (17, 15), (15, 26), (13, 3), (19, 3), (9, 18), (8, 8), (19, 23), (4, 21), (17, 13), (12, 8), (11, 25), (15, 14), (2, 1), (10, 7), (22, 22), (3, 3), (5, 26), (17, 5), (22, 14), (4, 13), (22, 12), (0, 5), (11, 18), (0, 7), (18, 15), (12, 13), (11, 12), (3, 21), (11, 4), (1, 8), (13, 20), (11, 0), (14, 11), (20, 14), (21, 19), (22, 15), (9, 26), (13, 8), (3, 20), (13, 13), (3, 14), (18, 20), (3, 25), (10, 21), (14, 14), (1, 27), (16, 13), (6, 14), (20, 18), (20, 13), (11, 11), (6, 20), (19, 17), (16, 12), (20, 5), (4, 24), (0, 11), (2, 2), (11, 1), (12, 25), (21, 4), (6, 18), (4, 15), (18, 3), (20, 0), (22, 0), (13, 1), (22, 9), (18, 13), (15, 11), (18, 22), (8, 10), (16, 4), (5, 25), (2, 19), (10, 27), (18, 16), (11, 9), (1, 17), (11, 22), (13, 15), (20, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "463680", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 18), (22, 4), (22, 13), (9, 0), (12, 16), (2, 19), (6, 20), (21, 19), (12, 17), (17, 13), (17, 8), (12, 10), (4, 7), (11, 13), (4, 1), (13, 1), (6, 13), (4, 19), (15, 16), (6, 2), (0, 13), (18, 9), (22, 16), (13, 10), (16, 14), (2, 9), (9, 7), (15, 3), (2, 10), (5, 8), (4, 2), (3, 6), (1, 2), (3, 1), (19, 11), (16, 12), (14, 13), (3, 17), (2, 1), (8, 4), (14, 16), (18, 0), (1, 16), (7, 6), (22, 14), (8, 14), (11, 18), (9, 2), (1, 9), (20, 4), (17, 7), (7, 20), (11, 5), (17, 6), (9, 1), (16, 20), (13, 16), (14, 14), (3, 7), (9, 18), (12, 5), (13, 14), (9, 19), (16, 3), (7, 10), (10, 5), (14, 1), (14, 4), (12, 6), (21, 14), (5, 12), (18, 19), (15, 17), (4, 3), (20, 15), (19, 7), (16, 15), (14, 10), (19, 9), (13, 5), (8, 15), (20, 7), (20, 10), (2, 17), (5, 19), (3, 15), (17, 19), (12, 1), (15, 4), (13, 18), (7, 11), (17, 14), (3, 18), (18, 7), (20, 19), (0, 7), (4, 5), (12, 2), (8, 5), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999455", "dataset": "MATH"}
{"messages": [{"content": "In a 26x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 13), (1, 0), (8, 10), (24, 4), (22, 4), (4, 3), (18, 18), (12, 2), (2, 15), (4, 0), (10, 14), (10, 12), (24, 21), (22, 9), (1, 4), (0, 20), (12, 1), (19, 0), (16, 1), (22, 16), (3, 19), (7, 10), (21, 16), (14, 8), (2, 2), (14, 3), (18, 16), (4, 5), (15, 8), (13, 10), (5, 18), (0, 21), (20, 3), (1, 1), (8, 2), (21, 12), (17, 21), (9, 0), (2, 0), (7, 1), (14, 14), (4, 6), (17, 14), (16, 5), (21, 19), (6, 0), (24, 1), (10, 3), (0, 10), (7, 21), (5, 13), (17, 1), (25, 8), (22, 8), (7, 8), (8, 0), (15, 0), (16, 2), (17, 9), (8, 18), (8, 20), (9, 5), (19, 14), (19, 21), (5, 1), (23, 2), (18, 1), (6, 6), (22, 18), (25, 15), (17, 8), (19, 6), (11, 17), (11, 20), (6, 14), (22, 14), (9, 9), (7, 3), (6, 19), (5, 6), (1, 11), (3, 16), (2, 20), (3, 2), (21, 5), (20, 9), (19, 19), (13, 3), (6, 3), (14, 5), (17, 2), (2, 1), (15, 12), (22, 19), (3, 21), (1, 9), (23, 19), (3, 4), (25, 5), (24, 18), (10, 6), (17, 15), (24, 14), (12, 4), (12, 6), (14, 17), (7, 5), (18, 2), (16, 3), (14, 19), (18, 13), (25, 19), (15, 6), (20, 11), (18, 20), (4, 7), (1, 16), (24, 12), (4, 20), (22, 7), (9, 1), (21, 17), (14, 16), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "598040", "dataset": "MATH"}
{"messages": [{"content": "In a 29x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 24), 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), (0, 9), (23, 6), (28, 0), (9, 21), (25, 12), (18, 19), (0, 4), (5, 12), (28, 7), (11, 15), (15, 11), (16, 12), (24, 3), (12, 14), (22, 24), (7, 1), (4, 1), (13, 2), (10, 16), (17, 0), (25, 6), (18, 21), (4, 7), (9, 7), (3, 14), (20, 23), (26, 14), (5, 4), (19, 21), (14, 10), (14, 17), (9, 8), (19, 20), (17, 18), (13, 16), (27, 9), (13, 22), (4, 17), (24, 15), (1, 20), (1, 8), (19, 22), (26, 23), (7, 3), (9, 12), (28, 16), (27, 21), (20, 22), (7, 15), (1, 4), (8, 2), (11, 8), (25, 17), (5, 1), (16, 4), (8, 5), (20, 3), (11, 9), (28, 17), (20, 2), (6, 11), (12, 16), (5, 20), (28, 13), (16, 15), (21, 1), (18, 13), (14, 1), (15, 0), (6, 8), (1, 21), (22, 7), (17, 10), (17, 11), (28, 19), (28, 18), (12, 8), (18, 4), (6, 18), (14, 19), (26, 3), (15, 3), (4, 13), (17, 9), (4, 9), (4, 12), (10, 1), (7, 17), (24, 14), (11, 0), (10, 11), (1, 22), (20, 19), (7, 13), (4, 16), (24, 4), (2, 24), (24, 11), (19, 0), (20, 0), (16, 7), (7, 4), (19, 17), (15, 9), (6, 2), (15, 13), (16, 22), (18, 23), (2, 10), (21, 2), (3, 20), (12, 1), (21, 15), (1, 1), (12, 23), (14, 7), (23, 12), (15, 12), (20, 24), (15, 4), (6, 0), (19, 5), (16, 19), (3, 7), (24, 23), (16, 23), (2, 12), (4, 21), (13, 14), (15, 20), (21, 0), (0, 16), (28, 20), (14, 6), (13, 3), (27, 5), (8, 9), (25, 0), (12, 3), (10, 21), (15, 16), (6, 1), (9, 11), (3, 15), (7, 24), (13, 0), (16, 18), (15, 22), (25, 10), (7, 5), (28, 5), (24, 19), (10, 23), (1, 13), (13, 5), (19, 16), (25, 20), (21, 18), (26, 17), (12, 15), (8, 13), (0, 24), (26, 8), (28, 22), (25, 5), (1, 12), (2, 4), (26, 20), (16, 0), (27, 10), (24, 5), (11, 18), (11, 7), (20, 21), (7, 9), (17, 4), (13, 13), (5, 0), (7, 10), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "849944", "dataset": "MATH"}
{"messages": [{"content": "In a 26x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 19), 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), (15, 17), (3, 4), (8, 19), (14, 9), (22, 8), (9, 9), (19, 6), (18, 13), (18, 2), (2, 11), (12, 6), (3, 5), (17, 6), (21, 17), (2, 2), (0, 9), (24, 10), (20, 1), (24, 5), (1, 16), (11, 2), (16, 7), (4, 5), (1, 10), (23, 15), (23, 13), (18, 11), (10, 3), (2, 5), (11, 9), (6, 17), (12, 9), (12, 0), (17, 0), (14, 5), (23, 6), (8, 2), (0, 18), (7, 7), (7, 12), (11, 1), (9, 18), (18, 12), (6, 1), (15, 18), (20, 13), (0, 15), (1, 4), (1, 15), (4, 3), (16, 10), (0, 10), (7, 17), (15, 10), (23, 1), (0, 14), (20, 7), (17, 1), (1, 17), (1, 9), (19, 8), (15, 3), (8, 11), (22, 2), (13, 0), (17, 4), (7, 14), (9, 11), (16, 3), (11, 8), (12, 4), (11, 7), (7, 19), (23, 12), (1, 13), (3, 2), (5, 18), (17, 2), (13, 15), (25, 0), (1, 19), (12, 14), (16, 5), (16, 12), (2, 4), (4, 12), (15, 5), (20, 0), (7, 8), (6, 10), (18, 19), (18, 17), (0, 6), (22, 7), (1, 18), (12, 3), (8, 4), (16, 14), (2, 0), (14, 16), (22, 12), (0, 4), (7, 18), (11, 16), (10, 11), (12, 2), (9, 14), (9, 8), (11, 13), (22, 0), (2, 19), (12, 19), (5, 11), (19, 2), (3, 13), (5, 4), (24, 3), (23, 4), (4, 6), (4, 8), (7, 0), (8, 7), (17, 10), (19, 19), (21, 12), (21, 9), (9, 4), (19, 5), (22, 11), (14, 3), (10, 13), (23, 9), (14, 17), (17, 13), (2, 17), (20, 8), (10, 14), (0, 13), (10, 2), (17, 16), (25, 15), (3, 18), (12, 1), (2, 7), (25, 10), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508480", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), 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), (5, 24), (9, 23), (8, 20), (8, 10), (9, 11), (3, 23), (20, 2), (10, 18), (11, 5), (1, 24), (9, 4), (1, 22), (14, 17), (19, 24), (6, 2), (20, 8), (4, 8), (18, 8), (13, 9), (20, 5), (8, 16), (3, 8), (7, 9), (3, 2), (6, 10), (4, 12), (14, 2), (5, 7), (6, 22), (5, 4), (10, 21), (11, 27), (0, 27), (11, 10), (21, 22), (5, 8), (20, 19), (10, 5), (4, 25), (14, 6), (1, 9), (5, 11), (16, 21), (7, 11), (9, 20), (2, 3), (18, 1), (19, 8), (16, 16), (13, 13), (9, 12), (1, 10), (20, 3), (13, 3), (0, 16), (8, 4), (11, 19), (21, 1), (10, 12), (5, 21), (15, 12), (17, 2), (21, 19), (17, 27), (9, 14), (2, 6), (13, 11), (7, 10), (10, 17), (13, 8), (7, 13), (2, 2), (13, 10), (21, 18), (1, 21), (6, 17), (16, 18), (14, 13), (19, 16), (14, 11), (2, 22), (17, 6), (5, 0), (12, 13), (13, 24), (21, 11), (3, 6), (3, 9), (9, 13), (20, 20), (11, 18), (11, 1), (10, 19), (7, 0), (19, 13), (21, 21), (19, 1), (19, 9), (12, 0), (21, 23), (17, 22), (6, 12), (4, 24), (5, 2), (1, 20), (18, 19), (16, 26), (1, 25), (15, 0), (12, 3), (6, 15), (7, 24), (5, 12), (13, 27), (21, 26), (7, 1), (16, 12), (4, 26), (20, 21), (17, 13), (5, 16), (6, 11), (2, 19), (18, 26), (15, 25), (14, 4), (7, 7), (9, 18), (14, 12), (14, 18), (0, 20), (3, 7), (3, 1), (19, 27), (16, 17), (18, 15), (9, 26), (11, 22), (2, 9), (10, 15), (12, 27), (10, 6), (5, 1), (3, 0), (13, 26), (15, 19), (13, 2), (10, 10), (15, 9), (2, 26), (8, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623700", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), 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), (4, 17), (3, 11), (6, 9), (0, 3), (4, 7), (17, 15), (9, 7), (4, 1), (6, 7), (0, 4), (15, 3), (12, 10), (21, 9), (19, 8), (13, 13), (19, 0), (19, 4), (11, 7), (4, 13), (2, 3), (13, 15), (8, 0), (19, 3), (1, 15), (17, 17), (10, 16), (9, 6), (2, 6), (12, 0), (18, 2), (2, 10), (18, 17), (5, 6), (16, 0), (5, 8), (22, 12), (7, 15), (21, 16), (15, 8), (22, 14), (23, 3), (23, 11), (7, 17), (12, 4), (8, 1), (12, 12), (21, 6), (11, 4), (13, 14), (12, 14), (12, 5), (2, 18), (10, 12), (1, 10), (21, 7), (9, 11), (8, 8), (7, 0), (21, 11), (22, 2), (10, 15), (4, 18), (13, 0), (6, 16), (5, 19), (22, 7), (19, 13), (8, 18), (4, 4), (13, 12), (23, 16), (23, 8), (11, 14), (10, 8), (19, 6), (15, 11), (5, 3), (23, 17), (16, 12), (16, 13), (8, 4), (1, 19), (19, 5), (0, 2), (7, 6), (7, 5), (2, 16), (10, 11), (9, 16), (0, 13), (22, 16), (16, 3), (0, 19), (16, 15), (15, 19), (7, 9), (5, 12), (15, 4), (2, 0), (3, 3), (12, 18), (19, 11), (15, 9), (3, 12), (14, 11), (17, 6), (17, 0), (3, 8), (5, 10), (10, 13), (1, 5), (9, 13), (5, 13), (10, 19), (7, 18), (2, 14), (5, 4), (11, 0), (2, 5), (18, 19), (21, 14), (12, 1), (19, 2), (14, 8), (14, 1), (19, 7), (8, 12), (9, 8), (1, 8), (21, 13), (3, 1), (0, 5), (12, 3), (6, 18), (7, 7), (21, 1), (7, 1), (11, 3), (9, 12), (22, 11), (7, 16), (22, 18), (2, 7), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572952", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 23), (22, 23), (13, 14), (18, 4), (19, 22), (7, 5), (0, 21), (10, 16), (10, 11), (4, 0), (20, 24), (16, 15), (17, 19), (8, 18), (4, 1), (7, 0), (0, 18), (18, 14), (21, 23), (21, 10), (18, 6), (21, 2), (10, 4), (9, 1), (2, 23), (22, 11), (2, 11), (25, 14), (12, 5), (23, 18), (0, 5), (1, 8), (10, 7), (12, 11), (23, 11), (6, 8), (10, 14), (3, 17), (13, 16), (14, 4), (5, 0), (19, 17), (17, 16), (9, 0), (12, 3), (20, 2), (12, 9), (25, 18), (17, 4), (5, 20), (7, 9), (11, 9), (13, 13), (14, 8), (22, 7), (4, 20), (1, 16), (13, 0), (22, 2), (20, 7), (2, 15), (21, 21), (15, 8), (24, 10), (6, 17), (11, 21), (9, 9), (21, 4), (0, 9), (21, 24), (18, 15), (10, 13), (25, 8), (20, 5), (7, 4), (23, 14), (8, 2), (5, 11), (23, 0), (23, 19), (4, 11), (23, 15), (0, 2), (9, 2), (8, 14), (23, 21), (6, 24), (20, 11), (9, 23), (23, 24), (25, 9), (16, 6), (2, 7), (8, 15), (10, 12), (16, 23), (14, 10), (9, 13), (13, 2), (8, 10), (7, 15), (17, 14), (16, 10), (0, 13), (13, 7), (25, 10), (6, 6), (6, 23), (1, 14), (3, 18), (23, 7), (2, 3), (3, 13), (1, 23), (4, 14), (10, 24), (19, 20), (10, 3), (17, 0), (21, 9), (4, 22), (20, 20), (19, 16), (3, 8), (10, 23), (20, 12), (6, 4), (22, 24), (15, 1), (13, 17), (24, 0), (25, 3), (3, 22), (10, 9), (18, 10), (8, 4), (5, 14), (21, 11), (19, 5), (16, 17), (8, 0), (3, 24), (20, 18), (15, 11), (23, 9), (5, 4), (6, 14), (20, 23), (1, 5), (20, 13), (14, 16), (18, 8), (3, 9), (20, 17), (12, 8), (0, 3), (3, 10), (9, 16), (24, 4), (2, 5), (20, 22), (25, 1), (19, 8), (3, 12), (1, 24), (22, 18), (0, 12), (0, 16), (21, 7), (5, 15), (6, 5), (18, 7), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "662256", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), 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), (6, 2), (14, 6), (7, 25), (8, 6), (7, 24), (4, 11), (15, 15), (8, 5), (4, 26), (18, 16), (8, 12), (12, 21), (3, 20), (13, 15), (8, 7), (16, 7), (1, 28), (8, 17), (9, 18), (12, 19), (5, 10), (10, 5), (8, 22), (14, 23), (5, 28), (3, 19), (17, 21), (5, 26), (14, 5), (5, 22), (10, 21), (1, 10), (4, 15), (3, 22), (14, 28), (19, 0), (1, 2), (9, 12), (6, 3), (10, 17), (1, 18), (0, 26), (19, 9), (3, 1), (13, 16), (0, 16), (15, 19), (5, 13), (3, 27), (12, 12), (13, 26), (2, 9), (9, 21), (0, 23), (18, 13), (15, 25), (8, 26), (19, 18), (2, 4), (11, 5), (9, 23), (4, 21), (14, 8), (11, 21), (16, 1), (19, 23), (18, 21), (4, 8), (8, 19), (12, 18), (6, 18), (19, 27), (11, 28), (17, 11), (10, 8), (17, 9), (16, 20), (7, 11), (9, 9), (7, 28), (12, 14), (5, 4), (4, 22), (5, 0), (13, 3), (17, 1), (7, 22), (5, 5), (2, 14), (10, 11), (14, 2), (10, 24), (1, 27), (14, 17), (5, 9), (14, 24), (17, 6), (10, 26), (10, 14), (4, 23), (6, 22), (15, 13), (9, 19), (18, 5), (4, 12), (11, 12), (16, 15), (8, 4), (6, 24), (1, 13), (19, 17), (13, 17), (0, 2), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168700", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), 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), (14, 1), (12, 18), (19, 0), (14, 17), (12, 7), (10, 11), (0, 4), (15, 3), (22, 16), (18, 10), (18, 2), (7, 5), (5, 5), (12, 6), (17, 7), (18, 16), (15, 17), (7, 15), (21, 13), (1, 11), (0, 19), (11, 23), (6, 20), (17, 15), (12, 5), (21, 23), (4, 16), (11, 1), (5, 8), (24, 14), (9, 21), (22, 18), (0, 9), (14, 14), (23, 22), (1, 1), (5, 0), (7, 23), (4, 10), (22, 10), (0, 23), (8, 4), (20, 7), (1, 6), (20, 10), (5, 22), (0, 7), (13, 6), (14, 8), (5, 11), (1, 8), (7, 11), (2, 20), (12, 15), (17, 23), (1, 12), (10, 12), (22, 21), (18, 7), (5, 1), (14, 10), (6, 2), (17, 12), (6, 16), (23, 7), (13, 22), (0, 11), (5, 13), (24, 13), (0, 3), (15, 5), (18, 13), (9, 4), (19, 8), (19, 6), (4, 14), (22, 8), (11, 0), (14, 9), (7, 9), (12, 8), (21, 9), (21, 11), (18, 14), (0, 14), (7, 0), (6, 13), (3, 2), (19, 10), (15, 15), (4, 8), (8, 18), (16, 1), (16, 14), (22, 23), (20, 15), (5, 9), (23, 21), (24, 23), (22, 2), (5, 17), (13, 18), (7, 4), (15, 16), (19, 22), (8, 19), (10, 15), (13, 4), (15, 4), (14, 21), (10, 10), (4, 24), (2, 15), (11, 7), (13, 12), (9, 3), (0, 15), (13, 8), (10, 9), (7, 8), (23, 0), (16, 8), (24, 16), (3, 11), (5, 20), (19, 24), (3, 14), (20, 1), (6, 22), (21, 7), (5, 14), (20, 11), (5, 12), (10, 7), (24, 20), (17, 20), (1, 3), (17, 0), (0, 17), (22, 5), (1, 10), (21, 10), (9, 23), (7, 21), (19, 12), (6, 12), (12, 23), (11, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "808760", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 12), (8, 23), (4, 1), (21, 24), (19, 0), (26, 23), (2, 26), (10, 24), (1, 6), (17, 22), (14, 3), (2, 23), (14, 6), (21, 23), (25, 27), (13, 18), (5, 27), (18, 15), (25, 13), (12, 15), (26, 11), (7, 3), (25, 17), (0, 15), (5, 21), (22, 18), (1, 18), (6, 0), (19, 1), (24, 16), (21, 14), (0, 14), (20, 2), (26, 18), (9, 18), (1, 25), (9, 0), (7, 9), (6, 26), (24, 20), (5, 1), (25, 6), (1, 1), (12, 20), (21, 22), (13, 22), (5, 25), (20, 11), (11, 18), (24, 13), (3, 7), (22, 10), (26, 16), (2, 0), (17, 6), (22, 14), (6, 12), (17, 10), (10, 10), (16, 12), (1, 12), (4, 26), (17, 12), (25, 0), (1, 10), (16, 18), (10, 6), (13, 20), (23, 22), (7, 12), (18, 3), (9, 5), (8, 27), (17, 25), (11, 1), (1, 19), (7, 2), (25, 14), (16, 8), (10, 2), (15, 8), (9, 7), (20, 4), (11, 21), (14, 4), (26, 22), (8, 26), (7, 16), (18, 25), (0, 4), (17, 27), (11, 6), (7, 19), (25, 18), (26, 24), (9, 23), (9, 9), (23, 16), (15, 19), (3, 5), (3, 24), (12, 16), (22, 19), (20, 27), (6, 5), (6, 3), (25, 26), (16, 16), (3, 27), (2, 22), (12, 1), (21, 20), (3, 23), (6, 11), (14, 1), (14, 23), (17, 8), (24, 14), (6, 9), (25, 7), (11, 17), (12, 26), (4, 2), (20, 18), (24, 24), (1, 21), (21, 7), (18, 16), (9, 11), (17, 14), (23, 6), (12, 23), (23, 20), (19, 9), (21, 2), (2, 8), (12, 25), (2, 24), (17, 3), (10, 17), (4, 25), (12, 22), (13, 7), (14, 26), (11, 9), (23, 18), (24, 21), (15, 15), (5, 22), (8, 1), (22, 24), (19, 22), (0, 7), (7, 8), (1, 22), (17, 18), (3, 6), (18, 24), (24, 5), (8, 18), (18, 6), (13, 24), (20, 20), (0, 13), (26, 15), (26, 6), (23, 21), (9, 3), (8, 10), (22, 8), (9, 19), (20, 22), (16, 4), (8, 21), (2, 6), (12, 4), (14, 16), (26, 0), (10, 3), (4, 23), (9, 10), (18, 4), (2, 10), (23, 0), (7, 27), (24, 7), (5, 19), (22, 22), (18, 1), (7, 26), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371256", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 19), (23, 10), (17, 0), (6, 17), (19, 25), (1, 20), (14, 5), (10, 8), (18, 25), (25, 9), (9, 23), (23, 11), (20, 22), (10, 14), (7, 7), (15, 20), (16, 3), (4, 8), (13, 24), (6, 19), (20, 1), (7, 1), (17, 23), (23, 2), (16, 19), (26, 11), (19, 15), (21, 22), (19, 18), (22, 16), (2, 16), (10, 6), (15, 26), (10, 17), (24, 0), (1, 11), (0, 6), (2, 3), (12, 11), (6, 4), (15, 4), (24, 21), (20, 15), (4, 15), (5, 25), (3, 4), (4, 10), (10, 16), (20, 21), (25, 6), (1, 1), (12, 18), (21, 26), (21, 7), (13, 25), (10, 26), (0, 18), (4, 23), (1, 7), (24, 22), (13, 7), (24, 17), (5, 6), (18, 21), (26, 14), (0, 9), (4, 5), (8, 11), (14, 12), (10, 21), (11, 18), (17, 14), (7, 10), (5, 16), (7, 23), (18, 26), (4, 3), (19, 13), (22, 21), (8, 3), (10, 12), (26, 8), (3, 9), (9, 14), (25, 2), (22, 6), (7, 0), (20, 24), (11, 7), (1, 24), (7, 9), (3, 24), (17, 11), (12, 6), (1, 22), (0, 3), (8, 20), (21, 19), (19, 7), (25, 15), (0, 22), (0, 17), (8, 25), (24, 8), (11, 19), (19, 3), (15, 9), (22, 24), (23, 9), (3, 25), (17, 8), (21, 14), (4, 0), (3, 3), (4, 16), (2, 1), (17, 16), (19, 10), (10, 7), (23, 12), (13, 2), (2, 4), (2, 26), (14, 22), (16, 22), (19, 9), (5, 5), (26, 23), (19, 17), (5, 1), (3, 16), (7, 16), (10, 23), (17, 17), (18, 15), (26, 18), (25, 26), (12, 13), (5, 21), (1, 23), (4, 21), (4, 26), (10, 24), (9, 9), (16, 18), (9, 22), (0, 12), (9, 12), (24, 5), (19, 6), (0, 19), (8, 15), (21, 16), (16, 20), (15, 15), (20, 19), (17, 7), (14, 11), (21, 23), (6, 14), (14, 4), (9, 26), (11, 15), (2, 17), (1, 2), (20, 13), (17, 21), (22, 7), (11, 10), (4, 7), (16, 23), (1, 21), (14, 24), (25, 13), (5, 18), (3, 22), (6, 26), (19, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980100", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 2), (2, 20), (17, 14), (7, 23), (15, 5), (19, 9), (18, 17), (11, 4), (13, 6), (4, 10), (12, 22), (7, 19), (6, 17), (19, 1), (4, 13), (3, 17), (6, 9), (4, 19), (22, 8), (11, 11), (8, 6), (3, 5), (2, 24), (16, 12), (1, 17), (22, 11), (16, 4), (8, 20), (22, 9), (2, 12), (11, 1), (5, 17), (9, 5), (6, 12), (5, 22), (20, 17), (19, 22), (19, 14), (2, 17), (2, 10), (7, 15), (17, 2), (21, 2), (7, 21), (10, 16), (2, 16), (22, 21), (7, 11), (5, 15), (15, 22), (0, 19), (20, 14), (6, 14), (17, 11), (4, 6), (3, 4), (12, 1), (13, 15), (7, 20), (13, 11), (8, 12), (9, 11), (21, 8), (13, 4), (6, 8), (11, 10), (18, 14), (19, 7), (11, 13), (3, 3), (15, 11), (10, 22), (20, 6), (15, 13), (12, 0), (1, 2), (20, 11), (14, 7), (21, 15), (9, 9), (21, 12), (5, 5), (10, 21), (17, 3), (12, 21), (21, 6), (17, 0), (20, 8), (10, 7), (18, 4), (1, 22), (16, 3), (9, 13), (12, 23), (8, 2), (21, 14), (6, 22), (19, 15), (18, 12), (16, 23), (10, 18), (9, 23), (8, 16), (2, 19), (7, 9), (11, 8), (4, 3), (6, 11), (5, 24), (13, 23), (18, 13), (20, 13), (6, 10), (7, 13), (8, 24), (20, 9), (1, 19), (18, 7), (11, 23), (14, 3), (20, 7), (7, 3), (17, 7), (5, 12), (21, 9), (14, 8), (1, 16), (0, 10), (20, 3), (16, 24), (21, 5), (16, 16), (14, 16), (16, 14), (22, 0), (8, 11), (22, 4), (10, 10), (1, 20), (8, 3), (5, 0), (8, 23), (0, 8), (10, 11), (20, 12), (7, 14), (3, 18), (16, 17), (8, 13), (5, 1), (5, 21), (9, 24), (8, 4), (17, 20), (13, 20), (22, 12), (1, 15), (21, 18), (17, 23), (21, 16), (4, 12), (20, 18), (19, 3), (21, 20), (1, 12), (7, 16), (1, 21), (20, 10), (18, 9), (17, 1), (10, 23), (14, 20), (17, 16), (14, 12), (13, 16), (15, 10), (7, 2), (19, 24), (4, 16), (11, 21), (12, 17), (18, 3), (16, 5), (6, 21), (19, 6), (5, 10), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787500", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (21, 10), (13, 8), (14, 21), (5, 9), (0, 6), (13, 20), (22, 11), (3, 3), (18, 17), (11, 4), (9, 4), (0, 4), (11, 0), (11, 8), (15, 20), (3, 13), (15, 12), (14, 16), (13, 12), (16, 17), (11, 14), (13, 22), (4, 4), (20, 1), (7, 14), (17, 4), (20, 10), (0, 7), (1, 13), (17, 17), (20, 0), (22, 10), (5, 14), (17, 9), (15, 7), (19, 19), (6, 15), (14, 10), (6, 20), (5, 10), (17, 2), (2, 3), (16, 4), (14, 5), (3, 11), (0, 10), (10, 2), (5, 5), (10, 22), (18, 12), (2, 15), (21, 16), (22, 5), (11, 10), (14, 17), (15, 8), (10, 10), (22, 21), (22, 16), (17, 12), (19, 21), (18, 5), (16, 9), (12, 3), (17, 13), (6, 19), (12, 15), (9, 3), (8, 9), (11, 21), (2, 11), (1, 8), (9, 16), (2, 6), (19, 22), (17, 15), (4, 15), (6, 11), (4, 9), (6, 12), (0, 17), (3, 18), (21, 5), (22, 19), (11, 19), (0, 21), (4, 7), (5, 0), (6, 10), (12, 12), (9, 5), (16, 10), (21, 18), (1, 21), (20, 15), (9, 6), (18, 22), (1, 7), (7, 21), (0, 5), (8, 17), (7, 12), (22, 14), (17, 21), (20, 14), (3, 12), (11, 13), (16, 7), (3, 16), (12, 9), (21, 11), (7, 8), (20, 19), (3, 22), (2, 17), (0, 14), (13, 16), (20, 7), (7, 0), (17, 20), (6, 6), (12, 11), (15, 11), (7, 18), (14, 20), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510384", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 15), (18, 2), (6, 7), (4, 22), (14, 1), (14, 9), (4, 10), (8, 4), (20, 21), (16, 24), (3, 24), (1, 4), (10, 25), (4, 15), (0, 16), (19, 11), (14, 22), (4, 9), (18, 27), (21, 11), (20, 0), (18, 8), (9, 13), (13, 26), (0, 3), (4, 19), (14, 26), (0, 14), (0, 27), (18, 14), (12, 10), (8, 5), (16, 2), (5, 7), (1, 21), (8, 6), (11, 24), (11, 23), (5, 9), (19, 26), (0, 12), (4, 13), (18, 26), (17, 7), (20, 24), (1, 6), (15, 23), (5, 16), (11, 20), (11, 5), (10, 19), (17, 3), (13, 12), (2, 6), (4, 1), (17, 17), (9, 3), (21, 19), (8, 2), (8, 19), (0, 23), (0, 4), (20, 6), (20, 13), (10, 27), (21, 24), (11, 3), (21, 6), (21, 5), (6, 0), (3, 7), (10, 14), (18, 6), (0, 1), (3, 18), (17, 22), (7, 12), (11, 19), (11, 8), (3, 12), (1, 7), (12, 13), (10, 15), (10, 8), (3, 16), (15, 19), (16, 25), (19, 12), (17, 2), (10, 13), (13, 2), (7, 6), (17, 25), (7, 11), (6, 27), (3, 25), (12, 12), (12, 4), (1, 10), (8, 18), (3, 14), (15, 5), (3, 26), (6, 13), (5, 11), (16, 14), (10, 10), (15, 18), (13, 27), (13, 22), (10, 22), (20, 11), (11, 25), (15, 26), (17, 14), (15, 3), (18, 3), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315624", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 22), (9, 20), (5, 11), (9, 17), (10, 24), (8, 24), (14, 17), (14, 14), (3, 20), (17, 15), (17, 0), (17, 17), (4, 18), (20, 2), (19, 6), (16, 3), (2, 24), (16, 10), (18, 15), (18, 17), (1, 8), (6, 3), (15, 5), (17, 4), (14, 9), (14, 5), (11, 13), (18, 9), (18, 16), (11, 3), (2, 16), (14, 18), (9, 2), (8, 7), (9, 21), (9, 0), (20, 24), (17, 2), (19, 1), (15, 25), (6, 16), (5, 6), (6, 6), (2, 10), (10, 20), (13, 9), (16, 9), (0, 24), (14, 16), (12, 21), (7, 25), (13, 11), (21, 23), (3, 13), (8, 23), (16, 19), (7, 5), (0, 14), (9, 16), (15, 11), (10, 25), (11, 6), (15, 21), (18, 0), (7, 12), (16, 13), (15, 19), (3, 15), (6, 5), (19, 11), (21, 22), (5, 4), (0, 11), (18, 19), (10, 1), (20, 6), (11, 24), (4, 2), (10, 12), (6, 9), (15, 9), (10, 18), (11, 0), (18, 4), (1, 15), (6, 10), (21, 17), (10, 23), (0, 13), (16, 17), (20, 1), (11, 7), (9, 19), (9, 14), (2, 25), (5, 15), (2, 6), (19, 5), (10, 13), (11, 25), (12, 1), (7, 13), (12, 0), (12, 22), (6, 2), (3, 2), (18, 13), (13, 8), (12, 15), (13, 4), (13, 16), (16, 24), (5, 2), (5, 12), (10, 11), (18, 3), (1, 13), (0, 15), (12, 24), (2, 15), (15, 1), (20, 3), (14, 15), (21, 1), (1, 6), (4, 10), (1, 17), (14, 2), (16, 12), (6, 19), (20, 5), (19, 3), (16, 7), (21, 19), (21, 12), (18, 5), (6, 25), (17, 20), (11, 4), (5, 25), (20, 9), (6, 20), (12, 19), (5, 9), (13, 19), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "716736", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (11, 21), (11, 14), (3, 0), (9, 21), (16, 15), (3, 6), (0, 16), (15, 8), (22, 5), (11, 16), (8, 21), (3, 11), (15, 9), (12, 7), (1, 1), (1, 8), (8, 11), (16, 12), (6, 3), (7, 3), (1, 6), (17, 11), (15, 16), (12, 0), (11, 25), (11, 5), (18, 14), (15, 3), (13, 2), (10, 13), (23, 20), (1, 9), (21, 20), (14, 21), (20, 12), (5, 19), (15, 6), (5, 8), (13, 9), (22, 3), (5, 12), (16, 25), (20, 16), (8, 8), (1, 3), (21, 15), (13, 3), (23, 3), (10, 19), (9, 22), (22, 2), (19, 2), (16, 13), (2, 13), (22, 24), (1, 20), (17, 5), (2, 19), (17, 25), (16, 22), (16, 16), (10, 9), (18, 21), (8, 12), (14, 7), (14, 11), (0, 27), (8, 13), (15, 4), (11, 26), (3, 17), (8, 15), (3, 26), (14, 9), (14, 28), (5, 23), (16, 8), (11, 11), (19, 11), (0, 25), (7, 23), (6, 9), (11, 10), (21, 2), (12, 11), (4, 17), (23, 6), (12, 21), (17, 3), (12, 4), (6, 24), (23, 4), (11, 23), (23, 13), (20, 24), (20, 22), (14, 20), (8, 22), (5, 16), (13, 17), (9, 13), (16, 5), (1, 26), (19, 15), (7, 26), (20, 23), (6, 22), (23, 12), (4, 14), (11, 8), (17, 16), (4, 25), (10, 24), (21, 3), (14, 1), (1, 5), (2, 23), (18, 27), (22, 11), (10, 15), (20, 15), (6, 25), (2, 27), (14, 4), (11, 0), (16, 21), (19, 16), (7, 17), (22, 21), (22, 20), (14, 23), (1, 12), (0, 15), (19, 13), (11, 27), (12, 18), (1, 7), (1, 24), (17, 18), (17, 23), (7, 8), (17, 7), (11, 19), (22, 14), (7, 6), (14, 25), (7, 2), (5, 14), (4, 4), (23, 22), (7, 0), (21, 27), (13, 23), (9, 23), (1, 10), (2, 14), (6, 17), (8, 2), (18, 0), (4, 21), (2, 0), (15, 24), (16, 18), (9, 3), (18, 16), (17, 26), (23, 26), (17, 15), (0, 8), (20, 6), (4, 27), (0, 9), (18, 20), (14, 14), (17, 6), (1, 2), (12, 15), (11, 4), (23, 18), (19, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "881284", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 21), (11, 0), (6, 10), (1, 6), (15, 12), (18, 6), (9, 10), (23, 17), (9, 20), (8, 13), (24, 14), (8, 19), (0, 8), (4, 0), (6, 17), (5, 16), (11, 10), (17, 16), (15, 6), (10, 3), (8, 4), (17, 17), (3, 1), (18, 11), (23, 0), (24, 15), (13, 0), (18, 18), (11, 2), (22, 0), (22, 17), (21, 17), (7, 2), (1, 16), (17, 15), (8, 15), (0, 16), (10, 18), (21, 4), (18, 0), (24, 1), (3, 7), (23, 2), (4, 16), (11, 20), (23, 13), (11, 5), (5, 11), (22, 4), (14, 16), (17, 11), (8, 18), (22, 19), (17, 0), (10, 17), (24, 9), (22, 18), (14, 9), (5, 1), (19, 16), (21, 9), (23, 11), (10, 12), (12, 20), (7, 8), (5, 5), (2, 16), (6, 14), (12, 16), (8, 7), (12, 21), (6, 12), (7, 18), (10, 11), (16, 21), (12, 14), (11, 1), (20, 7), (22, 1), (10, 9), (0, 3), (12, 9), (8, 10), (16, 20), (18, 7), (18, 13), (15, 21), (17, 5), (2, 7), (13, 9), (15, 16), (8, 6), (22, 3), (7, 7), (1, 11), (17, 9), (20, 12), (18, 12), (15, 2), (16, 6), (20, 9), (3, 3), (2, 19), (5, 17), (4, 11), (14, 3), (19, 15), (9, 0), (7, 20), (9, 12), (17, 21), (2, 20), (1, 15), (23, 3), (10, 7), (4, 21), (23, 9), (8, 0), (15, 10), (14, 0), (20, 19), (10, 19), (13, 7), (22, 2), (4, 17), (5, 6), (13, 11), (0, 7), (2, 18), (13, 15), (4, 15), (12, 12), (7, 0), (22, 15), (0, 17), (1, 7), (6, 7), (1, 5), (6, 2), (9, 1), (13, 8), (12, 0), (3, 2), (12, 5), (15, 20), (14, 20), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "597552", "dataset": "MATH"}
{"messages": [{"content": "In a 26x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (21, 6), (18, 22), (6, 3), (17, 3), (15, 12), (4, 10), (17, 16), (14, 23), (19, 19), (2, 19), (4, 2), (9, 7), (8, 11), (2, 0), (9, 4), (5, 13), (11, 17), (8, 7), (3, 0), (16, 17), (2, 13), (20, 23), (9, 16), (0, 13), (4, 21), (1, 8), (18, 20), (15, 0), (3, 14), (11, 0), (16, 21), (13, 16), (6, 19), (20, 14), (0, 4), (3, 21), (23, 16), (3, 3), (3, 7), (15, 22), (9, 5), (11, 20), (22, 16), (25, 6), (20, 18), (9, 12), (20, 22), (0, 15), (22, 0), (18, 12), (24, 18), (11, 8), (13, 18), (8, 17), (5, 11), (25, 0), (2, 17), (8, 24), (16, 1), (25, 2), (5, 10), (3, 19), (3, 5), (24, 16), (13, 11), (22, 4), (7, 15), (5, 23), (16, 23), (2, 24), (21, 14), (6, 11), (25, 10), (2, 20), (1, 16), (5, 2), (23, 1), (23, 2), (3, 22), (23, 3), (10, 22), (14, 6), (21, 4), (22, 13), (1, 19), (3, 11), (20, 1), (16, 12), (5, 19), (20, 8), (7, 20), (13, 15), (17, 18), (15, 9), (19, 16), (4, 24), (7, 16), (3, 10), (10, 4), (17, 2), (12, 4), (23, 11), (25, 20), (2, 12), (17, 10), (11, 1), (23, 17), (18, 3), (1, 5), (18, 15), (20, 3), (10, 19), (24, 7), (3, 2), (16, 4), (17, 15), (22, 2), (25, 23), (14, 12), (24, 21), (23, 19), (3, 13), (5, 3), (24, 3), (6, 20), (15, 16), (24, 9), (20, 13), (22, 7), (19, 8), (8, 5), (2, 10), (5, 16), (1, 6), (8, 10), (23, 4), (2, 23), (3, 18), (16, 15), (12, 19), (15, 17), (18, 19), (0, 14), (8, 20), (17, 11), (9, 13), (9, 0), (21, 10), (4, 7), (18, 14), (19, 0), (9, 15), (6, 9), (13, 1), (20, 5), (2, 3), (19, 20), (8, 0), (19, 22), (25, 4), (21, 7), (5, 14), (24, 10), (18, 21), (23, 21), (18, 1), (0, 17), (22, 11), (5, 12), (25, 13), (8, 2), (14, 10), (9, 14), (15, 10), (14, 13), (6, 22), (19, 3), (1, 11), (23, 13), (14, 22), (13, 3), (22, 14), (17, 19), (23, 23), (23, 6), (12, 10), (17, 24), (1, 15), (3, 1), (0, 24), (10, 21), (7, 10), (13, 6), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "859344", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 22), (6, 3), (2, 22), (14, 12), (9, 15), (13, 7), (13, 13), (11, 5), (14, 13), (20, 24), (19, 2), (2, 23), (8, 0), (2, 14), (8, 6), (18, 16), (22, 6), (18, 8), (1, 0), (4, 20), (20, 11), (23, 7), (14, 20), (14, 1), (18, 17), (12, 3), (10, 3), (18, 22), (1, 7), (8, 24), (4, 16), (22, 16), (19, 11), (6, 24), (14, 8), (13, 9), (18, 14), (12, 6), (10, 15), (3, 1), (23, 24), (8, 2), (7, 20), (21, 5), (8, 19), (13, 0), (14, 0), (3, 12), (10, 5), (10, 25), (10, 2), (12, 1), (16, 7), (16, 8), (15, 15), (11, 24), (14, 25), (16, 23), (22, 14), (9, 20), (23, 12), (22, 2), (21, 24), (16, 6), (10, 21), (4, 4), (7, 0), (17, 10), (2, 3), (23, 16), (5, 9), (18, 21), (13, 8), (9, 18), (10, 18), (10, 20), (23, 19), (11, 20), (1, 3), (11, 13), (21, 9), (5, 5), (17, 20), (8, 4), (1, 16), (0, 22), (4, 3), (3, 23), (4, 14), (5, 10), (4, 21), (22, 4), (17, 4), (7, 24), (5, 15), (20, 8), (23, 18), (12, 23), (10, 0), (4, 10), (17, 17), (23, 15), (22, 11), (9, 9), (6, 10), (2, 13), (5, 24), (17, 24), (7, 3), (21, 1), (6, 22), (19, 10), (16, 13), (5, 12), (4, 25), (3, 21), (6, 18), (6, 16), (9, 5), (15, 8), (23, 1), (3, 2), (7, 25), (6, 21), (14, 19), (6, 0), (17, 23), (21, 11), (11, 4), (4, 11), (20, 5), (11, 9), (16, 12), (18, 5), (11, 7), (3, 18), (6, 8), (5, 7), (6, 9), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48475", "dataset": "MATH"}
{"messages": [{"content": "In a 27x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 20), (23, 23), (7, 20), (11, 10), (21, 11), (26, 23), (23, 20), (12, 27), (5, 5), (6, 2), (14, 17), (19, 7), (13, 4), (5, 27), (9, 20), (6, 21), (2, 17), (20, 6), (5, 11), (3, 15), (17, 21), (1, 17), (26, 0), (9, 17), (6, 9), (24, 3), (21, 16), (22, 9), (11, 24), (1, 3), (2, 24), (26, 5), (9, 26), (4, 27), (9, 1), (16, 6), (5, 23), (26, 17), (20, 16), (7, 17), (12, 11), (3, 16), (0, 13), (1, 1), (17, 0), (19, 27), (10, 5), (11, 6), (21, 8), (16, 25), (13, 20), (26, 16), (5, 25), (1, 8), (2, 14), (11, 1), (16, 10), (20, 15), (12, 19), (7, 12), (9, 9), (9, 4), (26, 22), (14, 28), (22, 18), (22, 16), (13, 21), (26, 1), (10, 2), (4, 19), (1, 10), (2, 28), (5, 20), (25, 2), (4, 3), (22, 0), (19, 15), (2, 11), (15, 22), (14, 12), (18, 6), (8, 0), (26, 8), (7, 19), (26, 11), (0, 20), (25, 26), (18, 2), (23, 13), (8, 11), (16, 8), (25, 23), (10, 3), (26, 6), (6, 8), (15, 8), (8, 25), (21, 0), (19, 23), (0, 23), (9, 7), (26, 7), (17, 9), (11, 5), (22, 10), (14, 11), (6, 10), (9, 27), (26, 24), (16, 11), (22, 2), (25, 16), (5, 9), (1, 20), (6, 15), (21, 1), (25, 6), (3, 3), (20, 10), (21, 12), (9, 16), (11, 11), (12, 23), (19, 10), (0, 7), (17, 10), (8, 21), (14, 19), (2, 7), (19, 14), (23, 22), (7, 27), (12, 3), (11, 3), (18, 20), (25, 8), (1, 19), (21, 26), (15, 21), (4, 15), (9, 21), (8, 2), (12, 22), (24, 15), (25, 19), (21, 20), (8, 3), (11, 2), (15, 14), (15, 6), (17, 27), (24, 26), (21, 28), (21, 17), (7, 16), (18, 9), (10, 22), (13, 16), (17, 8), (5, 28), (15, 15), (19, 9), (2, 22), (24, 13), (17, 16), (0, 19), (13, 23), (0, 3), (15, 19), (15, 1), (19, 0), (0, 21), (5, 7), (5, 18), (6, 17), (10, 10), (14, 8), (3, 12), (17, 15), (13, 7), (24, 5), (12, 21), (7, 22), (0, 18), (26, 10), (6, 27), (22, 6), (23, 18), (2, 0), (0, 4), (24, 6), (13, 19), (6, 18), (23, 0), (1, 24), (20, 18), (20, 8), (9, 18), (14, 2), (6, 14), (1, 14), (0, 11), (3, 4), (14, 13), (14, 26), (2, 26), (12, 1), (8, 9), (14, 14), (13, 15), (23, 9), (14, 15), (2, 12), (4, 7), (14, 4), (8, 17), (18, 27), (17, 6), (2, 25), (13, 1), (0, 16), (6, 0), (1, 18), (20, 23), (13, 17), (22, 22), (3, 8), (24, 12), (23, 17), (19, 20), (10, 24), (4, 21), (20, 3), (0, 22), (24, 8), (22, 1), (20, 4), (7, 2), (7, 21), (16, 0), (3, 24), (8, 23), (9, 25), (18, 3), (10, 28), (20, 0), (18, 17), (24, 11), (13, 14), (18, 22), (14, 16), (6, 5), (5, 2), (20, 11), (8, 26), (25, 1), (14, 24), (15, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "678708", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), 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), (4, 8), (22, 0), (7, 12), (7, 8), (0, 19), (4, 10), (6, 0), (25, 8), (18, 7), (5, 0), (6, 10), (3, 6), (21, 12), (24, 16), (17, 17), (16, 2), (13, 18), (16, 21), (6, 7), (13, 13), (1, 2), (26, 0), (13, 21), (13, 8), (1, 23), (23, 19), (3, 20), (18, 18), (3, 8), (20, 21), (21, 0), (18, 6), (24, 10), (9, 8), (11, 6), (7, 19), (23, 12), (9, 9), (13, 2), (14, 0), (24, 20), (17, 14), (7, 17), (20, 11), (8, 13), (19, 5), (5, 14), (13, 22), (6, 4), (10, 13), (13, 14), (2, 5), (23, 6), (18, 21), (1, 9), (8, 9), (12, 6), (13, 15), (14, 16), (22, 10), (20, 17), (23, 4), (20, 4), (22, 14), (25, 12), (25, 22), (6, 5), (1, 15), (12, 5), (19, 19), (9, 10), (4, 21), (15, 9), (15, 16), (7, 13), (9, 20), (10, 3), (2, 11), (18, 9), (10, 7), (6, 14), (18, 1), (3, 17), (2, 21), (3, 12), (17, 9), (24, 13), (22, 6), (25, 10), (20, 0), (18, 4), (22, 17), (10, 22), (17, 16), (0, 7), (1, 0), (8, 12), (9, 3), (10, 2), (10, 1), (19, 22), (3, 19), (9, 23), (22, 15), (0, 8), (16, 20), (6, 16), (18, 13), (3, 21), (24, 19), (19, 3), (24, 18), (26, 11), (23, 0), (26, 8), (20, 14), (12, 11), (6, 3), (3, 13), (9, 14), (8, 11), (20, 23), (16, 19), (4, 16), (5, 23), (26, 20), (5, 16), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82368", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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), (4, 10), (20, 23), (5, 17), (8, 11), (7, 23), (20, 24), (21, 19), (23, 9), (9, 7), (1, 18), (2, 12), (13, 14), (13, 18), (19, 11), (4, 7), (18, 23), (10, 22), (1, 16), (22, 17), (20, 21), (15, 3), (15, 6), (8, 8), (14, 16), (6, 24), (6, 13), (21, 11), (1, 10), (21, 15), (21, 12), (8, 23), (11, 17), (18, 14), (19, 4), (23, 7), (15, 10), (10, 17), (14, 23), (21, 24), (13, 16), (17, 17), (7, 20), (10, 3), (13, 17), (13, 22), (8, 4), (15, 17), (8, 2), (2, 23), (23, 18), (12, 4), (7, 1), (16, 8), (2, 0), (21, 1), (2, 16), (9, 19), (20, 9), (2, 3), (23, 8), (16, 3), (3, 17), (15, 13), (3, 18), (4, 4), (10, 13), (3, 14), (16, 19), (0, 8), (4, 0), (9, 16), (6, 12), (15, 7), (14, 4), (15, 8), (19, 10), (22, 19), (2, 17), (5, 16), (10, 4), (7, 16), (23, 10), (8, 21), (18, 8), (12, 13), (18, 12), (22, 7), (20, 0), (16, 24), (9, 15), (15, 11), (22, 24), (19, 2), (18, 24), (9, 14), (4, 20), (1, 7), (11, 8), (3, 0), (21, 2), (8, 9), (11, 10), (13, 4), (6, 0), (7, 24), (23, 20), (16, 10), (20, 19), (22, 11), (17, 3), (18, 21), (1, 24), (6, 9), (11, 3), (14, 0), (12, 2), (4, 6), (4, 18), (8, 15), (11, 15), (0, 24), (11, 14), (5, 12), (21, 10), (15, 24), (8, 7), (14, 19), (8, 10), (10, 11), (9, 20), (12, 6), (17, 6), (7, 19), (15, 18), (14, 20), (14, 10), (4, 2), (5, 7), (15, 20), (16, 18), (11, 24), (4, 19), (1, 4), (20, 1), (23, 3), (7, 14), (18, 10), (15, 12), (23, 1), (16, 20), (2, 4), (6, 19), (23, 14), (13, 23), (13, 2), (17, 15), (13, 24), (23, 11), (10, 2), (18, 3), (16, 9), (9, 10), (14, 11), (12, 14), (6, 20), (23, 4), (10, 1), (16, 7), (19, 21), (14, 2), (8, 5), (12, 15), (14, 8), (11, 12), (16, 12), (17, 19), (10, 12), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606240", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (4, 19), (18, 19), (3, 5), (10, 3), (9, 18), (3, 3), (14, 20), (1, 13), (3, 1), (19, 14), (12, 12), (1, 17), (5, 17), (9, 1), (13, 3), (12, 19), (13, 14), (11, 7), (12, 20), (11, 14), (9, 9), (4, 15), (16, 11), (11, 5), (11, 3), (18, 10), (11, 18), (4, 11), (9, 20), (10, 8), (20, 11), (13, 0), (16, 7), (18, 1), (15, 7), (18, 17), (19, 12), (19, 7), (13, 17), (20, 4), (20, 9), (7, 16), (3, 7), (12, 3), (18, 13), (13, 18), (3, 11), (13, 8), (18, 11), (5, 14), (16, 17), (6, 16), (10, 13), (16, 6), (6, 20), (22, 14), (17, 4), (4, 2), (7, 19), (2, 11), (15, 17), (3, 2), (8, 3), (12, 16), (1, 4), (21, 11), (20, 6), (12, 9), (20, 16), (10, 5), (15, 0), (3, 13), (4, 17), (12, 15), (8, 6), (9, 0), (6, 17), (21, 8), (6, 10), (8, 15), (21, 14), (19, 10), (2, 9), (10, 16), (4, 20), (0, 3), (6, 5), (22, 2), (22, 19), (19, 1), (6, 15), (5, 3), (14, 0), (16, 15), (21, 15), (12, 7), (17, 10), (9, 17), (2, 8), (6, 1), (7, 18), (2, 16), (19, 8), (9, 14), (16, 19), (3, 6), (16, 4), (14, 9), (15, 10), (4, 8), (8, 12), (2, 19), (8, 2), (9, 4), (3, 8), (10, 2), (6, 12), (8, 13), (20, 20), (17, 1), (5, 2), (19, 15), (21, 2), (10, 12), (5, 8), (17, 0), (14, 8), (5, 1), (4, 5), (3, 12), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "697956", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (1, 8), (13, 17), (18, 2), (0, 9), (6, 22), (17, 8), (8, 16), (12, 5), (12, 4), (9, 2), (8, 2), (2, 12), (16, 13), (12, 19), (9, 10), (2, 24), (20, 20), (12, 2), (1, 12), (21, 22), (19, 2), (7, 7), (6, 1), (7, 16), (4, 14), (18, 1), (15, 9), (4, 22), (12, 8), (21, 6), (2, 5), (3, 4), (2, 14), (18, 3), (20, 1), (14, 24), (18, 10), (10, 0), (9, 0), (5, 12), (15, 17), (14, 22), (5, 23), (1, 11), (6, 13), (7, 5), (9, 5), (0, 21), (3, 6), (19, 6), (6, 9), (20, 13), (6, 14), (7, 23), (12, 11), (20, 4), (17, 14), (5, 14), (19, 17), (14, 6), (13, 20), (9, 21), (5, 19), (0, 5), (15, 0), (19, 11), (2, 7), (6, 17), (20, 7), (11, 4), (21, 13), (7, 3), (19, 7), (5, 5), (7, 18), (11, 2), (0, 14), (4, 18), (12, 24), (3, 19), (3, 17), (10, 7), (15, 1), (9, 20), (3, 2), (1, 10), (17, 3), (13, 0), (19, 16), (2, 13), (10, 1), (7, 24), (1, 0), (21, 20), (2, 9), (10, 16), (4, 21), (21, 17), (11, 14), (0, 15), (10, 20), (18, 8), (6, 19), (13, 9), (7, 19), (19, 14), (1, 23), (14, 1), (8, 3), (17, 18), (10, 17), (14, 5), (16, 22), (2, 20), (20, 8), (13, 7), (17, 10), (3, 18), (5, 11), (7, 22), (20, 15), (19, 5), (1, 13), (8, 7), (13, 10), (21, 15), (17, 11), (9, 3), (17, 1), (15, 24), (14, 12), (5, 16), (0, 22), (9, 15), (2, 10), (6, 3), (19, 3), (9, 17), (8, 17), (0, 19), (11, 5), (5, 6), (11, 19), (20, 16), (1, 24), (21, 18), (2, 17), (18, 5), (12, 15), (20, 23), (10, 21), (8, 18), (11, 9), (11, 7), (18, 24), (18, 21), (2, 2), (17, 21), (17, 24), (2, 0), (20, 14), (20, 10), (21, 7), (12, 9), (15, 7), (17, 15), (12, 21), (0, 24), (3, 14), (21, 14), (15, 11), (11, 17), (21, 4), (18, 12), (6, 5), (15, 2), (8, 14), (11, 21), (21, 3), (7, 15), (3, 1), (4, 11), (0, 16), (18, 4), (5, 0), (8, 23), (13, 2), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767748", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 22), (3, 1), (13, 15), (14, 13), (13, 6), (17, 9), (10, 18), (21, 13), (19, 12), (21, 7), (20, 14), (1, 5), (7, 19), (0, 6), (7, 12), (9, 14), (13, 21), (16, 15), (6, 12), (10, 20), (19, 8), (20, 8), (4, 11), (19, 5), (8, 16), (3, 14), (11, 18), (15, 1), (16, 6), (15, 5), (0, 11), (2, 6), (17, 21), (14, 19), (20, 18), (6, 3), (8, 17), (17, 2), (3, 4), (0, 2), (4, 20), (4, 16), (5, 9), (4, 3), (2, 19), (6, 4), (13, 12), (8, 14), (19, 3), (17, 14), (7, 21), (12, 5), (3, 7), (11, 17), (6, 20), (0, 1), (9, 2), (14, 16), (18, 17), (4, 1), (1, 4), (2, 12), (17, 18), (13, 22), (4, 21), (12, 0), (7, 5), (12, 3), (7, 4), (20, 5), (7, 18), (12, 9), (14, 14), (2, 22), (16, 18), (4, 10), (13, 2), (2, 13), (17, 3), (5, 5), (14, 6), (1, 9), (11, 11), (1, 17), (1, 20), (12, 11), (2, 18), (12, 13), (3, 9), (5, 21), (12, 15), (0, 9), (6, 13), (19, 14), (5, 4), (11, 16), (19, 7), (5, 18), (15, 8), (10, 14), (21, 15), (6, 2), (20, 2), (11, 8), (20, 1), (3, 18), (10, 19), (14, 22), (2, 5), (0, 17), (0, 21), (7, 11), (9, 11), (6, 6), (21, 1), (20, 4), (5, 22), (3, 6), (12, 20), (10, 1), (2, 1), (1, 13), (9, 16), (12, 22), (8, 2), (3, 12), (13, 10), (8, 10), (14, 18), (14, 15), (1, 2), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822921", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), 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), (6, 22), (6, 27), (13, 7), (7, 11), (12, 19), (17, 24), (19, 24), (5, 14), (8, 16), (0, 27), (14, 28), (0, 1), (15, 11), (13, 24), (1, 25), (1, 10), (6, 15), (0, 20), (6, 13), (2, 19), (19, 21), (6, 17), (9, 27), (16, 11), (10, 19), (12, 22), (4, 15), (13, 14), (12, 14), (0, 17), (12, 0), (7, 5), (17, 26), (11, 4), (6, 28), (2, 16), (1, 24), (0, 8), (13, 3), (13, 10), (15, 15), (3, 13), (8, 17), (6, 4), (9, 5), (18, 13), (6, 2), (11, 13), (0, 18), (5, 13), (13, 4), (13, 22), (1, 17), (1, 19), (4, 10), (1, 16), (4, 17), (15, 10), (19, 5), (15, 12), (13, 26), (5, 11), (7, 7), (1, 12), (2, 17), (12, 18), (1, 22), (14, 0), (11, 14), (4, 12), (8, 25), (16, 8), (7, 16), (7, 8), (14, 21), (12, 28), (15, 5), (5, 10), (1, 13), (9, 8), (14, 20), (8, 9), (5, 15), (14, 22), (11, 0), (15, 22), (18, 20), (8, 3), (6, 18), (18, 7), (3, 25), (15, 14), (0, 10), (4, 16), (9, 13), (2, 4), (7, 14), (1, 9), (14, 2), (11, 1), (19, 11), (9, 4), (11, 5), (6, 6), (7, 2), (13, 16), (0, 28), (7, 27), (4, 14), (9, 28), (6, 19), (6, 25), (11, 16), (19, 12), (10, 16), (15, 13), (5, 20), (8, 14), (10, 8), (14, 1), (19, 15), (17, 14), (11, 15), (13, 17), (19, 25), (7, 15), (7, 26), (17, 5), (9, 1), (11, 12), (10, 28), (0, 13), (10, 14), (5, 7), (13, 19), (17, 17), (19, 16), (18, 24), (9, 17), (18, 10), (18, 28), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464780", "dataset": "MATH"}
{"messages": [{"content": "In a 20x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 23), (8, 4), (5, 23), (7, 5), (1, 22), (6, 8), (3, 24), (15, 1), (16, 2), (4, 22), (13, 14), (0, 2), (3, 13), (0, 13), (13, 3), (17, 24), (2, 2), (13, 20), (10, 24), (15, 14), (14, 2), (8, 16), (9, 6), (14, 12), (17, 11), (19, 9), (16, 6), (3, 1), (14, 3), (2, 18), (6, 9), (1, 15), (9, 7), (19, 7), (18, 20), (11, 13), (14, 5), (12, 2), (14, 20), (9, 24), (17, 7), (8, 5), (14, 21), (18, 6), (3, 16), (18, 18), (13, 6), (10, 10), (8, 22), (7, 0), (13, 10), (13, 8), (3, 11), (18, 23), (8, 17), (14, 9), (0, 3), (6, 10), (15, 3), (14, 6), (2, 11), (18, 11), (15, 2), (0, 5), (3, 19), (16, 24), (19, 18), (10, 6), (2, 19), (6, 21), (15, 21), (11, 3), (16, 15), (12, 0), (10, 17), (4, 11), (10, 13), (0, 19), (19, 13), (16, 17), (11, 4), (18, 21), (7, 22), (1, 5), (13, 0), (6, 23), (10, 18), (1, 23), (18, 24), (3, 6), (13, 17), (13, 7), (1, 4), (5, 2), (4, 3), (9, 8), (10, 12), (15, 17), (1, 8), (12, 16), (9, 23), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366738", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), 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), (4, 8), (13, 3), (1, 20), (11, 11), (10, 2), (19, 21), (12, 9), (5, 25), (0, 4), (9, 16), (0, 15), (6, 26), (6, 14), (9, 1), (19, 22), (0, 12), (18, 12), (2, 11), (5, 11), (1, 19), (9, 14), (7, 17), (11, 12), (19, 9), (5, 26), (9, 22), (0, 14), (11, 10), (15, 3), (9, 18), (0, 17), (3, 14), (14, 15), (17, 12), (5, 16), (11, 16), (10, 7), (0, 5), (4, 21), (11, 17), (14, 20), (3, 26), (3, 7), (4, 2), (8, 23), (12, 19), (7, 1), (11, 18), (17, 25), (18, 26), (10, 12), (13, 15), (7, 9), (9, 26), (6, 1), (4, 1), (18, 8), (14, 11), (18, 23), (8, 19), (12, 16), (6, 10), (2, 2), (7, 15), (11, 6), (15, 21), (13, 17), (12, 22), (1, 1), (10, 17), (5, 15), (17, 11), (6, 20), (2, 9), (16, 16), (8, 17), (17, 17), (7, 10), (14, 13), (7, 23), (0, 9), (13, 22), (11, 19), (14, 19), (9, 7), (8, 5), (19, 15), (15, 18), (10, 6), (11, 21), (18, 4), (14, 3), (13, 19), (0, 21), (12, 15), (7, 12), (5, 9), (9, 21), (6, 18), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199752", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 20), (12, 10), (2, 14), (18, 11), (19, 4), (15, 9), (9, 5), (12, 1), (1, 9), (5, 20), (9, 18), (8, 1), (5, 5), (19, 21), (9, 20), (16, 15), (17, 17), (14, 4), (10, 19), (3, 13), (4, 3), (7, 16), (19, 18), (5, 17), (9, 4), (14, 21), (17, 22), (13, 17), (16, 7), (9, 16), (5, 11), (1, 21), (13, 1), (1, 12), (15, 2), (6, 8), (3, 6), (19, 19), (18, 22), (17, 12), (19, 3), (12, 21), (9, 9), (2, 8), (9, 23), (9, 19), (18, 17), (0, 16), (8, 7), (0, 21), (9, 13), (14, 10), (8, 13), (17, 5), (15, 8), (4, 5), (6, 7), (7, 19), (7, 23), (9, 22), (14, 9), (15, 11), (4, 8), (15, 6), (19, 10), (11, 13), (8, 19), (6, 13), (5, 7), (12, 12), (16, 13), (5, 13), (18, 3), (6, 14), (2, 20), (15, 12), (15, 4), (1, 8), (3, 2), (10, 9), (7, 17), (7, 9), (11, 5), (15, 21), (11, 4), (2, 4), (11, 16), (12, 16), (3, 23), (11, 22), (6, 0), (7, 10), (0, 4), (6, 19), (3, 18), (4, 1), (11, 20), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "503298", "dataset": "MATH"}
{"messages": [{"content": "In a 24x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 28), 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), (21, 8), (1, 4), (20, 0), (22, 26), (3, 7), (4, 14), (23, 21), (12, 5), (19, 23), (9, 15), (21, 15), (12, 6), (20, 15), (10, 23), (13, 17), (11, 24), (1, 25), (23, 4), (5, 7), (16, 20), (6, 3), (17, 11), (5, 12), (4, 23), (11, 27), (22, 21), (4, 2), (22, 18), (20, 27), (22, 2), (9, 13), (14, 9), (5, 20), (12, 8), (20, 12), (8, 21), (0, 24), (18, 7), (4, 17), (0, 4), (10, 22), (15, 2), (8, 22), (7, 22), (0, 8), (8, 18), (13, 23), (12, 27), (16, 27), (18, 17), (4, 7), (18, 1), (12, 22), (9, 22), (22, 25), (0, 26), (13, 8), (1, 19), (15, 25), (20, 4), (6, 0), (23, 25), (17, 1), (4, 12), (10, 9), (15, 7), (9, 25), (8, 12), (18, 23), (16, 24), (6, 2), (7, 0), (23, 23), (21, 14), (17, 20), (20, 18), (22, 24), (15, 6), (19, 12), (19, 25), (10, 5), (15, 28), (14, 15), (8, 7), (11, 15), (22, 9), (14, 21), (13, 16), (6, 20), (22, 19), (18, 27), (18, 6), (14, 25), (18, 9), (4, 6), (1, 5), (17, 9), (18, 8), (9, 11), (11, 13), (11, 8), (20, 24), (18, 16), (19, 27), (0, 1), (6, 28), (12, 9), (8, 4), (15, 16), (20, 16), (23, 14), (22, 14), (15, 14), (1, 11), (7, 8), (14, 18), (10, 16), (10, 25), (16, 3), (2, 18), (10, 3), (12, 26), (10, 20), (15, 4), (2, 7), (3, 16), (22, 13), (1, 27), (15, 0), (9, 14), (12, 14), (6, 10), (3, 15), (2, 12), (16, 5), (15, 19), (7, 1), (20, 8), (16, 28), (12, 12), (6, 14), (16, 9), (10, 14), (11, 14), (18, 10), (20, 9), (0, 27), (12, 13), (8, 3), (18, 4), (12, 19), (3, 28), (3, 2), (19, 20), (3, 3), (14, 20), (18, 12), (2, 27), (22, 8), (2, 28), (14, 19), (5, 27), (18, 25), (16, 13), (23, 18), (21, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50286", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 0), (19, 0), (12, 17), (23, 1), (17, 12), (12, 0), (14, 11), (0, 4), (6, 3), (22, 5), (14, 1), (9, 2), (6, 10), (16, 4), (16, 9), (8, 2), (7, 0), (19, 11), (1, 13), (19, 16), (18, 12), (21, 14), (3, 3), (10, 3), (2, 9), (15, 12), (17, 13), (10, 21), (14, 5), (9, 6), (18, 6), (7, 18), (18, 7), (13, 6), (10, 4), (12, 7), (5, 13), (6, 16), (20, 5), (1, 1), (22, 11), (6, 1), (14, 12), (20, 20), (21, 3), (8, 17), (15, 16), (2, 19), (4, 15), (13, 4), (11, 13), (4, 6), (3, 6), (2, 14), (14, 13), (0, 18), (15, 4), (1, 16), (8, 8), (12, 13), (19, 7), (15, 21), (2, 0), (17, 3), (21, 18), (7, 11), (12, 3), (21, 17), (9, 13), (5, 5), (13, 17), (23, 6), (9, 17), (4, 16), (8, 0), (4, 1), (5, 14), (21, 11), (23, 14), (1, 14), (23, 20), (21, 5), (12, 16), (2, 13), (4, 10), (20, 16), (16, 3), (12, 20), (8, 16), (8, 20), (15, 10), (1, 10), (17, 14), (12, 4), (8, 7), (7, 10), (22, 15), (13, 18), (4, 4), (6, 15), (21, 0), (20, 9), (20, 18), (19, 9), (16, 17), (7, 3), (2, 18), (2, 2), (2, 7), (14, 8), (19, 13), (3, 18), (19, 8), (11, 19), (6, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670010", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), 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), (8, 7), (5, 20), (16, 25), (12, 15), (9, 20), (8, 14), (7, 21), (3, 11), (19, 19), (4, 17), (7, 7), (15, 12), (2, 3), (5, 1), (1, 18), (0, 2), (13, 10), (15, 6), (2, 23), (4, 1), (23, 20), (10, 17), (10, 20), (7, 3), (18, 6), (10, 0), (15, 4), (9, 22), (18, 18), (19, 24), (19, 23), (17, 19), (3, 21), (6, 24), (2, 11), (17, 24), (12, 12), (15, 0), (23, 0), (17, 18), (6, 1), (16, 15), (2, 22), (17, 2), (15, 22), (20, 16), (0, 5), (21, 2), (19, 17), (15, 24), (12, 1), (12, 16), (20, 8), (19, 9), (1, 22), (15, 2), (22, 19), (4, 23), (10, 11), (21, 11), (1, 7), (12, 14), (15, 5), (10, 23), (19, 4), (16, 5), (10, 3), (7, 0), (11, 25), (3, 6), (5, 23), (4, 4), (23, 23), (7, 14), (14, 13), (4, 12), (3, 4), (23, 2), (15, 16), (21, 5), (7, 25), (0, 7), (21, 10), (8, 10), (18, 11), (14, 23), (20, 11), (11, 24), (8, 9), (6, 19), (4, 11), (7, 9), (10, 8), (2, 8), (12, 23), (0, 11), (7, 16), (0, 19), (8, 15), (0, 9), (1, 25), (11, 10), (6, 10), (1, 17), (3, 22), (5, 14), (3, 23), (7, 6), (8, 17), (21, 16), (14, 5), (3, 24), (3, 18), (5, 7), (14, 25), (4, 20), (10, 14), (17, 5), (19, 16), (5, 22), (6, 9), (12, 8), (23, 18), (13, 0), (8, 4), (11, 5), (22, 18), (13, 11), (8, 3), (8, 24), (4, 15), (22, 13), (16, 12), (16, 4), (2, 6), (13, 5), (19, 12), (17, 4), (20, 1), (7, 5), (11, 20), (21, 1), (10, 24), (12, 20), (1, 4), (12, 10), (13, 24), (17, 13), (3, 15), (21, 4), (14, 19), (0, 21), (16, 24), (14, 16), (13, 16), (11, 18), (5, 0), (3, 25), (13, 17), (17, 9), (4, 24), (21, 8), (6, 13), (6, 20), (20, 18), (18, 24), (3, 20), (0, 17), (15, 10), (8, 16), (3, 3), (7, 10), (5, 18), (21, 21), (16, 11), (0, 3), (4, 22), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104256", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 16), (15, 18), (15, 14), (0, 4), (6, 3), (18, 16), (15, 1), (5, 6), (19, 17), (7, 11), (6, 6), (15, 20), (3, 22), (5, 13), (20, 13), (20, 4), (4, 4), (12, 5), (15, 11), (18, 19), (15, 9), (20, 2), (2, 23), (3, 2), (0, 20), (16, 2), (18, 3), (0, 6), (3, 1), (14, 18), (12, 14), (11, 0), (15, 6), (2, 21), (18, 7), (14, 3), (10, 18), (8, 20), (13, 16), (3, 10), (16, 9), (5, 12), (0, 18), (1, 21), (2, 14), (9, 19), (7, 4), (1, 8), (10, 12), (4, 12), (7, 8), (4, 6), (5, 16), (9, 6), (2, 18), (0, 19), (13, 12), (8, 0), (16, 23), (2, 20), (4, 0), (7, 14), (4, 16), (20, 3), (5, 8), (2, 12), (12, 10), (16, 18), (10, 0), (17, 16), (7, 16), (7, 20), (15, 5), (10, 20), (17, 7), (0, 14), (16, 0), (19, 7), (1, 6), (6, 19), (9, 11), (18, 1), (13, 21), (2, 5), (8, 6), (10, 1), (8, 12), (5, 4), (17, 3), (17, 10), (18, 20), (0, 15), (1, 22), (16, 6), (0, 5), (17, 1), (6, 17), (19, 11), (8, 23), (3, 20), (18, 18), (7, 17), (15, 16), (3, 8), (17, 2), (10, 10), (13, 22), (14, 8), (5, 7), (7, 9), (1, 11), (7, 10), (11, 17), (13, 2), (13, 23), (7, 6), (10, 21), (1, 4), (1, 7), (1, 14), (12, 23), (11, 20), (5, 23), (15, 7), (1, 23), (6, 2), (20, 21), (18, 0), (20, 12), (5, 21), (19, 10), (10, 8), (9, 14), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410256", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), 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), (1, 18), (1, 6), (12, 1), (21, 13), (18, 4), (7, 23), (2, 21), (15, 22), (4, 12), (11, 16), (14, 2), (12, 18), (14, 6), (3, 0), (16, 14), (11, 23), (15, 21), (18, 8), (8, 4), (17, 19), (7, 6), (0, 13), (18, 22), (11, 5), (11, 22), (16, 7), (19, 4), (8, 22), (11, 7), (0, 23), (8, 1), (0, 5), (11, 0), (6, 5), (14, 12), (7, 8), (1, 12), (13, 6), (10, 4), (2, 8), (17, 18), (9, 6), (4, 18), (21, 12), (20, 7), (16, 3), (11, 18), (0, 17), (18, 19), (16, 17), (4, 15), (15, 6), (16, 4), (16, 2), (19, 5), (17, 23), (14, 7), (5, 13), (4, 19), (11, 14), (18, 17), (6, 13), (21, 14), (21, 10), (19, 7), (10, 10), (4, 16), (13, 19), (6, 6), (20, 4), (10, 19), (2, 19), (10, 1), (1, 14), (13, 4), (9, 14), (21, 2), (2, 2), (0, 3), (19, 19), (10, 16), (12, 13), (18, 10), (1, 11), (7, 14), (2, 15), (5, 10), (20, 8), (15, 20), (17, 15), (20, 21), (14, 15), (18, 18), (13, 13), (10, 18), (18, 11), (1, 8), (10, 15), (17, 10), (11, 1), (17, 6), (0, 9), (19, 11), (21, 11), (3, 14), (19, 8), (4, 1), (6, 8), (1, 3), (12, 5), (1, 22), (20, 18), (20, 17), (2, 12), (1, 10), (19, 17), (14, 9), (13, 10), (12, 9), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867762", "dataset": "MATH"}
{"messages": [{"content": "In a 22x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 19), (8, 3), (20, 10), (9, 11), (4, 9), (9, 2), (17, 4), (7, 13), (12, 6), (8, 14), (10, 3), (12, 17), (16, 0), (2, 11), (4, 18), (21, 6), (18, 13), (11, 17), (14, 11), (8, 11), (17, 6), (16, 9), (11, 4), (5, 0), (5, 9), (19, 9), (13, 1), (4, 5), (20, 12), (4, 13), (15, 7), (3, 12), (9, 1), (11, 9), (5, 14), (7, 17), (8, 19), (0, 2), (20, 18), (5, 11), (17, 16), (7, 3), (13, 14), (4, 19), (14, 17), (13, 4), (11, 10), (18, 14), (6, 9), (10, 14), (21, 7), (13, 17), (2, 0), (9, 10), (6, 8), (4, 3), (6, 17), (3, 5), (13, 15), (2, 18), (2, 14), (9, 0), (7, 10), (5, 7), (14, 5), (12, 2), (0, 3), (16, 1), (15, 11), (17, 12), (1, 5), (8, 2), (19, 7), (3, 1), (18, 12), (3, 6), (21, 14), (19, 18), (15, 12), (5, 1), (2, 1), (8, 13), (16, 7), (12, 8), (20, 9), (1, 7), (14, 15), (0, 8), (15, 8), (21, 11), (9, 18), (11, 1), (1, 17), (20, 0), (11, 2), (4, 7), (2, 8), (6, 4), (8, 0), (15, 5), (10, 17), (5, 12), (8, 16), (16, 16), (21, 8), (11, 13), (0, 14), (3, 10), (6, 11), (13, 16), (13, 5), (7, 14), (7, 7), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542234", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 20), (4, 6), (9, 10), (10, 13), (13, 18), (27, 3), (19, 19), (0, 27), (28, 4), (24, 17), (5, 17), (0, 3), (27, 6), (18, 6), (20, 20), (20, 14), (6, 18), (12, 4), (21, 6), (7, 18), (17, 3), (23, 12), (20, 4), (13, 10), (4, 1), (4, 16), (21, 27), (10, 1), (9, 3), (13, 23), (13, 25), (11, 2), (25, 20), (4, 23), (2, 5), (27, 5), (11, 0), (28, 7), (11, 21), (21, 2), (23, 15), (17, 27), (3, 27), (7, 13), (18, 20), (26, 5), (6, 19), (19, 2), (24, 11), (15, 9), (21, 16), (3, 17), (12, 27), (22, 2), (21, 3), (23, 0), (11, 4), (24, 0), (18, 0), (13, 27), (22, 13), (15, 2), (21, 22), (19, 20), (25, 6), (10, 24), (14, 2), (7, 16), (16, 25), (9, 19), (7, 12), (19, 3), (20, 1), (28, 22), (28, 17), (21, 8), (10, 9), (10, 7), (15, 3), (22, 18), (1, 11), (21, 14), (2, 21), (22, 19), (18, 1), (26, 7), (4, 3), (19, 8), (17, 13), (10, 22), (27, 24), (14, 7), (7, 23), (7, 20), (28, 0), (13, 13), (1, 18), (6, 5), (12, 22), (21, 13), (9, 22), (22, 15), (11, 20), (19, 13), (6, 7), (11, 11), (10, 26), (7, 7), (24, 24), (9, 13), (5, 3), (20, 10), (28, 8), (7, 15), (13, 24), (16, 22), (10, 8), (20, 15), (0, 18), (18, 13), (4, 13), (10, 17), (27, 15), (6, 6), (3, 22), (5, 27), (16, 7), (6, 8), (8, 25), (27, 17), (15, 5), (6, 9), (3, 21), (11, 1), (20, 2), (26, 9), (15, 10), (21, 1), (11, 5), (13, 0), (18, 8), (6, 20), (24, 25), (24, 12), (7, 17), (3, 15), (28, 10), (7, 14), (18, 17), (15, 19), (6, 22), (18, 19), (5, 23), (23, 17), (25, 8), (8, 19), (26, 25), (2, 6), (21, 11), (11, 27), (9, 4), (16, 4), (4, 27), (3, 3), (25, 21), (1, 22), (16, 2), (7, 11), (25, 23), (21, 17), (25, 10), (14, 23), (8, 24), (12, 5), (28, 1), (27, 18), (9, 27), (21, 10), (18, 18), (9, 1), (18, 11), (11, 22), (20, 26), (16, 15), (27, 22), (6, 11), (11, 16), (10, 4), (22, 14), (13, 12), (24, 20), (0, 16), (22, 1), (19, 11), (18, 25), (24, 19), (18, 27), (28, 14), (20, 11), (5, 16), (24, 15), (16, 12), (7, 22), (18, 5), (8, 26), (15, 16), (3, 16), (19, 10), (4, 10), (26, 14), (16, 17), (23, 11), (15, 27), (15, 21), (15, 1), (10, 21), (26, 26), (1, 27), (2, 22), (11, 19), (7, 27), (23, 23), (22, 17), (28, 5), (7, 10), (12, 20), (25, 27), (20, 9), (8, 0), (28, 19), (27, 12), (18, 3), (13, 2), (4, 21), (23, 1), (21, 26), (27, 10), (18, 21), (23, 4), (14, 17), (9, 18), (8, 16), (20, 23), (6, 24), (7, 8), (9, 9), (5, 21), (17, 25), (10, 10), (21, 5), (11, 7), (2, 3), (24, 7), (6, 25), (3, 23), (17, 17), (8, 23), (20, 17), (17, 22), (23, 25), (22, 20), (16, 23), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934920", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (6, 15), (9, 2), (0, 11), (13, 9), (6, 11), (2, 10), (12, 14), (8, 11), (17, 2), (10, 14), (8, 6), (2, 9), (19, 6), (17, 6), (1, 7), (5, 16), (9, 15), (1, 11), (6, 17), (19, 11), (17, 19), (16, 10), (0, 17), (11, 16), (14, 15), (5, 12), (17, 3), (2, 17), (12, 4), (16, 9), (6, 22), (2, 16), (0, 8), (6, 21), (15, 2), (3, 20), (1, 2), (0, 15), (3, 16), (20, 14), (19, 1), (9, 8), (17, 10), (9, 16), (14, 7), (6, 12), (8, 8), (15, 1), (3, 21), (19, 18), (5, 0), (6, 10), (6, 9), (10, 15), (13, 3), (2, 6), (20, 7), (13, 17), (18, 5), (16, 19), (16, 1), (20, 2), (6, 2), (14, 22), (1, 0), (0, 22), (3, 4), (17, 14), (2, 3), (6, 3), (8, 13), (11, 1), (19, 14), (3, 7), (19, 13), (5, 19), (7, 4), (17, 12), (13, 4), (0, 18), (10, 9), (8, 15), (0, 13), (8, 5), (18, 10), (1, 21), (15, 18), (18, 2), (10, 4), (16, 22), (18, 7), (9, 4), (11, 22), (17, 16), (10, 1), (11, 0), (7, 20), (20, 10), (9, 18), (3, 2), (7, 18), (8, 10), (0, 20), (12, 16), (18, 21), (12, 18), (19, 16), (5, 18), (12, 19), (1, 16), (5, 15), (13, 10), (1, 5), (7, 5), (13, 15), (14, 9), (11, 13), (12, 12), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "740209", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), 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, 8), (21, 18), (13, 20), (14, 4), (2, 19), (15, 1), (5, 18), (16, 8), (6, 9), (6, 6), (2, 8), (8, 15), (11, 21), (5, 19), (20, 4), (1, 13), (0, 8), (7, 1), (18, 0), (14, 6), (10, 20), (0, 13), (17, 7), (19, 4), (20, 13), (17, 16), (13, 12), (16, 21), (20, 5), (19, 20), (19, 11), (7, 6), (19, 1), (18, 8), (3, 2), (11, 7), (12, 5), (9, 13), (14, 22), (8, 11), (15, 21), (17, 2), (17, 1), (4, 18), (2, 16), (9, 3), (5, 16), (13, 4), (22, 3), (19, 7), (19, 12), (8, 5), (13, 13), (2, 21), (5, 11), (16, 15), (19, 19), (11, 5), (7, 8), (0, 11), (5, 15), (16, 7), (4, 15), (14, 9), (15, 4), (5, 5), (11, 11), (0, 20), (0, 5), (14, 0), (10, 9), (5, 3), (17, 21), (20, 8), (20, 22), (12, 14), (0, 10), (10, 13), (6, 16), (17, 0), (15, 6), (6, 1), (7, 16), (16, 5), (16, 6), (2, 12), (18, 13), (19, 5), (3, 11), (3, 18), (21, 6), (8, 20), (13, 3), (6, 18), (20, 1), (8, 14), (4, 4), (12, 12), (12, 2), (11, 15), (13, 18), (5, 12), (12, 7), (7, 21), (1, 16), (20, 3), (5, 8), (3, 9), (21, 21), (1, 9), (21, 2), (5, 20), (18, 1), (21, 20), (10, 0), (12, 9), (0, 22), (7, 11), (11, 16), (13, 5), (2, 4), (18, 2), (0, 2), (8, 8), (14, 11), (7, 10), (12, 8), (1, 14), (16, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867723", "dataset": "MATH"}
{"messages": [{"content": "In a 23x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 16), (18, 0), (10, 6), (17, 20), (18, 15), (7, 18), (14, 3), (11, 8), (2, 12), (20, 18), (14, 12), (1, 2), (12, 3), (14, 19), (22, 10), (9, 18), (10, 16), (1, 18), (11, 17), (6, 2), (10, 14), (12, 19), (22, 5), (10, 22), (8, 5), (13, 3), (8, 16), (14, 13), (5, 4), (15, 4), (16, 10), (9, 4), (6, 1), (11, 11), (7, 1), (21, 3), (21, 22), (10, 7), (11, 18), (2, 11), (16, 2), (11, 20), (4, 4), (8, 2), (6, 14), (22, 7), (14, 15), (13, 5), (3, 0), (17, 1), (0, 9), (19, 7), (16, 16), (14, 7), (15, 12), (17, 10), (4, 0), (16, 19), (10, 3), (8, 13), (16, 9), (5, 9), (12, 13), (16, 17), (20, 16), (3, 12), (13, 11), (20, 14), (19, 2), (6, 8), (13, 6), (5, 5), (4, 20), (16, 4), (15, 6), (10, 18), (8, 6), (8, 21), (3, 11), (5, 7), (11, 19), (0, 3), (21, 13), (20, 3), (16, 22), (19, 9), (6, 3), (15, 9), (12, 2), (5, 8), (2, 4), (11, 9), (20, 17), (12, 0), (4, 19), (4, 18), (17, 4), (10, 20), (18, 10), (15, 11), (10, 15), (0, 17), (9, 7), (19, 19), (10, 17), (19, 1), (13, 21), (6, 19), (22, 11), (18, 13), (9, 10), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369360", "dataset": "MATH"}
{"messages": [{"content": "In a 28x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 23), 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), (11, 5), (2, 7), (4, 21), (23, 11), (5, 4), (12, 21), (22, 14), (26, 16), (0, 10), (9, 15), (15, 0), (3, 3), (27, 16), (26, 20), (24, 5), (6, 3), (4, 13), (4, 2), (27, 8), (27, 12), (22, 18), (14, 8), (7, 20), (3, 5), (8, 23), (3, 9), (25, 19), (21, 2), (2, 18), (21, 23), (24, 1), (5, 7), (9, 22), (19, 9), (21, 13), (27, 1), (16, 19), (17, 13), (13, 5), (1, 2), (21, 4), (17, 16), (25, 22), (7, 15), (25, 5), (13, 4), (12, 1), (0, 7), (23, 13), (26, 9), (9, 19), (9, 2), (22, 17), (5, 18), (18, 5), (6, 22), (13, 10), (0, 22), (3, 23), (17, 9), (6, 13), (12, 7), (24, 8), (3, 1), (10, 7), (19, 21), (14, 17), (9, 14), (15, 4), (6, 23), (27, 9), (12, 4), (13, 3), (21, 14), (10, 10), (25, 23), (14, 19), (21, 11), (23, 18), (14, 20), (7, 7), (1, 5), (13, 8), (23, 12), (1, 11), (5, 17), (8, 2), (14, 22), (27, 7), (18, 16), (7, 11), (6, 12), (15, 15), (3, 11), (0, 21), (26, 19), (4, 1), (23, 19), (17, 11), (1, 14), (19, 17), (11, 11), (0, 9), (14, 0), (14, 14), (26, 4), (13, 23), (25, 21), (23, 6), (17, 20), (8, 1), (16, 6), (3, 12), (19, 23), (18, 12), (7, 21), (25, 9), (21, 16), (20, 1), (19, 7), (4, 14), (23, 2), (22, 15), (15, 1), (3, 20), (20, 16), (17, 14), (7, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626250", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), 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, 3), (25, 17), (11, 15), (6, 15), (5, 5), (13, 15), (21, 7), (19, 2), (1, 14), (11, 7), (21, 10), (1, 3), (1, 7), (0, 6), (26, 16), (12, 8), (7, 9), (15, 18), (16, 13), (3, 17), (3, 5), (22, 18), (25, 0), (27, 7), (13, 3), (10, 18), (17, 17), (2, 7), (15, 12), (0, 9), (4, 5), (26, 3), (12, 0), (24, 8), (7, 0), (23, 3), (8, 0), (7, 1), (27, 11), (5, 4), (24, 14), (20, 11), (4, 17), (26, 9), (14, 15), (19, 0), (11, 17), (0, 11), (23, 4), (7, 3), (27, 19), (0, 5), (8, 2), (16, 19), (1, 8), (24, 1), (16, 0), (19, 13), (24, 20), (1, 13), (22, 11), (16, 7), (18, 3), (21, 18), (26, 4), (17, 1), (1, 6), (7, 6), (13, 4), (3, 1), (14, 4), (26, 14), (9, 12), (6, 19), (9, 11), (26, 18), (18, 17), (24, 11), (27, 16), (21, 19), (22, 14), (21, 16), (25, 9), (13, 0), (7, 17), (26, 15), (16, 4), (26, 7), (20, 16), (23, 9), (3, 19), (24, 9), (19, 7), (24, 13), (13, 12), (9, 0), (20, 15), (0, 19), (24, 7), (25, 8), (3, 15), (2, 19), (15, 20), (12, 1), (24, 15), (15, 8), (1, 17), (0, 13), (19, 14), (24, 18), (26, 6), (0, 1), (13, 19), (8, 4), (10, 9), (18, 2), (7, 5), (15, 14), (16, 3), (25, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656163", "dataset": "MATH"}
{"messages": [{"content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), 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, 4), (2, 9), (5, 3), (14, 9), (19, 1), (16, 11), (19, 15), (16, 9), (19, 7), (8, 12), (0, 1), (2, 18), (17, 14), (17, 15), (8, 3), (1, 16), (9, 11), (0, 15), (13, 1), (6, 8), (18, 13), (13, 3), (9, 7), (3, 16), (14, 19), (14, 15), (0, 18), (8, 10), (1, 6), (16, 8), (16, 18), (7, 19), (3, 0), (7, 3), (6, 7), (19, 13), (1, 8), (13, 18), (13, 2), (10, 9), (8, 19), (17, 7), (17, 10), (7, 7), (0, 6), (0, 9), (0, 13), (2, 3), (19, 11), (17, 17), (13, 15), (13, 5), (10, 15), (6, 5), (15, 14), (17, 3), (2, 19), (18, 18), (6, 1), (7, 10), (7, 8), (4, 12), (15, 11), (8, 14), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616132", "dataset": "MATH"}
{"messages": [{"content": "In a 29x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 19), (10, 0), (22, 2), (16, 17), (3, 12), (27, 10), (2, 9), (7, 12), (2, 16), (4, 18), (2, 8), (22, 3), (25, 19), (15, 9), (4, 10), (8, 19), (19, 10), (21, 3), (24, 2), (18, 15), (18, 7), (6, 7), (20, 3), (6, 1), (11, 8), (2, 7), (2, 19), (13, 8), (27, 7), (16, 18), (22, 10), (18, 8), (26, 0), (22, 4), (14, 1), (3, 1), (1, 13), (2, 2), (22, 15), (14, 6), (27, 3), (25, 17), (20, 11), (1, 11), (6, 14), (10, 10), (21, 1), (7, 9), (7, 4), (21, 2), (3, 14), (13, 13), (20, 13), (11, 3), (14, 16), (7, 15), (8, 8), (9, 10), (21, 16), (12, 16), (4, 11), (11, 7), (24, 10), (16, 8), (18, 0), (15, 13), (26, 1), (16, 4), (6, 0), (1, 17), (18, 6), (22, 16), (11, 17), (28, 14), (1, 18), (20, 19), (15, 15), (4, 14), (27, 15), (3, 9), (20, 15), (7, 0), (26, 5), (15, 14), (12, 11), (8, 0), (13, 10), (19, 5), (24, 4), (4, 13), (10, 19), (10, 13), (25, 11), (9, 17), (1, 14), (20, 0), (20, 5), (19, 18), (16, 1), (13, 3), (15, 0), (13, 0), (11, 0), (17, 7), (23, 11), (1, 15), (24, 17), (21, 6), (1, 2), (23, 0), (13, 19), (19, 2), (5, 2), (7, 11), (23, 10), (16, 2), (28, 1), (19, 0), (10, 2), (27, 6), (12, 0), (1, 9), (7, 5), (1, 4), (26, 15), (15, 10), (15, 19), (9, 13), (9, 18), (26, 19), (12, 5), (5, 8), (15, 2), (28, 3), (25, 15), (1, 1), (9, 7), (0, 12), (24, 1), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "995652", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 8), (13, 2), (17, 14), (18, 16), (1, 4), (13, 17), (12, 9), (18, 3), (24, 11), (0, 21), (16, 18), (5, 13), (17, 7), (11, 9), (22, 4), (15, 11), (13, 6), (16, 4), (0, 16), (3, 11), (22, 6), (11, 0), (25, 12), (22, 14), (23, 20), (16, 14), (6, 11), (7, 8), (14, 3), (8, 10), (9, 6), (19, 8), (4, 12), (16, 9), (5, 0), (10, 9), (14, 13), (8, 11), (7, 7), (12, 7), (10, 18), (15, 9), (19, 17), (28, 15), (10, 21), (12, 2), (1, 10), (26, 13), (8, 21), (13, 7), (26, 6), (0, 7), (1, 0), (9, 21), (27, 4), (26, 20), (3, 1), (1, 14), (5, 12), (23, 10), (18, 7), (12, 21), (1, 15), (13, 4), (21, 8), (13, 3), (12, 10), (3, 16), (1, 16), (14, 4), (10, 4), (17, 11), (27, 12), (24, 10), (7, 20), (5, 20), (14, 2), (16, 16), (7, 15), (9, 7), (8, 18), (2, 10), (22, 8), (0, 4), (5, 3), (17, 3), (24, 17), (26, 18), (21, 15), (17, 19), (23, 15), (17, 18), (22, 13), (26, 8), (22, 17), (18, 2), (0, 20), (19, 3), (22, 11), (24, 6), (5, 9), (26, 3), (12, 20), (23, 18), (4, 6), (4, 20), (21, 18), (27, 11), (16, 8), (23, 3), (15, 20), (2, 14), (22, 18), (12, 13), (10, 11), (12, 5), (15, 4), (16, 1), (25, 10), (10, 19), (9, 15), (1, 9), (17, 12), (14, 7), (21, 11), (23, 13), (2, 8), (0, 12), (14, 6), (12, 16), (24, 8), (2, 2), (13, 15), (25, 3), (23, 6), (11, 7), (24, 0), (13, 1), (14, 20), (17, 13), (5, 18), (6, 20), (25, 14), (19, 12), (17, 16), (25, 4), (15, 2), (15, 8), (20, 13), (27, 10), (9, 20), (12, 8), (3, 9), (26, 7), (11, 5), (2, 4), (6, 1), (5, 14), (28, 5), (27, 15), (23, 14), (5, 1), (7, 17), (11, 2), (1, 12), (2, 5), (24, 9), (7, 21), (4, 7), (10, 3), (7, 9), (13, 9), (25, 20), (10, 6), (20, 3), (28, 13), (27, 18), (3, 20), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "885120", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 9), (0, 10), (10, 11), (5, 23), (22, 2), (8, 0), (1, 11), (11, 1), (4, 24), (18, 5), (15, 22), (17, 6), (1, 22), (0, 20), (5, 14), (21, 18), (25, 14), (9, 17), (5, 2), (25, 3), (21, 3), (8, 25), (16, 18), (24, 18), (16, 0), (15, 12), (2, 27), (6, 14), (8, 26), (12, 20), (8, 1), (8, 9), (13, 25), (16, 16), (3, 7), (19, 21), (4, 17), (17, 14), (21, 17), (2, 2), (11, 7), (0, 25), (8, 21), (24, 24), (21, 27), (4, 8), (22, 11), (10, 9), (18, 14), (3, 1), (5, 22), (16, 24), (14, 21), (19, 4), (24, 4), (22, 17), (22, 14), (15, 13), (15, 10), (8, 6), (17, 9), (6, 27), (18, 21), (23, 22), (5, 13), (3, 14), (17, 19), (14, 20), (0, 1), (9, 7), (13, 26), (20, 3), (12, 21), (4, 21), (2, 23), (25, 5), (11, 20), (2, 4), (6, 8), (11, 25), (17, 10), (7, 20), (17, 26), (22, 22), (13, 18), (21, 13), (16, 2), (20, 6), (19, 3), (9, 18), (8, 8), (3, 3), (7, 23), (7, 12), (10, 23), (7, 21), (15, 1), (24, 16), (5, 24), (17, 1), (13, 11), (15, 7), (19, 5), (5, 16), (18, 1), (2, 18), (25, 19), (21, 19), (13, 2), (21, 1), (16, 3), (9, 14), (22, 25), (10, 10), (20, 12), (12, 18), (15, 25), (5, 6), (6, 5), (9, 4), (23, 0), (2, 10), (13, 8), (20, 24), (9, 1), (22, 15), (2, 7), (3, 8), (8, 18), (7, 22), (0, 3), (5, 21), (19, 11), (13, 3), (23, 27), (21, 5), (25, 13), (10, 17), (14, 14), (8, 7), (10, 2), (11, 26), (15, 0), (4, 18), (1, 3), (5, 27), (2, 1), (20, 7), (20, 21), (24, 23), (20, 0), (18, 19), (20, 14), (0, 7), (1, 25), (8, 12), (24, 2), (5, 8), (0, 26), (1, 16), (0, 21), (14, 22), (11, 21), (24, 13), (6, 9), (15, 16), (0, 5), (1, 26), (19, 1), (4, 16), (16, 23), (18, 18), (22, 8), (13, 21), (22, 12), (4, 6), (12, 2), (22, 0), (6, 20), (0, 16), (17, 2), (23, 20), (23, 26), (21, 10), (21, 12), (6, 12), (0, 23), (4, 10), (20, 26), (23, 2), (6, 13), (4, 2), (10, 27), (0, 2), (12, 16), (25, 24), (4, 1), (14, 8), (10, 0), (6, 26), (18, 15), (18, 17), (12, 0), (17, 21), (19, 2), (3, 17), (9, 24), (14, 11), (20, 10), (17, 18), (6, 4), (12, 19), (25, 2), (4, 20), (22, 27), (19, 6), (3, 15), (15, 2), (9, 3), (13, 10), (5, 15), (16, 27), (25, 11), (10, 4), (19, 26), (13, 12), (1, 5), (21, 8), (6, 2), (0, 15), (2, 20), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "326889", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), 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), (19, 20), (0, 1), (19, 0), (3, 13), (18, 6), (2, 19), (10, 11), (10, 0), (1, 4), (4, 2), (7, 11), (3, 15), (17, 11), (12, 7), (14, 14), (12, 19), (14, 15), (10, 6), (10, 3), (4, 16), (12, 11), (15, 2), (6, 13), (13, 4), (18, 5), (2, 16), (2, 17), (17, 0), (10, 17), (0, 13), (8, 11), (1, 9), (6, 17), (10, 13), (12, 21), (0, 20), (1, 17), (5, 20), (12, 1), (5, 9), (3, 8), (11, 8), (7, 7), (8, 7), (9, 15), (3, 7), (5, 16), (4, 4), (4, 13), (16, 18), (17, 16), (3, 21), (4, 6), (1, 10), (0, 8), (1, 11), (8, 9), (15, 0), (19, 12), (16, 0), (19, 19), (1, 16), (16, 6), (3, 0), (15, 14), (17, 6), (2, 18), (11, 20), (1, 12), (7, 5), (18, 18), (2, 6), (3, 5), (7, 1), (14, 6), (15, 3), (13, 5), (0, 4), (7, 18), (5, 15), (16, 4), (0, 11), (8, 13), (12, 0), (6, 11), (6, 0), (15, 10), (5, 8), (16, 16), (9, 7), (3, 1), (5, 14), (16, 14), (6, 12), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932610", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), 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), (5, 1), (4, 6), (8, 12), (7, 13), (4, 0), (10, 13), (21, 12), (19, 13), (4, 3), (2, 9), (21, 18), (10, 14), (7, 25), (12, 11), (24, 10), (4, 21), (14, 11), (11, 21), (4, 1), (15, 24), (1, 20), (19, 21), (17, 27), (5, 24), (10, 0), (20, 10), (7, 14), (5, 6), (5, 19), (11, 17), (11, 10), (18, 21), (21, 0), (14, 1), (9, 20), (18, 16), (17, 8), (1, 16), (15, 18), (24, 14), (3, 2), (4, 23), (21, 26), (8, 20), (2, 27), (13, 16), (16, 26), (5, 25), (0, 24), (17, 19), (17, 11), (1, 2), (17, 25), (6, 0), (11, 13), (10, 18), (19, 26), (18, 26), (2, 7), (14, 9), (21, 16), (9, 24), (9, 15), (18, 14), (10, 12), (8, 11), (1, 14), (9, 17), (16, 10), (15, 11), (20, 7), (8, 9), (4, 19), (17, 0), (21, 5), (3, 20), (3, 14), (11, 12), (13, 17), (7, 27), (22, 24), (11, 27), (22, 3), (20, 6), (9, 19), (16, 9), (18, 15), (17, 23), (21, 10), (14, 7), (3, 8), (20, 24), (3, 26), (18, 3), (23, 2), (9, 10), (18, 12), (4, 14), (11, 7), (13, 2), (7, 26), (19, 16), (22, 12), (12, 18), (5, 22), (6, 20), (9, 1), (7, 18), (0, 14), (13, 21), (3, 16), (12, 2), (18, 5), (4, 15), (8, 23), (20, 1), (6, 21), (22, 27), (22, 2), (6, 5), (7, 0), (1, 1), (9, 9), (5, 27), (16, 20), (13, 15), (1, 0), (17, 20), (12, 4), (24, 11), (12, 5), (19, 6), (19, 7), (10, 21), (20, 2), (6, 3), (4, 5), (13, 13), (4, 17), (23, 4), (0, 6), (21, 3), (2, 18), (19, 0), (5, 17), (13, 23), (11, 2), (10, 4), (6, 16), (20, 17), (22, 18), (5, 26), (16, 4), (17, 13), (13, 0), (12, 16), (16, 8), (14, 6), (9, 26), (9, 4), (11, 5), (12, 9), (2, 20), (16, 5), (9, 23), (9, 0), (18, 13), (6, 17), (2, 24), (9, 16), (17, 4), (8, 19), (21, 19), (11, 4), (20, 11), (5, 18), (23, 24), (16, 1), (9, 13), (20, 23), (24, 3), (7, 21), (12, 20), (4, 27), (10, 9), (20, 4), (22, 16), (24, 16), (16, 23), (0, 10), (23, 21), (8, 24), (24, 22), (8, 5), (4, 4), (0, 26), (21, 23), (12, 19), (24, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26600", "dataset": "MATH"}
{"messages": [{"content": "In a 20x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 28), 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), (15, 0), (16, 28), (12, 26), (16, 6), (5, 10), (18, 25), (10, 23), (6, 28), (9, 20), (16, 15), (8, 1), (4, 16), (14, 6), (19, 10), (17, 7), (11, 10), (1, 25), (6, 12), (11, 1), (18, 22), (18, 17), (16, 1), (11, 11), (17, 3), (16, 14), (5, 6), (19, 27), (5, 8), (8, 9), (15, 20), (17, 28), (12, 11), (7, 15), (15, 5), (9, 6), (0, 21), (13, 21), (0, 20), (5, 24), (15, 6), (4, 10), (0, 13), (7, 12), (14, 24), (6, 9), (0, 23), (10, 0), (10, 21), (4, 2), (9, 7), (1, 12), (10, 27), (12, 12), (7, 8), (1, 11), (5, 4), (19, 7), (17, 20), (13, 19), (11, 19), (4, 25), (14, 18), (1, 13), (18, 1), (17, 26), (8, 17), (19, 18), (18, 5), (12, 2), (2, 12), (8, 21), (6, 16), (4, 18), (3, 11), (6, 23), (1, 21), (17, 23), (14, 0), (10, 4), (13, 18), (11, 27), (10, 26), (15, 17), (6, 15), (14, 17), (4, 14), (19, 15), (3, 18), (1, 19), (1, 26), (11, 3), (14, 13), (4, 17), (0, 9), (15, 15), (11, 2), (14, 5), (8, 26), (11, 4), (11, 6), (15, 3), (9, 21), (4, 1), (5, 25), (9, 16), (3, 17), (9, 15), (11, 9), (6, 26), (10, 15), (12, 4), (16, 21), (6, 18), (16, 3), (16, 10), (14, 23), (15, 2), (6, 7), (16, 16), (8, 18), (1, 0), (19, 26), (13, 10), (10, 2), (14, 15), (10, 19), (19, 25), (14, 21), (2, 16), (19, 21), (6, 17), (5, 14), (14, 27), (13, 22), (9, 22), (17, 1), (16, 18), (14, 22), (13, 3), (7, 25), (12, 6), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820260", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 18), (9, 14), (21, 21), (15, 16), (16, 5), (11, 21), (16, 11), (15, 4), (10, 11), (6, 0), (1, 14), (7, 13), (4, 23), (9, 13), (18, 6), (21, 19), (18, 0), (9, 15), (2, 10), (18, 14), (19, 10), (5, 5), (7, 16), (8, 6), (0, 11), (11, 14), (18, 15), (10, 4), (9, 24), (9, 10), (20, 24), (20, 15), (8, 0), (21, 11), (13, 2), (4, 20), (16, 20), (21, 9), (3, 6), (19, 23), (6, 21), (7, 21), (14, 15), (19, 21), (9, 19), (2, 5), (17, 5), (2, 8), (12, 21), (11, 24), (1, 17), (14, 11), (1, 20), (5, 17), (7, 1), (4, 14), (10, 14), (8, 1), (11, 7), (21, 15), (12, 19), (16, 23), (4, 7), (15, 0), (17, 24), (17, 15), (2, 23), (3, 0), (7, 22), (17, 11), (4, 1), (20, 8), (3, 2), (14, 12), (7, 14), (19, 14), (13, 21), (11, 11), (20, 14), (1, 8), (18, 5), (18, 23), (6, 20), (11, 1), (21, 7), (8, 5), (13, 5), (0, 23), (7, 10), (5, 18), (15, 24), (12, 17), (10, 9), (9, 18), (7, 6), (7, 7), (16, 0), (16, 15), (6, 10), (13, 23), (9, 12), (21, 17), (3, 14), (3, 3), (12, 14), (20, 1), (9, 8), (18, 13), (10, 24), (18, 7), (6, 6), (9, 7), (16, 18), (7, 3), (1, 19), (20, 6), (8, 4), (5, 10), (18, 21), (1, 18), (16, 12), (3, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534412", "dataset": "MATH"}
{"messages": [{"content": "In a 21x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 18), (6, 17), (8, 8), (15, 11), (7, 0), (3, 0), (4, 8), (17, 6), (17, 5), (8, 19), (2, 17), (11, 11), (16, 11), (10, 0), (16, 19), (9, 10), (5, 4), (13, 13), (14, 8), (1, 16), (16, 10), (10, 18), (10, 12), (2, 9), (16, 17), (0, 12), (5, 20), (14, 7), (3, 11), (0, 5), (17, 13), (13, 14), (18, 2), (20, 2), (4, 5), (6, 12), (15, 2), (19, 17), (0, 19), (12, 4), (17, 11), (1, 4), (9, 16), (11, 17), (6, 8), (19, 7), (4, 20), (17, 15), (19, 15), (8, 4), (12, 0), (9, 14), (18, 8), (10, 11), (6, 19), (11, 3), (15, 15), (12, 18), (1, 9), (9, 1), (15, 13), (4, 0), (0, 20), (4, 3), (3, 17), (12, 20), (9, 5), (20, 10), (16, 5), (14, 15), (11, 20), (17, 3), (2, 1), (19, 9), (1, 17), (8, 2), (19, 0), (4, 16), (18, 11), (20, 7), (13, 18), (9, 11), (16, 14), (6, 20), (0, 7), (7, 17), (9, 0), (4, 19), (8, 18), (13, 9), (4, 9), (16, 9), (9, 17), (10, 10), (0, 2), (5, 13), (12, 12), (10, 1), (6, 7), (0, 9), (3, 15), (14, 2), (8, 11), (5, 2), (10, 4), (11, 6), (17, 16), (16, 20), (3, 2), (19, 8), (20, 9), (2, 7), (2, 11), (6, 16), (19, 11), (14, 1), (4, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "795280", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 27), (24, 13), (2, 4), (12, 9), (10, 10), (11, 27), (26, 14), (5, 4), (10, 6), (23, 23), (3, 14), (15, 0), (18, 10), (13, 9), (1, 16), (8, 12), (6, 25), (16, 1), (16, 9), (18, 25), (2, 26), (12, 28), (22, 12), (21, 10), (20, 14), (26, 17), (12, 12), (3, 25), (9, 19), (17, 24), (25, 28), (9, 2), (26, 26), (13, 16), (9, 9), (21, 11), (18, 17), (15, 7), (9, 26), (9, 16), (20, 22), (1, 0), (14, 3), (6, 8), (24, 19), (7, 19), (24, 9), (17, 11), (15, 13), (8, 28), (1, 4), (26, 4), (7, 10), (10, 28), (20, 3), (25, 9), (4, 20), (21, 27), (8, 5), (16, 2), (24, 4), (14, 17), (17, 25), (25, 20), (19, 24), (13, 1), (17, 17), (24, 26), (0, 5), (27, 8), (25, 6), (2, 7), (14, 11), (20, 6), (25, 10), (25, 3), (0, 8), (22, 7), (14, 9), (14, 23), (21, 17), (3, 9), (10, 12), (9, 12), (9, 25), (15, 25), (23, 14), (7, 25), (27, 6), (27, 1), (19, 7), (9, 28), (5, 24), (24, 23), (3, 27), (23, 28), (25, 1), (13, 14), (6, 13), (6, 26), (19, 17), (16, 19), (13, 23), (23, 27), (7, 5), (2, 17), (4, 15), (0, 26), (5, 13), (4, 26), (19, 16), (21, 23), (23, 20), (21, 8), (13, 24), (19, 22), (4, 13), (12, 6), (7, 27), (20, 4), (13, 28), (22, 13), (2, 21), (13, 4), (8, 26), (22, 2), (3, 1), (1, 7), (10, 4), (19, 21), (6, 14), (24, 18), (22, 1), (12, 4), (13, 26), (15, 6), (3, 8), (2, 14), (25, 4), (19, 5), (6, 12), (2, 15), (10, 24), (11, 10), (12, 25), (12, 26), (18, 19), (19, 27), (21, 13), (0, 12), (2, 5), (14, 14), (5, 19), (21, 20), (4, 19), (14, 6), (2, 28), (19, 14), (25, 17), (2, 8), (4, 16), (1, 26), (16, 8), (13, 0), (10, 14), (7, 6), (10, 11), (15, 5), (27, 5), (27, 14), (16, 27), (16, 16), (14, 1), (12, 18), (19, 9), (15, 12), (7, 20), (26, 24), (13, 7), (1, 19), (3, 22), (13, 27), (5, 3), (10, 16), (11, 13), (11, 3), (22, 14), (0, 15), (19, 25), (26, 11), (4, 12), (18, 18), (7, 16), (22, 6), (5, 5), (0, 22), (12, 10), (23, 8), (12, 23), (19, 18), (22, 22), (10, 15), (25, 8), (6, 18), (11, 1), (3, 17), (15, 28), (26, 20), (9, 4), (10, 26), (17, 7), (9, 11), (20, 0), (20, 10), (24, 20), (22, 5), (21, 0), (4, 10), (5, 6), (22, 26), (0, 21), (11, 16), (27, 13), (2, 20), (24, 25), (15, 15), (11, 11), (26, 12), (22, 19), (12, 20), (24, 17), (26, 1), (25, 7), (17, 14), (23, 16), (26, 10), (22, 17), (26, 8), (17, 21), (5, 2), (1, 13), (14, 12), (6, 9), (19, 12), (4, 0), (15, 17), (11, 26), (26, 6), (12, 13), (14, 0), (24, 21), (8, 2), (17, 15), (23, 2), (26, 15), (25, 23), (11, 17), (19, 2), (21, 18), (3, 2), (17, 18), (4, 22), (25, 13), (0, 3), (10, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160200", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 19), (8, 22), (1, 7), (17, 24), (10, 7), (3, 19), (13, 5), (18, 2), (7, 5), (4, 20), (12, 18), (2, 9), (17, 5), (6, 22), (0, 8), (9, 2), (18, 18), (1, 11), (4, 16), (0, 22), (9, 9), (14, 20), (10, 2), (13, 25), (6, 5), (0, 17), (0, 18), (5, 11), (8, 9), (0, 24), (13, 21), (7, 6), (17, 19), (11, 18), (3, 15), (13, 7), (4, 7), (7, 21), (18, 7), (3, 24), (15, 5), (12, 11), (0, 5), (17, 3), (9, 4), (15, 9), (10, 1), (9, 5), (6, 19), (13, 23), (19, 0), (16, 5), (6, 1), (13, 2), (16, 8), (1, 24), (9, 3), (19, 13), (4, 5), (4, 4), (19, 1), (9, 15), (4, 14), (2, 2), (13, 14), (15, 0), (5, 12), (10, 24), (1, 21), (0, 15), (5, 5), (4, 19), (8, 8), (6, 16), (13, 18), (6, 0), (10, 12), (19, 24), (4, 12), (1, 17), (3, 1), (19, 9), (7, 1), (6, 15), (19, 22), (9, 12), (10, 6), (12, 1), (9, 7), (7, 14), (15, 25), (13, 16), (12, 4), (13, 12), (11, 14), (16, 1), (3, 13), (6, 18), (14, 14), (5, 25), (15, 6), (9, 13), (5, 6), (8, 16), (16, 6), (7, 22), (3, 22), (0, 11), (14, 16), (7, 20), (18, 3), (6, 14), (6, 13), (15, 17), (5, 3), (11, 13), (17, 17), (17, 6), (9, 6), (5, 23), (11, 0), (11, 11), (3, 7), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570000", "dataset": "MATH"}
{"messages": [{"content": "In a 23x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 21), 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), (6, 0), (15, 14), (13, 17), (16, 12), (21, 11), (12, 3), (11, 12), (4, 13), (21, 6), (20, 11), (5, 14), (22, 19), (10, 15), (20, 16), (3, 19), (16, 16), (5, 20), (5, 8), (9, 6), (19, 9), (11, 4), (22, 12), (0, 17), (9, 10), (4, 17), (21, 7), (12, 16), (6, 14), (5, 18), (13, 10), (8, 19), (2, 0), (22, 20), (9, 2), (2, 9), (2, 3), (8, 12), (14, 0), (9, 14), (12, 15), (16, 10), (6, 20), (6, 21), (14, 4), (18, 10), (2, 10), (5, 4), (0, 7), (8, 15), (18, 11), (5, 16), (22, 8), (11, 11), (13, 1), (20, 14), (21, 1), (22, 15), (9, 4), (18, 1), (21, 16), (17, 3), (7, 15), (9, 1), (6, 7), (19, 4), (18, 4), (14, 1), (20, 1), (16, 4), (4, 3), (13, 9), (14, 16), (17, 11), (8, 21), (3, 20), (4, 6), (4, 10), (1, 5), (17, 0), (11, 19), (11, 18), (10, 11), (0, 21), (10, 7), (14, 3), (14, 6), (1, 16), (2, 19), (12, 14), (7, 19), (15, 3), (15, 2), (0, 9), (8, 18), (15, 19), (19, 16), (20, 19), (7, 12), (3, 9), (17, 1), (21, 2), (8, 7), (8, 1), (1, 7), (10, 9), (18, 12), (21, 3), (16, 19), (11, 16), (19, 13), (15, 13), (0, 14), (8, 13), (18, 16), (12, 11), (19, 15), (19, 10), (21, 19), (5, 21), (1, 6), (3, 16), (19, 21), (7, 21), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776000", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 17), (7, 6), (18, 11), (17, 8), (14, 13), (4, 3), (21, 15), (19, 25), (10, 8), (19, 5), (17, 20), (1, 4), (0, 12), (2, 20), (18, 5), (16, 16), (16, 11), (13, 5), (11, 8), (18, 0), (3, 6), (15, 12), (15, 1), (21, 21), (19, 17), (3, 1), (12, 18), (4, 24), (20, 13), (8, 1), (19, 15), (7, 9), (11, 21), (17, 2), (17, 6), (3, 18), (10, 16), (14, 8), (10, 12), (10, 21), (12, 22), (3, 15), (6, 25), (9, 8), (11, 24), (17, 12), (19, 0), (8, 9), (16, 4), (6, 16), (7, 27), (8, 8), (3, 3), (7, 22), (17, 10), (0, 19), (18, 21), (20, 25), (11, 14), (20, 27), (7, 16), (21, 5), (6, 14), (19, 24), (9, 0), (11, 1), (10, 2), (6, 23), (2, 2), (7, 0), (21, 6), (12, 17), (3, 17), (11, 15), (7, 20), (0, 2), (11, 26), (10, 18), (16, 22), (3, 24), (14, 26), (13, 8), (5, 0), (19, 12), (20, 24), (7, 21), (14, 0), (0, 14), (1, 19), (18, 23), (4, 16), (3, 22), (17, 19), (5, 5), (18, 4), (3, 21), (11, 4), (12, 16), (19, 18), (19, 26), (9, 13), (6, 0), (16, 9), (14, 23), (10, 1), (3, 10), (1, 20), (0, 4), (18, 8), (2, 14), (14, 14), (6, 21), (14, 11), (19, 21), (0, 17), (9, 11), (4, 17), (0, 5), (15, 18), (4, 4), (0, 10), (21, 8), (11, 7), (8, 18), (14, 24), (9, 27), (21, 17), (16, 3), (4, 15), (2, 23), (16, 12), (2, 22), (9, 6), (15, 27), (14, 15), (14, 5), (3, 19), (4, 11), (5, 4), (14, 22), (20, 12), (12, 12), (17, 24), (20, 6), (11, 0), (12, 8), (21, 0), (11, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613410", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 15), (20, 14), (15, 23), (6, 10), (3, 7), (0, 6), (0, 4), (5, 3), (20, 22), (4, 22), (0, 10), (12, 9), (15, 8), (1, 17), (1, 9), (3, 13), (12, 4), (11, 4), (2, 23), (20, 11), (2, 14), (15, 4), (21, 13), (20, 19), (4, 21), (11, 12), (17, 13), (17, 7), (8, 24), (15, 10), (16, 12), (17, 0), (1, 8), (12, 7), (0, 12), (7, 14), (13, 9), (9, 11), (8, 20), (8, 15), (13, 5), (6, 15), (23, 4), (20, 6), (1, 11), (16, 9), (7, 6), (10, 15), (14, 16), (17, 17), (4, 5), (8, 11), (13, 12), (13, 14), (0, 13), (19, 13), (20, 2), (18, 8), (5, 9), (14, 22), (3, 9), (9, 6), (16, 21), (11, 13), (17, 19), (21, 24), (0, 22), (3, 2), (20, 7), (2, 0), (15, 22), (14, 12), (10, 7), (8, 6), (3, 8), (14, 6), (15, 9), (0, 3), (18, 6), (10, 19), (19, 0), (21, 0), (2, 12), (12, 15), (14, 7), (10, 1), (14, 9), (3, 4), (22, 19), (3, 16), (12, 12), (3, 5), (3, 21), (1, 12), (6, 5), (6, 1), (9, 16), (4, 14), (22, 1), (6, 23), (6, 0), (2, 7), (22, 14), (15, 12), (12, 5), (0, 7), (9, 23), (11, 24), (2, 3), (15, 15), (2, 16), (13, 2), (17, 5), (18, 9), (13, 19), (19, 15), (9, 21), (20, 3), (4, 2), (11, 16), (22, 7), (18, 3), (6, 12), (10, 12), (7, 23), (9, 19), (8, 0), (9, 12), (8, 5), (19, 6), (8, 17), (19, 22), (10, 23), (21, 16), (23, 23), (22, 15), (19, 3), (18, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47088", "dataset": "MATH"}
{"messages": [{"content": "In a 29x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 26), 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), (9, 7), (8, 8), (14, 26), (24, 5), (25, 3), (1, 13), (15, 23), (13, 7), (15, 17), (22, 20), (19, 4), (17, 13), (26, 23), (14, 4), (6, 14), (8, 7), (21, 23), (17, 1), (1, 20), (26, 14), (1, 4), (18, 21), (18, 24), (3, 5), (12, 26), (1, 12), (5, 7), (27, 1), (13, 16), (28, 20), (12, 18), (25, 21), (27, 21), (17, 20), (18, 20), (22, 0), (11, 19), (7, 16), (16, 20), (28, 15), (3, 10), (26, 10), (3, 19), (16, 18), (28, 7), (14, 16), (18, 2), (16, 25), (23, 18), (7, 20), (8, 2), (14, 22), (21, 13), (24, 11), (2, 8), (13, 3), (16, 21), (8, 23), (1, 10), (12, 19), (20, 1), (22, 2), (9, 20), (8, 0), (19, 22), (0, 23), (7, 14), (20, 12), (5, 8), (7, 15), (6, 2), (14, 8), (18, 19), (26, 5), (12, 24), (11, 20), (1, 25), (3, 16), (21, 3), (11, 10), (3, 20), (20, 13), (6, 1), (19, 10), (19, 0), (7, 22), (0, 11), (12, 5), (18, 25), (13, 17), (9, 25), (11, 5), (26, 18), (18, 12), (15, 14), (21, 8), (9, 0), (24, 8), (14, 19), (8, 10), (17, 2), (1, 18), (11, 1), (6, 13), (10, 26), (24, 23), (28, 12), (1, 1), (6, 15), (8, 17), (4, 20), (3, 8), (14, 10), (1, 19), (19, 20), (16, 16), (8, 19), (10, 13), (2, 6), (3, 1), (5, 16), (15, 20), (8, 14), (21, 19), (16, 22), (15, 22), (2, 16), (13, 19), (15, 13), (8, 1), (15, 24), (6, 19), (4, 13), (15, 25), (9, 26), (18, 26), (25, 13), (20, 24), (21, 6), (10, 21), (5, 18), (0, 15), (15, 3), (12, 15), (7, 23), (28, 4), (3, 25), (8, 5), (7, 24), (25, 4), (11, 13), (14, 23), (18, 15), (3, 2), (22, 1), (16, 9), (2, 18), (6, 10), (3, 11), (8, 16), (18, 4), (17, 5), (10, 2), (7, 0), (6, 24), (15, 2), (13, 10), (11, 3), (10, 4), (23, 7), (17, 14), (21, 18), (28, 2), (22, 15), (12, 4), (17, 3), (28, 17), (3, 6), (0, 8), (10, 9), (6, 6), (16, 26), (26, 9), (22, 8), (26, 11), (15, 0), (6, 0), (24, 10), (17, 11), (22, 26), (15, 19), (20, 4), (2, 24), (5, 12), (22, 3), (25, 18), (4, 23), (5, 6), (15, 12), (14, 14), (27, 6), (18, 14), (25, 7), (26, 24), (28, 10), (11, 11), (16, 11), (20, 8), (23, 25), (3, 14), (15, 8), (19, 14), (27, 24), (28, 16), (14, 17), (22, 19), (8, 12), (27, 4), (6, 7), (27, 13), (4, 24), (28, 0), (20, 5), (21, 21), (16, 19), (9, 14), (22, 12), (9, 23), (24, 24), (23, 19), (23, 12), (20, 0), (26, 1), (25, 6), (3, 13), (4, 17), (8, 26), (6, 17), (26, 25), (4, 21), (14, 24), (0, 5), (11, 2), (1, 23), (13, 0), (19, 7), (17, 6), (6, 20), (13, 18), (2, 5), (23, 24), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941400", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 15), (2, 10), (0, 15), (4, 20), (20, 20), (18, 23), (9, 17), (3, 23), (18, 10), (21, 18), (27, 23), (27, 26), (20, 21), (2, 27), (17, 16), (3, 22), (11, 14), (21, 13), (23, 17), (2, 21), (5, 27), (19, 0), (8, 20), (1, 16), (21, 16), (11, 9), (25, 2), (2, 18), (3, 14), (8, 13), (1, 25), (3, 24), (9, 27), (14, 10), (13, 21), (25, 20), (28, 10), (25, 6), (1, 12), (23, 5), (13, 26), (18, 9), (26, 20), (19, 8), (5, 24), (17, 10), (19, 21), (19, 24), (28, 1), (25, 15), (25, 7), (9, 9), (2, 6), (18, 25), (15, 20), (28, 17), (11, 11), (6, 11), (18, 4), (27, 5), (18, 7), (4, 3), (14, 3), (20, 6), (28, 8), (0, 19), (28, 5), (16, 13), (18, 8), (28, 15), (5, 13), (2, 20), (21, 22), (6, 23), (21, 2), (18, 20), (13, 24), (10, 4), (26, 2), (7, 5), (1, 2), (14, 23), (14, 15), (11, 21), (12, 6), (26, 26), (14, 26), (28, 4), (17, 21), (25, 23), (25, 10), (7, 16), (2, 3), (25, 9), (13, 2), (11, 18), (27, 25), (4, 16), (15, 24), (4, 8), (6, 24), (12, 18), (16, 1), (21, 0), (0, 12), (21, 9), (19, 15), (19, 13), (14, 0), (22, 24), (22, 6), (19, 11), (19, 12), (21, 7), (15, 15), (3, 9), (14, 4), (5, 4), (0, 18), (14, 7), (11, 7), (9, 26), (11, 6), (3, 8), (19, 18), (11, 20), (12, 24), (26, 15), (1, 9), (12, 27), (7, 20), (13, 9), (28, 23), (10, 20), (11, 19), (23, 16), (15, 17), (27, 14), (17, 18), (12, 14), (8, 8), (26, 5), (11, 23), (6, 13), (0, 7), (17, 5), (4, 6), (28, 0), (20, 16), (15, 16), (16, 2), (19, 23), (19, 9), (20, 9), (24, 3), (24, 14), (24, 15), (24, 21), (3, 11), (17, 8), (15, 14), (4, 7), (9, 20), (13, 11), (1, 17), (7, 6), (9, 0), (1, 13), (10, 18), (5, 14), (20, 27), (7, 12), (11, 12), (9, 6), (12, 22), (19, 7), (17, 20), (3, 2), (0, 11), (8, 9), (9, 5), (4, 11), (24, 16), (10, 0), (9, 3), (1, 10), (26, 23), (13, 16), (27, 17), (23, 6), (27, 13), (4, 14), (7, 23), (15, 0), (11, 16), (22, 22), (9, 22), (11, 8), (25, 4), (22, 14), (15, 22), (6, 16), (2, 14), (22, 0), (9, 15), (16, 23), (20, 23), (10, 12), (20, 0), (17, 27), (19, 26), (24, 0), (12, 20), (13, 3), (1, 18), (26, 14), (4, 2), (23, 19), (5, 8), (28, 7), (27, 27), (12, 26), (9, 11), (11, 25), (17, 9), (19, 14), (2, 15), (16, 16), (0, 1), (22, 20), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447900", "dataset": "MATH"}
{"messages": [{"content": "In a 28x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 20), (1, 9), (8, 11), (0, 8), (4, 17), (17, 17), (4, 2), (6, 15), (24, 5), (13, 0), (0, 11), (15, 18), (19, 5), (23, 10), (6, 18), (9, 14), (17, 11), (3, 14), (0, 16), (10, 4), (16, 0), (11, 7), (7, 13), (15, 3), (11, 11), (24, 2), (5, 17), (26, 2), (5, 15), (3, 17), (26, 6), (17, 9), (27, 14), (3, 8), (13, 13), (27, 15), (16, 9), (0, 13), (6, 3), (26, 19), (21, 11), (21, 14), (8, 8), (20, 18), (25, 15), (15, 19), (11, 18), (22, 20), (21, 2), (7, 0), (6, 19), (15, 12), (24, 19), (2, 2), (23, 9), (11, 3), (21, 1), (1, 7), (5, 16), (21, 12), (9, 12), (13, 11), (22, 19), (25, 3), (12, 20), (10, 8), (10, 20), (14, 9), (0, 5), (17, 16), (17, 7), (22, 17), (16, 4), (23, 3), (2, 12), (23, 14), (10, 7), (0, 3), (11, 8), (23, 7), (15, 15), (24, 6), (0, 9), (12, 4), (15, 17), (12, 14), (19, 0), (16, 3), (16, 13), (22, 2), (1, 4), (15, 7), (22, 11), (11, 6), (18, 5), (7, 10), (5, 11), (14, 4), (13, 6), (14, 18), (22, 9), (20, 8), (16, 16), (22, 18), (14, 1), (24, 0), (5, 6), (27, 11), (24, 17), (16, 8), (6, 14), (8, 12), (0, 12), (14, 2), (2, 7), (23, 13), (13, 19), (16, 20), (2, 18), (12, 18), (17, 13), (11, 10), (0, 10), (1, 16), (24, 15), (9, 20), (23, 17), (13, 17), (12, 15), (27, 1), (23, 16), (8, 13), (3, 15), (21, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178752", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 18), (4, 18), (27, 25), (13, 12), (22, 23), (4, 10), (2, 12), (17, 25), (25, 19), (14, 7), (5, 27), (10, 18), (2, 2), (19, 28), (25, 7), (2, 15), (25, 16), (27, 7), (21, 0), (6, 26), (16, 1), (12, 10), (23, 21), (18, 4), (11, 12), (22, 4), (17, 9), (23, 24), (7, 22), (3, 27), (0, 18), (7, 20), (5, 20), (13, 28), (17, 17), (27, 4), (0, 10), (26, 16), (4, 7), (23, 4), (2, 19), (6, 23), (17, 28), (9, 2), (18, 28), (21, 15), (25, 21), (15, 26), (5, 16), (4, 5), (19, 4), (18, 20), (7, 19), (15, 18), (19, 2), (2, 5), (23, 22), (2, 23), (20, 10), (16, 6), (9, 19), (1, 25), (27, 17), (21, 28), (9, 3), (16, 3), (10, 5), (0, 23), (14, 9), (11, 16), (3, 24), (14, 19), (12, 3), (21, 5), (15, 20), (13, 7), (1, 18), (6, 22), (20, 8), (15, 12), (10, 20), (24, 20), (26, 7), (7, 10), (1, 4), (10, 28), (19, 18), (26, 10), (25, 15), (8, 11), (12, 14), (27, 9), (12, 11), (15, 16), (0, 5), (26, 1), (16, 10), (3, 5), (12, 28), (14, 21), (8, 15), (26, 28), (6, 4), (26, 15), (3, 8), (0, 12), (7, 1), (4, 6), (15, 1), (11, 3), (17, 12), (6, 0), (17, 14), (18, 5), (24, 7), (3, 14), (3, 0), (12, 26), (4, 9), (0, 22), (24, 2), (17, 10), (15, 15), (5, 21), (2, 1), (15, 21), (22, 24), (15, 27), (27, 1), (5, 22), (9, 11), (5, 24), (20, 26), (25, 22), (23, 7), (6, 11), (8, 16), (14, 15), (9, 21), (22, 1), (17, 15), (25, 1), (24, 25), (7, 8), (19, 24), (23, 11), (25, 6), (17, 3), (15, 4), (22, 7), (0, 21), (9, 13), (6, 1), (5, 4), (25, 2), (14, 28), (8, 10), (27, 26), (24, 12), (16, 17), (11, 8), (21, 24), (23, 19), (0, 11), (22, 8), (1, 6), (26, 14), (1, 5), (9, 10), (16, 5), (2, 16), (7, 16), (0, 7), (19, 19), (12, 6), (3, 23), (1, 7), (17, 6), (14, 5), (12, 20), (12, 19), (16, 4), (24, 24), (19, 23), (17, 5), (10, 10), (4, 0), (23, 15), (20, 17), (11, 21), (10, 24), (16, 24), (4, 28), (0, 3), (22, 6), (2, 17), (1, 20), (25, 14), (2, 24), (1, 19), (23, 10), (13, 17), (4, 22), (8, 21), (19, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "773280", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), 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), (7, 22), (18, 27), (3, 2), (2, 22), (8, 5), (16, 18), (4, 10), (15, 0), (6, 11), (4, 22), (0, 15), (21, 3), (21, 6), (10, 23), (14, 14), (6, 0), (0, 25), (14, 5), (11, 9), (6, 4), (6, 10), (20, 21), (2, 20), (9, 0), (6, 15), (5, 15), (15, 13), (21, 12), (16, 20), (5, 8), (2, 6), (21, 1), (12, 9), (3, 24), (19, 24), (6, 5), (15, 2), (6, 16), (3, 8), (1, 13), (4, 24), (18, 25), (3, 12), (14, 21), (16, 21), (12, 18), (9, 15), (21, 4), (21, 17), (2, 14), (9, 12), (17, 26), (9, 14), (10, 11), (17, 3), (8, 6), (15, 26), (13, 4), (10, 26), (0, 2), (21, 7), (11, 14), (5, 22), (17, 13), (6, 7), (8, 22), (8, 18), (4, 20), (2, 12), (21, 16), (4, 13), (17, 21), (11, 2), (9, 4), (12, 13), (10, 18), (5, 25), (0, 17), (12, 22), (8, 19), (20, 13), (17, 4), (1, 16), (3, 10), (21, 14), (16, 5), (4, 21), (9, 25), (15, 12), (11, 27), (4, 0), (6, 22), (15, 24), (13, 18), (21, 23), (10, 2), (7, 19), (19, 6), (11, 1), (9, 7), (11, 5), (13, 8), (12, 26), (20, 14), (15, 1), (0, 26), (20, 5), (20, 1), (11, 12), (19, 3), (8, 16), (20, 20), (19, 25), (19, 9), (19, 4), (13, 20), (9, 21), (17, 12), (17, 1), (12, 24), (5, 9), (11, 7), (14, 20), (6, 27), (16, 3), (16, 27), (14, 9), (7, 21), (19, 7), (12, 21), (13, 13), (8, 10), (10, 25), (9, 17), (1, 9), (5, 13), (4, 14), (12, 16), (19, 10), (2, 15), (10, 21), (7, 23), (11, 11), (6, 19), (0, 21), (2, 26), (15, 25), (12, 11), (12, 5), (4, 26), (0, 8), (3, 0), (6, 12), (8, 2), (19, 15), (2, 27), (13, 7), (18, 23), (1, 11), (20, 11), (0, 13), (1, 23), (11, 25), (11, 8), (7, 26), (10, 15), (20, 25), (14, 19), (1, 7), (2, 4), (4, 18), (17, 23), (15, 5), (20, 3), (20, 10), (11, 3), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891180", "dataset": "MATH"}
{"messages": [{"content": "In a 20x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 14), (18, 21), (5, 23), (4, 9), (19, 21), (4, 1), (3, 21), (15, 15), (18, 17), (4, 21), (19, 13), (12, 13), (2, 17), (6, 5), (5, 17), (12, 22), (8, 13), (19, 14), (14, 19), (15, 5), (19, 20), (10, 9), (0, 9), (5, 10), (6, 13), (14, 13), (16, 15), (6, 0), (11, 17), (16, 16), (15, 11), (2, 2), (5, 22), (1, 7), (14, 16), (13, 15), (5, 14), (13, 16), (13, 21), (9, 18), (8, 1), (10, 3), (0, 19), (1, 3), (0, 10), (15, 2), (4, 7), (4, 11), (7, 4), (8, 6), (15, 9), (0, 2), (10, 20), (19, 19), (1, 18), (13, 14), (13, 12), (1, 16), (8, 14), (11, 16), (1, 17), (7, 19), (14, 0), (6, 22), (3, 1), (8, 23), (3, 12), (15, 7), (9, 11), (12, 10), (9, 7), (9, 10), (2, 10), (10, 21), (18, 19), (18, 4), (5, 13), (3, 6), (6, 10), (16, 7), (12, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832435", "dataset": "MATH"}
{"messages": [{"content": "In a 26x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 27), 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, 11), (12, 22), (20, 12), (0, 23), (0, 4), (13, 19), (18, 18), (19, 26), (24, 0), (18, 16), (2, 11), (6, 9), (15, 20), (1, 10), (5, 4), (1, 4), (2, 20), (5, 25), (11, 14), (10, 0), (4, 7), (7, 8), (11, 23), (19, 27), (5, 14), (15, 19), (23, 5), (4, 0), (24, 17), (6, 22), (23, 21), (3, 5), (3, 14), (0, 19), (22, 20), (12, 15), (1, 19), (10, 14), (24, 6), (22, 11), (11, 9), (18, 12), (21, 3), (16, 2), (22, 26), (0, 7), (20, 18), (17, 12), (19, 9), (14, 25), (11, 5), (6, 6), (8, 19), (16, 12), (25, 6), (0, 16), (25, 20), (15, 22), (3, 24), (12, 25), (18, 2), (10, 22), (6, 4), (15, 9), (22, 5), (20, 17), (2, 27), (4, 18), (6, 14), (8, 8), (24, 12), (0, 6), (21, 21), (13, 4), (21, 13), (2, 3), (8, 9), (2, 7), (14, 2), (19, 12), (14, 14), (1, 14), (23, 26), (17, 6), (12, 13), (1, 26), (17, 13), (14, 11), (22, 16), (12, 27), (19, 13), (12, 7), (20, 15), (3, 21), (18, 3), (9, 11), (25, 3), (18, 4), (14, 22), (4, 27), (24, 2), (15, 11), (4, 4), (17, 24), (10, 6), (21, 18), (2, 17), (3, 0), (14, 20), (18, 25), (0, 27), (24, 18), (14, 17), (13, 25), (24, 24), (13, 14), (14, 10), (12, 26), (9, 7), (7, 25), (9, 6), (22, 15), (7, 6), (1, 17), (24, 21), (6, 24), (3, 26), (23, 8), (15, 14), (4, 16), (13, 23), (13, 1), (18, 19), (9, 25), (8, 24), (14, 26), (3, 2), (11, 2), (20, 5), (21, 26), (16, 0), (9, 20), (5, 9), (22, 1), (22, 4), (7, 1), (17, 23), (19, 0), (0, 11), (5, 27), (11, 10), (20, 4), (5, 19), (3, 4), (8, 14), (4, 12), (8, 25), (19, 16), (7, 10), (16, 21), (4, 22), (14, 18), (22, 19), (6, 12), (14, 4), (11, 7), (25, 19), (5, 0), (16, 15), (18, 6), (1, 9), (3, 27), (18, 9), (23, 20), (24, 5), (3, 11), (25, 10), (23, 22), (15, 15), (19, 21), (22, 7), (0, 20), (19, 4), (17, 26), (21, 1), (15, 6), (10, 21), (19, 1), (3, 19), (1, 15), (5, 23), (5, 5), (23, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87480", "dataset": "MATH"}
{"messages": [{"content": "In a 22x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 25), 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), (20, 18), (0, 14), (3, 13), (1, 17), (0, 17), (17, 23), (15, 23), (14, 4), (15, 10), (18, 17), (6, 8), (2, 17), (1, 24), (20, 8), (1, 13), (12, 23), (8, 8), (9, 22), (17, 14), (8, 23), (18, 25), (15, 3), (20, 20), (8, 22), (15, 13), (18, 11), (12, 5), (15, 18), (1, 9), (2, 2), (9, 16), (19, 20), (14, 20), (13, 22), (11, 21), (18, 8), (2, 13), (1, 11), (2, 3), (12, 4), (1, 25), (0, 5), (20, 9), (13, 8), (18, 7), (7, 19), (19, 14), (7, 5), (8, 5), (3, 7), (11, 13), (1, 2), (19, 7), (4, 1), (4, 20), (13, 3), (19, 0), (12, 18), (12, 20), (20, 6), (18, 9), (4, 10), (10, 19), (16, 7), (6, 11), (0, 16), (18, 20), (1, 4), (17, 7), (3, 5), (7, 8), (19, 5), (6, 22), (1, 20), (19, 13), (3, 2), (15, 12), (2, 10), (16, 13), (1, 23), (12, 9), (9, 10), (16, 22), (7, 24), (5, 23), (15, 4), (13, 14), (7, 17), (14, 2), (0, 1), (3, 18), (4, 18), (6, 19), (5, 11), (20, 1), (13, 25), (21, 0), (10, 12), (17, 17), (2, 14), (14, 14), (17, 1), (11, 17), (8, 18), (5, 4), (11, 2), (9, 7), (20, 19), (20, 10), (9, 9), (2, 20), (8, 12), (19, 3), (0, 21), (7, 1), (0, 2), (8, 25), (6, 18), (6, 24), (7, 2), (6, 13), (3, 10), (8, 21), (6, 16), (1, 15), (11, 24), (13, 21), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758256", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), 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), (13, 10), (2, 11), (19, 15), (19, 14), (18, 21), (9, 22), (2, 8), (15, 16), (19, 2), (12, 14), (8, 6), (2, 10), (4, 21), (20, 23), (9, 19), (16, 6), (6, 9), (3, 1), (22, 0), (0, 2), (2, 18), (10, 20), (11, 16), (8, 16), (17, 15), (3, 14), (7, 12), (12, 11), (22, 1), (0, 23), (17, 2), (13, 1), (15, 15), (16, 2), (10, 7), (20, 18), (7, 7), (16, 13), (1, 2), (13, 7), (19, 3), (3, 17), (18, 4), (22, 8), (4, 10), (18, 10), (11, 10), (7, 17), (1, 6), (11, 14), (3, 4), (4, 12), (15, 1), (6, 4), (13, 13), (21, 7), (21, 3), (10, 5), (7, 18), (6, 23), (16, 22), (21, 8), (4, 3), (1, 16), (14, 9), (9, 10), (16, 12), (16, 10), (15, 7), (15, 18), (14, 2), (3, 18), (1, 5), (14, 11), (16, 19), (20, 15), (3, 20), (1, 9), (10, 12), (16, 20), (13, 9), (3, 9), (1, 10), (0, 15), (9, 13), (5, 22), (0, 11), (21, 16), (7, 10), (17, 21), (9, 18), (11, 8), (17, 7), (22, 7), (5, 11), (19, 1), (14, 6), (5, 9), (16, 17), (2, 3), (9, 0), (20, 0), (4, 4), (19, 16), (1, 15), (13, 21), (7, 8), (14, 19), (10, 22), (15, 0), (14, 4), (12, 23), (15, 9), (11, 11), (21, 20), (13, 2), (18, 20), (21, 2), (14, 12), (6, 15), (1, 19), (4, 2), (10, 21), (3, 5), (21, 0), (8, 12), (14, 16), (7, 16), (15, 21), (17, 9), (18, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643740", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (4, 17), (7, 24), (4, 5), (15, 8), (16, 0), (18, 18), (2, 19), (2, 8), (17, 20), (19, 12), (0, 5), (3, 10), (4, 20), (0, 24), (15, 0), (6, 21), (2, 9), (3, 1), (16, 22), (9, 23), (18, 13), (21, 14), (7, 22), (9, 11), (5, 7), (2, 10), (14, 3), (1, 21), (18, 3), (14, 15), (21, 3), (9, 5), (14, 16), (10, 4), (10, 22), (16, 4), (11, 15), (19, 7), (7, 10), (7, 20), (10, 5), (13, 9), (1, 24), (20, 14), (7, 9), (10, 15), (5, 11), (13, 0), (21, 11), (10, 8), (15, 21), (7, 0), (11, 11), (4, 16), (4, 7), (3, 3), (4, 4), (14, 5), (2, 17), (8, 7), (2, 7), (6, 0), (0, 23), (16, 21), (9, 24), (15, 10), (6, 24), (16, 19), (5, 21), (21, 12), (4, 9), (12, 18), (15, 13), (18, 19), (13, 15), (7, 11), (12, 4), (3, 16), (8, 17), (2, 3), (12, 5), (13, 7), (3, 13), (7, 5), (8, 6), (11, 21), (1, 13), (17, 14), (12, 1), (13, 8), (17, 19), (10, 10), (7, 16), (16, 10), (14, 6), (3, 9), (16, 20), (13, 14), (14, 7), (17, 12), (5, 16), (11, 4), (10, 6), (15, 19), (10, 3), (14, 11), (4, 23), (11, 23), (6, 4), (0, 22), (7, 18), (0, 10), (11, 12), (14, 14), (21, 13), (6, 6), (3, 0), (20, 23), (15, 14), (1, 18), (18, 16), (3, 18), (8, 1), (5, 0), (17, 17), (8, 24), (12, 17), (20, 15), (2, 6), (10, 18), (3, 24), (7, 7), (8, 12), (3, 8), (7, 19), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "498520", "dataset": "MATH"}
{"messages": [{"content": "In a 22x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 26), 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), (20, 18), (12, 2), (0, 12), (7, 3), (20, 3), (9, 17), (21, 8), (17, 6), (7, 5), (13, 12), (4, 15), (13, 0), (3, 23), (7, 6), (17, 7), (19, 23), (4, 13), (5, 10), (19, 13), (18, 9), (15, 15), (7, 25), (5, 26), (9, 16), (11, 24), (14, 21), (1, 0), (15, 25), (18, 10), (13, 3), (12, 21), (7, 10), (14, 12), (14, 8), (21, 10), (15, 22), (2, 11), (4, 21), (21, 13), (10, 20), (17, 3), (1, 21), (13, 21), (10, 11), (1, 15), (14, 1), (2, 9), (7, 2), (16, 25), (20, 25), (20, 8), (20, 6), (16, 23), (9, 8), (2, 12), (12, 1), (19, 21), (7, 12), (6, 24), (20, 13), (7, 14), (15, 16), (2, 24), (9, 21), (15, 3), (2, 22), (12, 3), (16, 17), (3, 21), (15, 7), (7, 8), (12, 4), (6, 1), (2, 0), (13, 6), (16, 3), (15, 19), (1, 8), (14, 18), (16, 10), (7, 11), (10, 25), (11, 16), (2, 25), (13, 7), (18, 20), (11, 19), (16, 14), (0, 4), (18, 6), (6, 4), (9, 22), (0, 10), (10, 2), (11, 8), (8, 8), (10, 6), (18, 23), (3, 3), (0, 3), (3, 6), (9, 19), (4, 8), (9, 13), (4, 10), (20, 21), (8, 10), (8, 6), (19, 6), (4, 14), (4, 22), (15, 1), (18, 18), (20, 4), (16, 20), (14, 10), (2, 13), (8, 3), (11, 7), (11, 25), (2, 21), (12, 18), (4, 20), (8, 9), (1, 23), (20, 12), (9, 3), (7, 17), (5, 20), (10, 9), (13, 2), (20, 22), (18, 8), (14, 14), (5, 14), (0, 22), (14, 4), (15, 0), (12, 13), (13, 11), (3, 1), (18, 24), (11, 22), (14, 7), (20, 9), (12, 12), (10, 26), (15, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734306", "dataset": "MATH"}
{"messages": [{"content": "In a 26x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 21), (10, 6), (19, 25), (0, 24), (0, 21), (18, 7), (1, 20), (6, 26), (4, 5), (3, 17), (15, 6), (6, 20), (24, 10), (23, 18), (14, 15), (15, 24), (20, 0), (16, 1), (7, 18), (13, 0), (10, 7), (1, 1), (5, 15), (12, 20), (1, 5), (13, 8), (20, 9), (21, 25), (4, 8), (23, 2), (11, 3), (5, 23), (24, 16), (19, 26), (21, 2), (23, 17), (17, 12), (13, 3), (4, 12), (16, 18), (18, 5), (22, 8), (10, 14), (1, 23), (1, 0), (15, 1), (20, 13), (0, 3), (13, 6), (1, 12), (20, 18), (6, 8), (5, 5), (7, 13), (1, 4), (23, 24), (3, 7), (23, 16), (4, 25), (2, 13), (12, 12), (15, 17), (24, 18), (18, 15), (10, 15), (11, 14), (23, 25), (10, 10), (19, 20), (22, 3), (7, 16), (8, 23), (23, 10), (17, 17), (7, 5), (23, 23), (22, 9), (18, 24), (13, 15), (21, 11), (20, 1), (9, 15), (22, 6), (20, 15), (3, 18), (16, 17), (5, 16), (10, 18), (5, 1), (9, 5), (7, 9), (5, 13), (0, 9), (7, 19), (1, 13), (14, 1), (3, 21), (18, 18), (18, 26), (5, 9), (9, 12), (24, 12), (6, 24), (12, 18), (7, 15), (14, 19), (11, 16), (15, 23), (10, 3), (19, 14), (3, 11), (4, 6), (6, 9), (10, 0), (3, 14), (13, 16), (10, 13), (4, 11), (22, 12), (18, 9), (2, 5), (8, 6), (16, 0), (7, 4), (25, 6), (23, 20), (8, 20), (8, 22), (12, 11), (14, 20), (24, 14), (21, 14), (17, 19), (5, 7), (13, 7), (0, 7), (19, 18), (21, 23), (15, 2), (25, 7), (0, 25), (12, 2), (11, 25), (10, 16), (3, 0), (13, 21), (16, 6), (4, 26), (17, 10), (18, 10), (14, 24), (6, 19), (6, 17), (6, 15), (19, 17), (5, 22), (12, 16), (12, 15), (11, 19), (20, 22), (17, 11), (5, 25), (21, 26), (23, 4), (15, 7), (21, 8), (9, 11), (23, 7), (22, 20), (15, 14), (24, 25), (8, 1), (20, 26), (8, 16), (4, 17), (9, 13), (16, 10), (2, 1), (3, 19), (8, 7), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779324", "dataset": "MATH"}
{"messages": [{"content": "In a 27x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (21, 22), (26, 7), (17, 20), (18, 1), (15, 4), (2, 14), (15, 9), (5, 1), (11, 8), (4, 8), (20, 2), (18, 18), (9, 10), (18, 11), (13, 14), (20, 1), (20, 5), (0, 7), (25, 0), (16, 21), (10, 0), (0, 3), (25, 19), (13, 9), (24, 9), (19, 12), (15, 1), (16, 5), (1, 26), (5, 18), (26, 11), (11, 13), (2, 15), (2, 19), (15, 11), (0, 8), (20, 8), (14, 14), (3, 25), (11, 15), (3, 24), (23, 20), (3, 13), (18, 9), (13, 21), (14, 13), (11, 3), (12, 17), (0, 13), (22, 7), (16, 23), (10, 26), (7, 26), (1, 9), (9, 22), (1, 16), (4, 14), (10, 25), (7, 18), (8, 18), (22, 4), (2, 18), (5, 14), (16, 22), (19, 4), (2, 11), (18, 12), (26, 15), (11, 6), (25, 8), (9, 4), (8, 19), (5, 5), (23, 14), (26, 0), (19, 25), (22, 26), (10, 11), (2, 8), (3, 9), (21, 1), (23, 21), (10, 19), (12, 15), (12, 23), (8, 12), (14, 11), (1, 20), (18, 0), (17, 24), (24, 8), (6, 20), (13, 6), (10, 13), (17, 13), (7, 21), (13, 7), (9, 3), (25, 16), (19, 18), (3, 21), (21, 25), (4, 25), (15, 10), (24, 6), (5, 17), (5, 26), (3, 11), (9, 17), (25, 2), (19, 17), (25, 1), (24, 20), (13, 3), (18, 17), (18, 2), (8, 5), (5, 2), (19, 16), (13, 13), (25, 11), (12, 16), (12, 1), (19, 13), (0, 16), (3, 8), (13, 11), (2, 5), (26, 18), (10, 6), (14, 19), (5, 23), (22, 11), (25, 12), (4, 0), (4, 7), (23, 23), (15, 22), (3, 22), (0, 17), (17, 7), (11, 12), (18, 21), (4, 26), (2, 3), (21, 8), (5, 9), (8, 2), (11, 16), (16, 19), (18, 20), (14, 18), (21, 10), (20, 7), (1, 12), (23, 9), (5, 11), (16, 6), (3, 7), (16, 10), (23, 4), (5, 8), (4, 4), (7, 20), (25, 3), (7, 10), (15, 23), (0, 12), (14, 7), (23, 5), (25, 4), (15, 19), (1, 7), (17, 3), (13, 8), (1, 5), (17, 22), (16, 8), (23, 6), (15, 16), (1, 3), (18, 14), (14, 20), (24, 10), (4, 24), (1, 18), (6, 16), (13, 15), (15, 17), (11, 1), (0, 9), (12, 20), (20, 6), (3, 16), (7, 13), (21, 5), (19, 20), (1, 21), (17, 8), (5, 12), (1, 13), (6, 26), (23, 10), (11, 26), (20, 14), (10, 4), (4, 17), (20, 0), (19, 24), (26, 25), (20, 25), (8, 9), (10, 16), (16, 3), (22, 6), (12, 4), (5, 10), (17, 5), (21, 20), (17, 6), (18, 4), (23, 15), (22, 19), (24, 2), (3, 18), (14, 0), (8, 13), (10, 8), (21, 23), (11, 22), (2, 17), (25, 20), (20, 15), (21, 0), (24, 25), (22, 8), (12, 26), (4, 9), (9, 1), (2, 7), (3, 26), (26, 9), (9, 0), (13, 25), (26, 20), (18, 8), (25, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "611952", "dataset": "MATH"}
{"messages": [{"content": "In a 21x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 23), (0, 3), (11, 17), (18, 2), (9, 17), (3, 20), (19, 13), (0, 5), (15, 11), (11, 13), (10, 16), (19, 5), (8, 8), (13, 0), (19, 7), (18, 16), (1, 18), (20, 7), (2, 11), (0, 12), (2, 15), (17, 2), (16, 5), (2, 10), (16, 6), (5, 8), (13, 15), (1, 9), (12, 11), (17, 18), (12, 1), (14, 4), (19, 16), (0, 1), (15, 10), (12, 20), (3, 16), (9, 16), (0, 4), (4, 10), (13, 23), (16, 1), (12, 12), (2, 3), (8, 15), (16, 22), (1, 22), (0, 20), (14, 15), (15, 3), (8, 13), (10, 14), (5, 7), (15, 17), (10, 2), (15, 8), (11, 23), (9, 5), (12, 10), (6, 4), (3, 14), (16, 3), (3, 0), (17, 9), (2, 9), (1, 10), (4, 16), (13, 18), (0, 19), (17, 6), (17, 22), (14, 3), (3, 13), (6, 1), (6, 22), (8, 16), (13, 14), (20, 20), (1, 5), (11, 1), (14, 7), (6, 19), (2, 1), (14, 12), (15, 13), (4, 12), (8, 21), (2, 13), (13, 13), (4, 17), (19, 22), (16, 7), (14, 0), (5, 21), (0, 16), (14, 10), (8, 1), (3, 4), (18, 6), (20, 14), (9, 4), (1, 7), (9, 9), (5, 10), (2, 18), (5, 3), (5, 12), (20, 19), (10, 5), (16, 12), (18, 12), (15, 14), (1, 13), (2, 17), (20, 2), (1, 19), (11, 12), (7, 1), (9, 1), (13, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914071", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), 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), (15, 15), (7, 22), (4, 10), (0, 10), (9, 13), (0, 18), (23, 3), (23, 2), (0, 12), (8, 2), (4, 3), (17, 12), (19, 20), (6, 17), (7, 24), (5, 8), (12, 14), (4, 16), (11, 6), (11, 18), (16, 9), (11, 9), (10, 5), (6, 0), (3, 17), (3, 2), (9, 10), (21, 6), (15, 22), (2, 5), (11, 16), (11, 7), (7, 2), (18, 3), (8, 5), (12, 0), (5, 6), (16, 23), (18, 23), (17, 18), (20, 24), (7, 12), (7, 19), (6, 8), (12, 21), (1, 0), (18, 24), (2, 16), (0, 21), (12, 4), (16, 3), (15, 4), (8, 4), (21, 17), (14, 1), (15, 24), (14, 20), (4, 9), (19, 6), (2, 23), (0, 14), (10, 23), (13, 17), (5, 22), (10, 22), (11, 14), (18, 8), (2, 4), (1, 22), (5, 4), (6, 23), (18, 19), (18, 16), (13, 16), (22, 18), (22, 4), (18, 13), (17, 10), (22, 2), (4, 1), (15, 21), (3, 6), (19, 10), (18, 7), (3, 18), (14, 15), (15, 3), (19, 8), (22, 9), (11, 0), (10, 20), (13, 0), (7, 8), (7, 20), (15, 11), (21, 3), (15, 0), (10, 17), (9, 2), (14, 19), (11, 22), (20, 5), (18, 11), (3, 0), (7, 3), (3, 13), (16, 0), (16, 15), (15, 10), (22, 1), (14, 11), (17, 14), (9, 23), (14, 22), (23, 1), (12, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72921", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (16, 4), (21, 15), (10, 20), (16, 16), (15, 16), (9, 3), (3, 2), (5, 5), (10, 7), (14, 20), (16, 11), (18, 5), (2, 20), (12, 6), (3, 10), (1, 13), (15, 13), (5, 4), (5, 6), (7, 20), (13, 5), (22, 3), (13, 7), (7, 9), (4, 18), (21, 3), (7, 2), (22, 6), (12, 2), (21, 12), (14, 14), (4, 8), (6, 13), (13, 4), (9, 20), (22, 4), (10, 8), (10, 3), (9, 15), (4, 10), (18, 17), (12, 9), (2, 17), (5, 0), (6, 3), (1, 5), (20, 19), (14, 11), (14, 10), (16, 13), (2, 15), (22, 17), (1, 6), (1, 1), (4, 2), (15, 7), (0, 4), (4, 19), (12, 5), (18, 6), (6, 19), (10, 0), (12, 17), (15, 3), (1, 12), (20, 2), (18, 2), (20, 9), (22, 14), (11, 10), (21, 9), (8, 16), (0, 2), (17, 8), (22, 2), (11, 11), (21, 18), (18, 3), (7, 12), (9, 8), (22, 5), (13, 20), (15, 10), (6, 1), (4, 1), (13, 6), (14, 19), (9, 18), (2, 14), (17, 7), (18, 7), (19, 17), (5, 8), (11, 19), (14, 3), (9, 5), (6, 8), (8, 1), (7, 7), (10, 11), (13, 11), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592802", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 20), (5, 11), (4, 9), (6, 20), (9, 13), (14, 21), (14, 2), (19, 4), (11, 17), (9, 16), (2, 9), (1, 18), (9, 5), (15, 10), (14, 18), (19, 15), (3, 13), (13, 11), (8, 0), (17, 16), (19, 11), (19, 7), (1, 10), (14, 3), (3, 2), (8, 19), (14, 17), (4, 4), (12, 15), (19, 14), (18, 19), (16, 20), (17, 3), (6, 3), (3, 16), (9, 7), (6, 9), (3, 3), (9, 9), (11, 2), (20, 7), (11, 13), (17, 11), (1, 0), (2, 12), (11, 19), (16, 1), (16, 0), (2, 4), (8, 17), (10, 8), (10, 18), (9, 3), (18, 9), (8, 6), (10, 7), (3, 10), (5, 0), (15, 16), (6, 21), (12, 2), (16, 3), (18, 0), (10, 11), (5, 20), (4, 13), (13, 6), (5, 19), (11, 15), (4, 6), (7, 20), (7, 7), (10, 16), (17, 12), (18, 6), (14, 19), (3, 15), (7, 8), (0, 6), (14, 0), (6, 16), (0, 9), (11, 6), (8, 8), (19, 10), (19, 5), (17, 17), (15, 18), (4, 0), (12, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986106", "dataset": "MATH"}
{"messages": [{"content": "In a 23x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 27), 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), (21, 8), (14, 16), (11, 17), (4, 8), (18, 4), (15, 16), (7, 16), (18, 26), (10, 24), (12, 13), (1, 7), (11, 2), (13, 12), (19, 27), (6, 2), (3, 14), (3, 26), (13, 21), (3, 21), (7, 10), (4, 1), (9, 0), (18, 9), (5, 24), (20, 1), (12, 7), (11, 23), (21, 23), (6, 12), (22, 16), (22, 19), (15, 27), (11, 11), (22, 22), (5, 14), (5, 22), (6, 1), (3, 3), (21, 26), (18, 13), (12, 1), (3, 4), (7, 1), (2, 8), (0, 18), (18, 6), (1, 5), (3, 25), (17, 6), (9, 16), (2, 13), (18, 11), (17, 16), (6, 24), (6, 4), (14, 2), (2, 27), (22, 15), (12, 18), (8, 22), (2, 22), (6, 6), (0, 27), (4, 20), (6, 23), (8, 27), (22, 8), (6, 26), (6, 9), (22, 5), (3, 7), (15, 7), (21, 27), (2, 19), (6, 0), (2, 3), (13, 13), (18, 25), (12, 17), (8, 1), (16, 19), (16, 6), (5, 5), (13, 10), (4, 2), (9, 7), (18, 21), (18, 20), (1, 19), (13, 0), (2, 16), (4, 25), (5, 12), (2, 20), (14, 23), (4, 17), (13, 23), (1, 12), (17, 12), (21, 3), (13, 1), (1, 27), (7, 2), (19, 25), (4, 9), (1, 17), (9, 9), (14, 3), (11, 0), (9, 21), (20, 18), (10, 25), (3, 22), (15, 21), (20, 22), (4, 6), (15, 18), (14, 5), (16, 21), (13, 14), (21, 24), (4, 3), (11, 7), (13, 18), (12, 12), (17, 21), (0, 5), (21, 19), (20, 7), (19, 13), (22, 17), (9, 25), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836650", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), 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), (1, 13), (16, 23), (4, 2), (2, 1), (8, 11), (14, 21), (15, 8), (13, 9), (14, 23), (4, 18), (12, 0), (6, 23), (18, 9), (6, 24), (12, 1), (0, 16), (4, 11), (13, 23), (13, 7), (8, 12), (18, 4), (0, 6), (19, 5), (13, 8), (0, 22), (13, 25), (16, 20), (1, 19), (15, 11), (14, 9), (12, 8), (10, 24), (9, 18), (7, 8), (4, 5), (7, 3), (6, 18), (13, 17), (1, 20), (12, 5), (17, 2), (17, 8), (13, 11), (16, 2), (18, 14), (12, 19), (18, 24), (9, 17), (12, 16), (18, 3), (7, 7), (6, 6), (11, 5), (14, 4), (4, 6), (0, 24), (9, 0), (17, 0), (12, 10), (11, 19), (7, 4), (16, 1), (5, 2), (8, 1), (13, 20), (17, 23), (11, 16), (18, 0), (12, 6), (19, 12), (18, 7), (10, 23), (17, 21), (15, 21), (8, 5), (11, 13), (1, 3), (18, 10), (3, 2), (18, 17), (14, 1), (14, 14), (19, 2), (2, 11), (0, 9), (18, 6), (6, 22), (1, 10), (16, 21), (7, 19), (18, 20), (9, 14), (0, 18), (17, 13), (15, 10), (7, 1), (17, 9), (6, 21), (17, 1), (5, 11), (2, 14), (7, 2), (5, 22), (17, 15), (16, 14), (6, 10), (8, 7), (16, 19), (6, 25), (17, 5), (9, 22), (5, 7), (14, 0), (16, 12), (8, 10), (6, 11), (6, 3), (3, 9), (16, 9), (19, 10), (13, 3), (9, 16), (11, 10), (4, 0), (13, 1), (11, 11), (18, 16), (0, 12), (12, 22), (0, 20), (0, 8), (7, 13), (5, 5), (10, 9), (8, 15), (8, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760506", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), 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, 7), (2, 12), (15, 2), (19, 22), (1, 4), (16, 18), (16, 16), (9, 7), (8, 2), (5, 23), (4, 24), (11, 17), (5, 5), (19, 13), (18, 10), (13, 11), (4, 4), (0, 8), (14, 11), (7, 18), (10, 22), (18, 12), (8, 8), (17, 16), (11, 16), (17, 3), (7, 17), (1, 18), (5, 20), (6, 18), (18, 15), (10, 23), (4, 20), (11, 10), (7, 9), (11, 20), (11, 15), (17, 14), (16, 4), (10, 10), (11, 24), (0, 13), (1, 22), (4, 14), (7, 16), (12, 20), (1, 0), (14, 8), (10, 1), (13, 16), (15, 17), (14, 12), (18, 5), (3, 3), (12, 7), (1, 23), (0, 23), (13, 19), (2, 14), (13, 15), (11, 25), (4, 13), (17, 10), (4, 18), (0, 5), (9, 4), (7, 23), (12, 5), (1, 11), (4, 11), (15, 8), (17, 18), (12, 6), (6, 13), (10, 4), (10, 5), (4, 17), (19, 19), (11, 7), (8, 24), (17, 19), (8, 1), (3, 2), (9, 0), (16, 7), (16, 19), (18, 21), (1, 12), (3, 15), (15, 19), (14, 16), (7, 0), (0, 21), (19, 16), (18, 4), (15, 12), (18, 18), (0, 4), (2, 16), (2, 20), (1, 20), (17, 6), (2, 15), (7, 14), (19, 1), (8, 5), (16, 14), (10, 21), (8, 12), (15, 20), (15, 10), (12, 21), (3, 18), (14, 23), (19, 12), (19, 23), (10, 24), (12, 19), (18, 11), (1, 14), (15, 0), (16, 9), (9, 21), (18, 13), (14, 9), (14, 15), (0, 14), (6, 19), (16, 15), (15, 18), (16, 13), (0, 25), (11, 14), (6, 12), (6, 6), (12, 24), (16, 20), (9, 2), (17, 2), (13, 2), (13, 17), (5, 0), (16, 10), (10, 19), (3, 12), (9, 18), (18, 24), (15, 3), (19, 11), (12, 14), (18, 8), (4, 2), (8, 0), (10, 6), (4, 1), (19, 15), (8, 20), (13, 20), (15, 5), (19, 24), (17, 13), (0, 19), (11, 6), (0, 18), (19, 2), (14, 4), (17, 21), (6, 0), (12, 1), (13, 10), (6, 2), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870480", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), 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), (13, 1), (16, 7), (10, 8), (9, 17), (6, 1), (20, 3), (5, 4), (23, 4), (9, 10), (11, 13), (14, 17), (9, 1), (5, 17), (20, 8), (0, 8), (14, 9), (7, 2), (10, 13), (8, 7), (2, 9), (10, 4), (6, 6), (11, 5), (2, 19), (0, 1), (12, 8), (19, 3), (9, 16), (5, 2), (0, 18), (16, 14), (13, 0), (19, 16), (8, 13), (19, 12), (22, 13), (16, 11), (0, 5), (15, 18), (9, 6), (15, 11), (14, 20), (8, 12), (22, 6), (1, 9), (18, 15), (16, 3), (21, 12), (23, 18), (15, 1), (24, 5), (11, 21), (20, 6), (12, 1), (8, 11), (2, 7), (19, 9), (5, 13), (17, 14), (16, 19), (17, 11), (18, 7), (2, 17), (23, 3), (24, 0), (16, 4), (2, 3), (3, 7), (6, 17), (24, 10), (19, 14), (1, 20), (3, 3), (12, 11), (8, 15), (9, 8), (10, 9), (4, 1), (17, 7), (14, 0), (13, 2), (16, 13), (2, 11), (6, 11), (3, 18), (3, 21), (11, 12), (13, 3), (10, 15), (17, 18), (8, 19), (11, 14), (15, 8), (23, 20), (14, 16), (18, 2), (4, 9), (16, 15), (18, 12), (23, 9), (4, 5), (3, 19), (13, 6), (24, 9), (0, 10), (17, 13), (19, 15), (20, 20), (9, 13), (13, 7), (0, 11), (5, 10), (13, 21), (18, 10), (5, 20), (24, 6), (5, 8), (10, 19), (17, 15), (18, 9), (20, 13), (5, 0), (2, 6), (1, 12), (22, 18), (8, 1), (13, 18), (22, 15), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749264", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (12, 14), (14, 15), (9, 9), (0, 14), (13, 19), (12, 15), (19, 23), (13, 3), (7, 15), (14, 18), (11, 23), (10, 6), (1, 7), (1, 4), (5, 8), (11, 12), (8, 20), (7, 21), (3, 1), (8, 7), (13, 21), (1, 0), (4, 14), (19, 3), (5, 6), (14, 21), (4, 7), (0, 22), (5, 18), (11, 16), (15, 16), (8, 23), (9, 12), (8, 16), (4, 22), (18, 5), (18, 11), (11, 24), (4, 23), (10, 13), (16, 19), (9, 2), (11, 9), (10, 16), (11, 17), (8, 10), (8, 15), (6, 15), (6, 16), (1, 14), (18, 10), (1, 17), (6, 1), (17, 4), (4, 15), (5, 9), (18, 19), (6, 14), (5, 25), (12, 1), (4, 9), (10, 18), (8, 24), (15, 10), (14, 0), (0, 12), (18, 1), (9, 11), (7, 11), (12, 5), (13, 8), (5, 15), (0, 20), (11, 3), (0, 11), (3, 6), (11, 22), (10, 20), (8, 18), (5, 7), (11, 19), (9, 0), (2, 22), (16, 20), (0, 25), (18, 4), (14, 22), (2, 16), (14, 2), (19, 18), (16, 14), (3, 23), (12, 21), (9, 7), (15, 20), (4, 24), (8, 5), (5, 2), (18, 20), (18, 14), (9, 16), (16, 9), (2, 0), (0, 13), (4, 25), (8, 21), (18, 22), (0, 3), (17, 6), (19, 8), (2, 10), (0, 6), (17, 9), (1, 11), (3, 4), (2, 13), (0, 5), (5, 10), (12, 25), (4, 6), (10, 14), (19, 7), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895885", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), 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), (14, 3), (12, 24), (8, 21), (18, 22), (7, 12), (18, 21), (19, 9), (19, 14), (13, 6), (18, 18), (10, 7), (15, 23), (10, 24), (11, 4), (2, 18), (19, 20), (0, 20), (12, 23), (13, 2), (3, 9), (24, 12), (12, 9), (0, 12), (10, 2), (23, 5), (11, 19), (16, 12), (15, 11), (1, 11), (7, 3), (5, 19), (7, 20), (19, 23), (0, 16), (17, 21), (9, 17), (3, 7), (4, 23), (10, 22), (21, 0), (16, 2), (20, 19), (22, 18), (9, 23), (16, 15), (14, 16), (20, 15), (16, 5), (7, 4), (15, 8), (17, 2), (1, 25), (18, 24), (12, 2), (14, 12), (22, 4), (21, 21), (2, 21), (11, 25), (21, 23), (8, 25), (15, 22), (8, 5), (7, 5), (2, 15), (0, 9), (24, 11), (6, 15), (18, 25), (19, 22), (2, 16), (9, 18), (24, 21), (1, 9), (12, 16), (10, 23), (20, 5), (3, 18), (10, 0), (10, 19), (5, 12), (12, 1), (16, 7), (12, 6), (16, 3), (22, 2), (14, 11), (23, 22), (15, 19), (12, 10), (23, 18), (0, 3), (5, 20), (18, 17), (11, 22), (14, 25), (22, 1), (9, 9), (6, 4), (0, 21), (13, 26), (2, 10), (4, 19), (5, 26), (8, 23), (17, 15), (4, 13), (3, 19), (19, 13), (9, 12), (23, 24), (17, 8), (19, 6), (22, 12), (5, 3), (1, 21), (9, 3), (6, 0), (16, 19), (23, 23), (0, 17), (4, 7), (14, 13), (0, 11), (13, 13), (1, 2), (17, 22), (14, 22), (6, 17), (23, 17), (9, 5), (20, 7), (18, 16), (10, 18), (24, 19), (10, 10), (3, 22), (18, 10), (19, 25), (2, 24), (6, 23), (16, 6), (3, 13), (1, 12), (23, 10), (16, 21), (16, 11), (8, 20), (1, 18), (9, 25), (8, 16), (16, 18), (1, 15), (16, 9), (10, 3), (9, 0), (3, 11), (20, 12), (9, 16), (15, 1), (5, 5), (6, 13), (6, 12), (3, 20), (22, 0), (9, 20), (21, 8), (21, 9), (23, 0), (10, 26), (13, 7), (20, 4), (1, 4), (4, 16), (18, 13), (23, 9), (15, 26), (2, 6), (14, 1), (15, 13), (5, 8), (20, 6), (15, 24), (2, 20), (8, 24), (12, 7), (22, 5), (20, 21), (19, 21), (18, 0), (12, 11), (18, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34254", "dataset": "MATH"}
{"messages": [{"content": "In a 23x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 28), 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), (22, 10), (6, 3), (21, 6), (0, 19), (3, 1), (20, 26), (14, 18), (21, 27), (20, 7), (8, 14), (1, 27), (12, 5), (12, 25), (1, 1), (10, 25), (3, 3), (8, 7), (21, 25), (21, 16), (17, 0), (11, 7), (5, 1), (14, 7), (19, 15), (21, 17), (22, 17), (7, 25), (18, 8), (20, 22), (16, 16), (0, 11), (10, 28), (21, 26), (19, 16), (6, 13), (15, 1), (2, 22), (22, 1), (14, 17), (8, 1), (8, 23), (4, 25), (6, 22), (1, 3), (5, 25), (17, 13), (3, 16), (5, 26), (13, 10), (8, 24), (9, 3), (6, 25), (15, 23), (11, 26), (13, 17), (10, 14), (16, 28), (4, 10), (21, 22), (12, 23), (18, 15), (10, 11), (9, 1), (22, 6), (17, 16), (1, 6), (17, 8), (14, 27), (16, 21), (9, 19), (3, 13), (7, 20), (2, 9), (0, 14), (12, 20), (13, 1), (22, 8), (4, 28), (4, 20), (20, 10), (16, 14), (9, 20), (16, 23), (17, 14), (11, 8), (16, 0), (7, 17), (4, 2), (15, 16), (0, 9), (15, 20), (14, 5), (6, 8), (4, 8), (15, 19), (19, 27), (14, 21), (19, 0), (17, 23), (18, 4), (5, 15), (10, 0), (6, 15), (0, 6), (20, 11), (19, 13), (0, 17), (4, 7), (20, 8), (0, 23), (12, 24), (19, 8), (6, 11), (8, 12), (1, 13), (10, 15), (13, 23), (15, 9), (2, 25), (13, 5), (8, 6), (16, 22), (15, 25), (18, 7), (11, 10), (17, 24), (5, 4), (5, 23), (15, 14), (3, 4), (12, 6), (2, 24), (8, 10), (20, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376200", "dataset": "MATH"}
{"messages": [{"content": "In a 27x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 2), (16, 12), (25, 9), (1, 12), (17, 8), (20, 18), (10, 21), (8, 14), (11, 6), (1, 4), (20, 9), (7, 5), (14, 7), (14, 22), (20, 11), (1, 6), (9, 5), (24, 20), (18, 14), (5, 2), (25, 11), (0, 9), (26, 15), (23, 17), (6, 23), (0, 17), (26, 9), (0, 12), (18, 1), (14, 9), (17, 19), (3, 5), (13, 24), (21, 5), (24, 11), (16, 7), (1, 13), (4, 17), (21, 7), (14, 11), (15, 1), (3, 21), (18, 17), (1, 16), (20, 21), (11, 23), (22, 2), (19, 13), (14, 12), (1, 1), (20, 2), (7, 22), (12, 9), (15, 16), (8, 8), (13, 1), (15, 8), (7, 3), (24, 12), (5, 16), (4, 21), (17, 22), (8, 5), (26, 23), (22, 23), (18, 23), (3, 20), (3, 8), (20, 16), (8, 23), (13, 23), (9, 2), (21, 1), (16, 19), (10, 20), (5, 14), (10, 4), (9, 4), (5, 23), (1, 11), (17, 6), (17, 10), (25, 20), (19, 24), (6, 16), (10, 13), (21, 19), (5, 17), (11, 2), (15, 6), (2, 2), (4, 4), (22, 18), (26, 0), (21, 4), (25, 0), (23, 6), (9, 7), (19, 12), (15, 13), (6, 2), (12, 11), (12, 21), (5, 12), (4, 20), (12, 19), (25, 2), (14, 24), (7, 17), (13, 13), (0, 11), (25, 14), (9, 15), (3, 4), (4, 24), (13, 19), (23, 15), (25, 21), (3, 15), (22, 13), (9, 1), (23, 11), (11, 12), (18, 19), (11, 5), (2, 3), (0, 2), (18, 18), (25, 10), (6, 24), (16, 20), (10, 15), (18, 3), (6, 3), (10, 12), (25, 22), (26, 14), (13, 0), (12, 3), (22, 11), (11, 18), (10, 14), (15, 18), (2, 19), (15, 11), (8, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231840", "dataset": "MATH"}
{"messages": [{"content": "In a 21x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 27), 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), (8, 17), (4, 10), (6, 24), (5, 13), (6, 15), (5, 19), (16, 21), (0, 4), (15, 26), (3, 11), (20, 20), (3, 15), (16, 11), (6, 5), (11, 12), (15, 8), (5, 2), (17, 0), (18, 10), (8, 11), (14, 14), (6, 10), (20, 4), (5, 25), (0, 21), (4, 15), (12, 0), (18, 22), (7, 19), (12, 16), (10, 19), (11, 17), (3, 7), (13, 20), (17, 12), (7, 26), (5, 8), (6, 19), (7, 9), (12, 6), (5, 23), (15, 2), (4, 18), (18, 27), (8, 5), (20, 21), (14, 18), (13, 4), (20, 23), (18, 9), (7, 4), (17, 15), (3, 26), (15, 3), (10, 27), (0, 18), (16, 26), (7, 21), (19, 4), (9, 0), (13, 15), (15, 14), (5, 14), (9, 21), (14, 1), (2, 0), (2, 15), (18, 23), (20, 18), (6, 13), (19, 17), (19, 25), (8, 22), (11, 10), (9, 23), (13, 8), (1, 3), (18, 6), (6, 0), (14, 27), (8, 21), (18, 20), (14, 19), (20, 25), (13, 3), (16, 22), (18, 17), (1, 21), (7, 16), (1, 17), (9, 24), (17, 2), (13, 2), (10, 8), (5, 4), (17, 16), (9, 4), (4, 22), (19, 18), (9, 26), (5, 10), (1, 8), (8, 4), (15, 15), (8, 20), (5, 26), (16, 27), (4, 1), (8, 2), (20, 5), (10, 22), (16, 9), (5, 6), (20, 2), (11, 22), (15, 23), (12, 27), (4, 12), (4, 20), (7, 20), (16, 12), (10, 13), (11, 9), (18, 24), (19, 5), (7, 27), (7, 22), (0, 17), (12, 8), (2, 9), (0, 8), (5, 24), (2, 1), (7, 5), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16560", "dataset": "MATH"}
{"messages": [{"content": "In a 23x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 23), (6, 0), (13, 11), (13, 12), (11, 2), (12, 24), (4, 3), (1, 10), (19, 16), (11, 0), (19, 7), (4, 12), (15, 24), (19, 6), (7, 11), (14, 6), (19, 9), (12, 12), (13, 18), (19, 14), (22, 21), (21, 21), (5, 24), (11, 13), (21, 5), (16, 5), (15, 19), (14, 17), (4, 21), (20, 8), (1, 8), (9, 22), (5, 18), (7, 20), (15, 5), (10, 9), (8, 15), (12, 19), (10, 18), (3, 10), (2, 13), (15, 18), (5, 6), (6, 2), (11, 16), (16, 13), (5, 22), (0, 7), (8, 7), (9, 15), (4, 22), (20, 3), (2, 23), (1, 16), (7, 23), (0, 1), (2, 6), (6, 7), (18, 23), (17, 15), (5, 2), (14, 13), (20, 23), (12, 16), (11, 4), (6, 6), (22, 14), (2, 11), (17, 8), (9, 8), (2, 10), (19, 22), (12, 20), (5, 15), (2, 3), (17, 0), (7, 3), (6, 9), (3, 19), (14, 2), (19, 15), (0, 17), (8, 10), (13, 7), (17, 12), (10, 3), (7, 9), (21, 1), (7, 2), (1, 4), (14, 22), (3, 5), (17, 2), (19, 5), (13, 13), (6, 17), (17, 20), (7, 17), (15, 2), (9, 16), (22, 18), (1, 20), (19, 8), (15, 10), (4, 8), (11, 7), (7, 24), (4, 18), (20, 20), (0, 10), (12, 0), (18, 22), (2, 16), (9, 12), (21, 12), (18, 15), (21, 20), (20, 6), (0, 22), (12, 21), (5, 0), (14, 20), (18, 17), (19, 24), (20, 16), (8, 18), (20, 13), (1, 9), (0, 15), (10, 22), (21, 13), (13, 4), (18, 10), (14, 8), (9, 18), (1, 11), (14, 14), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "809712", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), 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), (18, 6), (18, 22), (21, 16), (0, 21), (3, 8), (24, 7), (23, 12), (10, 26), (26, 3), (5, 22), (16, 6), (2, 12), (13, 18), (4, 14), (9, 22), (19, 8), (8, 13), (21, 3), (11, 10), (25, 4), (9, 7), (25, 16), (21, 14), (5, 20), (18, 7), (10, 10), (19, 4), (19, 3), (18, 16), (23, 2), (21, 20), (22, 9), (3, 14), (7, 26), (10, 27), (11, 24), (23, 18), (12, 1), (10, 12), (4, 4), (24, 8), (20, 24), (26, 4), (17, 12), (2, 11), (6, 4), (0, 23), (5, 27), (27, 20), (28, 5), (9, 0), (7, 23), (7, 21), (18, 5), (8, 16), (19, 23), (4, 2), (1, 12), (26, 21), (20, 8), (7, 5), (27, 17), (16, 3), (1, 2), (9, 25), (15, 13), (26, 2), (16, 15), (6, 26), (5, 0), (8, 19), (25, 21), (11, 19), (17, 5), (8, 17), (16, 0), (25, 5), (12, 11), (4, 15), (13, 10), (14, 20), (21, 22), (22, 25), (19, 12), (5, 7), (5, 13), (21, 10), (4, 6), (10, 8), (15, 26), (28, 25), (4, 18), (23, 21), (21, 11), (7, 25), (13, 0), (28, 22), (4, 10), (28, 3), (27, 5), (25, 26), (15, 14), (10, 0), (17, 14), (20, 27), (16, 25), (24, 24), (21, 9), (27, 4), (24, 20), (28, 23), (20, 16), (16, 17), (0, 7), (13, 2), (22, 2), (14, 6), (7, 18), (11, 8), (2, 10), (1, 26), (7, 11), (0, 17), (18, 27), (15, 0), (0, 12), (12, 24), (14, 18), (8, 26), (20, 21), (16, 8), (11, 18), (15, 6), (17, 18), (11, 12), (13, 23), (18, 1), (17, 15), (15, 9), (14, 12), (7, 24), (0, 22), (14, 0), (11, 25), (28, 11), (21, 0), (19, 13), (9, 27), (2, 15), (5, 10), (5, 3), (21, 21), (15, 21), (14, 1), (20, 1), (10, 24), (6, 17), (22, 6), (21, 18), (0, 13), (22, 19), (23, 22), (28, 21), (9, 17), (2, 8), (4, 17), (23, 24), (3, 11), (16, 11), (23, 6), (17, 13), (15, 12), (17, 21), (25, 13), (12, 12), (21, 5), (27, 0), (28, 4), (26, 8), (27, 7), (23, 10), (10, 25), (28, 2), (14, 23), (9, 6), (27, 1), (11, 23), (12, 7), (7, 1), (2, 3), (28, 12), (27, 2), (18, 4), (21, 4), (27, 23), (9, 8), (0, 10), (0, 27), (23, 27), (4, 20), (17, 3), (14, 25), (28, 10), (2, 20), (22, 24), (27, 22), (6, 23), (6, 7), (18, 14), (24, 13), (18, 0), (3, 15), (22, 26), (3, 9), (5, 21), (4, 5), (7, 16), (24, 1), (10, 11), (2, 1), (27, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941520", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), 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), (7, 16), (11, 9), (4, 23), (6, 14), (3, 6), (1, 17), (5, 17), (6, 16), (14, 1), (15, 21), (14, 13), (8, 12), (3, 3), (16, 12), (8, 7), (11, 20), (19, 17), (8, 22), (14, 3), (17, 0), (0, 10), (4, 9), (12, 17), (9, 6), (13, 19), (4, 0), (10, 20), (9, 10), (15, 11), (8, 14), (11, 2), (4, 18), (10, 22), (3, 10), (9, 24), (6, 4), (7, 0), (5, 9), (11, 16), (13, 21), (10, 12), (17, 23), (6, 21), (0, 18), (11, 23), (7, 14), (5, 4), (8, 3), (10, 21), (18, 24), (10, 10), (4, 5), (14, 23), (16, 14), (10, 6), (11, 22), (7, 2), (8, 10), (2, 24), (1, 24), (14, 18), (12, 15), (5, 1), (6, 17), (17, 19), (3, 4), (3, 0), (0, 5), (5, 13), (4, 12), (10, 1), (17, 12), (5, 18), (13, 22), (4, 2), (17, 16), (17, 15), (17, 7), (4, 4), (16, 13), (6, 13), (7, 12), (10, 7), (4, 16), (8, 13), (8, 24), (3, 2), (13, 10), (1, 1), (15, 1), (17, 10), (10, 8), (19, 21), (8, 18), (7, 10), (6, 2), (19, 10), (9, 5), (18, 16), (4, 24), (2, 14), (16, 18), (16, 2), (8, 25), (18, 12), (7, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777426", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 17), (17, 15), (21, 10), (10, 7), (13, 15), (10, 0), (0, 10), (28, 6), (17, 10), (7, 0), (1, 8), (23, 8), (22, 2), (8, 19), (6, 1), (5, 5), (22, 10), (22, 18), (16, 6), (9, 5), (9, 14), (4, 18), (6, 0), (14, 11), (27, 0), (25, 0), (4, 3), (26, 7), (6, 5), (6, 7), (15, 2), (11, 10), (24, 17), (24, 3), (19, 5), (26, 13), (7, 18), (9, 4), (14, 6), (16, 20), (7, 12), (28, 18), (8, 4), (10, 19), (12, 5), (10, 15), (16, 19), (0, 5), (20, 20), (6, 14), (21, 15), (9, 10), (12, 15), (23, 18), (12, 17), (25, 10), (22, 3), (18, 0), (11, 13), (26, 10), (21, 0), (5, 19), (6, 10), (18, 13), (17, 19), (1, 13), (13, 12), (10, 5), (21, 11), (2, 12), (24, 1), (20, 3), (16, 13), (19, 12), (27, 13), (16, 3), (26, 17), (25, 12), (5, 20), (24, 15), (26, 2), (27, 8), (8, 10), (8, 15), (3, 18), (11, 17), (26, 16), (22, 14), (27, 18), (19, 11), (23, 15), (4, 10), (17, 18), (25, 8), (12, 9), (3, 1), (3, 7), (21, 13), (0, 13), (16, 10), (28, 15), (19, 13), (13, 0), (7, 19), (28, 5), (24, 19), (20, 18), (16, 11), (1, 10), (16, 2), (4, 14), (28, 12), (7, 3), (8, 17), (11, 11), (20, 4), (8, 5), (16, 15), (14, 0), (4, 5), (7, 8), (18, 4), (11, 2), (27, 9), (12, 10), (25, 15), (19, 8), (16, 14), (18, 17), (12, 8), (24, 0), (1, 2), (14, 18), (16, 18), (0, 14), (24, 16), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545292", "dataset": "MATH"}
{"messages": [{"content": "In a 27x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 27), 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), (24, 20), (17, 2), (12, 20), (25, 24), (2, 24), (23, 25), (6, 26), (23, 6), (19, 27), (9, 6), (2, 19), (14, 23), (5, 23), (21, 5), (23, 8), (12, 6), (2, 11), (8, 22), (6, 15), (14, 13), (22, 1), (25, 26), (13, 5), (10, 21), (2, 23), (4, 14), (12, 5), (1, 4), (19, 17), (20, 13), (13, 2), (22, 16), (15, 4), (12, 17), (17, 0), (25, 9), (2, 15), (8, 21), (11, 13), (26, 14), (12, 0), (6, 2), (22, 26), (4, 10), (22, 18), (26, 4), (1, 19), (13, 19), (25, 0), (24, 12), (2, 12), (15, 10), (17, 15), (13, 24), (10, 10), (6, 14), (6, 6), (4, 24), (15, 16), (4, 6), (13, 9), (18, 23), (23, 23), (8, 26), (10, 27), (20, 8), (14, 3), (18, 3), (23, 26), (20, 3), (22, 13), (14, 1), (21, 24), (1, 1), (5, 27), (17, 8), (18, 7), (13, 18), (18, 18), (21, 22), (3, 25), (11, 22), (11, 12), (6, 10), (9, 9), (8, 11), (12, 26), (9, 26), (0, 8), (16, 0), (13, 4), (0, 10), (26, 13), (25, 2), (13, 23), (20, 5), (24, 2), (10, 9), (5, 0), (21, 2), (26, 8), (19, 20), (17, 4), (5, 1), (7, 3), (25, 8), (11, 2), (16, 4), (0, 13), (19, 21), (5, 25), (10, 0), (13, 14), (14, 18), (19, 2), (5, 4), (22, 5), (5, 19), (0, 21), (22, 11), (14, 9), (13, 26), (4, 27), (23, 19), (12, 13), (25, 15), (23, 3), (19, 14), (3, 13), (18, 19), (12, 23), (3, 14), (8, 15), (19, 15), (12, 18), (14, 16), (15, 21), (1, 2), (0, 14), (1, 11), (18, 10), (23, 22), (8, 14), (15, 15), (26, 1), (6, 25), (18, 2), (24, 17), (2, 13), (8, 5), (25, 10), (17, 13), (24, 25), (0, 12), (24, 6), (21, 16), (20, 9), (14, 6), (1, 21), (15, 18), (2, 8), (18, 14), (22, 0), (3, 16), (10, 19), (1, 14), (5, 6), (11, 18), (18, 1), (12, 4), (13, 17), (10, 18), (7, 2), (10, 12), (19, 16), (25, 17), (22, 15), (14, 4), (8, 20), (25, 19), (25, 16), (24, 8), (4, 19), (9, 15), (3, 27), (26, 24), (5, 21), (15, 7), (13, 22), (0, 25), (3, 15), (13, 25), (7, 21), (21, 23), (4, 16), (6, 20), (17, 17), (4, 9), (14, 14), (13, 0), (7, 25), (20, 15), (7, 14), (7, 0), (2, 14), (6, 7), (12, 16), (23, 21), (14, 26), (10, 4), (25, 6), (6, 12), (8, 2), (18, 0), (9, 24), (15, 17), (17, 23), (1, 25), (9, 16), (22, 8), (21, 25), (23, 17), (12, 27), (14, 22), (1, 12), (13, 6), (9, 17), (20, 12), (10, 5), (21, 10), (15, 23), (0, 1), (9, 11), (14, 0), (1, 20), (24, 9), (4, 3), (6, 1), (10, 16), (11, 11), (11, 26), (9, 25), (11, 23), (3, 1), (1, 17), (8, 9), (1, 15), (18, 27), (26, 12), (8, 12), (10, 25), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726300", "dataset": "MATH"}
{"messages": [{"content": "In a 23x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 23), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 0), (19, 1), (14, 1), (9, 2), (18, 20), (13, 4), (12, 15), (19, 19), (22, 3), (0, 19), (14, 11), (20, 22), (7, 22), (14, 18), (1, 21), (8, 23), (0, 23), (14, 10), (8, 17), (10, 19), (17, 20), (11, 6), (2, 15), (18, 5), (12, 7), (4, 1), (8, 4), (15, 14), (8, 12), (19, 17), (20, 18), (13, 12), (20, 8), (1, 6), (20, 11), (21, 18), (21, 17), (19, 16), (18, 3), (18, 19), (22, 8), (18, 4), (9, 11), (5, 13), (1, 9), (4, 11), (16, 19), (9, 1), (16, 4), (16, 18), (5, 12), (20, 20), (20, 12), (14, 22), (22, 18), (20, 5), (0, 4), (19, 4), (1, 20), (7, 7), (14, 23), (9, 16), (19, 6), (13, 9), (4, 21), (8, 11), (6, 16), (13, 22), (14, 4), (7, 20), (3, 19), (16, 6), (10, 14), (9, 5), (18, 12), (8, 10), (17, 14), (22, 0), (21, 16), (9, 19), (10, 4), (2, 12), (6, 15), (5, 21), (16, 7), (6, 17), (20, 0), (10, 7), (5, 7), (21, 14), (17, 9), (5, 15), (11, 9), (17, 15), (16, 5), (22, 20), (0, 6), (15, 15), (22, 21), (2, 13), (15, 6), (21, 8), (15, 18), (8, 6), (2, 1), (0, 18), (17, 13), (18, 21), (14, 8), (7, 19), (2, 20), (9, 13), (22, 14), (9, 20), (10, 15), (21, 22), (10, 22), (16, 8), (1, 10), (4, 10), (3, 20), (2, 8), (0, 21), (14, 20), (9, 9), (2, 3), (10, 8), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514670", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 10), (15, 21), (6, 19), (14, 25), (12, 24), (21, 4), (21, 25), (19, 13), (7, 20), (6, 23), (0, 22), (17, 14), (25, 5), (10, 18), (1, 7), (9, 7), (24, 9), (19, 21), (24, 16), (24, 6), (11, 25), (7, 17), (10, 10), (15, 11), (6, 27), (16, 16), (3, 24), (25, 23), (16, 11), (9, 3), (24, 11), (6, 7), (2, 9), (20, 17), (23, 14), (5, 0), (12, 6), (14, 17), (21, 20), (3, 3), (3, 23), (14, 21), (6, 3), (7, 6), (16, 4), (20, 25), (9, 5), (0, 5), (21, 21), (3, 8), (25, 21), (2, 5), (20, 26), (5, 10), (25, 12), (10, 6), (10, 1), (14, 15), (12, 25), (22, 17), (14, 0), (18, 10), (11, 0), (17, 6), (9, 15), (1, 0), (23, 12), (12, 4), (12, 19), (16, 21), (9, 4), (2, 17), (24, 22), (15, 12), (0, 8), (17, 13), (3, 11), (24, 2), (13, 18), (25, 7), (23, 20), (7, 18), (13, 19), (2, 19), (6, 10), (22, 21), (9, 11), (1, 25), (4, 2), (16, 27), (1, 13), (10, 3), (11, 10), (19, 24), (9, 26), (18, 27), (6, 14), (8, 16), (4, 5), (8, 5), (20, 12), (5, 21), (12, 1), (22, 4), (14, 18), (0, 18), (5, 5), (25, 10), (20, 3), (20, 7), (11, 4), (2, 26), (15, 8), (12, 23), (17, 7), (13, 14), (24, 8), (18, 13), (9, 2), (2, 3), (23, 1), (4, 17), (4, 3), (16, 26), (16, 1), (5, 13), (14, 11), (15, 24), (19, 27), (1, 28), (11, 21), (16, 12), (24, 17), (16, 3), (14, 1), (24, 5), (10, 15), (22, 3), (13, 8), (13, 2), (24, 19), (1, 10), (25, 1), (9, 17), (17, 15), (17, 28), (12, 12), (6, 20), (21, 2), (19, 22), (25, 9), (14, 28), (4, 11), (19, 0), (22, 23), (19, 8), (15, 23), (23, 0), (7, 15), (18, 6), (22, 9), (3, 25), (8, 27), (5, 20), (16, 25), (8, 3), (10, 9), (0, 14), (13, 17), (1, 27), (25, 20), (17, 12), (17, 23), (4, 15), (22, 15), (4, 6), (23, 18), (13, 21), (16, 0), (12, 11), (23, 10), (15, 26), (14, 6), (3, 13), (16, 13), (4, 22), (21, 0), (10, 17), (25, 25), (12, 13), (2, 25), (12, 7), (18, 1), (24, 14), (22, 6), (5, 15), (3, 21), (13, 1), (21, 7), (7, 8), (20, 19), (9, 14), (13, 10), (3, 27), (0, 24), (25, 24), (20, 9), (0, 12), (25, 14), (21, 8), (2, 0), (21, 22), (7, 13), (1, 1), (20, 2), (14, 14), (22, 10), (12, 20), (0, 15), (4, 28), (23, 26), (18, 9), (16, 23), (12, 21), (22, 7), (0, 25), (23, 11), (2, 1), (3, 9), (5, 18), (4, 16), (22, 11), (9, 22), (8, 22), (0, 6), (21, 17), (7, 19), (4, 18), (13, 5), (16, 15), (9, 28), (20, 14), (15, 22), (2, 15), (15, 1), (2, 14), (2, 10), (20, 22), (18, 28), (17, 0), (2, 16), (25, 8), (11, 11), (15, 27), (12, 2), (10, 5), (11, 9), (15, 4), (17, 27), (12, 16), (24, 12), (12, 17), (6, 1), (24, 15), (23, 4), (9, 19), (1, 11), (25, 19), (8, 26), (23, 9), (13, 9), (24, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "806400", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), 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), (19, 17), (28, 18), (22, 13), (15, 16), (22, 10), (25, 4), (24, 14), (13, 0), (22, 16), (15, 20), (23, 16), (28, 14), (24, 19), (12, 2), (17, 11), (3, 12), (3, 6), (2, 12), (24, 6), (14, 20), (25, 1), (14, 3), (25, 11), (9, 5), (28, 3), (23, 4), (16, 16), (27, 4), (5, 11), (17, 12), (25, 12), (6, 6), (18, 14), (26, 10), (9, 15), (15, 12), (19, 15), (19, 7), (14, 14), (20, 14), (27, 15), (22, 12), (11, 8), (1, 15), (26, 18), (19, 1), (3, 9), (26, 11), (21, 15), (9, 14), (2, 20), (0, 7), (14, 18), (14, 11), (11, 1), (21, 6), (5, 5), (28, 8), (4, 15), (6, 4), (3, 10), (16, 4), (14, 13), (22, 9), (22, 14), (8, 0), (20, 5), (6, 11), (22, 3), (24, 4), (6, 18), (4, 17), (1, 20), (2, 13), (25, 16), (18, 18), (3, 18), (11, 16), (8, 10), (7, 2), (20, 19), (17, 4), (10, 1), (3, 13), (15, 19), (26, 19), (3, 7), (6, 16), (15, 2), (20, 7), (25, 19), (21, 0), (16, 5), (20, 20), (21, 10), (15, 0), (6, 17), (2, 11), (27, 20), (9, 7), (14, 10), (26, 0), (23, 20), (15, 3), (15, 5), (3, 5), (10, 2), (5, 9), (18, 6), (18, 20), (21, 1), (8, 2), (1, 5), (11, 2), (2, 16), (8, 11), (26, 7), (3, 0), (23, 12), (5, 17), (1, 11), (11, 20), (17, 8), (5, 6), (0, 12), (3, 20), (24, 0), (12, 11), (13, 11), (10, 4), (26, 12), (4, 20), (24, 3), (8, 13), (27, 3), (15, 9), (3, 17), (5, 3), (16, 0), (4, 0), (26, 13), (7, 16), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472812", "dataset": "MATH"}
{"messages": [{"content": "In a 28x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 20), (8, 0), (24, 15), (24, 10), (10, 15), (18, 8), (18, 14), (7, 18), (1, 3), (5, 24), (13, 12), (22, 2), (23, 5), (22, 23), (27, 2), (20, 20), (18, 22), (10, 20), (19, 24), (26, 11), (4, 0), (16, 24), (24, 0), (1, 21), (17, 24), (12, 20), (3, 2), (6, 1), (17, 2), (16, 11), (20, 21), (2, 16), (15, 10), (24, 16), (17, 9), (2, 24), (6, 24), (21, 25), (6, 25), (0, 21), (11, 20), (25, 17), (3, 20), (24, 20), (24, 18), (0, 7), (20, 9), (3, 23), (9, 23), (8, 8), (3, 4), (16, 0), (17, 1), (23, 19), (9, 11), (6, 19), (26, 20), (1, 16), (10, 21), (9, 15), (16, 1), (25, 24), (6, 3), (14, 21), (26, 5), (21, 9), (12, 12), (12, 13), (25, 11), (2, 14), (0, 18), (5, 4), (18, 16), (25, 22), (7, 22), (15, 3), (18, 24), (11, 25), (21, 23), (10, 23), (26, 1), (14, 13), (24, 11), (25, 23), (7, 11), (23, 22), (5, 7), (14, 0), (13, 8), (1, 25), (11, 8), (2, 11), (1, 13), (14, 22), (23, 12), (5, 2), (13, 1), (9, 16), (18, 7), (12, 19), (6, 6), (22, 24), (23, 17), (10, 14), (23, 23), (7, 21), (7, 17), (2, 9), (15, 13), (13, 4), (21, 24), (14, 7), (1, 9), (26, 21), (7, 23), (25, 4), (12, 3), (25, 16), (14, 6), (13, 9), (17, 21), (6, 13), (17, 11), (0, 13), (6, 11), (20, 2), (3, 7), (17, 5), (9, 4), (17, 22), (15, 23), (5, 16), (26, 18), (2, 17), (22, 11), (12, 0), (13, 20), (13, 11), (17, 14), (17, 3), (25, 2), (9, 12), (0, 4), (26, 19), (25, 7), (9, 22), (10, 12), (23, 8), (25, 14), (4, 22), (11, 9), (23, 2), (5, 1), (10, 25), (6, 15), (2, 18), (10, 18), (10, 2), (11, 10), (20, 8), (6, 2), (0, 11), (1, 14), (2, 23), (13, 17), (10, 24), (17, 13), (23, 7), (19, 4), (11, 19), (4, 15), (15, 8), (17, 17), (22, 25), (12, 23), (27, 1), (18, 17), (22, 0), (0, 17), (8, 16), (18, 1), (23, 9), (6, 23), (15, 19), (25, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27008", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), 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), (17, 6), (12, 18), (8, 24), (9, 4), (22, 16), (2, 0), (16, 24), (8, 10), (12, 1), (19, 22), (8, 2), (4, 4), (3, 20), (2, 6), (22, 0), (18, 1), (6, 10), (19, 14), (3, 11), (6, 24), (7, 23), (19, 21), (14, 15), (2, 23), (9, 1), (17, 17), (2, 8), (12, 10), (4, 15), (19, 10), (6, 8), (16, 9), (18, 3), (2, 22), (10, 15), (0, 4), (18, 22), (7, 20), (11, 1), (20, 2), (9, 17), (8, 18), (10, 5), (9, 16), (19, 16), (18, 7), (19, 12), (5, 4), (3, 15), (0, 9), (7, 11), (6, 11), (19, 24), (14, 14), (2, 18), (0, 3), (7, 6), (12, 24), (6, 0), (2, 4), (6, 1), (3, 24), (7, 4), (12, 12), (9, 25), (11, 15), (11, 14), (13, 11), (7, 17), (14, 17), (0, 21), (17, 22), (16, 7), (17, 5), (18, 24), (2, 3), (9, 12), (2, 25), (4, 12), (15, 1), (12, 14), (10, 17), (16, 10), (21, 22), (10, 21), (22, 17), (13, 5), (4, 0), (1, 8), (20, 7), (1, 5), (19, 20), (20, 23), (18, 16), (18, 20), (10, 10), (17, 20), (12, 21), (13, 21), (22, 22), (22, 15), (15, 21), (0, 25), (11, 10), (18, 6), (4, 3), (17, 16), (21, 23), (8, 7), (14, 12), (4, 2), (13, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757298", "dataset": "MATH"}
{"messages": [{"content": "In a 21x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (14, 0), (7, 5), (18, 8), (20, 20), (14, 8), (1, 17), (20, 2), (2, 1), (5, 19), (9, 20), (10, 5), (6, 15), (10, 12), (15, 14), (8, 20), (1, 2), (10, 1), (12, 12), (3, 6), (12, 20), (8, 16), (16, 16), (7, 0), (9, 7), (20, 6), (11, 0), (1, 10), (15, 3), (16, 4), (14, 6), (12, 16), (18, 15), (13, 0), (4, 1), (13, 9), (11, 2), (5, 10), (7, 3), (10, 7), (14, 13), (11, 9), (7, 11), (5, 9), (5, 8), (13, 2), (0, 15), (16, 8), (5, 5), (15, 13), (14, 3), (9, 16), (1, 9), (6, 9), (6, 19), (13, 5), (2, 16), (3, 5), (16, 3), (0, 7), (3, 19), (12, 3), (14, 17), (10, 2), (5, 17), (0, 17), (6, 14), (13, 3), (14, 14), (15, 4), (5, 18), (18, 3), (12, 1), (7, 19), (20, 16), (20, 13), (13, 13), (2, 10), (3, 12), (12, 19), (0, 2), (10, 17), (19, 1), (1, 6), (13, 7), (16, 12), (3, 1), (14, 15), (20, 9), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685464", "dataset": "MATH"}
{"messages": [{"content": "In a 26x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 10), (12, 17), (22, 17), (21, 1), (3, 4), (15, 20), (10, 12), (11, 18), (6, 9), (10, 16), (7, 14), (19, 22), (6, 5), (1, 13), (5, 11), (7, 19), (18, 8), (23, 17), (20, 12), (9, 3), (17, 4), (11, 3), (11, 13), (4, 12), (12, 10), (8, 12), (16, 18), (1, 7), (5, 5), (22, 10), (8, 15), (17, 3), (22, 6), (23, 2), (19, 19), (11, 7), (22, 4), (13, 16), (23, 4), (9, 5), (25, 16), (1, 14), (16, 6), (10, 18), (17, 11), (25, 19), (10, 20), (15, 11), (3, 8), (4, 4), (21, 14), (21, 8), (0, 1), (25, 20), (12, 22), (7, 11), (3, 22), (13, 4), (4, 8), (17, 13), (17, 15), (24, 0), (13, 0), (12, 3), (23, 18), (23, 16), (24, 13), (3, 5), (18, 12), (20, 17), (7, 5), (3, 17), (15, 10), (24, 7), (10, 3), (23, 11), (11, 20), (5, 13), (13, 1), (8, 3), (6, 22), (15, 19), (3, 1), (1, 20), (20, 16), (16, 16), (16, 1), (19, 9), (12, 2), (11, 8), (10, 21), (12, 9), (16, 3), (18, 7), (13, 11), (20, 3), (18, 16), (18, 19), (18, 18), (14, 16), (11, 21), (3, 10), (0, 6), (22, 19), (25, 12), (16, 13), (24, 18), (5, 1), (20, 21), (1, 8), (4, 7), (18, 14), (7, 6), (16, 11), (7, 17), (8, 20), (2, 18), (0, 22), (1, 4), (21, 0), (24, 5), (16, 10), (6, 20), (3, 19), (4, 17), (8, 8), (7, 2), (9, 1), (20, 22), (9, 2), (19, 8), (17, 0), (16, 12), (25, 5), (15, 4), (21, 7), (7, 12), (17, 1), (9, 22), (6, 13), (19, 7), (2, 19), (18, 6), (2, 2), (5, 6), (11, 22), (2, 13), (14, 17), (20, 9), (12, 5), (19, 20), (1, 18), (24, 1), (0, 13), (15, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973308", "dataset": "MATH"}
{"messages": [{"content": "In a 20x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 15), (1, 14), (14, 8), (14, 2), (14, 10), (1, 24), (6, 19), (5, 21), (16, 4), (5, 3), (12, 26), (16, 3), (18, 10), (16, 16), (5, 20), (12, 3), (3, 1), (19, 14), (7, 19), (17, 21), (15, 0), (5, 8), (3, 23), (11, 0), (15, 10), (7, 12), (5, 25), (17, 14), (18, 18), (2, 15), (16, 8), (13, 8), (4, 25), (6, 4), (10, 12), (16, 13), (4, 4), (13, 17), (14, 25), (12, 11), (2, 20), (6, 26), (16, 11), (19, 3), (7, 10), (2, 14), (18, 17), (18, 1), (17, 11), (11, 1), (17, 6), (8, 24), (9, 19), (3, 12), (2, 1), (18, 23), (5, 26), (11, 23), (3, 0), (8, 25), (19, 5), (10, 9), (11, 11), (9, 1), (3, 3), (11, 15), (1, 26), (3, 13), (10, 6), (10, 23), (17, 22), (5, 2), (2, 8), (8, 7), (1, 13), (2, 6), (6, 18), (13, 6), (17, 16), (13, 23), (2, 7), (5, 19), (15, 18), (3, 26), (3, 5), (4, 23), (6, 9), (11, 26), (15, 2), (9, 22), (12, 12), (15, 25), (8, 13), (19, 7), (19, 17), (1, 10), (13, 7), (11, 4), (13, 11), (19, 1), (3, 8), (11, 8), (7, 6), (17, 17), (13, 16), (3, 19), (8, 17), (5, 6), (8, 2), (12, 17), (7, 3), (5, 7), (6, 16), (17, 18), (15, 23), (19, 8), (9, 17), (0, 2), (19, 18), (19, 20), (12, 24), (10, 4), (14, 0), (19, 21), (18, 24), (16, 21), (13, 9), (0, 21), (5, 24), (12, 9), (13, 25), (9, 24), (15, 9), (14, 24), (7, 5), (14, 6), (4, 17), (12, 13), (16, 0), (0, 22), (18, 11), (1, 15), (13, 19), (0, 7), (17, 9), (4, 9), (6, 13), (4, 8), (14, 17), (10, 15), (8, 3), (4, 22), (16, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "745746", "dataset": "MATH"}
{"messages": [{"content": "In a 27x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 23), 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), (10, 0), (8, 21), (12, 23), (11, 23), (6, 4), (11, 16), (22, 9), (18, 4), (20, 19), (2, 15), (11, 12), (14, 22), (21, 23), (11, 8), (22, 8), (7, 22), (24, 4), (13, 2), (8, 9), (7, 19), (22, 10), (18, 10), (18, 19), (14, 10), (0, 8), (19, 3), (3, 6), (7, 13), (19, 8), (0, 2), (23, 16), (0, 11), (24, 21), (22, 17), (12, 22), (13, 10), (10, 15), (2, 5), (20, 20), (6, 15), (15, 4), (18, 8), (9, 0), (10, 3), (5, 6), (17, 21), (15, 6), (19, 21), (6, 11), (21, 8), (10, 17), (4, 5), (6, 14), (3, 8), (17, 14), (4, 23), (21, 3), (26, 2), (20, 18), (4, 6), (21, 13), (25, 19), (3, 17), (24, 1), (24, 15), (21, 6), (15, 17), (0, 18), (22, 23), (24, 14), (5, 18), (2, 14), (6, 3), (10, 19), (16, 4), (10, 13), (21, 16), (24, 22), (4, 21), (22, 14), (9, 16), (9, 12), (10, 20), (5, 12), (8, 1), (5, 3), (19, 5), (11, 17), (6, 23), (16, 2), (5, 0), (21, 11), (6, 8), (8, 19), (14, 8), (12, 11), (20, 15), (3, 19), (7, 7), (22, 11), (4, 2), (23, 1), (9, 13), (0, 5), (17, 8), (8, 6), (17, 4), (5, 8), (11, 6), (2, 0), (20, 21), (2, 1), (9, 23), (19, 11), (21, 2), (23, 20), (0, 6), (17, 18), (10, 14), (14, 16), (25, 6), (16, 20), (8, 18), (22, 15), (24, 2), (11, 18), (11, 15), (15, 2), (14, 3), (14, 7), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16128", "dataset": "MATH"}
{"messages": [{"content": "In a 25x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 26), 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), (6, 24), (13, 14), (1, 10), (3, 19), (2, 23), (17, 16), (6, 9), (3, 7), (7, 23), (3, 4), (0, 20), (9, 10), (6, 3), (0, 15), (4, 16), (15, 11), (17, 6), (11, 11), (8, 21), (12, 2), (7, 14), (12, 14), (19, 24), (18, 6), (19, 16), (21, 9), (16, 4), (19, 17), (7, 6), (15, 6), (2, 3), (14, 19), (3, 12), (1, 26), (18, 10), (23, 17), (5, 9), (17, 11), (14, 26), (24, 9), (17, 9), (1, 18), (6, 13), (22, 0), (6, 20), (21, 16), (16, 9), (20, 1), (2, 17), (15, 20), (18, 22), (0, 24), (9, 15), (5, 6), (16, 22), (13, 2), (10, 13), (7, 0), (11, 3), (12, 16), (15, 0), (4, 12), (23, 11), (0, 2), (18, 20), (23, 24), (20, 17), (11, 10), (16, 6), (22, 8), (20, 25), (5, 15), (2, 24), (8, 25), (4, 22), (11, 16), (23, 19), (19, 21), (13, 5), (5, 16), (13, 19), (10, 12), (8, 23), (3, 11), (9, 16), (19, 2), (21, 7), (15, 2), (5, 13), (8, 13), (24, 2), (19, 7), (15, 10), (22, 22), (1, 20), (23, 6), (3, 22), (19, 12), (6, 16), (0, 25), (7, 21), (13, 9), (23, 14), (20, 19), (4, 1), (7, 19), (4, 17), (12, 12), (15, 21), (18, 21), (18, 4), (21, 2), (15, 15), (16, 1), (4, 19), (1, 9), (12, 22), (12, 5), (17, 0), (17, 14), (2, 7), (13, 0), (20, 2), (7, 26), (10, 14), (24, 7), (13, 8), (9, 8), (20, 12), (22, 18), (9, 2), (7, 18), (0, 5), (4, 11), (22, 12), (9, 20), (22, 1), (21, 17), (19, 0), (3, 15), (21, 18), (8, 0), (9, 12), (10, 8), (2, 25), (13, 21), (4, 14), (9, 6), (3, 18), (1, 24), (21, 13), (13, 13), (22, 7), (1, 23), (1, 22), (8, 17), (23, 12), (18, 8), (1, 7), (10, 4), (0, 22), (12, 23), (6, 21), (10, 24), (22, 5), (4, 0), (8, 9), (9, 24), (3, 20), (19, 8), (12, 7), (24, 24), (0, 19), (23, 23), (14, 7), (21, 15), (12, 19), (12, 17), (21, 4), (10, 10), (0, 14), (23, 15), (7, 10), (12, 20), (19, 25), (24, 22), (6, 19), (10, 3), (5, 23), (9, 14), (4, 21), (20, 22), (12, 1), (8, 2), (12, 21), (4, 6), (3, 26), (20, 10), (18, 7), (4, 9), (20, 26), (24, 19), (17, 3), (21, 0), (4, 10), (18, 2), (9, 18), (8, 3), (12, 4), (1, 11), (2, 1), (22, 2), (1, 16), (15, 7), (19, 18), (21, 19), (2, 2), (10, 26), (11, 24), (6, 23), (10, 9), (16, 2), (15, 24), (18, 17), (19, 13), (15, 14), (9, 19), (0, 10), (14, 9), (17, 12), (4, 13), (6, 7), (18, 1), (21, 6), (20, 14), (19, 5), (13, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443820", "dataset": "MATH"}
{"messages": [{"content": "In a 24x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 15), (15, 17), (14, 0), (12, 8), (11, 2), (2, 6), (5, 17), (9, 7), (7, 0), (1, 5), (6, 3), (2, 7), (12, 0), (10, 16), (22, 7), (21, 10), (9, 5), (8, 19), (12, 15), (4, 10), (2, 19), (19, 10), (6, 15), (19, 9), (5, 11), (3, 6), (16, 19), (20, 19), (17, 9), (20, 3), (22, 18), (14, 10), (12, 19), (5, 0), (21, 9), (19, 18), (13, 16), (4, 8), (13, 4), (22, 3), (2, 15), (15, 3), (22, 19), (7, 16), (21, 0), (8, 5), (4, 17), (13, 15), (18, 5), (17, 2), (21, 3), (17, 12), (21, 8), (22, 0), (14, 1), (16, 18), (20, 13), (17, 8), (17, 4), (9, 15), (4, 13), (5, 3), (9, 9), (1, 13), (16, 3), (8, 4), (10, 17), (23, 1), (3, 1), (2, 1), (18, 14), (21, 7), (21, 12), (8, 18), (17, 0), (2, 3), (11, 14), (14, 8), (8, 7), (5, 8), (14, 18), (3, 19), (7, 9), (7, 7), (10, 18), (8, 14), (8, 16), (0, 4), (18, 3), (12, 4), (18, 1), (16, 16), (9, 3), (3, 0), (9, 6), (10, 4), (2, 0), (14, 5), (20, 17), (0, 1), (3, 9), (7, 17), (22, 2), (10, 2), (13, 14), (17, 1), (1, 19), (6, 12), (9, 0), (5, 10), (22, 8), (19, 0), (16, 12), (5, 1), (12, 5), (20, 6), (4, 9), (6, 11), (7, 4), (3, 13), (23, 6), (18, 6), (14, 17), (5, 4), (19, 1), (8, 12), (18, 18), (13, 2), (15, 16), (1, 7), (3, 12), (3, 14), (10, 11), (10, 3), (13, 7), (18, 19), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287700", "dataset": "MATH"}
{"messages": [{"content": "In a 24x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 25), 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, 16), (18, 6), (17, 22), (20, 10), (12, 21), (8, 8), (20, 19), (19, 19), (2, 23), (10, 12), (1, 19), (1, 7), (19, 9), (18, 23), (23, 5), (20, 23), (17, 2), (20, 9), (4, 12), (3, 6), (5, 22), (19, 25), (21, 14), (6, 21), (6, 4), (11, 22), (21, 7), (23, 23), (17, 6), (17, 0), (8, 5), (10, 2), (11, 9), (8, 18), (22, 2), (7, 20), (11, 7), (12, 11), (2, 25), (16, 19), (21, 25), (0, 11), (19, 4), (4, 24), (19, 11), (2, 0), (20, 18), (15, 6), (17, 14), (23, 22), (19, 17), (19, 18), (9, 1), (0, 4), (4, 5), (19, 15), (10, 9), (17, 16), (13, 0), (1, 3), (19, 20), (14, 4), (0, 25), (10, 17), (15, 3), (19, 1), (13, 19), (1, 14), (10, 23), (8, 1), (3, 7), (6, 12), (7, 24), (9, 2), (5, 14), (7, 0), (18, 12), (10, 20), (11, 16), (9, 18), (14, 16), (0, 7), (14, 23), (1, 4), (11, 12), (9, 25), (14, 10), (0, 22), (4, 13), (13, 25), (19, 6), (0, 15), (4, 21), (22, 18), (0, 19), (15, 2), (1, 21), (5, 9), (20, 2), (6, 22), (7, 16), (2, 20), (6, 11), (15, 25), (22, 20), (10, 6), (15, 19), (8, 12), (1, 1), (5, 20), (16, 9), (2, 16), (6, 2), (9, 16), (15, 11), (8, 21), (5, 19), (6, 23), (18, 19), (4, 23), (7, 19), (12, 0), (21, 13), (13, 8), (7, 15), (4, 25), (23, 3), (12, 6), (0, 10), (11, 1), (15, 8), (13, 23), (19, 10), (16, 11), (9, 23), (7, 14), (0, 16), (20, 4), (3, 16), (19, 23), (22, 3), (12, 14), (6, 0), (2, 24), (21, 17), (13, 13), (7, 9), (4, 18), (1, 20), (1, 13), (10, 0), (13, 24), (11, 18), (12, 8), (8, 6), (7, 25), (22, 11), (3, 3), (7, 22), (8, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844688", "dataset": "MATH"}
{"messages": [{"content": "In a 20x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 18), (16, 14), (18, 14), (0, 11), (6, 3), (9, 10), (17, 3), (8, 19), (11, 1), (18, 8), (7, 11), (7, 19), (9, 9), (17, 14), (10, 0), (1, 13), (16, 8), (12, 3), (1, 4), (11, 2), (2, 21), (11, 5), (11, 19), (7, 3), (7, 21), (2, 17), (2, 5), (9, 2), (19, 18), (12, 11), (13, 17), (5, 5), (13, 14), (11, 21), (0, 10), (4, 11), (18, 12), (9, 3), (6, 18), (18, 7), (8, 3), (0, 8), (8, 12), (16, 1), (14, 9), (18, 3), (13, 4), (11, 7), (9, 0), (11, 17), (6, 2), (6, 20), (8, 14), (8, 2), (10, 1), (4, 10), (19, 0), (12, 1), (12, 17), (2, 8), (10, 3), (7, 1), (0, 5), (3, 6), (5, 17), (6, 9), (2, 7), (13, 11), (2, 13), (10, 21), (5, 21), (5, 2), (19, 16), (10, 8), (15, 13), (1, 15), (6, 4), (14, 17), (13, 8), (16, 4), (17, 8), (19, 14), (0, 7), (2, 12), (10, 4), (12, 8), (12, 12), (11, 11), (14, 10), (11, 6), (15, 20), (16, 0), (6, 11), (0, 13), (12, 21), (19, 15), (18, 0), (1, 16), (7, 13), (10, 2), (12, 4), (4, 7), (9, 12), (14, 13), (4, 12), (19, 4), (7, 9), (1, 11), (17, 6), (13, 9), (19, 8), (3, 20), (0, 9), (11, 15), (3, 12), (8, 6), (17, 19), (15, 21), (6, 13), (13, 20), (0, 6), (17, 15), (18, 10), (8, 1), (11, 9), (14, 4), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109250", "dataset": "MATH"}
{"messages": [{"content": "In a 20x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 20), 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), (5, 1), (7, 16), (17, 15), (0, 9), (12, 20), (13, 15), (0, 11), (16, 4), (15, 7), (15, 15), (1, 1), (1, 16), (16, 6), (0, 16), (6, 19), (17, 10), (16, 1), (10, 3), (13, 18), (8, 10), (19, 16), (8, 16), (2, 5), (9, 2), (8, 2), (0, 3), (3, 2), (9, 12), (11, 18), (4, 2), (3, 18), (12, 9), (18, 11), (9, 1), (4, 8), (0, 14), (18, 13), (4, 0), (13, 12), (3, 10), (16, 11), (5, 7), (8, 18), (16, 13), (17, 4), (4, 13), (11, 8), (14, 8), (4, 20), (2, 4), (11, 3), (17, 7), (18, 16), (4, 16), (14, 15), (10, 12), (6, 2), (14, 1), (9, 13), (6, 13), (7, 1), (10, 7), (16, 12), (14, 17), (14, 3), (7, 8), (9, 11), (14, 5), (18, 5), (3, 20), (0, 15), (3, 4), (11, 14), (3, 5), (19, 15), (8, 6), (18, 10), (15, 1), (2, 10), (12, 2), (14, 16), (7, 10), (18, 17), (15, 3), (0, 17), (11, 15), (10, 15), (4, 19), (9, 5), (13, 11), (2, 17), (2, 9), (10, 19), (18, 1), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484773", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 23), (8, 13), (25, 23), (6, 14), (2, 11), (18, 17), (12, 20), (10, 17), (19, 21), (3, 18), (5, 12), (8, 15), (8, 21), (1, 17), (23, 7), (4, 19), (21, 19), (27, 23), (24, 19), (12, 1), (11, 1), (7, 20), (21, 14), (24, 11), (19, 13), (5, 20), (1, 10), (26, 3), (3, 22), (6, 9), (19, 22), (10, 18), (14, 17), (23, 19), (27, 4), (0, 14), (14, 9), (19, 16), (3, 17), (4, 0), (20, 19), (11, 10), (25, 5), (23, 9), (9, 16), (3, 3), (17, 6), (22, 6), (8, 5), (4, 21), (15, 16), (8, 8), (24, 2), (5, 9), (10, 2), (22, 13), (4, 16), (18, 20), (23, 5), (14, 19), (20, 17), (19, 4), (16, 14), (11, 22), (18, 21), (0, 4), (8, 3), (9, 11), (7, 8), (20, 9), (25, 1), (9, 9), (9, 6), (25, 16), (13, 1), (13, 12), (27, 5), (24, 17), (16, 18), (26, 14), (25, 18), (24, 8), (10, 15), (19, 1), (5, 16), (0, 24), (27, 1), (1, 21), (23, 0), (12, 17), (9, 19), (26, 1), (14, 11), (10, 4), (3, 6), (16, 21), (16, 2), (18, 7), (2, 20), (14, 0), (14, 6), (23, 22), (7, 18), (22, 3), (2, 19), (3, 13), (3, 23), (24, 4), (24, 16), (15, 9), (14, 18), (26, 8), (21, 23), (20, 14), (22, 23), (13, 3), (15, 24), (4, 9), (2, 9), (25, 2), (1, 13), (20, 6), (13, 22), (16, 9), (23, 21), (16, 13), (5, 4), (19, 9), (22, 15), (9, 22), (19, 18), (9, 8), (21, 15), (2, 8), (21, 16), (14, 10), (24, 22), (22, 21), (15, 15), (23, 16), (15, 6), (10, 24), (16, 4), (16, 16), (25, 11), (27, 16), (15, 2), (0, 21), (6, 6), (17, 15), (1, 6), (19, 5), (15, 3), (20, 16), (6, 20), (9, 13), (14, 16), (21, 12), (24, 6), (19, 3), (5, 19), (10, 20), (22, 4), (2, 21), (27, 17), (25, 9), (26, 11), (8, 0), (25, 24), (16, 0), (16, 11), (11, 15), (0, 18), (19, 7), (4, 23), (4, 15), (7, 7), (18, 3), (15, 12), (4, 17), (27, 8), (8, 9), (11, 20), (22, 24), (9, 21), (1, 11), (16, 8), (23, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926716", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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), (5, 13), (12, 24), (10, 11), (9, 17), (19, 2), (12, 19), (12, 26), (14, 0), (10, 5), (6, 6), (16, 16), (13, 7), (9, 23), (8, 17), (16, 10), (1, 10), (21, 19), (13, 25), (6, 16), (15, 24), (2, 18), (7, 20), (19, 19), (13, 24), (21, 15), (15, 18), (0, 22), (18, 15), (22, 9), (2, 15), (20, 6), (16, 7), (20, 25), (19, 4), (10, 2), (22, 10), (0, 9), (22, 4), (19, 12), (19, 3), (2, 22), (7, 1), (1, 1), (22, 17), (18, 22), (21, 24), (19, 8), (17, 16), (5, 0), (15, 13), (0, 20), (19, 25), (0, 13), (8, 0), (18, 0), (18, 16), (10, 8), (8, 6), (10, 23), (18, 10), (8, 1), (8, 2), (11, 2), (17, 17), (4, 16), (21, 17), (13, 20), (6, 9), (1, 13), (8, 16), (17, 5), (13, 5), (3, 19), (12, 25), (2, 4), (15, 7), (8, 15), (17, 22), (3, 1), (0, 21), (11, 7), (11, 21), (10, 25), (12, 16), (15, 5), (0, 15), (6, 10), (22, 6), (15, 12), (7, 16), (19, 18), (3, 5), (6, 7), (0, 24), (2, 17), (6, 22), (17, 15), (2, 21), (13, 22), (11, 9), (20, 4), (8, 11), (18, 14), (15, 20), (4, 26), (14, 22), (1, 3), (20, 14), (10, 24), (13, 11), (4, 14), (5, 8), (13, 12), (21, 13), (8, 20), (18, 9), (14, 15), (12, 4), (14, 16), (7, 14), (15, 1), (20, 21), (4, 12), (20, 13), (14, 8), (6, 25), (8, 8), (4, 24), (21, 7), (2, 20), (7, 6), (12, 17), (20, 2), (5, 12), (5, 21), (21, 10), (16, 23), (3, 11), (14, 5), (20, 12), (14, 18), (19, 1), (19, 20), (15, 8), (9, 21), (12, 7), (3, 10), (13, 6), (12, 1), (5, 10), (13, 10), (20, 11), (14, 17), (1, 26), (22, 13), (1, 7), (5, 4), (20, 5), (21, 6), (8, 14), (12, 3), (0, 19), (19, 13), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968366", "dataset": "MATH"}
{"messages": [{"content": "In a 28x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 19), (10, 2), (18, 9), (24, 5), (27, 7), (7, 7), (23, 1), (16, 23), (19, 23), (25, 8), (20, 3), (7, 22), (8, 13), (1, 9), (6, 14), (1, 2), (19, 10), (2, 8), (5, 20), (1, 6), (23, 17), (23, 14), (5, 6), (23, 4), (7, 11), (9, 4), (9, 23), (12, 22), (0, 11), (16, 0), (25, 11), (21, 12), (26, 19), (27, 3), (14, 7), (6, 18), (11, 10), (15, 14), (4, 14), (12, 3), (15, 13), (0, 3), (4, 17), (5, 1), (27, 22), (24, 17), (8, 8), (21, 9), (1, 10), (10, 5), (20, 15), (6, 21), (27, 13), (10, 8), (8, 22), (3, 14), (11, 18), (3, 3), (1, 7), (25, 16), (24, 18), (19, 4), (10, 13), (12, 4), (12, 5), (1, 17), (8, 16), (0, 16), (9, 2), (13, 18), (25, 9), (1, 1), (27, 20), (17, 9), (1, 11), (14, 16), (11, 13), (19, 1), (11, 17), (1, 21), (16, 16), (5, 8), (13, 20), (6, 5), (9, 7), (25, 2), (4, 15), (10, 9), (8, 19), (11, 14), (27, 1), (11, 8), (21, 3), (18, 22), (20, 5), (7, 12), (2, 7), (16, 12), (12, 12), (26, 11), (23, 23), (27, 5), (24, 6), (3, 23), (7, 20), (0, 17), (15, 24), (13, 12), (4, 16), (17, 6), (5, 5), (10, 19), (12, 14), (3, 22), (6, 11), (17, 13), (11, 24), (3, 13), (0, 20), (3, 18), (1, 16), (4, 7), (19, 2), (23, 24), (7, 2), (15, 0), (2, 20), (9, 21), (7, 19), (5, 21), (5, 10), (15, 23), (23, 9), (2, 24), (19, 15), (15, 3), (21, 4), (25, 1), (1, 18), (7, 13), (8, 1), (20, 4), (7, 16), (27, 15), (25, 7), (24, 3), (9, 6), (24, 10), (16, 19), (13, 2), (17, 16), (9, 13), (4, 6), (17, 18), (23, 13), (7, 9), (13, 7), (6, 8), (17, 19), (4, 12), (22, 17), (2, 6), (22, 21), (23, 2), (6, 22), (6, 2), (10, 11), (7, 5), (24, 7), (13, 8), (16, 7), (20, 21), (3, 9), (23, 11), (26, 8), (9, 0), (23, 15), (20, 0), (24, 4), (8, 2), (9, 9), (8, 14), (19, 7), (9, 11), (10, 12), (5, 22), (12, 16), (2, 1), (6, 20), (19, 22), (0, 4), (20, 13), (12, 7), (14, 5), (10, 21), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902040", "dataset": "MATH"}
{"messages": [{"content": "In a 23x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 21), (22, 9), (19, 23), (2, 9), (16, 22), (13, 22), (9, 12), (18, 3), (13, 19), (6, 24), (20, 24), (8, 20), (13, 2), (16, 24), (22, 4), (7, 16), (17, 3), (1, 20), (6, 3), (15, 11), (8, 11), (5, 23), (12, 21), (0, 13), (10, 21), (11, 2), (22, 24), (10, 7), (12, 2), (16, 7), (16, 1), (21, 10), (18, 24), (6, 4), (18, 18), (0, 18), (11, 18), (1, 23), (17, 13), (4, 21), (1, 22), (4, 0), (4, 5), (11, 15), (4, 23), (7, 10), (18, 14), (16, 2), (1, 24), (7, 0), (14, 6), (21, 1), (16, 9), (18, 22), (12, 4), (10, 11), (16, 19), (19, 13), (20, 21), (7, 24), (19, 0), (14, 17), (10, 25), (18, 13), (5, 16), (21, 16), (2, 10), (8, 4), (8, 5), (14, 24), (12, 22), (11, 9), (16, 12), (22, 13), (20, 12), (17, 4), (16, 23), (21, 11), (5, 15), (17, 22), (12, 12), (5, 5), (4, 3), (13, 10), (7, 3), (11, 22), (19, 10), (2, 20), (4, 4), (20, 17), (19, 24), (16, 15), (19, 9), (14, 2), (0, 14), (3, 15), (5, 24), (12, 23), (0, 10), (17, 10), (7, 7), (15, 6), (1, 10), (7, 1), (5, 9), (9, 6), (18, 21), (18, 10), (7, 9), (16, 10), (9, 20), (1, 14), (9, 15), (12, 9), (0, 1), (19, 6), (10, 9), (8, 1), (4, 12), (15, 3), (9, 7), (9, 18), (0, 7), (3, 7), (5, 0), (22, 23), (16, 25), (11, 1), (15, 9), (21, 17), (15, 16), (3, 4), (1, 8), (4, 9), (7, 22), (20, 25), (0, 24), (5, 3), (9, 9), (6, 20), (11, 17), (10, 19), (0, 8), (16, 18), (15, 17), (9, 10), (17, 9), (22, 21), (14, 16), (2, 25), (22, 17), (5, 14), (17, 24), (18, 5), (3, 16), (7, 21), (1, 11), (3, 13), (11, 0), (14, 22), (19, 3), (19, 1), (20, 10), (9, 13), (10, 3), (10, 12), (15, 15), (8, 0), (2, 23), (2, 24), (18, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807144", "dataset": "MATH"}
{"messages": [{"content": "In a 22x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 22), 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), (10, 17), (19, 10), (3, 22), (9, 2), (21, 6), (4, 14), (2, 2), (14, 1), (1, 3), (5, 6), (0, 10), (20, 2), (11, 3), (12, 22), (18, 6), (6, 7), (1, 7), (6, 11), (11, 9), (13, 3), (17, 3), (14, 17), (2, 1), (4, 12), (16, 4), (16, 22), (14, 19), (15, 8), (14, 5), (10, 1), (10, 6), (18, 8), (9, 8), (15, 17), (4, 19), (0, 20), (14, 3), (6, 15), (14, 15), (8, 19), (0, 14), (4, 0), (21, 13), (11, 11), (2, 9), (14, 6), (0, 16), (3, 17), (17, 13), (10, 15), (9, 18), (4, 22), (1, 19), (11, 20), (2, 16), (3, 0), (16, 5), (2, 13), (19, 4), (12, 12), (2, 7), (11, 15), (16, 14), (13, 1), (6, 21), (17, 10), (4, 20), (18, 0), (3, 2), (3, 11), (17, 21), (15, 21), (19, 5), (17, 8), (11, 7), (11, 22), (20, 12), (5, 9), (16, 9), (15, 22), (6, 17), (15, 14), (2, 0), (12, 3), (6, 20), (19, 20), (19, 6), (6, 18), (7, 0), (10, 18), (3, 12), (2, 21), (18, 5), (9, 6), (19, 14), (17, 22), (17, 0), (9, 5), (19, 8), (3, 13), (20, 4), (14, 7), (13, 12), (7, 8), (15, 19), (14, 18), (17, 20), (5, 22), (1, 8), (4, 21), (12, 18), (11, 21), (21, 18), (17, 5), (16, 17), (1, 0), (2, 22), (4, 16), (1, 20), (15, 18), (7, 21), (2, 15), (21, 9), (3, 9), (7, 12), (8, 9), (18, 22), (9, 0), (11, 1), (18, 16), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523934", "dataset": "MATH"}
{"messages": [{"content": "In a 25x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 17), (1, 15), (19, 7), (5, 21), (22, 0), (12, 16), (2, 15), (16, 17), (4, 18), (3, 6), (14, 11), (4, 0), (17, 1), (20, 0), (0, 3), (12, 14), (7, 20), (9, 15), (12, 13), (17, 4), (14, 7), (13, 3), (23, 7), (5, 16), (11, 16), (2, 3), (17, 13), (10, 18), (17, 12), (17, 5), (6, 2), (9, 6), (9, 3), (5, 19), (14, 12), (15, 14), (14, 13), (24, 16), (11, 10), (8, 16), (24, 0), (11, 13), (7, 6), (9, 13), (8, 8), (15, 9), (24, 17), (8, 21), (3, 4), (5, 5), (19, 4), (19, 17), (4, 4), (22, 20), (13, 9), (23, 14), (20, 9), (12, 21), (16, 9), (6, 10), (20, 1), (21, 10), (6, 7), (15, 10), (6, 19), (21, 18), (22, 7), (5, 0), (15, 3), (4, 2), (13, 11), (23, 9), (7, 0), (12, 17), (22, 19), (23, 16), (4, 16), (14, 2), (23, 3), (16, 7), (1, 4), (24, 8), (15, 1), (0, 15), (10, 7), (8, 1), (24, 2), (2, 9), (3, 17), (14, 21), (4, 9), (19, 12), (14, 5), (7, 16), (1, 20), (21, 2), (24, 7), (6, 17), (6, 20), (24, 13), (16, 0), (19, 21), (14, 10), (0, 6), (2, 6), (23, 10), (20, 18), (5, 3), (15, 16), (3, 9), (1, 13), (8, 9), (1, 8), (24, 9), (0, 12), (14, 1), (20, 8), (1, 19), (17, 14), (15, 4), (6, 6), (20, 11), (3, 18), (9, 21), (4, 7), (19, 5), (20, 5), (9, 12), (14, 6), (16, 21), (18, 8), (20, 2), (6, 13), (22, 5), (3, 11), (10, 0), (7, 5), (21, 16), (16, 13), (18, 7), (16, 12), (2, 21), (21, 0), (13, 2), (20, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "786780", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 14), (22, 17), (10, 7), (19, 16), (13, 15), (15, 12), (14, 15), (23, 8), (22, 7), (1, 0), (10, 1), (17, 16), (13, 2), (11, 19), (22, 20), (8, 12), (7, 11), (16, 11), (12, 1), (22, 18), (19, 5), (12, 5), (5, 17), (19, 17), (13, 14), (20, 12), (2, 11), (21, 7), (4, 3), (13, 17), (4, 8), (16, 1), (23, 15), (7, 10), (1, 10), (0, 13), (1, 4), (17, 19), (22, 9), (13, 12), (19, 1), (21, 9), (11, 15), (19, 11), (12, 8), (8, 4), (2, 19), (2, 8), (21, 2), (16, 0), (5, 9), (3, 18), (3, 3), (5, 18), (0, 18), (4, 10), (6, 5), (2, 16), (18, 9), (17, 7), (18, 5), (7, 4), (8, 20), (4, 9), (1, 11), (3, 15), (6, 6), (5, 8), (7, 13), (21, 18), (1, 13), (21, 6), (6, 0), (15, 15), (14, 14), (5, 1), (12, 12), (10, 2), (11, 16), (1, 7), (10, 15), (8, 2), (5, 7), (5, 3), (15, 18), (15, 5), (6, 4), (0, 9), (3, 1), (23, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845040", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 11), (0, 23), (12, 16), (19, 20), (9, 15), (9, 14), (13, 13), (3, 9), (23, 1), (21, 22), (14, 20), (22, 4), (20, 12), (4, 16), (11, 5), (7, 15), (13, 16), (23, 22), (17, 0), (13, 19), (22, 13), (1, 15), (0, 19), (15, 8), (2, 5), (7, 8), (14, 15), (5, 9), (0, 27), (4, 12), (7, 21), (7, 16), (7, 3), (16, 7), (0, 24), (12, 18), (3, 14), (11, 25), (17, 21), (20, 8), (9, 4), (10, 18), (16, 24), (3, 17), (5, 2), (23, 26), (15, 14), (23, 21), (9, 17), (21, 15), (14, 9), (18, 21), (2, 4), (13, 18), (18, 15), (9, 6), (9, 26), (9, 5), (21, 2), (18, 14), (5, 24), (6, 10), (23, 20), (8, 10), (10, 19), (11, 21), (6, 7), (18, 24), (8, 21), (12, 13), (18, 17), (0, 4), (14, 27), (15, 20), (22, 10), (1, 8), (0, 14), (20, 18), (1, 11), (17, 4), (13, 0), (9, 0), (16, 15), (21, 3), (7, 17), (22, 6), (3, 16), (9, 9), (7, 25), (8, 2), (3, 12), (16, 22), (2, 9), (1, 3), (9, 23), (21, 25), (13, 27), (10, 15), (16, 6), (13, 3), (13, 5), (17, 6), (22, 14), (11, 0), (20, 19), (19, 3), (9, 25), (11, 18), (9, 8), (3, 5), (5, 0), (14, 4), (5, 22), (9, 11), (15, 16), (17, 11), (4, 26), (9, 3), (4, 22), (17, 23), (12, 0), (1, 17), (0, 2), (12, 11), (3, 24), (1, 5), (23, 3), (0, 26), (19, 25), (15, 22), (20, 20), (13, 14), (18, 4), (14, 17), (23, 8), (20, 3), (16, 20), (11, 27), (16, 11), (5, 4), (15, 10), (11, 17), (20, 23), (4, 3), (4, 1), (0, 11), (20, 11), (16, 13), (4, 14), (8, 18), (16, 5), (4, 2), (19, 23), (12, 19), (9, 22), (22, 9), (6, 0), (22, 18), (14, 1), (19, 18), (13, 4), (12, 17), (12, 8), (21, 14), (13, 25), (20, 13), (16, 14), (7, 19), (5, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777280", "dataset": "MATH"}
{"messages": [{"content": "In a 20x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 25), 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), (14, 8), (15, 4), (8, 4), (3, 7), (14, 18), (17, 17), (17, 22), (10, 20), (10, 22), (9, 10), (6, 2), (2, 14), (14, 11), (17, 1), (4, 8), (9, 19), (7, 6), (10, 24), (7, 23), (14, 22), (11, 13), (16, 20), (11, 25), (7, 19), (2, 13), (10, 2), (4, 4), (15, 6), (14, 14), (13, 8), (19, 16), (18, 9), (14, 12), (7, 11), (11, 4), (12, 8), (19, 10), (0, 10), (3, 8), (18, 16), (12, 14), (9, 3), (17, 11), (10, 0), (14, 17), (6, 14), (0, 25), (3, 6), (1, 20), (12, 18), (8, 2), (11, 3), (10, 19), (5, 7), (4, 14), (6, 18), (8, 25), (11, 21), (10, 16), (16, 4), (13, 7), (13, 18), (17, 23), (0, 14), (13, 6), (13, 24), (14, 16), (7, 13), (2, 20), (9, 11), (5, 24), (18, 14), (3, 15), (6, 20), (5, 22), (16, 13), (16, 11), (11, 8), (15, 11), (15, 5), (5, 15), (19, 2), (10, 18), (0, 23), (0, 6), (4, 17), (19, 6), (3, 23), (1, 10), (9, 24), (1, 0), (1, 19), (9, 9), (5, 2), (17, 21), (13, 14), (11, 15), (14, 3), (12, 20), (4, 11), (16, 9), (12, 9), (0, 13), (17, 14), (18, 5), (16, 7), (18, 13), (10, 3), (18, 12), (18, 24), (12, 15), (17, 0), (8, 20), (10, 14), (15, 24), (15, 2), (3, 3), (19, 18), (12, 4), (19, 21), (6, 8), (5, 4), (2, 12), (15, 19), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950368", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 17), (18, 11), (1, 0), (2, 2), (6, 5), (13, 8), (17, 20), (13, 21), (11, 27), (3, 27), (5, 7), (9, 17), (23, 10), (22, 5), (18, 4), (13, 22), (21, 28), (10, 21), (14, 14), (5, 27), (19, 24), (18, 26), (16, 16), (9, 20), (7, 8), (14, 27), (6, 7), (6, 20), (17, 13), (1, 10), (7, 4), (22, 28), (25, 22), (23, 23), (8, 2), (18, 13), (24, 7), (2, 23), (19, 12), (11, 20), (8, 21), (3, 25), (13, 20), (17, 2), (19, 10), (9, 10), (15, 21), (17, 16), (1, 15), (22, 16), (18, 8), (20, 15), (11, 17), (5, 22), (19, 3), (19, 7), (12, 13), (10, 15), (21, 4), (19, 23), (15, 5), (4, 15), (24, 14), (8, 15), (15, 8), (7, 1), (15, 24), (23, 16), (18, 6), (3, 28), (15, 19), (25, 21), (16, 21), (14, 2), (21, 8), (13, 17), (23, 26), (16, 9), (12, 4), (10, 4), (20, 16), (21, 1), (2, 27), (0, 10), (14, 17), (5, 4), (11, 4), (4, 26), (17, 26), (11, 22), (1, 26), (13, 26), (25, 26), (21, 18), (0, 28), (1, 16), (10, 27), (0, 16), (23, 25), (19, 16), (6, 27), (25, 20), (12, 22), (20, 20), (15, 11), (11, 0), (8, 27), (11, 24), (23, 19), (15, 15), (11, 19), (10, 3), (7, 15), (4, 0), (6, 25), (20, 1), (11, 6), (16, 24), (9, 16), (24, 0), (15, 4), (22, 26), (0, 20), (10, 5), (10, 22), (15, 22), (9, 19), (23, 2), (12, 11), (21, 23), (5, 0), (25, 0), (4, 9), (19, 22), (18, 5), (7, 7), (9, 23), (5, 15), (3, 18), (12, 18), (10, 6), (18, 23), (24, 26), (8, 10), (0, 23), (5, 21), (9, 9), (23, 0), (14, 19), (24, 25), (24, 27), (24, 16), (25, 15), (2, 10), (7, 12), (0, 18), (5, 17), (16, 8), (17, 21), (10, 7), (25, 19), (23, 14), (3, 1), (6, 3), (19, 1), (1, 13), (24, 24), (20, 27), (14, 4), (1, 28), (11, 10), (11, 28), (18, 18), (17, 23), (12, 6), (6, 15), (17, 12), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847398", "dataset": "MATH"}
{"messages": [{"content": "In a 27x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 22), 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), (26, 8), (13, 22), (8, 4), (18, 17), (0, 5), (22, 8), (8, 2), (1, 22), (11, 19), (26, 11), (11, 8), (9, 21), (23, 18), (4, 13), (14, 19), (23, 1), (10, 11), (23, 11), (18, 9), (5, 3), (21, 14), (5, 14), (1, 19), (13, 2), (19, 14), (19, 19), (12, 20), (18, 11), (0, 22), (25, 14), (20, 2), (13, 16), (18, 10), (24, 7), (18, 14), (5, 8), (1, 16), (3, 20), (18, 3), (6, 2), (3, 18), (7, 12), (26, 19), (15, 10), (20, 15), (9, 10), (11, 11), (0, 13), (14, 15), (24, 22), (25, 15), (8, 15), (9, 3), (13, 0), (3, 14), (20, 18), (6, 6), (0, 17), (9, 22), (7, 10), (2, 4), (7, 16), (5, 22), (5, 21), (22, 2), (18, 15), (17, 14), (8, 19), (15, 0), (0, 4), (25, 5), (2, 13), (13, 7), (12, 16), (15, 16), (26, 5), (16, 19), (25, 20), (16, 18), (1, 7), (13, 11), (3, 15), (14, 6), (6, 16), (3, 2), (3, 1), (11, 21), (7, 7), (15, 4), (14, 8), (2, 19), (24, 17), (11, 4), (0, 15), (4, 21), (21, 4), (21, 16), (20, 16), (10, 16), (16, 3), (18, 2), (10, 8), (9, 1), (16, 15), (13, 13), (14, 4), (22, 16), (13, 21), (23, 9), (11, 3), (7, 1), (10, 2), (4, 6), (6, 18), (2, 21), (11, 10), (2, 11), (25, 16), (6, 15), (8, 0), (20, 11), (23, 7), (21, 6), (4, 12), (24, 0), (6, 17), (3, 22), (13, 12), (23, 19), (19, 11), (3, 8), (12, 11), (23, 3), (25, 1), (21, 12), (24, 19), (26, 21), (13, 1), (1, 1), (18, 8), (7, 3), (26, 10), (0, 20), (0, 8), (19, 6), (2, 9), (2, 15), (20, 7), (12, 7), (1, 13), (3, 16), (21, 20), (12, 0), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497576", "dataset": "MATH"}
{"messages": [{"content": "In a 20x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 27), 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, 2), (4, 15), (14, 14), (15, 19), (2, 6), (3, 23), (12, 27), (11, 12), (18, 18), (2, 22), (15, 1), (12, 1), (14, 21), (2, 15), (7, 18), (16, 17), (8, 6), (6, 12), (6, 19), (11, 18), (10, 10), (14, 13), (8, 23), (6, 20), (0, 25), (19, 8), (10, 23), (14, 24), (17, 3), (8, 14), (11, 27), (17, 8), (10, 16), (11, 2), (18, 3), (19, 0), (1, 3), (17, 22), (13, 24), (6, 27), (5, 23), (19, 23), (14, 4), (6, 13), (6, 15), (4, 26), (18, 12), (16, 23), (11, 23), (9, 22), (17, 16), (17, 6), (0, 22), (18, 15), (5, 8), (4, 22), (3, 0), (17, 15), (13, 18), (12, 10), (1, 14), (1, 16), (11, 13), (0, 23), (4, 9), (1, 11), (4, 16), (12, 26), (9, 11), (14, 6), (19, 15), (10, 9), (2, 10), (19, 24), (14, 7), (1, 6), (15, 25), (2, 27), (16, 8), (15, 8), (17, 25), (18, 23), (4, 14), (9, 16), (9, 26), (15, 11), (3, 13), (1, 22), (4, 11), (7, 27), (10, 2), (9, 8), (6, 7), (11, 22), (5, 20), (19, 16), (19, 9), (3, 21), (10, 11), (7, 12), (7, 7), (9, 1), (9, 20), (15, 14), (19, 13), (1, 17), (11, 24), (0, 19), (15, 6), (14, 11), (19, 14), (19, 19), (18, 10), (12, 15), (5, 11), (11, 19), (13, 11), (13, 23), (2, 25), (14, 10), (19, 4), (5, 25), (19, 25), (10, 22), (17, 18), (9, 21), (18, 8), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "975801", "dataset": "MATH"}
{"messages": [{"content": "In a 24x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 12), (19, 11), (2, 4), (2, 22), (15, 12), (22, 15), (12, 0), (23, 7), (8, 5), (23, 9), (8, 10), (20, 20), (16, 19), (1, 9), (11, 20), (14, 9), (19, 22), (15, 7), (4, 22), (19, 13), (0, 10), (1, 11), (15, 20), (6, 1), (21, 16), (11, 5), (13, 8), (14, 1), (21, 5), (2, 12), (1, 14), (4, 8), (6, 22), (1, 1), (1, 24), (10, 24), (21, 7), (7, 23), (17, 5), (2, 14), (10, 8), (2, 2), (20, 5), (12, 23), (4, 7), (18, 18), (1, 8), (12, 16), (20, 14), (12, 20), (9, 6), (6, 4), (16, 8), (7, 19), (14, 15), (22, 9), (5, 17), (21, 4), (20, 3), (6, 0), (1, 23), (19, 12), (6, 11), (0, 7), (20, 4), (8, 20), (15, 11), (1, 13), (15, 21), (18, 1), (23, 8), (14, 19), (0, 23), (15, 23), (8, 24), (19, 17), (20, 19), (16, 5), (6, 9), (23, 0), (2, 16), (7, 10), (8, 1), (7, 4), (20, 1), (15, 3), (10, 7), (12, 3), (10, 0), (4, 3), (13, 14), (5, 13), (8, 22), (20, 13), (6, 21), (6, 18), (1, 16), (14, 6), (8, 4), (9, 14), (14, 18), (16, 10), (15, 10), (11, 19), (2, 20), (16, 0), (11, 21), (2, 5), (1, 20), (13, 11), (11, 13), (0, 6), (13, 1), (4, 12), (17, 20), (9, 1), (21, 9), (17, 14), (9, 17), (5, 8), (12, 7), (19, 18), (20, 11), (22, 10), (18, 0), (9, 2), (5, 16), (13, 16), (3, 2), (13, 18), (23, 22), (20, 18), (17, 8), (22, 11), (3, 8), (23, 3), (16, 9), (17, 24), (15, 4), (13, 22), (5, 11), (9, 0), (4, 1), (22, 13), (18, 5), (17, 19), (9, 11), (17, 21), (22, 3), (11, 23), (4, 23), (0, 18), (3, 23), (2, 23), (23, 4), (4, 16), (10, 18), (10, 13), (22, 5), (22, 20), (10, 4), (17, 16), (1, 17), (5, 5), (23, 11), (20, 23), (6, 16), (3, 1), (6, 19), (11, 9), (2, 0), (10, 17), (1, 7), (4, 18), (21, 0), (8, 6), (16, 18), (12, 1), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15264", "dataset": "MATH"}
{"messages": [{"content": "In a 21x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 22), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 17), (1, 18), (0, 10), (15, 16), (15, 6), (11, 19), (13, 18), (12, 2), (3, 12), (2, 1), (15, 22), (20, 4), (12, 20), (20, 1), (18, 4), (18, 18), (3, 15), (19, 3), (3, 19), (15, 21), (2, 14), (12, 21), (15, 14), (8, 2), (4, 4), (19, 2), (9, 17), (11, 4), (16, 7), (0, 6), (2, 10), (3, 5), (14, 7), (6, 11), (17, 19), (13, 15), (11, 1), (9, 10), (3, 3), (10, 2), (0, 7), (10, 18), (16, 13), (9, 3), (16, 14), (0, 5), (1, 1), (17, 12), (7, 4), (19, 4), (5, 13), (1, 5), (3, 4), (19, 13), (14, 6), (14, 5), (19, 10), (20, 8), (11, 3), (15, 11), (4, 12), (11, 17), (1, 9), (13, 5), (19, 20), (8, 8), (16, 16), (20, 10), (14, 20), (3, 17), (20, 14), (20, 16), (18, 8), (16, 20), (14, 21), (2, 7), (18, 16), (1, 11), (17, 6), (16, 9), (0, 14), (17, 9), (17, 18), (12, 8), (19, 14), (14, 10), (2, 18), (15, 4), (17, 3), (13, 9), (7, 10), (1, 14), (14, 1), (3, 2), (14, 3), (12, 15), (19, 22), (4, 14), (4, 9), (12, 14), (16, 11), (17, 14), (1, 19), (9, 21), (12, 9), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "879861", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 12), (15, 7), (24, 10), (17, 5), (7, 11), (23, 13), (4, 14), (24, 13), (3, 20), (22, 3), (4, 16), (14, 18), (19, 3), (0, 8), (22, 19), (1, 11), (7, 9), (11, 4), (2, 13), (4, 21), (14, 11), (20, 2), (22, 8), (7, 6), (25, 15), (13, 13), (21, 20), (18, 7), (12, 13), (15, 14), (10, 3), (10, 18), (13, 7), (1, 12), (12, 16), (21, 2), (7, 5), (24, 21), (1, 15), (5, 9), (4, 4), (4, 20), (4, 1), (0, 9), (20, 4), (14, 14), (1, 14), (12, 21), (3, 21), (5, 16), (6, 11), (9, 17), (3, 15), (4, 7), (24, 12), (5, 17), (14, 10), (26, 3), (10, 0), (19, 17), (10, 12), (17, 11), (21, 17), (23, 1), (2, 2), (11, 16), (11, 21), (27, 4), (4, 10), (19, 21), (17, 1), (17, 12), (13, 15), (19, 7), (18, 12), (3, 13), (26, 5), (0, 3), (12, 18), (4, 13), (16, 2), (0, 18), (13, 17), (21, 19), (2, 10), (24, 2), (17, 18), (18, 6), (8, 19), (25, 16), (24, 6), (4, 15), (7, 1), (27, 7), (2, 1), (3, 3), (10, 8), (18, 21), (24, 3), (2, 16), (16, 12), (22, 16), (24, 16), (20, 16), (23, 8), (25, 19), (24, 18), (26, 9), (14, 7), (8, 20), (15, 9), (17, 13), (1, 1), (18, 16), (14, 17), (10, 21), (11, 1), (22, 1), (4, 2), (25, 17), (16, 11), (1, 4), (16, 19), (14, 6), (27, 9), (18, 3), (19, 1), (12, 3), (13, 16), (26, 13), (2, 6), (12, 7), (8, 17), (18, 18), (24, 17), (14, 5), (3, 7), (7, 18), (13, 8), (27, 14), (22, 0), (11, 0), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508860", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 10), (9, 18), (19, 19), (13, 18), (4, 7), (1, 6), (2, 4), (15, 4), (16, 14), (8, 3), (18, 5), (0, 20), (11, 6), (16, 11), (1, 9), (16, 4), (20, 6), (17, 11), (17, 20), (2, 6), (2, 16), (6, 14), (11, 4), (12, 10), (13, 20), (6, 11), (12, 5), (13, 4), (13, 10), (4, 9), (21, 20), (14, 2), (18, 3), (13, 14), (9, 4), (13, 11), (19, 13), (15, 19), (17, 13), (1, 12), (19, 6), (4, 11), (8, 0), (2, 19), (21, 13), (14, 6), (12, 0), (11, 20), (20, 19), (8, 16), (10, 3), (18, 16), (6, 7), (18, 20), (17, 4), (5, 3), (7, 16), (12, 13), (1, 2), (22, 20), (8, 20), (13, 9), (19, 4), (10, 14), (22, 4), (16, 2), (1, 19), (5, 4), (10, 0), (5, 16), (2, 5), (21, 7), (2, 2), (19, 9), (13, 0), (3, 5), (18, 7), (8, 10), (20, 20), (14, 13), (19, 7), (18, 11), (11, 14), (11, 8), (21, 0), (22, 3), (15, 13), (9, 3), (2, 8), (14, 7), (21, 16), (9, 20), (14, 14), (19, 12), (4, 0), (0, 1), (20, 11), (9, 1), (11, 15), (18, 6), (22, 9), (11, 10), (0, 14), (2, 11), (0, 10), (0, 6), (11, 13), (5, 1), (4, 4), (8, 8), (9, 0), (1, 16), (13, 17), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519966", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), 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), (15, 15), (15, 19), (11, 9), (25, 9), (19, 1), (25, 11), (13, 21), (12, 20), (9, 15), (17, 17), (7, 19), (6, 21), (8, 8), (3, 0), (0, 15), (2, 9), (19, 18), (16, 6), (24, 8), (7, 16), (27, 20), (4, 27), (2, 28), (20, 27), (6, 19), (16, 24), (13, 14), (15, 8), (13, 24), (23, 0), (24, 11), (28, 15), (9, 5), (28, 6), (1, 4), (24, 1), (0, 2), (28, 14), (19, 0), (5, 4), (12, 15), (6, 11), (2, 4), (19, 14), (19, 22), (17, 6), (0, 11), (23, 27), (5, 16), (20, 4), (10, 26), (21, 17), (3, 14), (6, 6), (13, 8), (6, 0), (10, 12), (21, 5), (24, 12), (9, 0), (12, 16), (23, 9), (26, 24), (2, 5), (5, 12), (9, 1), (14, 7), (22, 23), (7, 2), (7, 26), (14, 1), (18, 3), (22, 14), (23, 4), (25, 19), (1, 15), (6, 4), (27, 22), (19, 17), (5, 23), (6, 10), (3, 9), (18, 27), (18, 19), (21, 24), (1, 12), (14, 18), (22, 6), (16, 13), (8, 7), (14, 19), (0, 22), (7, 9), (18, 22), (12, 4), (16, 18), (22, 7), (28, 27), (22, 2), (23, 15), (21, 3), (0, 26), (18, 25), (22, 3), (1, 27), (22, 16), (27, 11), (5, 17), (23, 17), (28, 17), (5, 8), (3, 25), (19, 16), (12, 23), (3, 13), (13, 15), (4, 3), (22, 26), (10, 4), (8, 2), (3, 15), (4, 6), (17, 2), (1, 17), (24, 24), (27, 27), (22, 13), (27, 5), (10, 18), (7, 8), (14, 12), (25, 24), (24, 21), (11, 6), (23, 10), (8, 15), (3, 17), (13, 5), (12, 0), (4, 20), (4, 2), (26, 16), (27, 9), (25, 25), (13, 28), (2, 24), (17, 21), (4, 1), (10, 5), (1, 23), (2, 25), (4, 16), (13, 3), (10, 17), (0, 24), (20, 21), (21, 14), (14, 20), (12, 22), (27, 24), (27, 7), (11, 22), (19, 9), (26, 3), (6, 13), (13, 27), (21, 16), (8, 18), (4, 4), (22, 1), (11, 4), (8, 9), (28, 1), (28, 11), (28, 8), (16, 10), (12, 25), (4, 21), (10, 7), (28, 9), (28, 10), (26, 21), (9, 12), (4, 15), (20, 3), (18, 17), (9, 2), (12, 9), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28080", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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), (15, 5), (16, 2), (21, 9), (14, 0), (16, 16), (6, 4), (10, 13), (13, 2), (0, 7), (8, 4), (1, 7), (5, 14), (10, 19), (3, 0), (9, 14), (5, 0), (23, 1), (14, 20), (12, 7), (15, 9), (22, 9), (6, 13), (16, 6), (11, 0), (20, 13), (11, 19), (6, 15), (7, 11), (21, 17), (19, 0), (15, 17), (3, 3), (21, 7), (16, 3), (14, 16), (6, 2), (9, 9), (8, 10), (7, 15), (17, 17), (18, 1), (15, 7), (11, 20), (4, 9), (9, 6), (17, 5), (23, 14), (22, 19), (18, 17), (2, 4), (19, 17), (1, 19), (20, 9), (17, 6), (15, 1), (10, 6), (9, 12), (2, 1), (20, 0), (20, 15), (4, 13), (15, 18), (9, 10), (23, 3), (3, 20), (23, 19), (22, 5), (8, 6), (4, 20), (22, 2), (18, 5), (7, 0), (12, 14), (3, 10), (19, 4), (3, 11), (17, 20), (22, 1), (14, 5), (13, 5), (1, 14), (23, 11), (19, 5), (23, 15), (18, 4), (3, 1), (5, 10), (0, 19), (3, 14), (21, 19), (1, 8), (3, 15), (13, 8), (22, 12), (19, 8), (7, 16), (19, 16), (8, 13), (13, 1), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333198", "dataset": "MATH"}
{"messages": [{"content": "In a 25x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 24), (14, 7), (4, 20), (10, 9), (10, 4), (3, 23), (13, 24), (22, 3), (2, 15), (12, 26), (24, 15), (11, 7), (10, 7), (1, 22), (20, 11), (17, 15), (23, 4), (23, 10), (10, 19), (0, 15), (14, 12), (24, 10), (23, 9), (19, 18), (7, 21), (11, 16), (4, 10), (12, 16), (18, 21), (21, 22), (17, 21), (10, 24), (16, 25), (2, 2), (10, 8), (20, 4), (18, 20), (17, 23), (7, 0), (15, 21), (24, 18), (13, 7), (19, 6), (12, 23), (18, 15), (14, 1), (16, 11), (5, 6), (19, 3), (1, 27), (10, 15), (11, 12), (12, 10), (19, 11), (2, 21), (7, 12), (3, 10), (4, 17), (5, 12), (22, 11), (10, 25), (21, 8), (6, 21), (8, 6), (24, 24), (7, 18), (14, 16), (15, 14), (15, 24), (12, 12), (6, 2), (7, 22), (12, 4), (5, 2), (2, 9), (9, 6), (21, 20), (3, 12), (22, 2), (24, 17), (8, 8), (19, 13), (3, 24), (16, 20), (11, 18), (18, 3), (14, 0), (19, 0), (3, 4), (4, 19), (13, 22), (0, 14), (0, 1), (10, 22), (8, 4), (14, 10), (9, 13), (18, 27), (1, 17), (9, 20), (15, 3), (1, 7), (24, 4), (8, 17), (21, 7), (4, 25), (21, 9), (6, 14), (13, 14), (12, 19), (19, 9), (12, 8), (2, 4), (1, 20), (19, 19), (15, 11), (14, 20), (0, 19), (19, 8), (2, 0), (12, 27), (20, 25), (14, 5), (16, 27), (13, 16), (21, 19), (6, 20), (17, 10), (15, 22), (0, 25), (4, 18), (17, 7), (7, 9), (7, 19), (5, 11), (4, 8), (7, 15), (4, 22), (24, 8), (12, 1), (18, 14), (7, 6), (21, 16), (11, 17), (5, 24), (0, 20), (14, 9), (15, 25), (2, 8), (16, 3), (18, 16), (22, 1), (17, 24), (14, 24), (13, 3), (5, 9), (1, 4), (4, 27), (1, 24), (22, 18), (7, 20), (7, 23), (3, 26), (3, 14), (16, 1), (12, 9), (10, 13), (11, 23), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895856", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 6), (15, 12), (6, 2), (18, 20), (20, 24), (5, 7), (16, 17), (24, 0), (11, 6), (21, 4), (16, 12), (3, 20), (10, 5), (19, 5), (12, 2), (6, 20), (10, 2), (3, 19), (6, 16), (20, 18), (6, 5), (8, 4), (9, 17), (13, 8), (10, 20), (23, 14), (11, 16), (22, 0), (19, 7), (8, 19), (10, 6), (15, 20), (24, 21), (0, 11), (23, 2), (23, 0), (11, 12), (5, 15), (19, 12), (19, 15), (16, 10), (5, 24), (17, 6), (22, 10), (20, 14), (2, 11), (12, 6), (13, 2), (20, 20), (0, 22), (11, 22), (19, 10), (6, 21), (15, 8), (9, 4), (10, 1), (8, 17), (17, 1), (3, 1), (0, 5), (17, 20), (24, 1), (23, 15), (9, 20), (18, 8), (14, 12), (6, 17), (17, 21), (10, 4), (9, 12), (5, 13), (24, 2), (15, 22), (13, 10), (0, 19), (12, 23), (22, 7), (22, 1), (17, 24), (6, 18), (2, 0), (16, 13), (20, 15), (20, 9), (17, 4), (15, 14), (4, 1), (19, 16), (22, 19), (21, 15), (16, 3), (17, 19), (18, 7), (4, 20), (21, 18), (23, 9), (24, 12), (1, 8), (6, 24), (13, 12), (23, 8), (4, 18), (5, 9), (1, 0), (9, 14), (10, 21), (9, 1), (20, 6), (22, 9), (10, 7), (16, 4), (12, 14), (11, 19), (7, 13), (8, 5), (11, 17), (20, 17), (20, 7), (5, 19), (15, 3), (5, 5), (4, 13), (5, 14), (13, 7), (3, 5), (6, 13), (15, 16), (13, 20), (7, 8), (20, 23), (5, 0), (7, 16), (23, 10), (3, 3), (4, 9), (9, 0), (0, 17), (2, 7), (9, 13), (3, 17), (16, 15), (11, 13), (23, 17), (3, 24), (17, 10), (24, 4), (7, 10), (3, 16), (2, 21), (3, 18), (11, 3), (8, 24), (24, 5), (14, 1), (8, 3), (3, 4), (14, 9), (10, 10), (2, 13), (19, 21), (11, 14), (1, 14), (2, 18), (23, 6), (13, 11), (18, 13), (10, 16), (8, 21), (22, 16), (16, 14), (11, 9), (11, 4), (20, 16), (14, 14), (1, 23), (21, 21), (3, 13), (16, 9), (10, 13), (4, 22), (6, 15), (17, 13), (22, 2), (22, 14), (9, 23), (19, 8), (10, 23), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825930", "dataset": "MATH"}
{"messages": [{"content": "In a 22x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 24), 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), (16, 6), (1, 24), (21, 11), (1, 4), (11, 11), (1, 1), (4, 16), (12, 19), (13, 17), (1, 18), (11, 7), (19, 13), (4, 13), (14, 1), (13, 14), (18, 4), (17, 18), (19, 19), (0, 7), (3, 11), (20, 14), (20, 6), (18, 9), (14, 14), (10, 24), (5, 6), (16, 21), (11, 12), (13, 24), (4, 11), (11, 16), (3, 23), (13, 22), (5, 23), (20, 7), (2, 19), (8, 12), (11, 0), (9, 0), (17, 24), (14, 10), (0, 13), (20, 11), (11, 18), (21, 8), (14, 5), (8, 19), (6, 15), (3, 4), (18, 7), (14, 13), (4, 22), (6, 11), (2, 22), (12, 4), (3, 3), (1, 2), (9, 14), (21, 14), (5, 22), (3, 5), (0, 9), (19, 0), (5, 15), (0, 4), (18, 17), (3, 9), (17, 19), (11, 21), (8, 23), (6, 8), (11, 20), (19, 7), (18, 1), (16, 9), (15, 12), (4, 19), (6, 3), (2, 1), (8, 16), (16, 24), (13, 4), (11, 2), (5, 8), (3, 22), (19, 17), (20, 21), (12, 0), (0, 22), (11, 14), (0, 12), (19, 24), (12, 24), (15, 22), (16, 10), (2, 11), (21, 7), (5, 14), (2, 24), (13, 19), (10, 14), (7, 24), (8, 21), (9, 3), (3, 1), (7, 9), (21, 3), (1, 13), (7, 0), (3, 18), (11, 10), (14, 21), (8, 18), (4, 14), (21, 16), (11, 3), (6, 16), (14, 3), (10, 5), (13, 1), (4, 2), (18, 18), (19, 1), (12, 13), (17, 9), (5, 5), (5, 19), (9, 20), (19, 5), (1, 5), (4, 1), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779202", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), 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), (6, 24), (9, 16), (21, 11), (2, 7), (9, 10), (8, 12), (19, 12), (12, 11), (2, 14), (9, 3), (14, 0), (4, 21), (12, 13), (2, 9), (1, 26), (15, 23), (8, 4), (21, 18), (16, 5), (4, 17), (5, 6), (11, 16), (12, 15), (14, 10), (9, 19), (4, 4), (20, 17), (18, 14), (14, 12), (20, 27), (1, 27), (19, 14), (11, 8), (6, 6), (19, 25), (17, 23), (13, 13), (16, 3), (5, 22), (9, 23), (3, 11), (6, 7), (5, 5), (19, 20), (16, 20), (19, 0), (8, 18), (17, 15), (11, 3), (14, 21), (11, 4), (19, 18), (11, 21), (14, 3), (1, 2), (16, 9), (5, 15), (4, 26), (9, 0), (1, 15), (15, 15), (16, 10), (13, 12), (17, 2), (10, 12), (12, 9), (3, 8), (6, 26), (16, 22), (18, 12), (5, 1), (20, 18), (11, 13), (13, 0), (7, 23), (18, 18), (17, 24), (18, 24), (21, 14), (13, 7), (14, 27), (8, 22), (16, 6), (20, 22), (14, 20), (17, 3), (11, 2), (20, 7), (13, 1), (21, 10), (9, 11), (4, 14), (13, 4), (13, 20), (5, 14), (20, 10), (18, 26), (4, 9), (3, 0), (16, 4), (20, 12), (1, 6), (0, 16), (7, 21), (6, 20), (16, 7), (18, 20), (13, 26), (2, 26), (13, 18), (4, 1), (8, 16), (17, 16), (16, 8), (8, 17), (2, 5), (3, 25), (11, 7), (16, 27), (7, 9), (12, 12), (19, 9), (19, 22), (0, 9), (16, 25), (9, 9), (19, 26), (13, 11), (3, 9), (18, 15), (16, 24), (16, 19), (19, 15), (21, 0), (16, 13), (15, 27), (5, 11), (11, 12), (9, 27), (1, 23), (1, 25), (7, 11), (9, 17), (11, 25), (0, 17), (7, 10), (12, 4), (13, 19), (15, 17), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724656", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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), (4, 9), (22, 3), (20, 18), (16, 5), (0, 6), (8, 20), (19, 11), (6, 20), (0, 7), (16, 20), (3, 3), (13, 9), (1, 16), (15, 17), (0, 5), (3, 14), (6, 14), (2, 5), (17, 13), (8, 16), (8, 1), (1, 15), (14, 16), (7, 10), (22, 9), (11, 5), (13, 7), (20, 6), (5, 8), (10, 8), (2, 17), (2, 11), (23, 16), (17, 14), (9, 4), (10, 5), (14, 6), (7, 19), (6, 11), (9, 10), (23, 5), (13, 16), (3, 12), (19, 20), (8, 15), (11, 12), (13, 3), (10, 20), (6, 3), (16, 2), (19, 12), (18, 8), (12, 7), (14, 12), (16, 16), (14, 13), (23, 19), (14, 4), (5, 9), (14, 18), (17, 19), (4, 16), (23, 14), (16, 8), (18, 18), (5, 1), (16, 17), (12, 17), (17, 9), (18, 12), (15, 10), (10, 19), (10, 4), (20, 20), (12, 4), (15, 19), (8, 5), (18, 1), (14, 10), (20, 2), (0, 20), (1, 10), (20, 8), (2, 10), (11, 19), (6, 9), (8, 8), (2, 18), (7, 15), (7, 9), (23, 18), (5, 13), (21, 11), (0, 17), (1, 12), (18, 2), (21, 8), (6, 12), (15, 2), (7, 13), (17, 4), (23, 0), (13, 2), (7, 11), (22, 2), (17, 5), (11, 17), (21, 3), (20, 19), (10, 3), (9, 2), (4, 1), (22, 5), (8, 2), (21, 1), (6, 1), (22, 10), (11, 18), (9, 15), (19, 13), (14, 2), (10, 13), (7, 14), (9, 5), (10, 7), (19, 9), (15, 8), (10, 2), (19, 8), (11, 20), (14, 9), (2, 7), (23, 7), (19, 2), (2, 8), (22, 14), (7, 8), (14, 3), (2, 15), (16, 11), (14, 1), (7, 17), (20, 13), (0, 1), (21, 19), (23, 3), (3, 10), (1, 20), (13, 15), (23, 13), (8, 19), (11, 11), (18, 13), (2, 20), (0, 12), (3, 19), (6, 6), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228528", "dataset": "MATH"}
{"messages": [{"content": "In a 21x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 19), 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), (1, 9), (7, 19), (7, 0), (11, 18), (1, 11), (4, 10), (5, 12), (7, 7), (14, 3), (15, 0), (16, 17), (1, 15), (17, 15), (8, 19), (12, 13), (20, 1), (3, 10), (6, 8), (3, 16), (12, 9), (13, 17), (4, 7), (11, 13), (0, 4), (18, 1), (13, 14), (19, 15), (17, 8), (18, 13), (16, 9), (3, 6), (6, 5), (0, 5), (20, 9), (9, 0), (11, 17), (18, 17), (10, 11), (2, 4), (14, 19), (20, 14), (14, 9), (11, 9), (3, 11), (2, 6), (5, 18), (20, 17), (8, 6), (4, 6), (14, 5), (10, 10), (1, 13), (20, 0), (1, 17), (0, 17), (8, 8), (0, 18), (10, 4), (19, 18), (16, 11), (7, 1), (19, 14), (3, 9), (7, 8), (1, 2), (11, 7), (4, 2), (17, 10), (17, 5), (15, 11), (3, 14), (14, 0), (6, 18), (13, 8), (5, 14), (18, 11), (11, 10), (17, 18), (4, 13), (7, 5), (11, 4), (3, 2), (0, 15), (16, 6), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "621712", "dataset": "MATH"}
{"messages": [{"content": "In a 28x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 18), (23, 27), (20, 22), (18, 19), (19, 2), (18, 15), (5, 23), (3, 9), (12, 24), (25, 24), (5, 21), (21, 26), (12, 28), (4, 1), (3, 11), (10, 5), (12, 10), (15, 4), (27, 15), (14, 1), (13, 24), (13, 20), (12, 17), (24, 18), (10, 27), (14, 10), (0, 3), (7, 13), (3, 4), (11, 25), (14, 19), (19, 19), (25, 0), (21, 8), (21, 0), (25, 6), (24, 17), (2, 2), (9, 5), (12, 19), (1, 3), (19, 4), (7, 3), (14, 15), (17, 26), (24, 22), (25, 10), (13, 5), (13, 21), (0, 2), (10, 10), (6, 15), (1, 23), (7, 9), (26, 16), (13, 22), (13, 9), (5, 16), (13, 10), (20, 18), (8, 24), (10, 26), (15, 27), (6, 26), (26, 11), (23, 5), (6, 27), (20, 8), (8, 14), (25, 13), (1, 1), (27, 27), (1, 4), (10, 16), (15, 9), (18, 26), (14, 22), (2, 19), (4, 16), (3, 19), (10, 3), (4, 15), (24, 4), (16, 18), (0, 24), (21, 23), (17, 7), (4, 3), (8, 4), (21, 13), (17, 20), (15, 10), (26, 19), (17, 6), (2, 17), (21, 19), (23, 20), (11, 20), (11, 10), (0, 21), (22, 13), (3, 10), (24, 6), (18, 12), (23, 0), (11, 21), (27, 17), (8, 13), (22, 19), (3, 14), (2, 21), (26, 27), (9, 18), (4, 6), (27, 16), (16, 25), (19, 22), (16, 0), (14, 16), (20, 21), (14, 2), (0, 16), (9, 16), (2, 11), (23, 14), (23, 4), (10, 21), (10, 1), (21, 25), (4, 2), (26, 6), (14, 21), (2, 27), (16, 1), (17, 22), (20, 0), (23, 19), (11, 13), (20, 10), (8, 11), (23, 24), (9, 19), (24, 21), (9, 23), (3, 7), (27, 14), (6, 6), (27, 24), (26, 14), (8, 1), (24, 8), (3, 3), (13, 2), (7, 16), (18, 18), (14, 3), (24, 7), (3, 6), (20, 25), (5, 17), (21, 3), (15, 7), (7, 1), (2, 20), (13, 25), (8, 0), (24, 11), (1, 19), (27, 4), (22, 25), (2, 6), (4, 25), (1, 15), (8, 8), (18, 20), (24, 5), (22, 12), (15, 25), (24, 0), (14, 8), (10, 7), (22, 2), (21, 5), (21, 11), (9, 17), (23, 17), (0, 15), (8, 6), (16, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494412", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 24), (15, 11), (10, 20), (12, 2), (3, 14), (13, 0), (18, 13), (14, 19), (12, 25), (17, 13), (2, 16), (11, 14), (15, 20), (11, 21), (23, 18), (7, 7), (8, 21), (18, 15), (22, 10), (22, 15), (2, 7), (9, 26), (11, 12), (14, 9), (5, 10), (20, 17), (3, 26), (7, 9), (23, 19), (22, 3), (10, 14), (14, 8), (4, 10), (6, 6), (4, 24), (19, 11), (11, 22), (21, 10), (6, 18), (13, 20), (21, 18), (2, 14), (15, 10), (4, 5), (14, 21), (9, 18), (5, 14), (2, 19), (19, 20), (13, 8), (18, 18), (17, 10), (20, 4), (4, 0), (10, 1), (12, 21), (1, 23), (14, 13), (8, 18), (17, 15), (10, 26), (3, 15), (6, 25), (15, 21), (15, 1), (3, 13), (23, 22), (13, 3), (19, 3), (22, 26), (22, 0), (6, 24), (19, 26), (7, 2), (2, 3), (7, 16), (10, 19), (21, 9), (8, 26), (1, 16), (16, 4), (2, 9), (5, 11), (16, 26), (13, 21), (10, 8), (0, 14), (22, 12), (3, 23), (7, 12), (5, 19), (0, 1), (14, 17), (9, 19), (14, 14), (12, 7), (14, 10), (17, 3), (23, 15), (0, 6), (17, 25), (15, 16), (7, 23), (11, 17), (16, 24), (6, 19), (15, 9), (22, 5), (14, 12), (5, 7), (22, 24), (21, 12), (17, 21), (7, 24), (3, 18), (16, 7), (11, 3), (18, 6), (1, 3), (18, 0), (5, 24), (11, 6), (16, 18), (15, 25), (13, 24), (15, 4), (3, 4), (2, 18), (16, 9), (4, 22), (5, 4), (5, 6), (10, 21), (2, 17), (0, 24), (8, 17), (11, 8), (19, 23), (0, 23), (23, 2), (21, 23), (14, 7), (14, 2), (8, 23), (23, 13), (18, 16), (6, 17), (9, 21), (15, 14), (23, 23), (2, 15), (11, 0), (12, 26), (16, 16), (2, 20), (4, 25), (11, 15), (7, 22), (14, 26), (22, 9), (12, 18), (17, 9), (7, 4), (22, 6), (13, 2), (14, 0), (1, 10), (0, 7), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "668172", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (0, 12), (7, 7), (1, 4), (10, 9), (3, 10), (7, 12), (8, 1), (4, 23), (1, 9), (19, 1), (1, 13), (7, 5), (17, 2), (0, 11), (0, 1), (13, 19), (19, 24), (15, 4), (13, 18), (1, 17), (4, 13), (2, 9), (17, 4), (17, 7), (15, 9), (9, 21), (1, 24), (13, 20), (5, 5), (13, 10), (16, 21), (0, 18), (6, 10), (19, 0), (12, 22), (13, 22), (0, 4), (16, 20), (5, 23), (13, 11), (18, 15), (11, 15), (4, 1), (15, 17), (5, 16), (9, 15), (15, 10), (13, 13), (18, 2), (4, 20), (7, 21), (13, 7), (8, 14), (12, 0), (13, 23), (17, 5), (18, 11), (3, 7), (17, 3), (18, 10), (18, 12), (3, 4), (10, 10), (18, 24), (2, 23), (5, 12), (2, 19), (6, 6), (20, 22), (19, 8), (6, 13), (8, 3), (5, 19), (19, 2), (16, 5), (19, 13), (7, 1), (4, 15), (10, 15), (0, 23), (16, 23), (5, 18), (7, 8), (4, 6), (4, 3), (6, 22), (10, 22), (17, 19), (2, 11), (7, 10), (13, 9), (10, 14), (9, 12), (3, 20), (20, 7), (14, 20), (9, 20), (20, 10), (11, 2), (8, 9), (13, 21), (17, 16), (11, 21), (20, 14), (4, 17), (17, 1), (8, 4), (9, 1), (2, 22), (20, 21), (5, 25), (7, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284891", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (0, 8), (15, 14), (18, 11), (8, 7), (16, 20), (9, 20), (0, 2), (16, 18), (17, 2), (12, 0), (11, 7), (8, 0), (6, 11), (7, 19), (13, 16), (6, 1), (20, 9), (1, 6), (20, 5), (8, 20), (12, 4), (10, 6), (10, 8), (17, 5), (6, 16), (0, 18), (8, 4), (18, 1), (3, 1), (7, 2), (11, 20), (13, 7), (16, 4), (21, 11), (5, 9), (1, 9), (15, 1), (20, 8), (10, 1), (13, 2), (12, 1), (19, 9), (17, 16), (2, 15), (7, 10), (18, 17), (7, 14), (10, 14), (18, 7), (18, 20), (4, 18), (4, 20), (7, 6), (15, 20), (15, 10), (13, 0), (8, 9), (2, 4), (11, 8), (16, 16), (8, 13), (21, 10), (22, 5), (9, 15), (6, 17), (3, 18), (16, 1), (4, 8), (15, 13), (3, 10), (22, 9), (6, 20), (14, 17), (3, 13), (1, 12), (21, 5), (10, 5), (2, 20), (20, 15), (4, 4), (15, 18), (13, 19), (22, 8), (9, 16), (2, 10), (12, 7), (19, 18), (14, 4), (20, 12), (9, 6), (19, 6), (18, 0), (9, 4), (8, 17), (20, 16), (21, 16), (13, 12), (9, 1), (19, 20), (16, 12), (11, 6), (2, 1), (3, 4), (15, 3), (19, 12), (20, 0), (9, 17), (12, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "421626", "dataset": "MATH"}
{"messages": [{"content": "In a 26x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 28), 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), (5, 24), (24, 5), (20, 1), (10, 16), (6, 7), (9, 27), (6, 18), (5, 12), (3, 4), (19, 21), (2, 28), (8, 7), (25, 6), (25, 24), (14, 0), (17, 18), (7, 15), (6, 24), (3, 24), (3, 19), (1, 4), (25, 7), (23, 4), (14, 27), (7, 25), (18, 24), (5, 18), (20, 4), (13, 7), (0, 17), (20, 28), (20, 12), (13, 4), (20, 0), (17, 13), (16, 13), (10, 21), (13, 23), (15, 26), (3, 12), (22, 26), (17, 27), (16, 7), (17, 5), (23, 11), (2, 2), (11, 4), (2, 19), (17, 25), (17, 8), (20, 26), (21, 7), (21, 11), (23, 25), (14, 12), (12, 20), (0, 3), (17, 1), (11, 23), (25, 2), (17, 11), (8, 24), (23, 17), (10, 23), (4, 28), (12, 11), (13, 10), (7, 1), (15, 18), (1, 0), (15, 14), (8, 27), (14, 4), (13, 20), (24, 10), (18, 27), (19, 6), (14, 19), (2, 26), (23, 13), (22, 20), (15, 4), (17, 19), (22, 19), (12, 12), (21, 6), (4, 23), (25, 12), (16, 4), (23, 20), (15, 1), (10, 24), (14, 10), (10, 1), (1, 14), (7, 9), (4, 15), (22, 18), (7, 12), (2, 10), (12, 22), (24, 22), (7, 24), (7, 2), (6, 5), (3, 22), (13, 24), (2, 12), (11, 24), (10, 10), (13, 22), (17, 12), (2, 6), (10, 3), (24, 20), (0, 24), (6, 2), (23, 8), (1, 15), (9, 9), (5, 23), (23, 2), (9, 18), (25, 27), (4, 1), (10, 5), (9, 3), (20, 14), (18, 6), (12, 1), (4, 6), (9, 6), (7, 5), (11, 26), (0, 7), (4, 9), (4, 3), (8, 9), (4, 13), (22, 25), (8, 1), (16, 17), (19, 10), (17, 28), (25, 25), (25, 10), (0, 6), (10, 18), (21, 5), (17, 26), (1, 10), (19, 28), (23, 15), (13, 0), (17, 23), (4, 12), (13, 19), (12, 6), (19, 0), (25, 15), (17, 3), (11, 28), (22, 9), (19, 7), (8, 14), (4, 16), (10, 27), (18, 1), (5, 10), (22, 14), (4, 10), (21, 21), (25, 4), (23, 7), (14, 16), (8, 10), (11, 15), (19, 2), (3, 21), (18, 0), (20, 2), (7, 14), (3, 10), (18, 14), (17, 9), (1, 26), (21, 25), (23, 0), (8, 28), (14, 20), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "808328", "dataset": "MATH"}
{"messages": [{"content": "In a 29x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (20, 3), (19, 12), (21, 13), (0, 10), (20, 19), (17, 0), (21, 10), (11, 10), (11, 16), (28, 13), (11, 14), (22, 20), (9, 8), (3, 12), (22, 0), (28, 5), (26, 1), (17, 16), (28, 14), (24, 6), (11, 5), (7, 20), (24, 20), (23, 4), (11, 7), (23, 16), (17, 17), (20, 8), (8, 10), (6, 3), (13, 4), (27, 4), (12, 1), (5, 19), (17, 19), (1, 0), (18, 3), (12, 12), (13, 12), (12, 0), (14, 16), (20, 5), (11, 1), (4, 11), (8, 16), (4, 6), (21, 12), (16, 11), (18, 9), (25, 17), (12, 19), (1, 1), (18, 10), (19, 6), (15, 6), (26, 18), (19, 4), (14, 7), (19, 13), (26, 19), (12, 16), (14, 14), (5, 16), (20, 12), (18, 13), (6, 14), (20, 15), (13, 14), (2, 20), (16, 16), (0, 3), (8, 11), (16, 0), (21, 4), (21, 5), (13, 0), (27, 1), (13, 18), (11, 4), (9, 18), (1, 20), (6, 6), (12, 8), (2, 4), (24, 5), (23, 15), (6, 1), (7, 12), (8, 3), (4, 3), (6, 11), (16, 20), (11, 15), (12, 10), (21, 0), (9, 12), (28, 3), (13, 9), (8, 7), (20, 1), (16, 21), (24, 14), (27, 2), (1, 11), (20, 18), (16, 7), (28, 20), (8, 9), (4, 8), (14, 18), (22, 3), (24, 11), (9, 2), (12, 5), (2, 6), (26, 8), (17, 14), (16, 6), (22, 12), (25, 21), (25, 10), (11, 8), (25, 11), (22, 21), (25, 18), (3, 17), (6, 8), (15, 3), (28, 2), (24, 2), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694592", "dataset": "MATH"}
{"messages": [{"content": "In a 21x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (20, 25), 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), (5, 21), (1, 13), (1, 4), (0, 7), (1, 25), (20, 3), (11, 9), (16, 5), (10, 10), (15, 0), (9, 2), (7, 14), (8, 8), (7, 23), (2, 25), (3, 15), (6, 19), (13, 22), (20, 13), (17, 19), (14, 0), (12, 7), (6, 1), (10, 21), (2, 4), (3, 6), (10, 2), (17, 12), (8, 18), (4, 17), (0, 3), (17, 17), (13, 4), (12, 2), (19, 18), (15, 14), (6, 14), (12, 20), (18, 10), (4, 4), (5, 0), (12, 23), (2, 16), (12, 0), (1, 5), (20, 15), (3, 7), (14, 7), (11, 17), (17, 1), (6, 21), (5, 1), (6, 23), (16, 18), (15, 10), (7, 3), (14, 8), (16, 13), (3, 0), (14, 10), (8, 4), (18, 12), (14, 1), (6, 3), (1, 17), (19, 12), (15, 13), (10, 24), (15, 7), (9, 11), (10, 6), (11, 25), (14, 2), (11, 20), (20, 21), (0, 21), (9, 13), (2, 13), (19, 2), (17, 13), (13, 2), (7, 24), (11, 21), (3, 18), (9, 18), (13, 11), (0, 15), (19, 3), (10, 18), (6, 18), (13, 24), (7, 25), (4, 10), (18, 8), (0, 8), (14, 19), (18, 15), (0, 4), (5, 13), (13, 6), (19, 7), (8, 19), (20, 4), (7, 9), (10, 13), (20, 17), (10, 14), (8, 2), (19, 16), (2, 2), (10, 5), (5, 23), (12, 12), (8, 7), (15, 15), (18, 0), (12, 18), (3, 14), (15, 17), (5, 8), (12, 1), (17, 6), (10, 23), (15, 3), (11, 5), (17, 23), (14, 12), (17, 14), (5, 11), (16, 20), (9, 21), (8, 22), (17, 2), (7, 12), (4, 23), (13, 17), (13, 8), (4, 22), (8, 20), (14, 14), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417600", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 15), (9, 4), (9, 10), (15, 7), (17, 4), (24, 9), (20, 6), (19, 2), (13, 1), (4, 20), (2, 17), (18, 9), (26, 16), (17, 14), (14, 18), (13, 4), (22, 1), (11, 7), (25, 21), (5, 0), (2, 12), (1, 9), (17, 20), (21, 16), (26, 19), (25, 3), (18, 3), (10, 13), (9, 21), (2, 4), (25, 19), (8, 17), (22, 0), (14, 0), (23, 5), (11, 5), (12, 14), (3, 4), (21, 4), (24, 5), (5, 7), (6, 2), (17, 2), (25, 6), (0, 14), (11, 9), (23, 7), (27, 19), (21, 19), (19, 19), (12, 7), (10, 14), (0, 2), (13, 17), (7, 10), (14, 17), (0, 8), (2, 11), (1, 15), (11, 0), (1, 12), (4, 13), (14, 1), (14, 13), (10, 7), (10, 10), (7, 19), (13, 5), (17, 18), (2, 18), (14, 20), (7, 17), (22, 18), (5, 3), (16, 12), (25, 2), (0, 16), (27, 3), (21, 12), (24, 8), (8, 3), (8, 11), (9, 13), (17, 3), (10, 4), (9, 18), (15, 15), (19, 17), (11, 17), (11, 8), (12, 9), (11, 6), (21, 8), (15, 5), (5, 9), (7, 13), (27, 12), (0, 5), (9, 11), (0, 13), (24, 10), (6, 1), (13, 7), (20, 12), (21, 21), (8, 5), (2, 21), (0, 6), (8, 18), (25, 12), (7, 16), (22, 19), (15, 16), (23, 17), (2, 1), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "669552", "dataset": "MATH"}
{"messages": [{"content": "In a 24x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 6), (4, 10), (17, 27), (19, 16), (19, 14), (18, 12), (12, 16), (6, 21), (6, 6), (12, 3), (21, 9), (11, 6), (16, 7), (13, 19), (7, 19), (4, 1), (19, 6), (10, 19), (12, 27), (1, 15), (10, 16), (4, 25), (23, 16), (23, 12), (9, 12), (21, 12), (8, 24), (7, 21), (8, 7), (9, 26), (22, 5), (15, 6), (11, 17), (14, 8), (3, 7), (20, 11), (8, 0), (14, 20), (10, 10), (5, 14), (8, 3), (23, 8), (11, 20), (8, 2), (11, 4), (4, 4), (20, 14), (19, 0), (11, 9), (18, 24), (9, 14), (2, 20), (8, 5), (1, 4), (13, 14), (20, 20), (9, 9), (5, 8), (18, 22), (7, 16), (1, 3), (10, 1), (3, 23), (17, 25), (1, 12), (23, 1), (11, 15), (11, 12), (6, 10), (10, 5), (12, 23), (2, 23), (21, 4), (20, 15), (7, 2), (7, 0), (7, 3), (10, 12), (18, 7), (16, 27), (14, 3), (2, 6), (5, 27), (22, 12), (4, 22), (11, 7), (1, 1), (18, 1), (23, 9), (23, 10), (11, 11), (12, 14), (3, 19), (7, 23), (9, 23), (7, 24), (16, 15), (5, 0), (10, 25), (18, 13), (0, 22), (11, 8), (3, 11), (19, 10), (10, 23), (9, 27), (0, 1), (5, 23), (10, 13), (7, 12), (9, 1), (23, 11), (23, 0), (14, 25), (22, 25), (17, 20), (8, 25), (5, 17), (2, 27), (23, 26), (4, 17), (3, 17), (16, 24), (4, 3), (18, 3), (17, 16), (21, 3), (14, 7), (19, 25), (1, 23), (6, 12), (2, 8), (14, 24), (8, 8), (23, 14), (20, 0), (4, 16), (13, 16), (1, 21), (15, 15), (18, 23), (19, 8), (5, 19), (2, 7), (20, 6), (7, 4), (8, 10), (17, 1), (5, 22), (16, 0), (13, 4), (6, 16), (15, 12), (9, 8), (16, 23), (14, 16), (16, 1), (22, 17), (18, 16), (8, 21), (8, 17), (1, 17), (0, 19), (2, 16), (4, 23), (0, 13), (10, 6), (8, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744861", "dataset": "MATH"}
{"messages": [{"content": "In a 26x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (25, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 3), (21, 0), (7, 2), (17, 3), (16, 5), (1, 6), (23, 6), (6, 2), (2, 14), (18, 15), (17, 15), (16, 10), (20, 13), (15, 4), (17, 8), (13, 8), (11, 0), (12, 6), (2, 20), (0, 13), (24, 11), (17, 16), (8, 12), (4, 13), (21, 10), (12, 11), (2, 12), (16, 6), (8, 18), (8, 8), (11, 12), (22, 5), (13, 16), (12, 9), (0, 10), (7, 17), (1, 7), (25, 19), (24, 7), (1, 18), (17, 2), (6, 15), (0, 11), (11, 4), (0, 5), (9, 17), (6, 13), (16, 19), (9, 1), (1, 0), (14, 12), (5, 5), (6, 20), (5, 11), (6, 14), (0, 2), (2, 1), (22, 16), (14, 19), (15, 1), (14, 1), (1, 19), (14, 8), (15, 11), (1, 3), (0, 16), (19, 1), (11, 7), (8, 19), (5, 12), (11, 17), (15, 14), (10, 2), (20, 17), (3, 13), (16, 11), (6, 5), (8, 20), (16, 3), (20, 14), (3, 0), (4, 4), (23, 5), (7, 19), (7, 4), (3, 12), (12, 12), (25, 9), (1, 9), (25, 4), (18, 5), (9, 6), (23, 14), (5, 3), (15, 18), (1, 12), (10, 7), (4, 12), (4, 19), (19, 13), (2, 16), (1, 20), (9, 8), (20, 10), (18, 20), (1, 4), (20, 12), (18, 16), (23, 11), (6, 10), (15, 10), (25, 15), (13, 18), (25, 16), (24, 10), (7, 1), (14, 6), (5, 18), (8, 9), (22, 7), (23, 9), (0, 19), (13, 6), (20, 6), (4, 2), (15, 6), (13, 2), (10, 20), (5, 14), (9, 5), (22, 4), (16, 4), (21, 4), (16, 13), (19, 4), (25, 14), (22, 19), (14, 20), (24, 6), (23, 20), (6, 6), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971040", "dataset": "MATH"}
{"messages": [{"content": "In a 25x26 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 25), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 13), (6, 14), (18, 10), (4, 18), (23, 5), (8, 12), (5, 15), (19, 6), (1, 24), (23, 2), (12, 12), (8, 23), (18, 24), (9, 16), (5, 3), (5, 12), (17, 22), (1, 22), (21, 6), (20, 9), (12, 24), (22, 8), (23, 10), (17, 7), (22, 19), (18, 7), (4, 13), (10, 5), (4, 2), (0, 19), (20, 21), (5, 10), (6, 18), (24, 7), (7, 8), (13, 1), (13, 6), (23, 21), (3, 11), (23, 13), (12, 15), (7, 25), (12, 3), (4, 12), (19, 23), (8, 15), (7, 18), (14, 10), (18, 16), (11, 13), (23, 11), (12, 0), (4, 5), (7, 9), (2, 20), (11, 10), (21, 14), (13, 16), (11, 16), (23, 8), (22, 3), (4, 6), (18, 0), (10, 9), (0, 18), (6, 13), (24, 6), (13, 19), (21, 22), (0, 2), (11, 9), (13, 0), (10, 14), (24, 4), (10, 23), (0, 12), (0, 22), (2, 25), (12, 22), (24, 14), (17, 2), (15, 21), (24, 16), (8, 5), (21, 5), (1, 23), (3, 4), (2, 23), (21, 23), (24, 13), (12, 14), (16, 21), (19, 0), (21, 2), (17, 0), (22, 18), (18, 4), (14, 14), (0, 25), (4, 23), (1, 14), (13, 24), (16, 16), (4, 21), (14, 24), (8, 11), (13, 22), (6, 9), (6, 6), (15, 17), (20, 18), (18, 11), (18, 20), (2, 13), (24, 3), (12, 21), (19, 24), (5, 1), (8, 7), (7, 16), (1, 6), (10, 22), (18, 1), (21, 11), (22, 4), (5, 0), (1, 12), (9, 4), (21, 20), (3, 9), (19, 15), (14, 17), (11, 23), (1, 17), (19, 2), (0, 15), (14, 8), (8, 17), (4, 17), (17, 24), (16, 22), (13, 23), (0, 23), (3, 22), (13, 11), (6, 24), (0, 11), (17, 3), (20, 4), (14, 16), (17, 10), (10, 11), (9, 17), (10, 0), (9, 24), (1, 4), (9, 21), (5, 6), (23, 3), (11, 0), (13, 2), (6, 12), (21, 7), (5, 22), (6, 0), (7, 22), (16, 7), (1, 15), (7, 10), (18, 17), (24, 1), (18, 9), (19, 19), (8, 14), (19, 21), (10, 1), (23, 12), (15, 1), (16, 19), (5, 24), (9, 19), (4, 25), (18, 18), (21, 3), (16, 12), (9, 18), (3, 23), (23, 25), (17, 18), (7, 12), (9, 22), (22, 16), (10, 2), (15, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915102", "dataset": "MATH"}
{"messages": [{"content": "In a 29x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 15), (26, 25), (14, 17), (4, 17), (20, 9), (27, 22), (9, 13), (7, 20), (26, 14), (17, 9), (8, 26), (15, 17), (4, 8), (1, 7), (13, 14), (15, 8), (4, 15), (2, 14), (21, 27), (10, 14), (6, 25), (22, 22), (25, 2), (9, 14), (27, 20), (14, 25), (19, 20), (11, 23), (0, 12), (2, 1), (9, 23), (12, 18), (0, 11), (23, 1), (16, 25), (3, 1), (6, 5), (18, 24), (1, 4), (10, 4), (2, 13), (17, 7), (27, 9), (8, 19), (18, 3), (18, 25), (19, 9), (23, 6), (7, 10), (8, 5), (0, 6), (22, 3), (19, 2), (20, 23), (11, 11), (15, 25), (12, 13), (28, 3), (11, 6), (18, 12), (4, 3), (22, 14), (7, 19), (3, 10), (6, 9), (23, 2), (1, 5), (5, 25), (22, 17), (16, 26), (1, 19), (10, 22), (27, 8), (18, 7), (14, 20), (20, 3), (9, 7), (28, 14), (4, 19), (9, 27), (18, 18), (4, 27), (21, 11), (14, 11), (26, 20), (10, 18), (26, 10), (16, 3), (19, 1), (19, 27), (6, 26), (4, 18), (28, 21), (15, 13), (7, 13), (12, 24), (25, 6), (21, 24), (28, 13), (22, 2), (12, 27), (7, 22), (1, 2), (25, 15), (25, 14), (11, 4), (26, 2), (23, 3), (1, 20), (0, 8), (12, 19), (2, 27), (6, 11), (15, 6), (16, 21), (15, 0), (1, 13), (13, 10), (12, 22), (21, 3), (24, 20), (5, 22), (22, 12), (17, 15), (27, 15), (3, 18), (11, 19), (14, 27), (14, 8), (10, 21), (26, 23), (9, 20), (12, 10), (9, 25), (8, 20), (17, 22), (7, 6), (17, 11), (23, 27), (8, 15), (1, 12), (25, 26), (10, 9), (2, 10), (13, 22), (6, 15), (12, 23), (16, 2), (5, 11), (3, 17), (20, 16), (13, 12), (6, 1), (2, 24), (26, 18), (15, 1), (25, 21), (20, 1), (19, 13), (18, 10), (4, 11), (6, 21), (6, 19), (8, 10), (10, 23), (13, 15), (6, 14), (0, 1), (26, 26), (5, 14), (16, 12), (27, 23), (21, 14), (22, 16), (2, 8), (7, 0), (2, 2), (11, 12), (17, 5), (16, 9), (2, 23), (25, 4), (9, 17), (28, 5), (10, 5), (25, 19), (9, 8), (7, 7), (5, 10), (7, 23), (3, 16), (26, 22), (10, 24), (19, 0), (10, 15), (20, 26), (28, 10), (12, 1), (10, 10), (11, 10), (9, 2), (24, 6), (28, 2), (28, 6), (0, 16), (4, 22), (10, 3), (16, 0), (21, 23), (24, 21), (3, 8), (7, 12), (4, 23), (14, 1), (9, 19), (19, 11), (24, 9), (8, 21), (21, 5), (3, 3), (12, 12), (16, 19), (14, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948942", "dataset": "MATH"}
{"messages": [{"content": "In a 24x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 20), 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), (20, 16), (3, 0), (19, 16), (11, 5), (12, 16), (3, 10), (23, 18), (8, 10), (11, 8), (20, 8), (1, 4), (10, 3), (22, 18), (20, 10), (9, 4), (7, 13), (12, 14), (15, 20), (17, 0), (4, 3), (14, 9), (6, 7), (6, 14), (15, 13), (17, 13), (11, 3), (6, 10), (21, 9), (19, 6), (0, 4), (23, 4), (0, 18), (16, 10), (19, 3), (7, 6), (2, 10), (9, 14), (18, 16), (23, 9), (8, 18), (23, 16), (2, 1), (19, 2), (2, 16), (5, 8), (10, 7), (5, 19), (2, 9), (10, 12), (9, 2), (1, 19), (3, 13), (17, 20), (17, 10), (20, 5), (20, 6), (19, 10), (0, 8), (11, 7), (6, 8), (5, 20), (12, 19), (18, 4), (15, 11), (4, 11), (21, 10), (18, 3), (22, 10), (13, 10), (18, 17), (2, 14), (7, 4), (19, 18), (18, 18), (22, 1), (8, 17), (14, 19), (17, 11), (9, 20), (10, 15), (21, 18), (13, 3), (9, 8), (20, 12), (1, 6), (7, 0), (11, 19), (16, 1), (22, 11), (8, 13), (16, 3), (1, 14), (15, 19), (16, 0), (16, 8), (13, 14), (11, 13), (4, 6), (22, 17), (13, 17), (7, 14), (23, 1), (14, 3), (5, 18), (3, 8), (4, 10), (18, 14), (8, 5), (14, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183312", "dataset": "MATH"}
{"messages": [{"content": "In a 24x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 26), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 7), (22, 15), (14, 22), (1, 9), (6, 13), (0, 16), (17, 2), (9, 6), (15, 23), (22, 16), (5, 26), (3, 18), (1, 12), (18, 25), (11, 14), (5, 14), (21, 17), (17, 17), (2, 8), (20, 25), (2, 9), (15, 26), (17, 6), (3, 9), (0, 23), (17, 18), (11, 5), (15, 12), (1, 1), (3, 14), (1, 11), (16, 6), (17, 22), (22, 23), (21, 19), (15, 13), (15, 15), (6, 12), (18, 24), (2, 18), (19, 11), (4, 3), (15, 24), (22, 2), (0, 3), (4, 19), (20, 10), (3, 20), (15, 11), (7, 13), (1, 10), (19, 16), (21, 3), (6, 5), (19, 10), (11, 26), (2, 7), (8, 17), (10, 11), (1, 7), (0, 12), (15, 18), (9, 15), (10, 4), (18, 18), (20, 16), (20, 1), (11, 6), (22, 10), (18, 7), (12, 23), (20, 24), (20, 11), (20, 15), (5, 24), (14, 25), (19, 24), (18, 13), (7, 25), (2, 26), (1, 21), (13, 23), (13, 15), (2, 19), (4, 5), (2, 6), (10, 16), (12, 25), (3, 5), (11, 23), (13, 3), (16, 3), (13, 5), (1, 24), (6, 19), (5, 8), (3, 7), (17, 24), (12, 12), (7, 11), (9, 7), (6, 16), (0, 5), (20, 14), (14, 21), (21, 1), (15, 0), (6, 7), (16, 23), (22, 20), (9, 8), (22, 5), (5, 4), (5, 17), (7, 14), (12, 15), (21, 16), (8, 5), (0, 4), (13, 4), (18, 11), (7, 4), (14, 9), (19, 8), (4, 23), (1, 4), (17, 20), (5, 16), (15, 25), (10, 15), (4, 12), (1, 14), (6, 0), (0, 1), (13, 11), (11, 1), (22, 18), (7, 0), (23, 21), (7, 20), (17, 14), (23, 0), (12, 21), (16, 1), (13, 25), (10, 3), (16, 0), (2, 4), (20, 26), (19, 13), (1, 26), (17, 13), (13, 8), (23, 1), (7, 6), (12, 22), (23, 25), (1, 22), (17, 7), (1, 15), (6, 6), (8, 19), (16, 19), (3, 25), (0, 8), (12, 20), (5, 5), (7, 15), (0, 25), (2, 23), (20, 20), (21, 13), (20, 8), (23, 23), (12, 7), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789720", "dataset": "MATH"}
{"messages": [{"content": "In a 24x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (23, 21), 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), (19, 15), (15, 0), (7, 10), (21, 5), (8, 1), (9, 9), (6, 7), (9, 8), (6, 2), (13, 6), (8, 10), (19, 1), (6, 8), (17, 2), (5, 17), (7, 9), (19, 11), (14, 21), (18, 4), (16, 10), (5, 20), (7, 8), (11, 15), (12, 18), (5, 21), (8, 2), (14, 19), (14, 10), (18, 21), (3, 19), (9, 17), (17, 8), (14, 14), (16, 1), (1, 15), (18, 9), (10, 20), (16, 6), (19, 8), (13, 9), (18, 18), (21, 4), (3, 10), (14, 7), (15, 6), (2, 6), (10, 1), (12, 8), (22, 5), (23, 15), (8, 6), (0, 10), (7, 7), (12, 12), (11, 17), (14, 4), (10, 6), (3, 8), (17, 13), (8, 14), (18, 17), (21, 14), (8, 9), (4, 13), (23, 14), (23, 3), (13, 14), (18, 10), (16, 19), (3, 11), (0, 8), (3, 5), (6, 20), (4, 4), (15, 9), (23, 13), (6, 10), (17, 19), (18, 6), (6, 3), (2, 13), (9, 1), (8, 15), (23, 2), (12, 3), (22, 9), (9, 14), (19, 12), (18, 19), (23, 16), (14, 0), (11, 12), (0, 6), (14, 20), (6, 19), (20, 2), (23, 17), (15, 1), (8, 19), (3, 6), (15, 15), (0, 2), (10, 5), (6, 1), (22, 21), (8, 21), (13, 13), (4, 0), (19, 18), (21, 17), (14, 6), (11, 10), (23, 4), (22, 15), (4, 10), (21, 13), (21, 20), (1, 8), (12, 21), (7, 4), (4, 18), (8, 18), (15, 8), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497297", "dataset": "MATH"}
{"messages": [{"content": "In a 25x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 28), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 22), (13, 8), (21, 10), (4, 23), (23, 18), (12, 12), (11, 7), (24, 7), (7, 25), (20, 0), (0, 17), (5, 23), (5, 14), (3, 2), (7, 22), (20, 24), (13, 16), (1, 5), (14, 10), (20, 17), (24, 22), (9, 15), (13, 23), (5, 25), (24, 4), (5, 6), (7, 13), (3, 24), (21, 8), (18, 0), (1, 16), (9, 28), (23, 1), (2, 3), (14, 8), (5, 3), (3, 9), (13, 9), (19, 21), (7, 28), (0, 25), (10, 3), (0, 3), (1, 20), (15, 6), (10, 22), (15, 8), (24, 10), (24, 21), (21, 1), (10, 10), (9, 10), (10, 11), (0, 10), (15, 23), (14, 6), (6, 1), (5, 11), (4, 6), (6, 24), (2, 8), (1, 1), (3, 26), (8, 1), (14, 1), (3, 4), (15, 2), (6, 10), (5, 15), (8, 23), (0, 28), (6, 9), (13, 4), (9, 11), (12, 1), (9, 1), (15, 11), (6, 14), (3, 11), (19, 24), (13, 28), (1, 11), (17, 24), (16, 20), (9, 17), (17, 25), (7, 10), (3, 14), (23, 27), (18, 8), (13, 25), (1, 23), (0, 14), (14, 12), (13, 10), (23, 25), (12, 27), (3, 15), (5, 20), (18, 3), (21, 23), (13, 11), (12, 22), (24, 13), (4, 17), (7, 18), (2, 20), (16, 1), (12, 28), (19, 1), (19, 0), (1, 25), (4, 22), (20, 21), (9, 26), (15, 25), (19, 4), (2, 23), (12, 9), (16, 4), (3, 12), (5, 18), (11, 28), (10, 9), (6, 15), (23, 21), (16, 3), (16, 14), (21, 3), (13, 17), (0, 2), (18, 20), (6, 11), (22, 10), (4, 21), (16, 26), (24, 17), (15, 22), (19, 17), (1, 19), (2, 27), (12, 11), (15, 7), (22, 27), (3, 16), (4, 12), (4, 10), (3, 27), (16, 17), (22, 11), (11, 27), (10, 7), (21, 17), (5, 4), (20, 1), (5, 28), (6, 21), (10, 28), (17, 10), (4, 27), (16, 22), (24, 0), (11, 5), (0, 20), (14, 24), (18, 27), (21, 9), (8, 15), (17, 19), (11, 8), (4, 25), (14, 9), (4, 15), (0, 26), (2, 11), (11, 2), (12, 23), (9, 25), (14, 14), (12, 15), (4, 14), (19, 28), (19, 26), (22, 24), (5, 12), (24, 25), (20, 23), (23, 3), (12, 5), (21, 27), (3, 13), (21, 0), (23, 5), (0, 7), (14, 7), (10, 14), (6, 23), (16, 16), (24, 5), (13, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778800", "dataset": "MATH"}
{"messages": [{"content": "In a 23x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 19), (3, 3), (14, 11), (14, 15), (0, 10), (6, 8), (5, 4), (21, 11), (9, 7), (14, 0), (20, 1), (10, 9), (16, 5), (16, 9), (17, 8), (8, 4), (10, 12), (3, 15), (17, 19), (7, 8), (9, 11), (9, 10), (13, 12), (12, 5), (9, 13), (19, 9), (14, 7), (14, 6), (14, 16), (8, 19), (9, 15), (18, 0), (21, 8), (21, 17), (8, 7), (0, 19), (17, 11), (11, 8), (2, 1), (0, 2), (14, 3), (0, 16), (5, 9), (7, 10), (16, 16), (0, 7), (0, 1), (15, 8), (19, 19), (12, 13), (4, 2), (4, 12), (18, 4), (19, 5), (20, 17), (22, 9), (1, 12), (9, 19), (16, 17), (4, 8), (10, 13), (22, 15), (12, 18), (8, 12), (14, 1), (9, 17), (13, 9), (9, 4), (18, 17), (2, 7), (1, 6), (6, 16), (20, 5), (9, 5), (22, 4), (5, 11), (22, 5), (5, 14), (21, 6), (3, 9), (2, 13), (22, 7), (19, 13), (2, 8), (14, 9), (6, 18), (8, 11), (20, 16), (14, 17), (17, 7), (1, 15), (6, 13), (13, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999641", "dataset": "MATH"}
{"messages": [{"content": "In a 27x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (26, 21), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 5), (0, 15), (18, 20), (16, 4), (12, 5), (13, 17), (5, 10), (12, 18), (25, 21), (11, 5), (0, 5), (10, 7), (19, 5), (16, 7), (3, 15), (12, 11), (2, 6), (9, 9), (14, 12), (18, 6), (24, 20), (25, 7), (15, 11), (3, 0), (11, 14), (17, 20), (6, 19), (7, 8), (16, 10), (4, 18), (8, 20), (0, 16), (21, 1), (13, 4), (13, 8), (6, 0), (17, 11), (25, 8), (15, 14), (23, 13), (14, 18), (10, 12), (23, 3), (4, 9), (10, 21), (16, 3), (9, 19), (22, 19), (19, 9), (16, 16), (5, 13), (20, 15), (11, 7), (26, 3), (15, 21), (24, 11), (6, 18), (18, 7), (6, 8), (5, 7), (17, 7), (11, 17), (13, 3), (19, 18), (12, 7), (2, 8), (25, 18), (26, 17), (6, 7), (8, 19), (19, 13), (10, 0), (3, 19), (20, 9), (19, 12), (17, 8), (3, 13), (22, 12), (2, 1), (22, 21), (2, 16), (23, 1), (26, 0), (14, 11), (2, 3), (26, 2), (5, 21), (1, 20), (16, 15), (20, 14), (12, 14), (25, 9), (12, 17), (14, 19), (23, 4), (13, 1), (20, 7), (8, 12), (7, 1), (21, 7), (24, 17), (22, 6), (22, 11), (26, 19), (9, 17), (24, 18), (0, 14), (3, 1), (0, 7), (17, 15), (13, 15), (3, 6), (10, 19), (8, 11), (16, 21), (11, 10), (0, 10), (5, 12), (8, 1), (5, 15), (12, 15), (13, 12), (6, 15), (23, 6), (17, 19), (1, 9), (22, 18), (14, 3), (12, 12), (3, 7), (10, 15), (10, 11), (4, 8), (5, 1), (18, 9), (21, 9), (25, 6), (24, 1), (23, 2), (6, 20), (3, 21), (23, 10), (7, 3), (17, 16), (18, 8), (24, 10), (13, 14), (23, 14), (14, 7), (24, 12), (25, 17), (25, 11), (21, 8), (15, 12), (4, 21), (16, 5), (24, 16), (1, 12), (19, 3), (6, 21), (11, 13), (19, 8), (24, 15), (16, 13), (19, 4), (16, 14), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902398", "dataset": "MATH"}
{"messages": [{"content": "In a 22x24 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 23), 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, 21), (16, 6), (2, 15), (16, 19), (16, 15), (7, 0), (16, 21), (8, 4), (14, 16), (10, 11), (2, 11), (1, 3), (11, 6), (21, 1), (9, 0), (17, 15), (12, 6), (11, 3), (17, 20), (2, 7), (14, 20), (18, 1), (5, 19), (17, 6), (18, 17), (12, 19), (1, 1), (16, 18), (19, 8), (17, 14), (16, 20), (1, 22), (15, 7), (7, 3), (9, 3), (12, 4), (11, 17), (17, 2), (18, 7), (13, 17), (8, 17), (8, 18), (12, 9), (1, 16), (4, 16), (1, 6), (21, 3), (4, 20), (11, 5), (6, 9), (18, 12), (20, 7), (11, 15), (12, 12), (9, 7), (10, 5), (14, 6), (1, 12), (9, 19), (16, 23), (5, 14), (0, 21), (11, 14), (16, 5), (18, 23), (3, 0), (15, 19), (5, 10), (14, 19), (8, 11), (9, 9), (7, 18), (7, 20), (4, 10), (11, 4), (7, 11), (1, 20), (6, 23), (20, 20), (3, 11), (4, 5), (7, 6), (20, 11), (5, 3), (3, 2), (7, 1), (3, 18), (17, 11), (11, 0), (10, 20), (18, 20), (18, 9), (3, 21), (5, 16), (9, 5), (0, 5), (6, 1), (13, 14), (10, 22), (18, 5), (19, 21), (16, 12), (20, 13), (0, 16), (8, 0), (4, 22), (0, 20), (21, 18), (13, 9), (0, 1), (7, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "929016", "dataset": "MATH"}
{"messages": [{"content": "In a 29x29 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 28), 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), (26, 17), (3, 22), (5, 4), (3, 3), (0, 9), (27, 17), (24, 22), (12, 12), (26, 14), (5, 27), (1, 17), (3, 14), (12, 26), (15, 1), (26, 12), (24, 27), (17, 28), (2, 3), (8, 6), (13, 24), (5, 7), (26, 8), (15, 15), (12, 15), (6, 9), (4, 4), (21, 25), (19, 21), (17, 19), (17, 8), (5, 17), (2, 2), (5, 21), (0, 24), (19, 18), (16, 20), (14, 24), (10, 22), (22, 3), (19, 13), (20, 13), (25, 15), (9, 0), (6, 6), (8, 2), (7, 15), (21, 16), (14, 10), (2, 19), (21, 22), (0, 17), (9, 20), (23, 0), (3, 11), (2, 16), (18, 22), (20, 22), (21, 13), (28, 22), (20, 24), (0, 8), (1, 28), (1, 2), (10, 26), (3, 8), (20, 18), (5, 3), (22, 1), (25, 23), (18, 12), (2, 17), (9, 4), (19, 8), (13, 4), (25, 25), (3, 4), (13, 19), (7, 8), (24, 9), (9, 9), (10, 7), (28, 19), (21, 21), (26, 13), (27, 25), (17, 15), (6, 7), (28, 1), (17, 12), (20, 5), (18, 14), (22, 21), (21, 4), (3, 26), (9, 12), (16, 27), (5, 13), (23, 20), (18, 1), (26, 28), (0, 26), (10, 0), (25, 21), (11, 0), (0, 7), (1, 3), (15, 6), (23, 12), (11, 2), (16, 1), (18, 23), (8, 27), (18, 15), (22, 28), (7, 20), (18, 20), (25, 5), (17, 11), (10, 8), (13, 11), (25, 8), (17, 25), (25, 17), (5, 8), (22, 22), (7, 13), (19, 2), (19, 7), (16, 13), (26, 9), (26, 19), (21, 14), (2, 24), (24, 0), (28, 4), (9, 19), (20, 17), (10, 12), (14, 6), (7, 7), (20, 25), (28, 24), (24, 16), (23, 5), (4, 24), (22, 17), (8, 1), (8, 10), (11, 28), (22, 7), (16, 17), (24, 17), (27, 23), (25, 4), (12, 27), (17, 18), (22, 10), (13, 10), (27, 13), (18, 3), (28, 6), (1, 0), (3, 6), (20, 20), (16, 2), (15, 23), (17, 10), (11, 24), (22, 25), (1, 8), (7, 16), (27, 27), (28, 15), (6, 18), (19, 26), (5, 14), (22, 15), (12, 25), (24, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728736", "dataset": "MATH"}
{"messages": [{"content": "In a 23x27 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 26), 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, 1), (1, 7), (6, 16), (0, 21), (17, 18), (19, 8), (16, 1), (14, 25), (21, 4), (19, 11), (14, 16), (12, 25), (21, 26), (1, 17), (13, 24), (3, 15), (22, 23), (16, 16), (8, 11), (5, 5), (20, 26), (17, 13), (9, 13), (19, 4), (12, 6), (3, 21), (13, 13), (11, 5), (19, 7), (15, 14), (15, 13), (20, 5), (21, 8), (3, 4), (10, 8), (16, 2), (2, 2), (17, 22), (10, 11), (21, 6), (13, 17), (13, 21), (12, 20), (2, 17), (0, 4), (5, 14), (11, 18), (6, 1), (5, 8), (12, 19), (1, 23), (14, 0), (10, 9), (20, 16), (19, 5), (7, 18), (16, 25), (20, 23), (2, 26), (6, 14), (6, 6), (22, 0), (7, 25), (22, 22), (1, 19), (0, 19), (8, 25), (8, 24), (22, 3), (0, 24), (6, 15), (15, 16), (5, 9), (4, 24), (6, 23), (14, 9), (7, 21), (11, 11), (18, 11), (18, 21), (7, 6), (5, 10), (9, 3), (6, 20), (18, 16), (6, 22), (15, 17), (3, 8), (22, 12), (0, 12), (7, 12), (19, 2), (8, 6), (5, 3), (5, 24), (14, 19), (10, 14), (18, 25), (16, 20), (14, 24), (12, 2), (11, 19), (8, 26), (22, 20), (12, 22), (18, 17), (12, 0), (7, 9), (14, 7), (10, 21), (8, 5), (11, 14), (21, 16), (19, 15), (17, 19), (0, 8), (1, 12), (17, 6), (19, 0), (8, 2), (4, 4), (14, 13), (1, 25), (21, 17), (16, 22), (13, 3), (20, 10), (12, 18), (9, 16), (22, 4), (16, 0), (8, 23), (18, 7), (20, 13), (7, 11), (4, 10), (8, 20), (12, 13), (10, 12), (2, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851580", "dataset": "MATH"}
{"messages": [{"content": "In a 29x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (28, 20), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 14), (3, 3), (11, 13), (8, 17), (22, 18), (11, 16), (10, 18), (15, 12), (9, 14), (13, 20), (18, 12), (26, 5), (24, 0), (13, 1), (9, 11), (16, 8), (16, 2), (9, 0), (20, 6), (4, 1), (3, 1), (3, 15), (8, 10), (2, 19), (21, 7), (26, 11), (23, 10), (5, 14), (20, 14), (8, 19), (15, 8), (22, 7), (12, 3), (10, 8), (15, 4), (12, 4), (13, 12), (14, 15), (25, 4), (1, 20), (21, 12), (0, 20), (20, 10), (26, 20), (24, 7), (14, 7), (28, 6), (3, 12), (22, 0), (28, 7), (10, 3), (6, 18), (9, 5), (11, 3), (25, 14), (27, 9), (19, 5), (13, 19), (24, 9), (21, 20), (2, 11), (22, 20), (10, 10), (19, 12), (12, 1), (16, 5), (20, 11), (2, 8), (26, 8), (8, 8), (9, 12), (28, 9), (16, 20), (0, 17), (28, 4), (18, 2), (17, 5), (15, 15), (25, 12), (25, 5), (16, 14), (8, 4), (7, 4), (16, 17), (20, 16), (4, 15), (27, 13), (23, 6), (14, 4), (0, 4), (17, 3), (2, 12), (16, 7), (4, 8), (13, 18), (4, 19), (10, 4), (13, 16), (3, 16), (22, 2), (7, 8), (0, 10), (12, 6), (26, 18), (0, 7), (14, 16), (27, 18), (26, 2), (8, 11), (10, 0), (7, 11), (22, 13), (21, 15), (12, 5), (6, 4), (26, 1), (21, 10), (8, 3), (17, 0), (12, 7), (9, 18), (15, 13), (6, 12), (18, 11), (27, 20), (21, 19), (12, 8), (21, 13), (25, 18), (5, 1), (23, 17), (15, 20), (16, 18), (20, 7), (23, 20), (28, 12), (5, 9), (2, 20), (13, 17), (5, 2), (5, 8), (12, 20), (1, 11), (18, 0), (11, 11), (4, 16), (1, 9), (15, 10), (25, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807244", "dataset": "MATH"}
{"messages": [{"content": "In a 25x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 19), 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), (24, 18), (16, 17), (21, 13), (10, 15), (18, 15), (16, 3), (17, 5), (2, 7), (23, 0), (23, 16), (13, 3), (17, 18), (20, 10), (19, 8), (14, 7), (1, 6), (2, 2), (10, 19), (9, 14), (1, 3), (20, 17), (17, 6), (19, 19), (17, 4), (9, 10), (4, 4), (14, 11), (1, 10), (24, 2), (18, 17), (7, 1), (16, 16), (3, 1), (8, 15), (12, 17), (24, 9), (5, 18), (11, 13), (3, 2), (20, 12), (13, 0), (10, 4), (1, 5), (21, 14), (3, 11), (4, 17), (2, 1), (19, 12), (15, 7), (11, 6), (10, 12), (18, 2), (12, 12), (4, 13), (5, 8), (9, 19), (10, 3), (0, 14), (17, 19), (5, 16), (6, 7), (15, 11), (9, 15), (6, 19), (24, 15), (18, 11), (21, 2), (4, 8), (17, 15), (11, 3), (4, 16), (9, 12), (21, 16), (13, 9), (14, 0), (8, 3), (3, 0), (6, 0), (19, 16), (7, 9), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913248", "dataset": "MATH"}
{"messages": [{"content": "In a 25x25 grid, how many different paths are there from the bottom left (0, 0) to the top right (24, 24), 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), (17, 2), (19, 22), (12, 0), (24, 5), (5, 23), (19, 1), (12, 10), (14, 16), (16, 4), (7, 19), (6, 2), (22, 12), (9, 2), (3, 19), (14, 6), (21, 2), (17, 21), (12, 24), (12, 13), (9, 23), (4, 1), (5, 10), (7, 6), (19, 20), (22, 24), (24, 21), (14, 7), (1, 21), (14, 3), (19, 15), (12, 17), (23, 15), (15, 7), (1, 18), (4, 9), (24, 7), (9, 0), (22, 5), (5, 20), (19, 21), (13, 16), (5, 13), (21, 4), (0, 12), (4, 8), (15, 16), (1, 14), (10, 5), (20, 5), (16, 8), (13, 11), (5, 7), (10, 17), (1, 4), (16, 3), (23, 1), (24, 10), (13, 6), (3, 6), (20, 10), (6, 18), (16, 22), (11, 0), (2, 12), (1, 6), (0, 10), (14, 5), (1, 3), (10, 6), (9, 16), (1, 11), (14, 2), (17, 19), (18, 6), (5, 14), (11, 16), (19, 10), (5, 5), (5, 15), (21, 9), (10, 14), (14, 8), (15, 8), (6, 19), (22, 13), (24, 12), (6, 17), (9, 4), (7, 4), (6, 20), (14, 24), (8, 17), (15, 9), (23, 4), (14, 20), (9, 9), (0, 6), (12, 22), (11, 23), (11, 7), (7, 12), (19, 0), (12, 23), (19, 2), (10, 7), (15, 4), (2, 6), (11, 15), (18, 5), (2, 3), (20, 8), (18, 13), (13, 9), (24, 20), (13, 22), (8, 5), (20, 1), (12, 21), (18, 4), (10, 11), (4, 16), (14, 18), (14, 21), (5, 12), (20, 13), (1, 13), (2, 11), (17, 23), (11, 3), (23, 24), (5, 17), (16, 12), (21, 11), (21, 5), (18, 23), (17, 7), (20, 14), (2, 14), (2, 8), (19, 16), (6, 14), (10, 19), (0, 21), (13, 14), (23, 17), (11, 24), (9, 14), (20, 19), (3, 23), (19, 8), (1, 9), (16, 0), (1, 0), (10, 4), (17, 9), (20, 20), (16, 10), (2, 15), (1, 12), (6, 13), (3, 15), (17, 16), (15, 12), (18, 9), (21, 22), (15, 10), (17, 13), (1, 17), (2, 20), (24, 4), (16, 9), (10, 24), (2, 5), (11, 9), (20, 22), (22, 20), (6, 8), (0, 2), (4, 2), (23, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330372", "dataset": "MATH"}
{"messages": [{"content": "In a 22x28 grid, how many different paths are there from the bottom left (0, 0) to the top right (21, 27), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 21), (7, 12), (7, 4), (15, 11), (12, 21), (11, 19), (18, 26), (15, 23), (6, 26), (3, 14), (12, 10), (16, 11), (12, 19), (19, 27), (16, 16), (4, 1), (3, 16), (17, 19), (1, 14), (0, 24), (2, 17), (11, 1), (19, 8), (6, 23), (19, 14), (10, 22), (11, 11), (1, 18), (1, 15), (19, 7), (3, 20), (17, 21), (2, 0), (5, 15), (20, 14), (14, 15), (3, 10), (18, 0), (21, 20), (5, 8), (6, 8), (10, 13), (13, 18), (1, 27), (5, 13), (4, 3), (8, 13), (13, 6), (8, 5), (9, 22), (4, 2), (18, 1), (13, 24), (5, 25), (19, 25), (14, 17), (16, 9), (9, 3), (7, 1), (5, 4), (7, 10), (21, 23), (13, 12), (3, 2), (9, 18), (6, 0), (12, 17), (19, 20), (12, 12), (18, 11), (3, 11), (12, 7), (13, 10), (8, 3), (7, 18), (12, 13), (0, 18), (12, 18), (5, 5), (2, 19), (5, 23), (2, 21), (10, 4), (21, 2), (21, 21), (21, 24), (2, 24), (16, 17), (20, 6), (14, 11), (16, 2), (18, 16), (16, 15), (11, 2), (1, 8), (16, 14), (3, 4), (20, 18), (6, 6), (0, 5), (10, 5), (17, 26), (7, 9), (4, 0), (13, 8), (8, 12), (2, 5), (2, 15), (3, 22), (6, 15), (12, 22), (19, 22), (4, 24), (8, 16), (16, 4), (21, 18), (16, 0), (9, 26), (2, 3), (0, 26), (18, 4), (19, 3), (4, 10), (15, 17), (13, 19), (8, 10), (18, 23), (15, 24), (6, 3), (4, 17), (20, 20), (11, 8), (7, 2), (14, 18), (2, 25), (19, 16), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993150", "dataset": "MATH"}
{"messages": [{"content": "In a 28x22 grid, how many different paths are there from the bottom left (0, 0) to the top right (27, 21), 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, 9), (8, 16), (27, 14), (21, 12), (3, 6), (14, 2), (21, 17), (4, 4), (11, 3), (6, 16), (16, 14), (7, 2), (22, 17), (10, 13), (10, 10), (9, 12), (23, 4), (19, 19), (24, 9), (21, 4), (21, 15), (6, 19), (0, 13), (20, 11), (14, 1), (12, 18), (23, 15), (7, 10), (1, 16), (25, 8), (2, 16), (11, 5), (17, 15), (4, 19), (27, 4), (14, 4), (18, 13), (2, 3), (18, 19), (1, 8), (10, 6), (3, 16), (11, 14), (20, 4), (23, 8), (13, 5), (0, 16), (20, 5), (5, 7), (6, 12), (19, 11), (16, 19), (9, 17), (6, 20), (16, 5), (9, 14), (26, 11), (24, 5), (21, 13), (17, 14), (9, 20), (12, 4), (24, 12), (20, 9), (0, 5), (13, 6), (8, 8), (15, 11), (25, 10), (11, 1), (21, 11), (5, 12), (21, 10), (16, 20), (27, 17), (11, 18), (27, 5), (22, 4), (10, 19), (19, 6), (0, 12), (14, 6), (8, 2), (15, 7), (22, 15), (16, 18), (8, 12), (6, 1), (12, 10), (14, 21), (3, 14), (14, 17), (24, 15), (9, 1), (5, 8), (20, 3), (13, 20), (15, 3), (12, 14), (27, 20), (9, 18), (6, 0), (18, 8), (0, 4), (20, 8), (20, 16), (27, 16), (21, 20), (1, 19), (21, 2), (18, 12), (1, 6), (5, 16), (21, 19), (6, 7), (1, 17), (16, 16), (18, 1), (9, 5), (27, 1), (15, 6), (5, 13), (15, 15), (25, 20), (4, 21), (27, 2), (15, 18), (22, 9), (19, 4), (2, 7), (25, 21), (12, 17), (22, 7), (2, 18), (12, 15), (14, 14), (5, 14), (8, 4), (25, 19), (22, 1), (9, 4), (20, 21), (18, 2), (25, 12), (15, 20), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515188", "dataset": "MATH"}
{"messages": [{"content": "In a 23x21 grid, how many different paths are there from the bottom left (0, 0) to the top right (22, 20), 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), (21, 6), (7, 1), (8, 20), (21, 0), (20, 11), (18, 3), (1, 12), (16, 10), (22, 16), (19, 1), (6, 19), (17, 13), (11, 2), (9, 16), (13, 20), (11, 15), (11, 16), (19, 7), (20, 18), (13, 17), (13, 16), (8, 8), (4, 9), (12, 11), (17, 0), (1, 18), (14, 18), (6, 18), (12, 20), (11, 6), (15, 20), (10, 1), (0, 1), (14, 3), (20, 2), (8, 16), (17, 9), (6, 15), (8, 2), (12, 10), (7, 18), (18, 8), (5, 3), (13, 14), (15, 13), (6, 0), (19, 10), (7, 19), (9, 10), (6, 17), (7, 14), (16, 12), (12, 9), (16, 11), (5, 19), (9, 8), (15, 17), (13, 5), (3, 17), (10, 10), (1, 5), (21, 5), (21, 11), (12, 1), (16, 18), (22, 6), (4, 18), (4, 7), (20, 1), (9, 14), (12, 15), (0, 8), (11, 10), (22, 15), (14, 8), (0, 10), (0, 20), (11, 11), (18, 10), (1, 16), (15, 12), (18, 4), (12, 3), (12, 8), (18, 16), (7, 7), (19, 3), (2, 13), (8, 5), (1, 3), (20, 7), (9, 5), (14, 11), (4, 13), (1, 8), (4, 1), (19, 8), (10, 6), (20, 19), (12, 17), (1, 17), (3, 11), (16, 15), (17, 1), (9, 9), (7, 16), (22, 3), (6, 10), (11, 13), (0, 12), (14, 16), (12, 0), (15, 19), (5, 1), (3, 14), (16, 4), (21, 8), (17, 8), (17, 3), (13, 2), (1, 19), (19, 5), (11, 18), (16, 7), (20, 16), (19, 0), (6, 7), (18, 11), (21, 3), (21, 19), (14, 17), (6, 11), (22, 2), (15, 3), (3, 18), (20, 10), (18, 1), (9, 15), (11, 9), (14, 4), (9, 19), (22, 10), (5, 11), (10, 20), (5, 2), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865998", "dataset": "MATH"}
{"messages": [{"content": "In a 20x23 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 22), 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), (17, 8), (10, 1), (14, 10), (12, 4), (2, 18), (17, 2), (10, 11), (9, 5), (0, 19), (10, 3), (11, 21), (18, 6), (2, 5), (13, 6), (8, 5), (12, 1), (6, 9), (6, 8), (18, 2), (1, 3), (11, 17), (16, 22), (0, 20), (13, 3), (17, 0), (11, 2), (11, 11), (4, 9), (11, 3), (1, 0), (19, 11), (14, 14), (7, 11), (4, 4), (12, 0), (0, 3), (10, 16), (13, 20), (10, 0), (3, 8), (12, 17), (3, 13), (2, 7), (18, 5), (18, 3), (18, 18), (7, 1), (6, 20), (10, 13), (9, 21), (5, 21), (9, 4), (0, 2), (2, 9), (6, 2), (0, 14), (7, 21), (10, 9), (5, 0), (14, 6), (0, 8), (13, 10), (11, 13), (10, 15), (15, 18), (2, 10), (5, 13), (5, 9), (1, 5), (6, 15), (18, 12), (6, 22), (17, 3), (9, 10), (18, 1), (6, 19), (11, 19), (4, 15), (8, 17), (13, 17), (1, 11), (15, 1), (15, 21), (3, 14), (2, 21), (13, 4), (16, 8), (13, 21), (18, 20), (5, 11), (17, 17), (4, 5), (16, 1), (5, 1), (4, 3), (5, 19), (11, 8), (1, 21), (15, 6), (0, 5), (11, 1), (12, 20), (3, 12), (9, 2), (14, 21), (13, 11), (16, 16), (18, 0), (16, 0), (4, 21), (9, 3), (19, 9), (15, 11), (6, 14), (18, 7), (11, 16), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776160", "dataset": "MATH"}